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1. 20 6 6 3 Pre computation and check of variables 6 6 4 Master receiver position 6 6 5 Ambiguity estimation 6 6 6 The extended kalman filter il 23 23 24 25 26 27 27 28 28 28 30 30 31 31 33 34 35 36 37 38 38 39 System test and Conclusion TA Systemi Speed sipaya oo ok ee ee a GOR Ba Ed TAA Process speed s siet gi a dee ee ae A Bed 7 1 2 Receiver output rate 7 1 3 Modem transmission rate 7 2 Filter performance 0 2 000000 Conclusion Kinematic test The full ephemerids struct used Bibliography 111 61 61 61 62 62 63 65 67 73 Chapter 1 Introduction 1 1 Background Virtual Reality is a technology that tries to mimic the real world or an immersion in 3 D visual world The basic idea is to immerse a user inside an imaginary com puter generated virtual world For the immersion to appear realistic the virtual reality system should be able to accurately sense the users movement and what effect it would have on the scene being rendered Usually stereo images are pro jected onto two miniature screens and with the help of a Head Mounted Display HMD device one could experience fascinating 3 D objects Figure 1 1 Head Mounted Display For this technology to work means of position and motion tracking is needed One commonly used method in tracking position and orientation is by magne
2. Notice the input no 1 or 2 which is the sigh for whether it is rover or master data This procedure has shown to be very stable and especial useful for deciphering the measurements in the fast running working loop 6 6 Important system functions As earlier stated a selection of the essential functions in the system will be de scribed in some detail To understand their individual relations see the function diagram that has been developed In the description below we try to follow the chronological order according to the flow diagram 6 6 1 GPS time Reciever time and check time The first contact to the receiver is a query for GPS time done by running m file GPS_DateTime m Here year month day and time of measurement is collected It was also intended for these variables to be displayed if a graphical user interface GUI were to be made From these informations the day of week dow can be computed This is needed for conversion of time of day tod into second of week sow See equation 6 1 which is done in msgRT m that computes receiver time sow check_time dow 86400 tod 1000 6 1 The function check_t m will ensure that the time in sow is within the limits of 302400 for numerical reasons Nav95 6 6 2 GPS ephemerides Before any position computations can be made the satellites ephemerides are needed They are queried for and processed by running the function gettopconeph2 m This script can only
3. AYAB 3 9 ZB ZA AZAB CHAPTER 3 GLOBAL POSITION SYSTEMS 18 If simultaneous observation are made for two satellites j and k linear combi nation can be formed leading to single double and triple difference 3 5 1 Single difference Consider a simultaneous phase observation from receivers A and B to satellites 7 and k The phase equation for the two points are Pi p I T clot a t dt t 7 A ba to o to ANY 4 3 10 DL t p IL T clotg t 6 t 7 ba to 9 to 4 ANG e 3 11 As discussed earlier if the distance between the two receivers is not too large the errors due to ionosphere 17 troposphere T7 and the satellite clock error dt t T would be similar Taking the difference between the two observation we have the single difference Di p t pp cdtap t Adaw to ANAB eh 3 12 3 5 2 Double difference Consider now that observation is made to a second satellite k simultaneously the phase equation for this observation for another single difference would be 64 t Pag cOtap t AdaB to NAB ehg 3 13 Figure 3 2 Double difference observation CHAPTER 3 GLOBAL POSITION SYSTEMS 19 Taking the difference again between equation 3 12 and 3 13 which is called the double difference we have te of ANIE oR 3 14 Clearly it can seen that the receiver clock bias c t 4 g t as well as the non zero initial phases A
4. 5 1 Discrete Linear Kalman Filter One basic assumptions that the discrete Kalman filter makes is that the model must be linear and when non linearities exist a good engineering approach is to lin earize it about some trajectory This is because linear system are more easily manipulated with engineering tools than nonlinear Other assumptions are that the system and measurement noises are white and Gaussian This make the filter tractable and gives the engineer a knowledge of the first and second order statistics mean and variance of a noise process Given a system which can be modelled by an equation in the form Cet Pyare k 5 1 where F is the transition matrix relating the previous state x at time k and the current state x at time k 1 and Ek Y N 0 Dek And an observations measurements equation given by bg Hkk k 5 2 The basic equations that forms the engine of the recursive kalman filter are The measurement also known as corrector update equations given by Kalman Gain K P HE H P HE Rp State estimate ij amp Kg bg Hit 5 3 Covariance of state estimate Pp I KyHy P and the time update equations predictor given by State predict Ty Fit Fy PFT Qk 5 4 Covariance of state predict Py The element that minimizes the mean square error in the above equations is the Kalman gain K All terms have their usual meanings The sequence of computa tional step is
5. Al A2 Then the following 2 roundoff in the wide lane domain are executed 60N 77Na 4 13 K floor N Na Ko floor 60 N 77N2 4 14 These K values are expected to be the correct integers in the wide lane domain and can therefore be transformed back as integers for L1 and L2 This is done by the following equations _ 60K Ko 17 Ni K 4 No 4 15 The integers and Na for L1 and L2 are herby computed and can be rein serted in equation 4 12 for the float solution and a fixed position can be com puted 4 3 3 Evaluating the Goad method Since the method is based on a numbers of assumptions and a final roundoff there are no guaranties of a correct integer estimate No validations or test can be performed either Though it is highly probable that the method will produce the correct solution for good measurements Exactly how probable a correct solution is depends on the accuracy of the code and phase measurements The solution concept may be the optimal solution for the given system Keep ing in mind that accurate positions estimates are needed at a high rate meaning that the computation load must be minimized Whether or not this is the case only a test can prove Especially the possibility of wrong roundoff s which will produce a measurement bias of 0 86m will have to be investigated both analytical and through tests CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 31 4 3 4 Choice of inte
6. As a means of analyzing the quality of the float solution the variance covariance matrix 2 for the solution hat can be computed by the following equation rep resenting the law variance propagation for independent observations Es ATCA 4 5 The covariance matrix for the float solution will in this case look like this 0 9880 0 7465 9 1058 9 0701 0 7465 0 5999 7 0683 7 0947 9 1058 7 0683 84 9040 84 8549 9 0701 7 0947 84 8549 84 8866 CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 26 The standard deviations on the 4 un known p I N 1 and No which are located in the matrix diagonal have the following values p I N No y diag X 0 9940m 0 7745m 9 2143 cycles 9 2133 cycles The variances for the float solution of 1 and No will be used for later compar ison In meters the derivations are equivalent to 74 1 75m and o y 2 25m Compared to the wavelength of the two carriers this deviation is more than 9 times one cycle The float solution is therefore insufficient for estimation of integer am biguities but can be used as a first computation of the problem Hereafter more sophisticated methods must be implied 4 2 2 LAMBDA To improve the precision for DGPS the double differences for the phase obser vation are often used and preliminary a float solution is computed To further improve the precision the knowledge that ambiguities always are integers can be included in the solution This imp
7. 4p to has also been cancelled This is the reason why double difference is used Note here that the cancellation became possible because we make simultaneous observations i e same time tag of epoch measurement from both receivers and also assumed that the measurements were made on same fre quencies 3 5 3 Triple difference If we now consider double difference from two different epochs we can form the triple difference Figure 3 3 Triple Difference observation Let t1 and 2 denote the two epochs then from the double difference equation we have Dplti plti ANGR eae Dinlt slt ANY eip 3 15 subtracting one from the other we get o ti OF to pez ty pliz to 3 16 CHAPTER 3 GLOBAL POSITION SYSTEMS 20 The final equation for the triple difference is then given as Dip t12 Pip t12 3 17 This eliminate the time independent ambiguities the main advantage of the triple difference With the ambiguities cancelled the triple difference is now insensitive to changes in the ambiguities called cycle slips 3 5 4 Combination of Code and Phase Measurements So far our discussion on relative positioning has been based on measurements from a single frequency with phase observations We now consider measurement on L1 and L2 with both code and phase observations and then form the double difference equations This combination is to give an improvement in the position accuracy by eliminating
8. Addressing RX Address ON 0001 TX Address ON 0001 4 Serial port 1 ON 38400 8 bit data None 1 stop bit 5 Serial port 2 OFF 19200 8 bit data None 1 stop bit RS 232 6 Additional setup Error Correction OFF Repeater Function OFF SL commands OFF 7 Tests Test Mode Unactive 8 Restore factory settings E Exit Important SATEL modem issues Because of our rather large problems with the radio modem some issues that can not be found in the manual are described here Before disconnecting the modem in programing mode remember to push E for exit or Q for quit in old SATEL versions and then disconnect pin 12 The program session is ended and settings are saved Otherwise settings are not saved Also notice that the Topcon receiver will share its power supply with the radio modem which requires 300 mA when transmitting It will appear to be working just fine but will stop during trans mission It is therefore NOT possible to run both the receiver and the modem on a single net adapter Connect therefore a fully charged battery to the secondary power supply port on the receiver when using the radio modem 6 1 4 Hardware test The complete hardware setup were tested with different settings for baud rate and receiver output rate The purpose of the test were to ascertain how much we could expect of the radio link connection This connection test was supposed to be part of the background for the software design Unfortunate
9. Chapter 4 Ambiguity Estimation Concepts In the above description of DGPS it was explained how each phase observation equation for the double differences included an unknown integer number of ambi guities Ny and No for each observed satellite There are currently a large variety of approaches to deal with the integer ambiguity problem and the solution of this equation They are mainly divided in the following to groups one called a float solution where the integer nature of the ambiguities are ignored and the equations are solved by means of iterative least square or filter techniques The other is the much more accurate fixed solution where the correct integer number are found mainly by the use of a search and test method and then used in the equation so lution if found valid Another solution which is a mixture of both is the rather crude round off method Here the float solution is rounded towards the nearest in teger giving one of the many possible integer solutions This method is normally quite bad because of the float solution for the ambiguities N and Na are highly correlated making a correct round off impossible Still it is mentioned as a so lution because of its fast properties and combined with sophisticated wavelength manipulations it can produce a highly probable solution The group has no intentions of going through all the possible methods but have selected a few which are found appropriate as solutions for the gi
10. Currently there has been significant advances made in system and receiver technologies This advances have enhanced the effectiveness of satellite position technologies This chapter therefore gives a brief description of the GPS system measurement techniques errors that affects the accuracy of positioning and math ematical modelling of the measurements This theoretical algorithm analysis chapter became very necessary because it is the bases upon which our data processing are made We discussed some of the options available and the reason why some algorithm are preferred than others 3 1 GPS principles Global Position Systems GPS is a satellite based system that can be said to pro vide a high level of positioning accuracy It became fully operational in 1994 and has a worldwide coverage that benefits all nation GPS allows user with proper equipment mainly GPS receivers access to useful information such as position velocity and time anywhere on the globe Determination of the position velocity and time information is done by reception of the GPS signals from the satellites to obtain ranging information as well as other necessary transmitted messages The system consists of four satellite at each of six 12 hour orbital planes at altitudes of about 20200km making up the Space Segment Ideally four or more satellites is visible from anywhere in the world Periodic update of information that is disseminated by the satellites is done b
11. Disable all Measurement output dm What is actually queried for will be described in details in section 6 4 6 1 3 Data Link A radio modem Satelline 3AS was used as a data link in kinematic setup Detail information about these device can be found in the user s manual SATO1 The important things relevant to this project is described below The maximum data speed for an RS 232 serial interface for this modem is 38400bps This setting has to be the same for both the transmitting modem the receiving modem and the GPS receivers Data format is asynchronous RS 232 Also the link has to be a line of sight and has a range of about 20km depending on your antenna hight and transmit power level All settings of the modem was done by the program SATELLINE _SaTerm ver sion 3 1 21 To enable the program mode the modem must be connected to the the programs hyper terminal at baut rate 9600 bps and pin 12 on the comport must be connected to ground Here are shown the exact modem configurations used in the project Be advised that the power output level was turned down to the minimum of 10 mA when test was performed in the laboratory to reduce the noise level modem antenna distance was less that 5 m CHAPTER 6 SYSTEM DESCRIPTION 45 KKKKK SATEL 3AS kkkkxx SW Version 0 37 HW Version 01 01 1 Radio frequency 433 0000 MHz CF 433 0000 MHz Spacing 25 kHz 2 Radio settings Tx Power Level 100 mW Rx Sensitivity Level 110 dBm 3
12. Epoch m Uping Vector m Position Vector m 10 1 71 10 2 70 E 10 3 E D E S 10 4 5 63 10 5 68 10 6 67 0 200 400 600 800 21 22 23 24 25 26 Epoch m Easting m Figure A 2 Plot of the individual baseline components in easting northing and upping for the circle test File ALLENU correct eps The plot shows how the easting and northing making a sinusoidal motion when a round in the circle is made In between they are steady at the same potion The plot of the upping show the antenna movement vertically throughout the test The actual movement has also been shown by plotting the northing in relation to the easting Here is clear why the group would like to re measure the test It clearly could have been performed better APPENDIX A KINEMATIC TEST 70 Statevector Position XYZ Statevector Velocity XYZ Statevector Acceleration XYZ 34 0 5 3 u 36 2 4A 2 0 El 0 x gt 38 x 2 x lt 40 0 5 204 0 500 1000 500 1000 0 500 1000 66 1 lt 02 S E u 64 05 S e Oo o gt E el 62 Z 0 2 gt 60 0 5 0 2 0 500 1000 500 1000 500 1000 6 0 5 0 05 5 E o 3 Hi o N gt 4 N 3 0 5 0 05 St amp tevector NoPE Positior RYZ St levector NORM of Velocity PF ZtateYector NORMOY AcceleraflOAKYZ 76 j s S 0 2 me y gt o gt 05 gi Bott ys ME iM Ay O 2 2 APA O el W 500 1000 0 500 1000 0 500 1000 Epo
13. improves the position accuracy since the standard deviation on this pseudorange is about 0 3 m For further reference on the method see Asa02 6 6 5 Ambiguity estimation As described both in the DGPS theory and in the theory about ambiguity integer estimation the first objective in DGSP is to make a reliable float solution regarding the baseline components and the ambiguities for the frequencies used This is done in the function trkfloat m In this function the float solution is also feed to LAMBDA2 m where the fixed solution is computed my means of Least squares AMBiguity Decorrelation Adjustment method see section 4 2 2 Notice that the master position already has been solved at this stage To sim plify the function description it has been divided into the following steps e Find the best reference satellite According to the theory the best choice of reference satellite refsv is the one with the highest elevation All elevations for the common satellites are therefore computed and the refsv selected e Data collection By using above described methods for data collection and data checks 8 epochs of data from the rover and master are collected into a large data struct ALLOBS epoch obs1 and obs2 Notice that all epochs of data contains the same common satellites so the observation equations for each epoch can be computed in the same routine Also the epochs are spaced in time with 2 seconds to avoid too similar observation eq
14. the receivers could at anytime be reached by contacting the pc through the internet This feature gave great flexibility for running system test from our own pc s at home Since the system were intended to operate on the GPS system alone the Rus sian GLONASS system were disabled Implementing GLONASS into the system would also go far beyond the project scope When setting the internal measurement rate from the default value of 200ms to 100ms all measurement output rates in multiples of 100ms are made possible At this point the actual output rate from the GPS to the VR system has not yet been decided The comport baud rate has to be set according to all other devices used in the system Here the tight point of the system is the modem used for radio link which will be described later Choice of baud rate was imposed by the workable baud rate in the modem A final but rather important remark The time transmitted with each measured epoch is time of day in ms tod in a topcon receiver This has to be converted into seconds of week sow if this is the chosen time environment We chose to do so since the ephemerids data is designed to correspond to sow Another thing some receivers like Ashtech ZXtreem correct the clock offset constantly and outputs a smoothed GPS time This is different in the Topcon receiver which crudely resets the receiver clock every time the clock offset exceeds 1ms This is not important for DGPS applications since th
15. variance for X m 6 5 L L L L L 0 100 200 300 400 500 600 700 5 5 T T variance for Y m A al T gt L 0 100 200 300 400 500 600 700 N T L o T L variance for Z m 1 1 100 200 300 400 500 600 700 Time in epochs sampling rate 0 6 s oa o Figure A 5 Plot of the first 3 items in diagonal of the filtered state covari ance varinace matrix P File SxF_correct eps The plot shows how the variances converge form their initial values of zero to their final filtered values Depending of the used variances this values converged to differently values but always within the very first few epochs Using the current set of observation and system variances they tend to start growing or falling a bit The value range in the e x 107 so it is not much Appendix B The full ephemerids struct used Here an example of how the ephemerids structure looks like with real numbers included eph sat 1 x 37 struct sateph 4579 14 24 30 The fields eph sat can contain the orbit information for 37 different satellites The fields however contains 21 variables picked from the ephemerides message status 1 SU 4 toc 151200 af2 0 afl 1 81898940354586e 012 afo 0 000259119551628828 toe 151200 rootA 5153 56780052185 ecc 0 00520778668578714 m0 0 541087018325925 omegal 0 0708340788260102 incO 0 309338531922549 argPer 0 551645188126713 deln 1 344119
16. This is the time when measurement data becomes available and the time data is passed on to the filter Also a delay between Kalman filter computation time and time of data output to the needed place One way of going about this problem is to make a projection of the Kalman filter so that solution are delivered the VR system The danger here is that there is the likelihood that error covariance associated with the solution could be corrupted Another problem worth discussing in real time applications is the time interval between measurement If this time interval varies considerably or in cases where measurement data is not available a problem then arises on the state estimates Ly and error covariance Py One way is to predict consistently using the transition matrix Fy and the process noise covariance Q computed for a fixed change of time BH85 Chapter 6 System Description This chapter gives a detail description of the system we have developed The first section describes the hardware part of the system which consist of the GPS receiver being used computer hardware and the modem used as radio link This descrip tion is very relevant in that our choice of hardware has an imposed limitation on the performance of the RTK system Secondly a description of the hardware com ponent would give a better understanding of the final result obtained in the overall system setup The second part of this chapter describes the software developed for proces
17. and covariance matrix To E xo Po E ao o xo o The computational step is the same as the ordinary kalman filters and can show by Figure 5 2 Time update Measurement update C Project the state ahead 1 Compute the Kalman gain 2 Project the error covary iance ahead 2 Update estimates with measurements 3 Update the error covariance Initial estimates for state and error covariance Figure 5 2 Extended Kalman Filter Loop 5 3 Implementation of EKF It is worth discussing how we are using EKF in estimating the position of the user in VR by use of GPS measurement In this particular project two models were implemented and both will be discussed below Model 1 is a static receiver where the present estimates at time k 1 are expected to be the same as the previous estimate at time k The second model assumes a constant velocity and acceleration Hence the present estimates at time k 1 are definitely going to differ from the previous estimates at time k We now go into detail description of the two models CHAPTER 5 KALMAN FILTER 37 5 3 1 Model 1 Static In this model we have our states being position vector Xy k Yk zk The model equation can be derived as Xk 1 Xx 5 7 In kalman filter this model is govern by the following process equation Xp Fk Xk Q 5 8 where 100 F 0 1 0 00 1 Q is the process noise it s initialization
18. and the fixed solu tion is computed using the following equations b b Q Q 4 4 6 CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 27 Qi Qi Qaa Qia 4 7 4 2 3 De correlation of ambiguities If a search starting with the original ambiguities was to be preformed it could easily be a cumbersome process given the highly correlated state of the ambiguities If for instance the precision of the starting point was 1m equivalent to 11 x A1 there would be 23 spatial candidates per double difference With 6 satellites observed this would amount to 25 6436343 candidates to be evaluated Therefore a re parameterizing known as the Z transform is preformed before the search is engaged The original double difference ambiguities in the vector amp are de correlated by the following equation z Z xa 4 8 Where Z is defined by the Z transformed original variance covariance matrix Qa by following equation Qz ZQaZ 4 9 4 2 4 The search method The new variance covariance matrix Qz can now be use to define the search ellip soid with which the search will be performed The magnitude of the de correlation of the search space is illustrated in the 2 ellipses in the figure below Figure 4 1 Figure of the search ellipsoids being the de correlated CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 28 4 2 5 Summarizing LAMBDA Given the high precision of the integer ambiguities and therefore the fixed so lution this method
19. be executed if no other data is being printed to the comport and if all available data in the buffer has been collected To ensure stability all massages are disabled and the comport emptied by a special routine each time the function is being run A check is also done in the function so no error in flicted ephemerides will be allocated in the eph structure The ephemerids update function is called by chech_eph m where all common satellites are checked for CHAPTER 6 SYSTEM DESCRIPTION 55 available ephemerides The current age of the present ephemerides is checked as well The limit of ephemerids age is two hours which also is the normal ephemeris update rate at the GPS ground stations 6 6 3 Pre computation and check of variables Before any data is used for computation we check the data integrity in the m file precomvar m and compute the common satellites for the rover and master The variables commonSats and NoComSats common satellites and the number of common Satellites are assigned as global and used in all other computations for index purposes A check for cycle slips could also be implemented in this function The check is described in the theory section 4 4 but has not been implemented at this point 6 6 4 Master receiver position The position of the master receiver is computed in TCrecpos 1s m The method is an iterative least square computation on the P code pseudorange on L1 Using the P code instead of the C A code
20. code and phase obser vation P and it was shown that the following equation could be constructed d Ax error P 1 1 0 0 p l Dd 1 1 A1 0 I a El 4 1 P 1 f f 0 0 N 2 1 fi f2 0 A No E2 CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 25 The given observation equation can be solved by means of least square Since two different measurements with different accuracies are included a weight matrix C must be introduced before the float solution can be computed The weight matrix First it is assumed that the 4 observations P P2 1 Da are un correlated Next the accuracy relation between a code and a phase measurement on Ll are related to the different chipping rate on the carrier This relation is defined as k 154 Furthermore it is assumed that the accuracy on the two code and phase ob servations are similar That means that the accuracy on L2 phase measurement is given by the accuracy on L1 times f1 f2 These assumptions give the following weight matrix 2 0 0 0 C l ce i 7 4 2 1 Ogi 0 0 fi f2 k 0 0 0 0 an fi f2 With the standard deviation on phase L1 0 0027 the weight matrix look like this 0 308 o 0 0 Ga va S 4 3 0 3952 1 0 0 0 0 00262 Having established the weight matrix C the following least square solution to the above observation equation can be computed AECI Al Cd 4 4 4 2 1 The variance covariance on the float solution
21. for the float ambiguity solution on L1 was oy 9 2cycles or 1 75m In the wide lane domain the variance for the ambiguity dy 0 2841cycles In meters that is equivalent to o y 0 2355 0 86 0 25m This makes the wide lain solution much better to estimate the unknown integers by a roundoff method since the chance of a correct roundoff is much higher than in the normal L1 band If we assume that the integers in the wide lane are just as stochastic and nor mally distributed as in L1 95 of the integer estimations should be within 3 the deviation oN 3 3 0 25m 0 75m This is still well within the length of one wide lane wavelength 0 86m A correct roundoff by this method is therefore highly probable CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 30 4 3 2 Goad s integer estimation When the integer N is estimated in the wide lane domain it is necessary to estab lish a transformation to return back from the wide lane domain so the integers for L1 and L2 can be found This is done by another liner combination that is build on the frequency relation between L1 and L2 given like this identity 2 m The unknowns p and I from equation 4 12 is eliminated First J is removed from the equation because of the assumption that the ionospheric delay cancel in the DGPS environment Next p is eliminated by the above identity The so called ionospheric free combination is given as the following linear combination 600 77
22. is regarded as one of the better ways of solving the integer problem One downside to the method could be the relative heavy computing load represented by the search and validation procedure If the method is used only once during the initializing process to obtain the integer ambiguities as would be the case in the perfect environment without cycle slips and loss of satellite contact this would not be a problem But if it has to be run often in realtime processing it could be a problem How the method is behaving in realtime processing only a test can show 4 3 Goad Method The Goad method is built on a number of assumptions which validity is the root to the methods accuracy The probability of these assumptions will therefore also be the subject of discussion in this chapter The fact that the system layout is defined by relative short baselines means that the ionospheric delay can be said to cancel all together in the double difference environment This means that this unknown can be removed from the equation in the float solution If this is done the observation equation will look like this d Ax error Pi 1 0 0 y B 1 A 0 E1 P 10 0 N 9 Cy P 1 0 Aa 2 E2 This assumption will hold true as long as the baseline is kept under 20 km and there are no intentions of making a system with baselines much over a few km all together The method acknowledges that the float DD ambiguities and Na are strongly correlated The w
23. length of the signal in the tro posphere the lower the satellite the longer the path signal would travel and the greater the delay The apparent effect is that the signals are delayed depending on the elevation angle of the satellite This delay is common for both code and carrier phase at L1 and L2 To estimate the tropospheric delay precisely knowledge of pressure temperature and humidity along the signal path are needed To minimize the delay 1t is recommended to exclude measurements to satellites that have low elevation mask e g 15 3 4 3 Receiver Noise Measurement of the code and the carrier phase are all affected by random mea surement noise This noise is usually a white noise common to all radio frequency radiation The error due to receiver noise varies with the signal strength ME01 3 4 4 Multipath GPS signals may bounce off a nearby object causing two or more signal to reach the antenna First the direct one and a bunch of delayed ones The reflected de layed ones are usually weaker than the direct one This error usually depends on the strength of the reflected signal and delay Both code and carrier phase mea surement are affected by multipath Improving the site of the antenna is a way of minimizing the effect of multipath Good antenna design can reduced multipath to some extend as well CHAPTER 3 GLOBAL POSITION SYSTEMS 17 Satellite Clocks Ephemeris Atmospheric Delays Multipat
24. like the transformation of a baseline in ECEF coordinates into the easting northing and upping vector ENU The purpose of the system description will rather be to describe how the group managed to combine all of these function and to describe the most important ones like how we compute the float solution and how the extended kalman filter works A very large part of the program is error checking and using safe procedures that keeps the system running whatever happens We have selected the most im portant of these checks and safe procedures and they will be listed and explained in the next section 6 3 Checks and safe procedures When working with GPS technology and especially real time kinematic systems it is important to realize the different ways one could expect system failures We can not state that the system is cable of handling all possible situations since they are numerous Still it has been a large part of the system development to ensure that the system would be cable of handling any common error situation Instead of going into detail the most important ones are listed below in 3 cate gories How some of the errors are corrected will not be described since it is rather obvious System checks on the common satellites used e Check satellites for available ephemeris e Check the age of the ephemeris e Check satellites for fixed ambiguities System check on raw and processed data e Check if the length of the raw data
25. model uses the estimation of current parameters satellite position and clock status etc which are then used to predict the future values of these parameter This is then uploaded to the satellite and then broadcasted as navigation message ME01 However there are errors in both the estimation and prediction of these parameters This errors grows with the age of the ephemeris And therefore if the rate of upload to the satellite is high the error is kept minimal CHAPTER 3 GLOBAL POSITION SYSTEMS 16 3 4 1 Ionospheric Delay The ionosphere is the upper part of the earth s atmosphere extending from a height of about 50km to about 1000km It contains ionized gases GPS signals travelling through this medium are refracted by this ionized gases The code phase tends to delay while the carrier phase is advanced by the same amount This ionization is caused by the sun s radiation The amount of ionized gases in the ionosphere is determined by the intensity of the sun s radiation The higher the sun s radiation the greater the ionization meaning ionospheric delay is greater during the day and tends to decrease at night 3 4 2 Tropospheric Delay Troposphere is the part of the earth that extend to about 50km above the surface of the earth This part of the earth contains water vapor and dry gases mainly Na and O2 GPS signals travelling through this neutral molecules are also refracted The elevation angle of satellite determines the path
26. shown in Figure 5 1 Once the filter loop is entered the computation can go on indefinitely To enter the loop an initial estimate of state predict 2 and it s covariance matrix Pj are needed CHAPTER 5 KALMAN FILTER 35 Initializati Compute Kalman Input Measurements Gain Matrix Compute State Update State Predict and it s Error Estimates Covariance Compute Error Output State Covariance of State Updates Figure 5 1 Kalman Filter Loop 5 2 Extended Kalman Filter The kalman filter can also be used in situation where the system is not linear The approach is to linearized the system process and or the measurement process about some nominal trajectory Different ways exist by which this linearization can be done If the linearization is done about the current mean and covariance the result ing filter is call extended kalman filter EKF BH85 For the EKF given the state space equations egy f Tk Uk Vk 5 5 Yk h k wk 5 6 The inputs needed are the linearized state and observation equations given by k41 7 fl k Uk Up A k xp Ti F k vk Uk yk h Tk We CO k k Ex G k wk Wy where aL of a Uk UK 7 A k A la x _ OF Bk Up Y F k ON d a Ee ea da ce Ses w CHAPTER 5 KALMAN FILTER 36 The error covariance matrices associated with the equations above T Q Efugu T R Efwgw Initial estimates of state
27. some of the errors The setup is as shown in Figure 3 2 Two receivers A and B observe two satellites j and k at the same time Double difference code observation equation on L1 gives ss o ey a PAB Pag Tap Tar LAB 3 18 and on L2 gives P3 4B Pap fi fo Tib Tap AB 3 19 Similarly double difference phase observation equation on L1 and L2 gives dias Pas Tag Tapt AN AB ELAB 3 20 oip e T NB g Er ip 3 21 Note here that the ionospheric delay is frequency dependent hence the factor f1 f2 on L2 Also note the reverse sign of the ionospheric delay for the phase obser vation As discussed in the previous section on code observation the signal is delayed making measurement of code to long and on carrier phase it is advanced making measurement too short by equal amount SB97 Omitting subscript and superscript for all measurements we then write the four equations as Pi p I e Bi hgh E aie 3 22 Py P f f I e Dz p fi f2 I A2No E2 where p is the ideal pseudorange e and e are the observation errors Transforming equation 1 22 into matrix form CHAPTER 3 GLOBAL POSITION SYSTEMS 21 P 1 1 0 0 p l 1 1 Al 0 I E1 3 23 Po 1 f f 0 0 Ni 2 22 P2 1 fi fo 0 A N2 E2 For short baseline the ionospheric delay can be assumed to be the same at both receivers and therefore can be set to zero SB97 Also putting the measurement errors to zero equa
28. tem would become rather expensive and the full systems would be quite a heavy pack to carry around The further improvement of the technologies may solve this problem The prospects of actually finding any users for such a system is more difficult to predict Though only the fantasy can set the limits of the uses of such a system It may be a mandatory part of the navigating system on super tankers in the future for all we know or a delightful experience of the dinosaurs when going through a virtual theme park Appendix A Kinematic test A system test was performed using kinematic data from a measured circular mo tion filtered using model 2 Using a circular motion is an easy way to investigate whether or not the system computes the correct trajectory just by knowing the circle s radius Aim The purpose with this exercise was to record a kinematic motion which we could compare relatively easy to the known trajectory of the circle Also the center point is a good reference because when it is re measured after a kinematic motion it gives information of how fast the filtered state becomes steady again Procedure A radius of 2m was used which was controlled by a string attached to the center point The measurement of the circle was performed as described below e The center was measured accurately using a tripod e Then one full circle was made before returning to the center for a remeasure e Then two further rounds were mad
29. this test failed for all tried settings to our great frustration After a point the radio link was given up and it was decided to use normal comport connections to the master and rover receiver in the laboratory After the software had been developed the radio modem was investigated once again and a loose connection in one of the antenna cables were accidently found After this point the radio modems worked to some satisfaction But unfortunate the group had no time to investigate all the different settings once again It was decided to use one that worked which is described above A more stable connections are assumably possible and should the setup if the modem have been investigated further CHAPTER 6 SYSTEM DESCRIPTION 46 6 2 Application Software Design This section will describe how the software has been designed for the handling and processing of the measured GPS data to overcome the given task Before a detailed description of the individual systems steps and functions a few general remarks about the overall design are made and the guideline diagrams of the soft ware design will be shown Some guidelines regarding the system design to insure effective and standard ized coding were made First of all the group wanted to make the software product as stable sufficient and self explanatory as possible The following design concepts were listed e Standardized script style with explanatory comments e Use functions and subf
30. up an independent RTK system with CHAPTER 2 RTK SYSTEMS 10 two receivers and a radio link The reasons for this choice are trivial First it is the purpose of the semester to investigate the algorithms of DGPS and secondly a highly accurate positioning system is needed Secondly the group can not use any commercially broadcasted corrections since no agreement with any such system has been made by the AAU GPS department It would be quite interesting to investigate how well the system could work using commercially broadcasted corrections signals If the GPS guided VR system were to be produced and sold commercial this other approach would be highly appropriate because it would lower overall system cost and needed knowhow to use it Though such an investigation would be good for a full project alone Therefore the group does not intend to go into this matter Chapter 3 Global Position Systems As stated in the problem formulation we intend to investigate the possibility of using Global Position System GPS to meet the tracking requirement of the vir tual environment system Other methods for tracking in the virtual environment exist such as magnetic trackers and sound trackers However the interest of the group in using GPS stem from the background of the group members and also the requirement for this semester Hence we intend to concentrate on the use of GPS technology in meeting the position requirement in the virtual environment
31. would be discussed later The measure ment consist of pseudorange and phase observation and hence the relation between the measurements and the states position vector is not linear This equation can be given as by h k we 5 9 The linearized version of the measurement equation now becomes bk HXk 5 10 where H is the Jacobian 2n x 3 matrix given by equation 1 k eD H A B 5 11 ui uh where k k k Te TECEF TA YECEF YA ECEF A A k k J k PA PA PA The measurement vector b is a 2n x 1 given by Pi AB AN IAB kn kn DIAB AIN AB Note here that the superscripts are satellites and subscripts are receivers CHAPTER 5 KALMAN FILTER 38 5 3 2 Model 2 Kinematic In model two we have our states being the position vector velocity vector and acceleration vector Xy Lk Yk Zk k k Zk Eh Yes 2 This model can be represented mathematically by the equation 6 ay At Tk41 Tk Ata z Tk 0 AP Yk 1 Yk tyz z Uk 5 13 p ae Zk 1 Zk Ate 3 The relation between the previous states and and current states are govern by the transition matrix 1 0 0 At 0 0 AR 0 0 010 0 At 0 O MZ 0 001 0 0 A 0 0 At 2 000 1 0 0 At 0 0 F 0 00 05 1 0 0 At 0 000 0 0 1 0 0 At 0000 0 0 1 0 0 0000 0 0 0 1 0 0000 0 0 0 0 1 In this model the H matrix is the same as model 1 only that it is expanded with zeros to take care of velocity and acceleration vector
32. 2 LAMBDA o darig ate ee E 4 2 3 De correlation of ambiguities 4 2 4 The search method o 4 2 5 Summarizing LAMBDA 4 3 Goad Method o o 020000000004 4 3 1 Properties of the wide lane combination 4 3 2 Goad sintegerestimation 4 3 3 Evaluating the Goad method 4 3 4 Choice of integer solution 4 4 Cycle slip check and repair oo o Kalman Filter 5 1 Discrete Linear Kalman Filter 5 2 Extended Kalman Filter o 5 3 Implementation of EKF o JA Modell Static va a a ate Soka a 5 3 2 Model 2 Kinematic 5 3 3 Filter Initialization and Tuning 5 3 4 Real Time Implementation Issues of EKF System Description Gel Hardware o E A A A hang da A 6 1 1 PC and Application PlatforM 6 1 2 GPS Receivers o en o o e 0 000000 6 1 3 Data Linkanos ea dd do asa 6 1 4 HardwaretesSt o e e 6 2 Application Software Design o 6 2 1 System destan eras A A 6 3 Checks and safe procedures o o o 6 4 Data Handling d soa ce ai ee ar 6 5 Data processing 2 2 2 02 eee eee ee 6 6 Important system functions 0 6 6 1 GPS time Reciever time and check time 6 6 2 GPSephemerides
33. 48238267e 009 omegaDot 2 53089638135862e 009 incDot 3 97903932025656e 012 cre 268 375 crs 92 8125 cuc cus cic cis 4 74415719509125e 006 5 89154660701752e 006 5 40167093276978e 008 1 04308128356934e 007 73 Bibliography AB92 Asa02 BH85 Car98 Dan02 DOF93 Eis99 GA93 HW97 Joo01 Kap96 S Aukstakalnis and D Blatner Silicon Mirage The Art and Science of Virtual Reality Peachpit Press 1992 Kyndal T Asamoah S Gps monitor Technical report Aalborg Univer sity 2002 Report of group 848 G Brown and P Hwang Introduction to Random Signals and Applied Kalman Filtering John Wiley and Sons INC 1985 ISBN 0 471 12839 2 John Carnes Map Tools World Wide Web http www maptools com UsingUTM UTMdetails html 1998 URL visited 24 11 2002 Peter H Dana University of Texas Department of Geography World Wide Web http www colorado edu geography gcraft notes gps gps_f html 2002 URL visited 29 09 2002 DOF Interface control document gps 200c Technical report US DOF 1993 Claus Eisenhardt Reeltids kinematisk differentiel gps Asip design til kalman filtrering Technical report Aalborg University 1999 Report of group 1028 M Grewal and A Andrews Kalman Filtering Theory and Practice Prentice Hall 1993 ISBN 0 13 211335 X Lichtenegger H and Collins J Hofmann Wellenhof B Global Posit
34. HIGH PRECISION TRACKING SYSTEM FOR VIRTUAL REALITY USING GPS AALBORG UNIVERSITY INSTITUTE OF ELECTRONIC SYSTEMS GROUP 948 2002 AALBORG UNIVERSITY INSTITUTE OF ELECTRONIC SYSTEMS Fredrik Bajersvej 7 DK 9220 AALBORG ST TITLE PERIOD GROUP GPS 948 MEMBERS Tue Kluas Kyndal Stephen N Asamoah SUPERVISORS Lars G Johansen Kai Borre NUMBER OF COPIES 5 NUMBER OF PAGES _ 67 pages HANDED IN 03 January 2003 High Precision Tracking System For Virtual Reality Using GPS 01 September 2002 to 03 January 2003 Abstract The key elements of this project was to investi gate the dynamics of a kinematic system and the real time determination of the systems pose posi tion amp orientation To direct our investigations we choosed to focus on the development of a specific application For this we chose the virtual environ ment Some virtual environment systems require a spa tial tracking application for pose purposes Several methods are currently used such as magnetic track ers etc However most of these systems only work in a restricted laboratorial environment With the use of GPS technology an outdoor system could be made For such a system the orientation and position is rather critical and if there is a lag between head movement and visual feedback the user perceives a temporal distortions effect It is therefore neces sary to develop a system that includes a predictive filtering tec
35. allow it Also we don t have any facili ties to establish a scientific way of tracking the rovers real position in kinematic mode It is therefore impossible to evaluate a measured trajectory when it can t be compared with a true one 7 1 System Speed The speed of the system is according to the problem formulation rather critical We must keep in mind that an update rate of 25 30 Hz is needed in the VR system It is currently not possible to compute GPS measurements that fast but the faster an update rate we can achieve the more accurate the algorithm that extrapolate the positions needed in between the filtered state at time k and the predicted state for time k 1 27 1 The output rate of the system is dependent on the performance of three parts of the system They are listed below in order of importance When they all are stretched to their limits the final output rate of the system is equal to the slowest e The systems software performance Process speed e The modem transmission rate e The receiver measurement output rate 7 1 1 Process speed The most important thing to optimize in the system is the process speed Process speed is defined as the time it takes the system to compute one update loop If the 61 CHAPTER 7 SYSTEM TEST AND CONCLUSION 62 software process limit is 1 Hz it does not matter how fast the receiver and radio modem can perform the system would jam up with data if the data input
36. as one of the measurement checks that is done in each epoch How to react if a cycle slip is detected is another matter Either the full set of new integer ambiguities can be re calculated or the problem could be fixed by adding or subtracting the missing cycles to the now faulty integer value The satellite could also be left out off computation for a number of epochs until it is determined if the phase is regulated by the receiver itself If it is fixing it in the software would cause another failure of above described test if the receiver at some point also repairs the problem itself Then the newly adjusted integer ambiguity would have to be re adjusted back to its old value CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 32 The problem of cycle slip is therefore quite difficult and which solution to the problem is best can only be decided by trying different methods and testing their performance Chapter 5 Kalman Filter In meeting the requirements of the Virtual Reality system it is intended that real time kinematic position update is implemented The expected update rate that would meet the requirement is 24 30Hz The receiver in use is capable of up dating at a stable rate of 5Hz There is therefore the need for a predictive filtering techniques that is capable of estimating by use of predictor and corrector the po sition of the user from the available data i e the 5Hz inputs from the receiver To explain further a posit
37. avelength of the C A code chip 1s about 300m and has a chipping rate of 1 023MHz The P code has rather an extremely long 10 chips The chipping rate of the P code is ten times faster than the C A code and the chip width is about 30m The significantly smaller wavelength of the P code would therefore result in greater precision in range mea surement than the C A code MEO1 Usually a user segment consist of a GPS receiver whose basic function is to e capture the signal transmitted by the satellites that are visible e perform measurement of signal transit time and Doppler shift e decode the navigation message e estimate position velocity and receiver time offset MEO1 CHAPTER 3 GLOBAL POSITION SYSTEMS 13 The receiver in use by the group is 20 channel dual frequency GPS GLONASS receiver This receiver is capable of tracking almost all the satellites that are visible in the sky The receiver after getting an initial almanac data and a rough idea of it s location is able to determine the PRN numbers of the satellites in the sky After getting the ID of each satellite the receiver then generates a replica C A code It then shift this code in time until there is a correlation between the replica code and the incoming code The time required to do this shift gives the pseudo transit time of the signal This transit time multiplied with the vacuum speed of light gives pseudorange Usually four or more pseudoranges measured from satel
38. ay of handling this problem is forming a linear combination of the Ni and No also called the wide lane combination Nw N No 4 11 4 3 1 Properties of the wide lane combination The wide lane combination can be regarded as a measurement on a simulated 3 wave with its own properties and behavior The most important is the wavelength and the fact that it is nearly un correlated with the measurements on L1 and L2 individually CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 29 The wavelength of the wide lane combination can be computed like this 300000000m s 1573 MHz 1228M Hz 0 80 e fi fo A quite different wavelength compared with the L 0 19m and La 0 24m A narrow lane combination can also be computed where N M N The narrow lane has a wavelength of 0 1m and is not useful in the estimation of the integer ambiguity The wide lane is computed by the following linear combination which intro duces the transformation matrix T 1 0 0 p o T 0 1 1 Ny No 4 12 01 0 No No The variance co variance for the transformed state vector Z can now be com puted just like it was done in the float solution case S TA CTA SF 0 9880 0 0356 9 1058 X 0 0356 0 0807 0 0490 9 1058 0 0490 84 9040 Again the variances for the state vector are found in the diagonal p I Nw Nz diag D 0 9940m 0 2841 cycles 9 2143cycles Earlier it was found that the variance
39. ch Epoch Epoch Figure A 3 Plot of the full filtered state vector The norms for position velocity and acceleration has been included File xF_correct eps The plot clearly shows how the filter finds the correct stable state in the center of the circle after having been in motion How quick is not possible to tell since 1t can not be compared with any known values APPENDIX A KINEMATIC TEST 71 Inovations Kalman gain iP for Circle sigmaSys 0 005m sigmaObs 0 01m 0 4 T T T T T T 0 2 4 Inovations for X m o 1 0 4 J 1 fi i i 0 100 200 300 400 500 600 700 0 4 T T Inovations for Y m 0 4 J 1 fi fi 1 fi 0 100 200 300 400 500 600 700 0 2 T T Inovations for Z m 0 2 L L 1 L 1 L 0 100 200 300 400 500 600 700 Time in epochs sampling rate 0 6 s Figure A 4 Plot of the product of Kalman Gain K multiplyed with the double difference innovations File ino_correct eps Here the actual innovation vector which is added to the a prior state is shown for the full test We have only included innovations for position since the inno vations for the derivatives of the position show the same picture on a very smaller scale The plot clearly shows how the innovations nearly disappear when the rover is not moving in the center of the circle APPENDIX A KINEMATIC TEST 72 r x10 Circle diagonal of Co var matrix SxF sigmaSys 0 005m sigmaObs 0 01m T T T T T T
40. clock and satellite clock can be related to GPS Time GPST as tilt t 6t t t t T t 7 6t t 7 3 2 where t and t are the clock biases in the receiver and satellite respectively measured relative to GPST Kap96 Incorporating the clock biases ie equation 3 2 and into equation 3 1 the pseudorange can now be written as P t clt dts t t T 8t t T ej cr c dt t t t r e 3 3 The term cr can be modelled as cr pr t t T 13 T 3 4 where p t t T is the geometric distance between the receiver at time t and satellite at time t 7 I and T are the delays in the ionosphere and the troposphere respectively The model for the pseudorange now becomes P t pi t t 7 17 TP c t t 6t t 7 ej 3 5 The accuracy of our position estimation would however depends on how well we are able to eliminate or compensate for most of these biases and errors in the measured pseudorange CHAPTER 3 GLOBAL POSITION SYSTEMS 15 3 2 2 Carrier phase measurement This measurement is much more accurate than the pseudorange measurement and would therefore give a better position estimation The carrier phase f is given as the difference between the phase of the receiver generated carrier signal at the instant of reception and the phase of satellite generated carrier signal at the instant of transmission However only fractional carrier p
41. ct other approaches are needed to govern tracking of the system This requires a tracking technology that could work outdoor without a large hardware setup and independent of time and place The specifications for an outdoor system differ from the cave system given the different circumstances Most important is the distance to the augmented object that normally is assumed to be much longer than in the cave An example could be a session where a new windmill has to be visualized to the public The longer distance means that a bias on the position is less significant because a offset is impossible to distinguish meaning that a minor bias of the position would not matter as long as it does not flicker to much An approach that smoothes the position is needed The orientation on the other hand is a different matter Since an angular error of the orientation is enlarged proportional with the distance to the object One way of solving the above mentioned problems would be to restrain the users view point by using a special designed pair of binoculars set up in a unmov able frame so an accurate angular measurements could be preformed This could augment the object with great accuracy but will not give the user a real VR expe rience For this reason the system has to give up of the restrictions of a fixed set of position and frame and follow the user around It is hard to set up a final and realistic specification for such a moving VR system si
42. d two global structures one for the ephemerides data eph and one for the data measured data Allocation of ephemerides The global structure eph was used for all ephemerides data so they would be available for all function It is designed like this eph sat 1 x 37 struct sateph 4579 14 24 30 The fields eph sat can contain the orbit information for 37 different satellites The fields however contains 21 variables picked from the ephemerides message eph sat status SU toc y y cis The first cell in the sat field is status This is set to 0 or 1 depending whether or not the ephemeris for the satellite is available The rest of the variables are the 21 ephemerides elements defined in Nav95 See also the full array with value examples in the appendix B Allocation of measurements After all raw data has been processed it has to be allocated so it can be reached by the functions in the program Because similar data measurements for 2 different receivers has to be organized a global 1x2 structure called data with a number of field and cells were used This way measurements from the master receiver is allocated in data 1 and the rover data in data 2 The fields in data are organized like this data 2 nSats 7 position 4 x 1 double tod 45889 sow 132289 usi 457914 24 30 sat 1a30struct commonSats 4579 14 24 30 NoComSats 7 refsu 7 refkol 3 CHAPTER 6 SYSTEM DESCRIPTION 52 Like th
43. double differences P and Pa are computed for all satellites and the results are stored in the vector bk which finally will be a 2n x 1 vector where n is the number of satellites These computed double differences are used in the filter state update equation for time k like this iP bk bkk inovation residual State estimate fy Ky iP 6 3 The final routine is the EKF is a prediction of the filtered state for time k 1 Ly 1 This prediction is computed in the same way as the a prior state x CHAPTER 6 SYSTEM DESCRIPTION 60 tp F amp 6 4 The prediction of the filtered state into the future is meant to be used by an other function which would generate the 30 Hz position update needed by the VR system These positions are partly generated by extrapolate additional pseudo po sitions in between the filtered state and the prediction This part of the system has not been developed since the group has realized that another and quite different approach most likely is better This will be discussed in the conclusion Chapter 7 System test and Conclusion It has been decided to divide the system test in to categories One regarding the speed of the system where we will evaluate and discuss the achievable update rate Secondly the filter tuning and performance will be described and evaluated A test of the system accuracy would have been preferable as well but because of problems with the radio link time did not
44. e before returning to the center to finish It should be mentioned that the described measured session was not executed to our satisfaction and if time had allowed it we would have preferred to re measure the session until the circle motion was executed as flawless as possible Since we currently only have one usable kinematic measurement this will have to do Results All the results should be viewed by opening the eps file First because they are in color secondly because it helps to zoom in on the individual subplots The filename are included for that purpose The files are included on the CD and they can be downloaded on the home page 67 APPENDIX A KINEMATIC TEST 68 ENU baseline Components Test Cricle sigmaSys 0 005m sigmaObs 0 01m T Easting Northing Upping S a l a a State Vector Changes Relative to Initial Epoch m I o l ae oa 0 100 200 300 400 500 600 700 Epochs 0 6 s interval Figure A 1 Plot of easting northing and upping ENU for the circle test File ENU correct eps Here the northing easting and upping can be compared with each other They have been plotted with the known center of the circle as reference point APPENDIX A KINEMATIC TEST 69 Easting Vector m Northing Vector m 72 26 71 25 E 70 24 o 2 Z o 69 S 23 68 22 67 21 0 200 400 600 800 0 200 400 600 800 Epoch m
45. e clock offset cancels but worthy mentioning anyway Set and Query commands Within the application software a number of settings and querying were done These commands are all described in the GPS Interface Language GRIL which is reference for detailed information Top01 Here only the most common com mands used will be mentioned All set commands follow the same format The set commands are meant to be printed to the receiver through the comport An example of a set command that will reset the receiver General format set object name value Reset command set par reset yes The query for data output is also a set command that either enables or disables a Javad Positioning Systems JPS output file The handling of this file will be CHAPTER 6 SYSTEM DESCRIPTION 44 described later If one set of data is only needed once it has to be enabled by a set command properly processed and then disabled again Otherwise the data will be repeated with the default rate of 1s Any number of data types can also be enabled with a specific output rate All the query commands follow the format em cur log msg def The list below show how the three data quarries used in the system are designed Enable Disable Receiver Date and GPS Time em jps RD GT dm jps RD GT Enable Disable GPS Ephemerides data em jps GE dm jps GE Enable chosen data measurements at rate 0 6 sec em jps RT SLR1 R2 P1 P2 EE 0 6
46. e determined dynamically by some mathematical model defining the movement of the user in VR system On the whole an update rate of 24Hz can be said to be attainable with some few modification and also by making a parallel algorithm that takes an input from 65 CHAPTER 8 CONCLUSION 66 the the filter and extrapolate position in between measurement update The group has through the project period come to realize that using a state vec tor of positions velocities and accelerations to enable us to make a good prediction for time k 1 which will be used in some extrapolation routine properly could be done in a smarter way A better choice of method may have been to include a heading and heading speed in the state vector instead The filtered position the heading and its veloc ity could then be used by the extrapolating routine for any period of time until new data arrives from the GPS system The heading vector could also be updated continuously with input from the much faster INS system that is guiding the sys tem orientation A solution like this may both have been better to react on small position changes and it would definitely have been better at estimation the position during periods where the GPS system for some reason can not solve the position Prospects for the system The future prospect for combined GPS INS and VR system are highly dependent of the development of hardware and their market prices Currently the full sys
47. e eph sat data also has a fields called sat where all satellite specific data are stored according to the prn number This fields looks like this data 2 sat 1 x 30 struct prangel prange2 phasel phase2 elev To exemplified the use of these structures lets say that the system is tracking the 7 satellites in above examples A call for the ephemerids status for satellite 4 would be eph sat 4 status and the measured L1 pseudorange for the same satellite would be data 2 sat 4 prangel 6 5 Data processing Before the data from the receivers are processed a data integrity check is made to insure proper processing of the raw data A wrong data passed on to the system could either crash the program or give an error message The procedure used in checking data integrity is as follows In the receiver user s manual the following is stated about the binary output massage All messages begin with a unique message identifier which is two ASCII char acters This is followed by the length of the message body descriptor which is a three upper case hexadecimal digits This descriptor gives an indication of the length of the message in bytes Then the message body itself follows At the end of every message there is a checksum Top01 This knowledge was used in developing the code that check the integrity of the messages and also for parsing each message type to the correct decoding algorithm All the messages in an epoch has a unique identif
48. eiver output rate As has been mentioned in the hardware test the receiver output rate can be expected to be stable down to 10 Hz This was also our experience throughout the tests when the receiver was connected to the pe with comport cables Using the radio modem is another matter The measurement rate is therefore highly dependent of the radio link 7 1 3 Modem transmission rate Since the system requires a radio modem connection this was subject to a lot of investigations As has been explained a broken core in one of the cable plugs delayed any progress in this area till nearly the very end of the semester Finally the problem was solved and we took the time to make some additional test and found some workable settings which is described earlier in hardware setup The radio link was found to be stable when connected to a receiver with a measurement output rate all the way down to 5 Hz on short ranges Power level adjustments could properly solve the range problem It was also possible to use an output rate of 10 Hz but not without several prob lems First the fast output rate seemed to block the modem for incoming massages CHAPTER 7 SYSTEM TEST AND CONCLUSION 63 This means that when a message output has been enabled it can not be disabled again though the radio link This represents a major problem with the current soft ware designed where the massages from the rover and master always are enabled and disabled in sync With s
49. es see equation 5 11 In this process the distance p to and the position of the satellites in ECEF is computed in the function get rho with the previous filtered state 2 and the P code pseudorangeas as input The satellites positions are corrected for earth rotation during the signal travel time The observed P code pseudorange is used for this purpose e Observation Matrix The double differences b for the observations are computed according to equation 5 12 Furthermore a set of computed double differences bk is also prepared from the geometric distance p which is the geometric range from the two receivers at time k to all common satellites This is later used in the filter as the predicted observations in the filtered state update equation e Filter routine Finely the filter function kalman is called What happens in the filter will be described next section e Output The Easting Northing and Upping baseline ENU is computed by first trans forming the rover position in ECEF onto the geoid in togeod m Then an other transformation in the function xyz2enu completes the job The ENU vector is part for the function output CHAPTER 6 SYSTEM DESCRIPTION 59 The kalman routine In the function kalman m the actual filtering is done according to the filter equa tions 5 3 5 4 The routine has been moved into a subfunction for several reasons First it clarify exactly where and how the filtering is done Secondly the fu
50. full The tuning was performed by testing a long set of values for the observation and system variances used in the filter until the filter result became reasonable During the tuning and filter test the following parameters were recorded for post analysis e The filtered state 7 e Is covariance matrix Pp e The ENU baseline e A designed innovation vector Plots for the final tuned filter can be found in appendix A The purpose of the first three items are rather obvious since they are the direct output of the filter The innovation vector requires some explanation though CHAPTER 7 SYSTEM TEST AND CONCLUSION 64 The Kalman Gain K in the filter has the size of 9 x 2n because it contains information about the weighting of all the double differences in the measurements innovation vector bg bkk which is 2n x 1 It can therefore not be analyzed directly The product of K x bj bkg which is the actual innovation added to the filtered state can be analysed This innovation vector was used in the analysis The settings of the variances are still somewhat unclear and could most likely be improved through further testing Especially with a better set of kinematic mea surements Though the discussion is still the same The weighting of the observa tions vs the weighting of the system is essential Either you chose a filter that is quick in the response to sudden movements but also vulnerable to measurement errors and noise or
51. ger solution At this point the group has chosen to implement both the lambda and the goad method in the system code It will then be up to a number of system test to chose which approach is appropriate It is all together premature to chose a final solution since the filter theory has not jet been elaborated As mentioned in the introduction some means of filtering techniques must be applied to the solution for an optimal estimate How this is implemented will be described in the next section 4 4 Cycle slip check and repair As mentioned in the earlier discussion of ambiguities in the Topcon receiver cycle slips can and will occur in RTK systems The group has decided not to rely on the receivers capability to solve the problem and will therefore elaborate the following theory of how to deal with the problem First the cycle slip has to be detected somehow This is done rather easily when both the code and phase on a carrier is available A simple check on the observation innovations from one epoch to another can be made The factor of the innovations on both code and phase should be the same for both L1 and L2 In SB97 it has been formulated like this AO j APU AQ j AQ 1 APG AP To weigh down random errors and check both L1 and L2 at the same time the above j and P j is defined as follows AP j o1P 5 a2 Po j A j ai j ag o j 2 Gi ea 4 16 f 2 This tool can be implemented
52. h A Receiver Clocks etc gt gt Figure 3 1 Summary of errors 3 5 Relative Positioning Several methods exist for which one can use in computing the position of the re ceiver antenna Choice of method usually depends on the intended application and also the types of receivers one has at hand Method like static single point positioning has already been discussed in our earlier project Asa02 and would therefore be left out in this current project Taking the intended application into consideration we would limit our discussions on only the methods that could be used to meet the requirements We would therefore concentrate much more on Differential GPS DGPS The main idea behind DGPS is to assume that the er rors due to satellite clock ephemeris atmospheric errors ie ionosphere and tro posphere and receiver clock are the same for receivers separated by some few kilometers And so when we form measurement differences these errors are can celled We discussed a few of such methods in this section The objective is to determine coordinates of an unknown point with respect to a known point In other words we are determining the vector between the two points known as the baseline For example let point A with coordinates X 4 YA ZA be the known and B with coordinates X g Yg Zp the unknown And let b A B be the baseline vector The baseline vector b A p can be expressed as XB XaA AX AB bag Ye Ya
53. h of the message is unknown It is also impossible to skip the full length of a corrupted massage to jump to the next useful massage Therefore another and more sophisticated method is being used throughout out the rest of the project This new approach reads all the bytes available from the com port object into matlab and with the help of a number of special dll files developed in C we then processed each bytes according to their precision At typical script that would processed all the bytes from the com port object into matlab is as follows while sl BytesAvailable gt 0 add fread sl s1 BytesAvailable char receph 1 receph 1 char add and The above script would read everything in the com port object into matlab The variable receph recorded ephemerids data would then contain an array of all the raw ephemerids data This date could then be processed by a function designed specifically for that Let s for simplicity reasons reflect back to the above example showing the exact structure of receiver date RD The function msgRD m that would process this message from a recorded data stream would then look like this the old way of reading bitwise with fread is added for illustration CHAPTER 6 SYSTEM DESCRIPTION 54 function msgRD msg no global data year getu2 msg 1 2 Sfread c 1 uint106 month getul msg 3 Erecadiliey ll want 8 lt 4 day getul msg 4 S fread c 1 uint8
54. hase can be measured at signal reception time leaving an integer number N of whole cycles The estimation of N is the so called integer ambiguity resolution The carrier phase equation is given in the absence of clock bias as pi hi ot 7 Nf E 3 6 re writing the above equation taking into consideration of all measurement errors and also writing phase as a unit of distance we have D pf If T ef ti t 6t t r Mbilto 4 to HAN E BD Note that has been multiplied by the the nominal wavelength A of the carrier signal to give which is in units of distance A c fo 3 8 It can be seen that both the code and carrier phase measurement are corrupted by the same error However the carrier phase measurement which is said to be precise has to be resolved for integer ambiguity before the measurement can be used for any position estimation Determination of integer ambiguity is discussed in Chapter 4 3 3 GPS errors Most GPS measurement are corrupted with errors which tend to affect the accuracy of the position estimation Errors are usually noise or bias In this section we attempt to discuss most of these error sources briefly 3 4 Satellite clock amp Ephemeris error The control segment is usually responsible for the computation and updating of satellite clock parameters and the ephemeris broadcasted by each satellite This is usually being done by Kalman filtering KF techniques The KF
55. hniques such as the Kalman Filter Real Time Kinematic RTK GPS is used for the es timation of the user s position in the virtual environ ment The problems concerning system orientation was not addressed in this project Preface This report is the documentation of a 9th semester project at AAU Institute of Elec tronic Systems The project aimed at implementing a tracking system for virtual environment The first few chapters give a brief introduction into the requirement of the VR system and a detailed analysis of the algorithm used in implementation The remaining chapters give a description of the system test and result Most of the coding was done in Matlab and a lot of m files already done by Kai Borre was used with little modification Few C MEX files were also used in reading binary data from the com ports All the m files mentioned in the report together with the manual of the JPS receiver can be found on the attached CD or the url e http kom auc dk group 02gr948 Projects html e http tue kyndal dk Projects html e http uk geocities com sasamoah Projects html gt To run a test programme off line just type rtk at the matlab command prompt and enter Then choice off line mode Tue Klaus Kyndal Stephen Neuman Asamoah Contents 1 Introduction Leal Background zaradeni dl eek ae ee aged 1 2 Tracking requirementinVR 04 1 2 1 Requirements in a outdoor VR 1 3 Proble
56. ier which is used to identify the type of message to decipher for example GE for GPS ephemerides and P1 for Code observation on L1 If any particular message is corrupt then at least one of the unique message identifier would be It is only the message containing the receiver time RT which has as the identifier The message body descriptor three hexadecimal digits are decoded to get the length of the message in bytes The actual message is then processed and sent to it rightful cells Each message body type comes in as either an integer unsign inter float double etc etc depending on the content of the messages For example a data structure containing the receiver date data set is given by CHAPTER 6 SYSTEM DESCRIPTION 53 struct RevDate u2 year current year 1 65534 ul month current month 1 12 ul day current day 1 31 ul base receiver reference time enum 0 GPS 1 UTC_USNO 2 GLONASS 3 UTC_SU 4 254 Reserved ul cs checksum where u2 is a two bytes unsign integer and ul is just a byte of unsign integer In matlab this message type could be deciphered bitwise with the fread com mand like this variable fread location length precision This was done in the initial stages of the development but it was found to be slow reading bitwise Also this method of processing raw data is not very stable and it can be quite difficult to handle when the lengt
57. ime response from the system is required As earlier stated in the previous section accurate means of tracking the position and orientation of the user is needed in order to determine the user s view point This is then communicated to the graphics system of VR and appropriate images or scenes are then rendered and sent to the Head Mounted Device Display HMD Usually 24 30 frames per second are needed to experience a good visual effect Soc02 This update rate gives the basic requirements for the tracking system since every frame is computed as a function of position and orientation CHAPTER 1 INTRODUCTION 3 Current technologies for head tracking systems make use of magnetic trackers or audio systems with an update rate of about 180A z Soc02 These system must be set up and configured in a restricted environment because the use of magnetic trackers introduce errors caused by metal objects in the surroundings Likewise the audio systems can be confused by echoe s These errors appear as errors in position and orientation and can not easily be modelled The range of such a track ing system are also rather limited approximately 25m If the range is exceeded or the update rate is slowed down lags between the position and orientation esti mation and the rendering device could occur giving the user a temporal distortion experience Soc02 1 2 1 Requirements in a outdoor VR To move the VR outdoor which is the purpose of this proje
58. inverse instead of the normal inverse function if the matrix could be none singular e Built in a reset option in the system and in functions containing changing persistent variables if these variables can converge to infinity or simply misbehave 6 4 Data Handling In the following section the actual data handling procedures will be described We start with the allocation of system variables and measurement data As mentioned a predefined structure of all data arrays and variables were de signed It was decided to use structures with fields and cells which in some cases is equivalent to the pointers used in C programming Instead of handing over local copies of large arrays with data pointers are much faster and error safe Another difference between a normal array of variables and a structure with fields and cells is the knowledge of exactly where a specific piece of data is located Because the nature of the data in a GPS system large numbers of common data is present therefore this knowledge is very convenient Data for the satellites orbits and the measurements for a given epoch must be locates somewhere When using structures and fields to solve the problem it is possible to sort the data according to the satellite unique prn number That means no resources are needed to find data for a specific satellite it would be directly CHAPTER 6 SYSTEM DESCRIPTION 51 available and located according to the prn number The group define
59. ion ing System Theory and Practice Springer 1997 ISBN 3 211 83534 2 Peter Joosten The lambda method Matlab implementation Technical report Delft University of Technology The Netherlands 2001 Editor Kaplan Elliott D Understanding GPS Principles and Applica tions Artech House Publishers 1996 ISBN 0 89006 793 7 BIBLIOGRAPHY II May97 MEO01 Nav95 SATO1 SB97 Soc02 TA98 Top01 TRI02 Val02 Peter S Maybeck Stochastic Models Estimation and Control Aca demic Press INC 1997 P Misra and P Enge Global Positioning System Signals Measure ments and Performance Stanford Bookstore Custom Publishing 2001 GPS Navstar Gps sps signal specification Technical report GPS Navs tar 1995 Filename gpssps1 pdf SATEL OY SATELLINE 3AS Users Guide Version 2 1 2001 File name satel manual pdf G Strang and K Borre Linear Algebra Geodesy and GPS Wellesley Cambridge Press 1997 ISBN 0 9614088 6 3 Virtual Reality Society World Wide Web http www vrs org uk public past html 2002 URL visited 22 10 2002 P Teunissen and Kleusberg A GPS for Geodesy Springer 1998 ISBN 3 540 63661 7 Topcon GPS Receiver Interface Language Firmware Ver 2 2 2001 Filename Grill pdf TRIMBLE World Wide Web http www trimble com gps 2002 URL visited 20 09 2002 Jim Vallino World Wide Web http www se rit edu jrv research ar 2002 URL vis
60. ion update of at least 24Hz is required but the receiver in use is capable of updating at 5Hz In between this 5Hz update rate we are to predict the position for a few Hz until new epoch of measurement data is received from the receiver Hence a Kalman Filter KF is being used in estimating and predicting the position of the dynamic user in VR The preference of Kalman filter to other filters is because of the following reasons e Kalman filter make use of all measurement data available and with prior knowledge about the system and measurement device it produce an estimate of position in such a way that the error is minimized statistically e Apart from it being used as an estimator the kalman filter can be used in analysing the system error e It s recursive nature which is explain later make it a good tool for real time applications A Kalman Filter is an optimal recursive data processing algorithm Optimal in that it make use of all information that can be provided to it and recursive because storage of previous data is not necessary According to Maybeck Peter S Kalman filter uses e knowledge of the system and measurement device dynamics e the statistical description of the system noise measurement errors and un certainty in the dynamics model and 33 CHAPTER 5 KALMAN FILTER 34 e any available information about initial conditions of the state variables to estimate the current value of the variables of interest
61. is correct e Check if the raw data checksum is correct e Check if raw data ends with line feed e Check if any of the processed variables is NaN e Check if the data from rover and master are in sync e Check for cycle slips CHAPTER 6 SYSTEM DESCRIPTION 50 Specific safe procedures Some safe procedures are used especially where the system is expected to crash or stall One example could be the control of a conditioned loop Some algorithms and functions uses iterations to obtain their goal often governed by a conditioned while if or for loop which could continue infinitely if not stopped Other algo rithms like a matrix invention will go wrong occasionally with the occasionally unstable GPS data The following safe procedures are therefore used as much as possible in the system The ideal is normally just to skip the epoch and re try with new data if something turns out wrong Some times more drastic procedures are called for and both function or a full system reset should be possible Below is listed the most common safe procedures e Use the try catch and end procedure for all function call with an unstable nature For example LAMBDA which dos not always compute e Built in a set of default functions return values e g constants and correct sized vectors and matrixes of zeros that can be returned with an error flag if the function does not compute e Use stop counters in all conditioned iteration loops e Use the pseudo
62. ited 20 09 2002
63. ived from the two GPS receivers It is checked and processed into the struct data 1 and data 2 2 Common satellites for rover and master are found and all measurements are checked for integrity 3 Ephemerides are checked for all common satellites If a new satellite has appeared or an ephemerides is too old we exit the working loop to update 4 If all parameters are ok we compute the position in an Extended Kalman Filter 5 The position is then ready for output to the VR system As mentioned the work loop will be exited if an ephemerides update is needed Then the update loop is engaged Update loop 1 First a new set of ephemerides are collected and assigned to the struct eph 2 Then a set of 8 unique data specimens spaced with 2 seconds interval are collected All data is checked and must contain data from the same common satellites 3 This data is then feed to a least square solution algorithm and the float solu tion for baseline and ambiguities are obtained 4 This float solution is the input to the LAMBDA method which estimates the integers CHAPTER 6 SYSTEM DESCRIPTION 49 5 The baseline is corrected with the fixed integers and the solution is feed back to the work loop where we proceed The actual startup face work and update loop all contains a large number of functions and scripts It is not intended to describe all these functions and their algorithms Most of them are standard GPS algorithms
64. ke is speed of update with its corresponding accuracy and stability that can be achieved We would try to identify the required elements needed for the ap propriate tracking algorithm and also investigate the speed of update that can be achieved having in mind of a speed of 30H z The intended approach will be to vary parameters in the processing algorithm to verify the speed accuracy and stability that can be achieved 1 5 System platform and computing language The group have both a linux unix and a windows 2000 platform at its disposal It is intended to develop software so it is executable on both Mostly because the platforms will be tested individually for stability and speed For a start Matlab software is used to develop the needed algorithm for the tracking applications It should be stated here that this platform would slow down the processing time And this would be investigated in the first phase of the project It may be necessary to develop some or all of the software directly in C but this will not be part of the apparent task 1 6 Hardware limitations The group will be working with two Topcon Legacy receivers This receiver is according to the manual Top01 capable of giving an update rate of 100ms 50ms is possible but not recommendable This has been investigated by a test program in Matlab that only received and check output for the two receivers connected to comports at baud rate 115200bps The fastest update rate obtai
65. lites are used to compute position It is possible for us also to compute our velocity by the use of the Doppler shifts and the satellite velocity vector normally given in the ephemerides This doppler shift is caused by the relative motion of the user and the satellite It s value can be converted into pseudorange rate In computing our velocity measurement of four or more pseudorange rates to satellites as well as satellites velocity vectors are needed ME01 Accuracy Position accuracy is affected by noise by satellite geometry and by bias errors Usually the quality of the position determination depends on 1 the spatial ar rangement of the satellites in the sky called satellite geometry and 2 the quality of the measured pseudoranges known as bias Satellite geometry actually has to do with the spread or distribution of the satellite relative to the receiver as the satellites moves in the sky A good coverage in azimuth and elevation offer a good geometry The separation is described by the so call geometrical dilution of precision in our earlier project Asa02 Errors like delays in the ionosphere and troposphere multi path propagation reflection orbit error and clock offset affect the quality of the measured pseu doranges However most of these errors can be removed by using dual frequency receiver and employing Differential GPS DGPS measurement technique as ex plained in section 3 5 3 2 GPS observables We ca
66. m formulation o o e LA CODIEC IVES o oe ee hae ie a a Be 1 4 1 The current project o 1 5 System platform and computing language 1 6 Hardware limitations o o e 1 7 Expectations for the system o 2 RTK systems 2 1 Introduction to RTK systems 3 Global Position Systems 3 1 GPS principles rios sey ener eee es ena Be ow ak Sd Ae aye ed 3 2 GPS observables cui io a Geog ale wm ne gold Sha aa one 3 2 1 Code measurements Pseudorange 3 2 2 Carrier phase measurement 39 3 O A AR ae 3 4 Satellite clock amp Ephemeriserror 3 4 1 Ionospheric Delay o o 3 4 2 Tropospheric Delay o 3 43 Receiver Noise e e ee 344 Multipath 0 ara y e a a ark aad 3 5 Relative Positioning e 0 20000 3 5 1 Single difference o oo 3 5 2 Double difference o 3 5 3 Triple difference o oo 3 5 4 Combination of Code and Phase Measurements 3 5 5 Baseline Vector Estimation A Dd Du UB gyYNnN e pu 4 Ambiguity Estimation Concepts 4 1 Ambiguities in Topcon receivers what is the relevance of this sec 4 2 Elo dt SOLOMON 16 2 deg tage sop ie Gone il eo ee deca Ae ay ted 4 2 1 The variance covariance on the float solution 42
67. measurements and filtering has the same characteristics It has to settle on a steady direction within a fraction of a degree when the system is stationary and also quickly adjust on sudden movements For both position and orientation the capability of quickly finding a stable state is the overall important feature A minor bias can be accepted if the former is obtained The above discussion of outdoor VR has given ground for the following hy pothesis The positioning of an outdoor VR system can be obtained by the use of GPS measurements and filtering techniques Solution of the system orientation could be done simultaneously but would require more equipment and other measurements 1 3 Problem formulation It is the aim of this project to investigate whether or not the use of GPS technology can be used to achieve some of the requirements of the VR system especially regarding the positioning of the system In the case where the VR environment is moved outdoor from the normal cave like laboratory environment a more hybrid systems are needed Here GPS system could be investigated because current processing algorithm of the technology is able to give a fast and accurate position of the user in space nearly regardless of time and place Furthermore by using hi tech filtering technologies a filtered and predictive update of the position can be computed With extrapolation algorithms an even faster position update rate could be achie
68. n derived two types of measurements from a GPS system The first is a code tracking known as pseudorange which is a timing measurement that provides an es timation of ranges to the transmitting satellites The other is a carrier phase tracking which gives relative phase measurement between the received carrier phase and the one generated by the receiver Since the wavelength of the carrier signal is 19cm at L1 and 24cm at L2 it allows very precise measurements of the phase to be made In the next section we briefly discussed simple mathematical models relating these two measurements to their ranges to satellites CHAPTER 3 GLOBAL POSITION SYSTEMS 14 3 2 1 Code measurements Pseudorange Transit time is defined as the time difference between signal reception time by the receiver clock and the transmission time at the satellite MEO1 This quantity is mostly measured by the GPS receivers However it contains bias due to atmo spheric delays multi path etc Hence it is a pseudo transit time The pseudo transit time multiplied by vacuum speed of light gives the pseudorange P expressed math ematically as P t cl t t r e 3 1 where Pf is equal to the difference between receiver time t at signal reception and satellite time t at signal transmission multiplied by the vacuum speed of light c T is the transit time or travel time of the signal from the satellite to the receiver e is the pseudorange measurement error Receiver
69. n is called the returned fixed solution is checked for error flag and a test is performed to check the reliability of the fixed solution This is done by making the ratio between the squared norms of the best and the second best fixed solution The result is discarded if the ratio is above 0 7 This value was found by testing the function CHAPTER 6 SYSTEM DESCRIPTION 57 6 6 6 The extended kalman filter The final and most important of the function in our system is ekfrtk3 m which is the function preparing a call to the extended kalman filter in subfunction kalman m These functions will get our special attention in the rest of this system description Before the actual filter routine can be launched quite a lot of preparation is needed The most important of this preparation will be explained in the following The actual filter routine has been moved to a subfunction containing the 5 filter see Chapter 5 to enhance the control of the filter The main purpose of the filter is the computation of raw DGSP data into a state vector containing the position baseline and if chosen derivatives of this We work with a multiply of choices for the filter model e Model 1 is based on a 1 x 3 state space model Here the state vector contains the baseline in ECEF co ordinates e Model 2 contains an example of how to include the derivatives of the state we include the velocity and the acceleration giving a 1 x 9 state space mode The filter routi
70. nce in reality would depend on the users ability and will to accept some distortions in the augmentation It is a known fact that a VR system can cause nausia if the images flicker to much The system setup should be a balance between a system that automatically restrain the users movement giving very small image variations to a more free system which may temporally give the user image distortions especially at sudden movements In the latter case it will be up to the user to restrain and control the amplitude of the system movements in a degree that only give distortions that are found acceptable System that is good enough could likewise only be decided by user tests If CHAPTER 1 INTRODUCTION 4 the user is not capable of controlling the system in such a manner that image distortions can be avoided or if the system requires major movements restrictions to work the system clearly is ineffective Still a number of minimum demands are required to obtain a system that a user could accept First the position and orientation update rate must as a minimum follow the image update rate which is 24 30H z to enable a good augmented image The accuracy of the measured position must be good enough to ensure a steady filtered position on cm level when the system is stationary Secondly position filtering techniques has to ensure a quick reaction of position movements to enable a good tracking capability The accuracy of the orientation
71. nction output can be controlled better this way If you for some reason don t want to update the filtered state covarinace variance matrix P in one epoch P could be left out in the function return parameters To prevent one bad epoch destroying the filtered state covarinace variance matrix The filter equations are well described in the theory chapter i e chapter 5 Though one equation in the filter has been changed in order to cope with the DGPS measurements and that is the state update equation shown below State estimate 2 Ky bj Ha The innovation or residuals that are scaled by the kalman gain Ky are supposed to be the difference between the measurements by and the predicted measurements Hit This prediction is not possible to make because of the complex relation in the measurement equations Therefore a set of predicted double differences are computed in advance and used in the filter Here is an example of how one set of double differences are computed for rover and master and j and reference satellites and satellite m Remember that double differences has to be computed on both L1 and L2 and that the geometric distance p is computed using 2 as input The computation of the measurement prediction is therefore made around the current trajectory of the system which is the correct procedure according to the extended kalman filter theory l l m l m Pii Pi Pi Pi T Pj l l m l m Pij Pi Pi Pi T Pj The
72. ned in the test was 200ms or 5 Hz After a modem had been connected between one receiver and the computer another test was performed The modem could only be set to a limit baud rate of 38400bps CHAPTER 1 INTRODUCTION 7 1 7 Expectations for the system Given the above described platform possibilities and hardware performances the following expectations to the system has been formulated e a position with a standard deviation o of 0 3cm e an measurement update rate of 5H z e a filtered and predicted position capable of tracking a moving target with a maximum speed of 0 5km h and a constant acceleration Chapter 2 RTK systems Before we discussed all the different GPS algorithms and filtering techniques let us briefly describe how it is all used in one of the most common GPS applications namely Real Time Kinematic positing systems also called RTK systems 2 1 Introduction to RTK systems The real time kinematic technique is a way to use GPS measurements which pro vides real time centimeter positioning As such it can be considered as a precision measurement instrument which can be used by engineers topographers surveyors and other professionals requiring this kind of a tool in the same way as tradi tional instruments optical or optoelectronic are employed Used in this mode the GPS offers significant advantages compared to more classical devices especially in terms of productivity and more relaxed operational con
73. nes are the same for both models The only difference is the initialization of system transition matrix F its covariance variance matrix Lig and the size of the design matrix H and of course the state vector x and its covari ance varinace matrix P Filter initialization In the initialization of the function a number of variables are declared persistent This way the function will remember variables that are used and updated each time the filter is called These persistent variables are very important for the filter routine because they contain the information about the recursive procedure Some of these persistent variables will be reset and re initialized each time the input to the filter changes to fit the new size of the data Such a reset may seem a bit crude but it is the only thing we can do because a re sizing is needed when the satellite constellation changes This reset procedure is not regarded as a problem E g The filter covanrians variance matrix p will converge within few epochs after a reset to default values The previously computed state vector 2 is re used as normal so the next new state vector will not be influenced much by this reset since the innovations are quite small for each epoch anyway The description of the function rtkekf m will also be divided into individual steps for simplicity e Ambiguity check First the common satellites are checked for fixed solution If any fall out they are removed and will no
74. ng the data input are different on and off line In the following system description only the on line mode is explained For the specific functionality or design of mentioned functions and scripts we refer to the header and comments in the actual m file Initialization face After an online startup of the system the proper variables and comports settings are declared Then GPS time date and ephemerides data are collected from the CHAPTER 6 SYSTEM DESCRIPTION 48 GPS system The system is now ready to handle the first real GPS measurements The first objective is to compute the master position and fix the ambiguities for both L1 and L2 This is done in a script called startup which is meant to be executed only once though it can be re run if the system has to be fully reset and started In this procedure a single point position of the master is found by means of a least square solution on the code observation on L1 Then a float solution is computed using the code and phase observations on both L1 and 12 This solution contains a baseline vector and float ambiguities The float solution is then corrected by the LAMBDA method As mentioned the startup phase can be repeated Eg if no fixed solution can be obtained within a count of 10 the system is restarted Work loop The work loop is the central part of the system where the filtered position is com puted In short it is done by the following steps 1 New raw data is rece
75. ome changes of how to deal with the data from the comport object it may very well be possible to simply skip disabling the output message from the receiver connected by the radio modem One problem that might occur would for example be the stack overflow that could occur on the comport where the output massage has not been disabled This happens when the system is updating the ephemerides on the other comport Anyway time does not allow us to experiment with such changes The con clusion will have to be that an overall output rate of 10 Hz is possible if some problems regarding the radio link are solved 7 2 Filter performance In an attempt to make some form of controlled kinematic test a method was devel oped where knowledge about the true rover position was less significant Therefore a system test was performed using kinematic data from a measured circular motion filtered using model 2 Using a circular motion is an easy way to investigate whether or not the system computes the correct trajectory just by knowing the circle s radius See a description of the test in appendix A Filter tuning With above described measurements the filter was tuned in for kinematic motion The actual tuning of the filter parameters would be a far to big subject to de scribe in this report and could easily be a full subject of its own for a 9th semester project Furthermore the time in this semester was not spent on investigating the subject in
76. orts in Linux However for system stability and performance Linux may have been a better choice of system environment Matlab was chosen for the development of all software to the application The group finds this software good for developing new code because of all the ready to use features and easy readability of codes Also a comprehensive library of existing Matlab code were available for further development However it was realized that everything would have to be re coded into a different language and compiled as executable files if the system had to be used in a complete VR system C programming were investigated and was found to be good but was neglected in the development phase the first phase of this project CHAPTER 6 SYSTEM DESCRIPTION 42 6 1 2 GPS Receivers From a variety of different receivers Topcon Legacy receiver was chosen The reason for this choice was first because the group wanted to investigate a different receiver from the Ashtech that were used last semester Secondly the legacy is very compact and power efficient which makes it preferable for kinematic purposes After having investigated the manual it also became clear that it could provide the group with the measurements needed at a higher update rate than any of the receivers available in the department at the moment Figure 6 2 Topcon Legacy receiver The Topcon Legacy receiver in use is a 20 channel dual frequency GPS GLONASS receiver The recei
77. oses the problem of finding the correct integer value for each ambiguity A method for this has been introduced by P J G Teunis sen and is called the LAMBDA method Least squares AMBiguity Decorrelation Adjustment TA98 The LAMBDA method uses an ambiguity de correlation method by means of the Z transform Then pairs of integers for all the ambiguities are found by a dis crete search over an ellipsoidal region defined by the variance covariance matrix and the correct integers are estimated by means of minimizing by least squares After a validation of the result giving a ratio between the best solution and the sec ond best the integers are used to correct the float solution which was computed to establish the input argument to the LAMBDA procedure In steps the flow is as follows e First a float solution is computed for example as described in the section above The float ambiguities 1 and 2 and their variance covariance matrix Q are used as input to the LAMBDA function e Inthe Lambda function a de correlation is imposed on the variance covariance matrix Q by the Z transform giving the de correlated variance covariance matrix Z This is then used to de correlate the float ambiguities Then a search is preformed where a selected number of integer candidates are tested and the best pairs are found e After a validation of the integer solution the integers and their variance covariance are re inserted into the observation equation
78. rate was faster than the process speed We tested the system on both a 700 MHz and a 1000 MHz AMD processer Naturally the processer speed plays a critically role for the process speed The test was made using model 2 which clearly is the heaviest model regarding computa tions The result of the test was rather surprising The 700 MHz was cable of pro ducing a process speed of 0 21 s The 1000 MHz did much better and only used 0 08 seconds It should be mentioned that the process speed behaved rather strangely on any of the tested computers when running for a longer period of time At first the process speed would settle at e g 0 21 s Then the process speed would slowly decrease to nearly a third of the initial value during the next few hundred baseline computations to finely settle around 0 1 0 08 s We don t know why the com puters tends to get that much faster when repeating the same process The final process speed for a given setup is therefore rather difficult to define Since even the slowest computer The 600 MHz portable pc finally settled around 0 1 s it must be assumed that the actual process speed is around 10 Hz or less With the right computer and further improvement of the code a process speed faster than 10 hz is within reach It is important to note that the process speed should be a bit faster than the system update rate leaving some time so the system can catch up if getting behind for some reason 7 1 2 Rec
79. s H matrix in model 2 now becomes a 2n x 9 matrix Observation vector b is however the same as model 1 5 3 3 Filter Initialization and Tuning In both models the parameters used in initializing the filters are the same The only difference is the sizes of the matrix which are changed to reflect the state estimates The states estimates were initialized to zeros in both cases The measurement noise covariance R was measured prior to operation of filter This was done by taking the variance of measurements Choice of process noise covariance Q was quiet difficult because we do not have the ability to directly observe the process we are estimating A better approach would have been to change Q dynamically during the filtering process by use of mathematical model But time limit could not permit modelling of a random walk In our case where we are tracking the head of the user in virtual environment it would have been good to reduce the magnitude of Q as the user stand still and increase the magnitude as he start moving CHAPTER 5 KALMAN FILTER 39 5 3 4 Real Time Implementation Issues of EKF As have been said in the previous discursion the recursive nature of Kalman filter makes it suitable for real time applications This is because there s no need of storage of previous data used in computation therefore taking less time for the filter to execute However there is some kind of processing and transmission delays that should be addressed
80. sing and handling of GPS measurements 6 1 Hardware As discussed earlier the group intend to make an independent RTK system to govern the position for the VR application Since we have decided only to take GPS measurements into account this will include two receivers a radio link and a PC The system setup is shown in the figure below In this section the selected hardware is briefly described and system specific settings if any are listed and explained 40 CHAPTER 6 SYSTEM DESCRIPTION 41 ROVER GPS one H RTK setur Radio BASE REFERENCE GPS Figure 6 1 Independent RTK system setup Each part of the system will be described in detail regarding choices of hard ware their individual settings and practical setup 6 1 1 PC and Application Platform Pc The group had a stationary personal computer with a pentium III 700 MHz pro cessor for laboratory work and a portable laptop with a pentium III 600 processor for field work They both have the capability to perform the computations needed for the application The choice of computer were restricted to availability at the department Platform Both computers operate on a windows platform The group also had the possibil ity to use a Linux platform Windows were chosen primarily because the group has limited knowledge about the Linux system and also because the group experi enced large problems with the communication between Matlab and the com p
81. specification is therefore designed to meet only the requirements of the GPS part of the system That means that the real VR software would get input from the developed GPS system and a range of other sensors to achieve the much higher VR requirements 1 4 1 The current project Basically the current project would focus on tracking the position of the user s view point by using GPS technology The first phase of this project would concen trate on e Setting up a real time Double Differential GPS system DGPS similar to the Real Time Kinematic surveying systems RTK e Exploring software and system platforms for the system development e Investigating GPS and filtering algorithms and evaluating their capabilities in solving the stated problems CHAPTER 1 INTRODUCTION 6 e Development of a system that in real time will estimate the position of a moving target e Updating the position estimations by implementing filtering techniques e Configure the system to achieve the best possible result by comparing the rate of update that can be obtained vis a vis position accuracy and stability The group intends to use Real Time Kinematic GPS to solve the problem about position determination One aspect of this project is to verify the rate of update that can be achieved vis a vis accuracy and stability taking into consideration of the resources at hand Problem about orientation would be left out for future work The main issue at sta
82. straints GPS operates 24 hours a day in any weather or visibility conditions and can consequently in some cases result in actual complete replacement of the more traditional tools altogether Kinematic GPS can be used not only as a simple metrology instrument but also as a core for navigation systems or automatic machine guidance in a variety of application areas in civil engineering Technically speaking real time kinematic is a GPS differential mode of oper ation using carrier phase measurements as such it is a technique which makes use of the most accurate information delivered by the GPS system The actual phase observations taken require a preliminary ambiguity resolution before they can be made use of This ambiguity resolution is a crucial aspect of any kinematic sys tem especially in real time where the mobiles velocity should not degrade either the achievable positional performance or the systems overall reliability The RTK system setup is normally designed to overcome a given task in the best possible way regarding system requirements budgets and performance speci fications Overall two different approaches are common Either the system contains one single GPS receiver and a radio or GSM link from where special designed differential corrections can be received This systems require a subscription to CHAPTER 2 RTK SYSTEMS 9 receive the corrections and offers global note Some systems are indeed global and uses satelli
83. suc cessfully Hardware test was performed see section 6 1 4 which gave some few problems with the radio link However after the faulty modem antenna was detected and repaired everything worked as expected The next was the software test which was done by testing the main functions in the developed software The main functions that were tested are the function that computes the ambiguities LAMBDA and the extended kalman filter where the position vector is obtained The ambiguity function test was performed by running the script startup 200 times This way the master position is recomputed and new fixed ambiguities are estimated in each loop For all 200 loops the same fixed solution was found With the proper test routine we find the method as close to errorless as possible The lambda method only takes about 0 18 seconds which is nothing compared to the 15 20 seconds data collection After final debugging the procedure also worked to our satisfaction The GOAD method has therefore not been implemented or tested as we first assumed would be the case The next test was the kinematic test as described in Appendix A This test worked to some satisfaction also but time limit did not allow us to investigate fur ther to some details It should be stated here that in tuning the filter we assumed a constant velocity and acceleration However these would not be the case in actual implementation in the VR Hence the system noise covariance could b
84. t be used in the current epoch A flag is raised to ensure a re computation of ambiguities CHAPTER 6 SYSTEM DESCRIPTION 58 e Check the common satellites The next objective is to investigate how the filter should deal with the new data set if it has changed since the last run This is done by comparing the satellites used since in the filter so fare and the new set of common satellites from the data set The flowing scenarios could occur 1 The data set contains the same satellites as used in the filter so far 2 One or more satellites has disappeared 3 One or more satellites has re appeared 4 Both case 2 and 3 has occurred According to a case scenario test the filter is either run with data corre sponding to the previous filter setup or the filter is re initialized to cope with the new size of the new data set A filter reset will therefore occur serval times an hour depending on satellite coverage and especially the con stellation changes If the system is used in a environment with meany dis turbances of the satellite signal some satellites could re and disappear quite often which would re initialize the filter each time Still it is not regarded as a problem the fast update rate taken into account The filter should be fully converged within seconds Though a momentary distortion of the filtered state might occur e Design matrix The design matrix H is designed according to the model and the number of used satellit
85. te transmitted corrections but the most common are restricted to a specific area defined by boarders or geographical features real time centime ter positioning These systems are often used in the industry farming and other commercial branches where a reliable and fairly accurate position is needed Another approach is generating the corrections within a DGPS environment An example is shown in the figure below This requires a minimum of two receivers linked by radio communication and specially developed software to compute the corrections If one of the receivers is mobile it becomes a RTK system Such an independent system is often more accurate than those where the corrections are offered commercially Mainly because the setup of the master receiver can be done closer to the area where the rover is measuring giving shorter baselines and better error determination A local system is also normally more precise because it does not have the errors and bias introduced by a global system This method is often used by surveyors or entrepreneurs needing highly accurate positions The downside to the system is the need of a larger system setup which requires both equipment time and technical know how Figure 2 1 Independent DGPS system setup Beside an overall economical evaluation the choice of system type depends on the requirement of a given task the available hardware and the know how to use it In this case the group has chosen to set
86. tic CHAPTER 1 INTRODUCTION 2 sensors such as inertial boxes sonic discs and potentiometers Val02 This is needed to instruct the graphics system in virtual reality setup to render a view of the world from the users new view point Tracking the position and motion of the user in virtual reality has been a topic for major research projects And this is the focus of this project Virtual Reality can be made indoors as well as outdoors An example of an indoor VR is a Cave Automatic Virtual Environment CAVE in which illusion of fascinating 3 D objects are generated by projecting stereo images on the walls and floor of the room with library software linking all elements The user is free to walk anywhere within the room wearing stereo glasses and means of head tracking equipment An example of an outdoor VR is Augmented Reality In augmented reality the user can see the real world around him with computer graphics superimposed on it This make it looks like both the real world and the virtual world coexist This can normally be used in a historical site museums training etc In augmented reality the virtual world supplements the real world rather than replacing it Figure 1 2 Augmented Reality 1 2 Tracking requirement in VR Virtual Reality VR is defined as a computer generated interactive three dimensional environment in which a person is immersed AB92 For the user to effectively interact with this virtual world real t
87. tion 1 23 can now be written as Pi 1 0 0 e S 1A 0 P 10 0 eu Dd 1 0 A Z This equation can now be solved for the ideal pseudorange p and the ambiguities N and No Estimation of ambiguities is discussed in details in chapter 4 3 5 5 Baseline Vector Estimation The final step after the determination of the ambiguities is the baseline vector de termination It is intended in this project that a short baseline would be used Hence errors due to tropospheric and ionospheric delay are assumed to be elimi nated when the double difference is formed Double difference phase observation equations can then be written without the ionospheric and tropospheric term Op PaptAdNo ap ELAB 3 25 Setting the noise term a p to be zero The equation can be linearized to obtain the Jacobian matrix J from the derivatives of the double difference SB97 1 k kl kl k1 Uy UB PAD AWN AB PAB uA uk Ja Or ip ANG ap Pie ES ya 2 T 4 3 26 n k B kn kn kn Uy UB PAB T AN ZAB PAB where k k k ieS TECEF YA YECEF T YA ZECEF 7A 3 27 AT k y k y k i PA PA PA Approximate coordinates for the master station is needed Also preliminary values for the baseline estimation are needed Equation 3 26 can be solved by least square solution to obtain the baseline vector The general least square equa tion is given CHAPTER 3 GLOBAL POSITION SYSTEMS 22 om A AAT ATb A b In Matlab 3 28 as amp
88. tly and counts the number of full cycles the phase measurement is shifted with according to the movements of the satellite and the receiver These cycles are then either added or subtracted to the adjusted phase measurement in each epoch This means that the unknown number of integer ambiguities always will be the same as long the receiver can track the phase undisturbed If an obstruction of the carrier or a receiver measurement error occur the phase tracking can easily go wrong This causes a so called cycle slip and if it is not repaired somehow the phase measurement has a bios of one or more cycles This will be minimized it the position adjustment but will always inflict an error upon the position Especially because the weight on the phase measurements is so high The method to estimate the correct number of integers in the startup face must therefore be followed up some way of checking the phase measurements and cor rect any cycle slips It must be said that the technology in the Topcon receiver is known to do a good job in checking for cycle slips and repair them it self Newer the lees it will also be part of the group objective to find our own way of handling this problem Especially because cycle slips have an much higher chance of occurring on a RTK system which moves randomly around and therefore implies many obstructions to the carrier wave 4 2 Float solution Given the earlier stated double difference equations for the
89. uations If this is not done the CHAPTER 6 SYSTEM DESCRIPTION 56 variance covariance matrix would seem not positive definite because the values would be quite small This is a problem occurring only when using fast data output rate about 5 10 Hz e construction of observation equations In a loop all the epochs of collected data are computed according to the equations 5 12 and allocated in two large arrays which finally will contain all 8 epochs of observation equations How we create the design matrix H and observation vector b will be described in detail in the next section The matrix containing the full set of design matrixes is called N and the observation is rs right side e Least square computation The full set of observation equations are then processed in a least square adjustment Notice that we uses the safe pseudo inverse pinv to prevent a possible system mal function The least square equation is repeated for convenience The normal case Bxx b e ED With our re sized equations and safe procedure Nxzx rs PP pinw N zz PPxrs 6 2 e LAMBDA The next step is to feed the float ambiguities to the m file lambda2 m where the fixed solution is estimated Then float baseline vector is re computed with the fixed ambiguities This entire step is included in a try catch end loop where default values of O are returned with an error flag if the lambda function does not compute Every time the rtkfloat functio
90. ully it will also give our readers an ideal of how the system is designed CHAPTER 6 SYSTEM DESCRIPTION 47 Program Get GPS Time Get Ep eS mode Fie Ambito Initialization gt GaN ew ie Fix new ambiguity Data output Bg WS Pre compute a7 variables G Work Che ck data Update 100 l loo p N p j i yi 1 PS N Wie Check if oe Extended Kalman epherimedes need Filter No update Yes Figure 6 3 Data Flow Diagram Get new epherimedes Program Mode Before the actual processing loop is engaged the system needs to be started and initialized The user can choose a number of program modes which will initialize the system for different purposes It should be mentioned that this interface is meant for a development stage and would not be part of final application product The following choices are possible e On line process e On line process with data storage for postprocessing e Off line process of stored data The main reason for these choices are the possibility for easy debugging and postprocessing Notice that whatever the choice it is the same program and scripts that are being run It was deliberately decided to have both the on and off line procedures within the same program instead of making two different but nearly similar programs for each mode Even though it complicates things in the begin ning it makes development and testing much easier since only a few procedures concerni
91. unctions when possible e Use a predefined environment of structures and cells for data and variables e Make defensive coding to prevent system crash e Optimize coding regarding speed and stability The reason for these choices are mostly to help ourself throughout the program ming phase Without a strict coding style and explanatory comments the coding process would get far to difficult Secondly a predefined structure of all variables in the system ensured that individual developed bits of code easily could be in corporated Since the nature of the measurements are unstable the programming should be rather defensive including a large number of checks and safe procedures like using a try catch and end statement Finally the main goal is optimizing for update speed so unnecessary looping and computations should be avoided In this context it should be mentioned that developing some of the functions which requires a lot of time for computation in a C MEX file would have been advantageous But time limit could not permit that 6 2 1 System design Before we go on to any detailed descriptions of the system processes an overall and rather simplified model will be explained A selection of the most important of the mentioned functions and script will be described in detail afterwards A function flow diagram were developed at the early stages of the system de sign and it served as a guide throughout the system development Hopef
92. ved From the above discussion the following main and subproblems has been for mulated Main problem How can we obtain a system position at the update rate and accu racy required by the VR system CHAPTER 1 INTRODUCTION 5 Sub problems e What are the hardware limitations e Which software platform and computing language should we chose e Which GPS solutions are appropriate e Can we improve the speed and accuracy of the GPS solutions by filtering techniques e What is the optimal solution regarding measurement update rate and com puting load The given problems leads to a number of needed tasks that must be solved before a system can be developed which will meet the requirements of the VR system 1 4 Objectives The obvious background for the system specification is the mentioned demands of the VR system Keeping in mind that it requires a position update rate of at least 30Hz with an accuracy less than 1cm The project group acknowledges that this might not be possible without additional measuring equipment like accelera tion meters inertia navigation systems INS or angular measuring devices All of which would be a natural part of the complete outdoor augmented VR system computing real time position and orientation The project group have decided to skip the system orientation and does therefore not have the option to include out puts from the above mentioned measuring devices in the position computation The
93. ven problem The following section will therefore discuss the float solution one of the best integer estimation procedure called LAMBDA and finally a round off solution in the wide lane domain called the Goad s method 4 1 Ambiguities in Topcon receivers what is the relevance of this sec Before the different solutions are discussed lets briefly explain the nature of the ambiguities and how they are treated in the Topcon receiver The different re ceivers on the market all have their own way of dealing with the phase observation UN is used for the float solution for N 23 CHAPTER 4 AMBIGUITY ESTIMATION CONCEPTS 24 and therefore the ambiguities As mentioned in the DGPS theory a phase observation is only a fraction of a cycle of the carrier wave The full distance to the satellite is therefore this fraction plus an unknown number of full ambiguities in the range of 10e This number is impossible to measure and have to be computed or estimated somehow To keep the values in this computation in a numeric stable range the Top con receiver uses a special trick The fraction of the first phase measurement is adjusted with according to the geometric range to the satellite in cycles This pro duces phase observations in the 10e range and integers numbers for N in the range 50cycles hence the deviation on the C A code position solution After this fist adjustment of the phase on L1 and L2 the receiver tracks the phase constan
94. ver is capable of outputting raw measurement data at the rate of 50 ms or 20Hz though it is not recommendable to query for measure ments faster that 10Hz Any further detailed description of the receivers capabili ties can be found in the user manual Top01 Receiver setup According to the manual Top01 the receiver can be connected with up to 30m of antenna cable before any amplifying of the signal is needed and the cables used were only 15 m The extension of antenna cable does not influence the GPS measurements which also were confirmed by the Topcon service department when contacted about the topic Therefore permanent antennas were installed on the rooftop making GPS signals accessible in the department s laboratory The master receiver were permanently connected to one of these antennas and the rover the other for stationary measurements in the development phase Another portable rover setup were used for kinematic system tests Receiver settings The receivers used the standard default settings with only a few changes e Power standby mode if idle were disabled CHAPTER 6 SYSTEM DESCRIPTION 43 e The GLONASS satellite system was disabled e The internal measurement rate were set to 100 ms or 10 Hz e The com port baud rate were set to 38400 bps The power standby mode were disabled so the master would not shut down if idle during tests Secondly when both the master and the rover were connected to the pc in the laboratory
95. y the Control Segment Information given by each satellites includes satellites ephemerides health status and constellation 11 CHAPTER 3 GLOBAL POSITION SYSTEMS 12 almanac Each satellites transmits a base frequency generated by the satellite clock on which a number of other signal are modulated First the two microwave carrier frequencies with the following properties e Base 10 23 MHz A 30m e Ll 154 10 23 MHz 1575 42MHz A amp 0 1905m e L2 120 10 23 MHz 1227 60MHz A amp 0 1905m They are modulated by two binary codes a Coarse Acquisition C A code on L1 and a Precise Encryted P Y code on L1 and L2 C A code is available to all users The encrypted higher precision code called Y code is reserved for only authorized users e C A 0 1 10 23 MHz 1 023 MHz A amp 300m e P 1 10 23 MHz 10 23 MHz A amp 30m The signal structure of each signal consist of three components e A sinusoidal signal called Carrier with frequencies L1 or L2 e A unique pseudo random noise PRN called Ranging code and e A Navigation data consisting of a binary coded data on the satellites ephemeris health cloak bias parameters and almanac For our project a combination of these component of the signal structure will be used The reason for this choice is given in section 3 5 4 Each satellite transmits a unique C A code of 1023 bits called chips which is repeated every millisecond The chip width or w
96. you chose to configure the filter more restricted giving a smoother trajectory but slower response The following result was obtained after experimenting with the filter tuning The standard deviations on the different noise terms are e Observation noise 0 01 m e System position 0 005 m e System velocity 0 0005 m e System acceleration 0 0005 m The standard deviation of the observation noise could be derived from the ob served measurement by taking the variance of the observation The system covarinace variance matrix XQ was more difficult because we really had no idea of how they should be set It turned out that the best result was obtained by giving the system position a variance a bit less than the measurements When trying to give bigger values the system simply became too free and the filtered state became very jumpy The variances for velocity and acceleration were defined the same way If they were set larger than 0 0005 the system would simply run out of control Chapter 8 Conclusion In giving a better conclusion for the project it will be good to reflect on the objec tives set for for this current project in section 1 4 1 Our focus was to implement a tracking system for a VR system In summary the group was to concentrate on setting up an RTK system and to investigate the update rate that can be achieved in relation to accuracy and stability As described in chapter 6 a static and kinematic setup was implemented

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