paper - ENAC
Contents
1. 13 Se A aS ia M 4 y 039 deg 042 deg 100 deg 063 deg 36 Kts 16 Kts 49 Kts 31 Kts Le we he Incorrect Correct Incorrect Correct Figure 10 Cluster of outlier records create incorrect wind estimation 5 2 Data quality criteria and algorithm tuning In order to cope with some of the issues presented in the previous section we designed a quality criterion combining the entropy of the ground speed directions and a threshold on the mean square error after regression The entropy criterion ensures that we have a sufficient dispersion of the ground track angles whereas the mean square criterion limits the dispersion of velocities around the fitted sinusoidal curve Good entropy is sufficient to ensure that the associated matrix is well conditioned The entropy is computed as follows considering the distribution of the ground speed directions among n equal bins partitioning the interval 0 360 Ent 5 P In P 8 with the convention 0 x lnO 0 and where P is the empirical probability using normalized histograms that a ground speed direction falls in the i bin The entropy value is maximum for uniform distribution and falls when the distribution concentrates Taking into account these data quality criteria the wind extraction algorithm is the following 1 filter the data in time and space in the vicinity of P x y z t 2 assess the quality of the filtered data entropy criterion2. 30mn 1h 2h 3h Figure 2I shows the deviations in wind direction 100 L 100 50 L 50 L 50 L Relative wind magnitude error p c 0 1 Relative wind magnitude error p c 50 0 1 100 100 L LS MTO LS Mode S Mode S MTO LS MTO LS Mode S Mode S MTO a 30 minute time window b J hour time window 100 L 100 50 L 50 L 50 L Relative wind magnitude error p c 50 1 Relative wind magnitude error p c 0 fi 100 100 fi LS MTO LS Mode S Mode S MTO LS MTO LS Mode S Mode S MTO c 2 hour time window d 3 hour time window Figure 20 Boxplots of relative wind magnitude deviations in p c for a 4x4 grid at flight level 350 Considering sub figures 19d 20d and 21d where the time window 3 hours is the same as in Figure 18 we see that the differences in magnitude and direction between the three wind values at flight levels ranging from 350 to 400 are much closer one from the other than when considering all flight levels Time window size 30mn lh 2h 3h Number of valid cells 5 9 13 12 Table 1 Number of valid cells using a 4x4 grid at flight levels 350 400 for time horizons of 30mn 1h 2h and 3h In Figures 19 20 ana 21 we can see how the choice of the time
3. LS MTO LS Mode S Mode S MTO LS MTO LS Mode S Mode S MTO a Wind mag deviations in Kts Figure 18 Boxplots of wind deviations in magnitude left and middle and direction LS MTO LS Mode S Mode S MTO b Wind mag deviations in p c c Wind dir deviations in deg right for all flight levels with a 4x4 grid and a time window of 3h 22 Figure 18 shows boxplotd of the differences in wind magnitude in Knots left or in percentage of the reference wind middle and wind direction right obtained when comparing the three different wind values LS MTO and Mode S pairwise The results in Figure I8 were obtained considering all flight levels with a 4x4 grid and a time window of 3 hours Considering this pairwise comparison of the three different sources we can see that they all provide consistent wind values In Figure 18 the difference between the LS approximated wind and the wind obtained from the two other sources MTO and Mode S is higher than the difference between the wind computed from Mode S data and the M t o France wind This is because Figure I8 shows the results for all flight levels including the LS wind estimates obtained with low quality input data 5 L 0 L Wind magnitude error Kts Wind magnitude error Kts 5 fi o 20 15 10 L 20 15 10 L LS MTO L
4. and V right in Kts for altitudes ranging from flight level 350 to 400 We see that the order of magnitude of these confidence intervals is much smaller than the difference between the estimated wind LS and the other winds MTO and Mode S which comforts our analysis of the results presented in the previous section 26 8 4 Air traffic controllers feedback In order to assess the potential operational interest of our wind extraction process we conducted informal discussions with air traffic controllers from Aix ATC Our goal was to assess the validity of our wind extraction process and to understand how air traffic controllers use wind parameters in their aircraft monitoring tasks We performed three interviews Firstly we asked a set of simple questions e How is the wind important in your daily work activity e How do you retrieve wind parameters e How often do you verify wind parameters Secondly we gave a software demonstration and thirdly we explained our algo rithm s rationale During the interview all the controllers confirmed that wind parameters are impor tant to their daily activity but when we asked them how they retrieved these parameters their response was not unanimous They often estimate wind parameters only by look ing at the aircraft behavior When I compare how aircraft turn when facing north or south I can assess the wind direction and the wind speed This estimation is not acc
5. 3 if the entropy criterion is met apply the ordinary least squares method described in section 3 3 to find a suitable sinus shape 4 assess the quality of the sinus shape fitting mean square error criterion 5 if the quality criteria i e entropy and mean square error are not met then return to first step and filter data from a larger neighborhood up to a given max imum size of P x y z and repeat the procedure After several tests we empirically defined acceptable criteria with an entropy value above 1 7 with 20 bins and a mean square error below 0 35 5 3 Summary of our preliminary findings During our preliminary tests we found that the introduction of data quality cri teria solved the issues illustrated in Figures thus improving the efficiency of our extraction method However other issues still remain presence of outliers incorrect clustering and multiple solutions We are convinced that the automatic procedure could 14 be improved again for example by using robust estimation methods instead of the least squares approximation or by applying more efficient clustering and filtering techniques to the input data These improvements are left for future work In the current paper we propose to leave some decisions and choices to the human operator about the assessment of the quality of both the input data and the resulting wind estimates While experimenting with the automatic procedure we noticed that inconsistent w
6. also to Serge Roux ENAC for collecting and post processing the Mode S radar data References 1 SESAR Consortium Milestone Deliverable D3 The ATM Target Concept Tech nical report 2007 2 Harry Swenson Richard Barhydt and Michael Landis Next generation air trans portation system ngats air traffic management atm airspace project Reference Material External Release Version NASA 2006 3 Jean Marc Alliot Nicolas Durand and G raud Granger A statistical analysis of the influence of vertical and ground speed errors on conflict probe In 4th Air Traffic Management Research amp Development Seminar Santa Fe USA 2001 4 Daniel Delahaye and Stephane Puechmorel Tas and wind estimation from radar data In Digital Avionics Systems Conference 2009 DASC 09 IEEE AIAA 28th pages 2 B 5 1 2 B 5 16 2009 5 Stuart K Card Jock D Mackinlay and Ben Schneiderman Readings in informa tion visualization using vision to think Morgan Kaufmann 1999 6 Christophe Hurter Benjamin Tissoires and St phane Conversy Fromdady Spreading aircraft trajectories across views to support iterative queries Visual ization and Computer Graphics IEEE Transactions on 15 6 1017 1024 2009 7 Christophe Hurter Ozan Ersoy and Alexandru Telea Moleview An attribute and structure based semantic lens for large element based plots Visualization and Computer Graphics IEEE Transactions on 17 12 2600 2609 2011 8
7. board measurements made by aircraft and transmitted through the data link capabilities of the Enhanced Mode S radars these data will be detailed in the following They also show how these measurements can be used as input to meteorological models to improve the short term and small scale prediction of wind and temperature These are significant improvements when compared with the current weather forecasts used in Air Traffic Control ATC and they will probably benefit ATC operations in the future In the meantime it is still worthwhile to investigate whether basic radar measure ments position velocity are sufficient to estimate the wind Extracting the wind from radar tracks has already been tried in other works In 4 an extended Kalman filter is used to estimate the wind from simulated radar tracks This method requires two trajectory turns for a single cruising aircraft or if two aircraft are considered one turn per aircraft The airspeed and the turning rate in the air are supposed to be constant for each aircraft The influence of the wind on the trajectory is modeled by the wind triangle stating that the ground speed vector of each aircraft is the sum of its airspeed vector and the wind vector In 18 a multi aircraft trajectory prediction problem is ad dressed with sequential Monte Carlo methods focusing on the inaccuracies related to wind forecast errors The wind is modeled as the sum of two components the nominal weath
8. data South West of France which contains additional data that can be used to validate our wind extraction in addition to the M t o France data 8 1 Visual comparison with M t o France data no error 25 error 50 error 75 error 100 error f A Figure 16 Visual conventions for the display of speed or angle differences In order to ease parameter comparisons we used two different designs to compare wind speeds and directions Both designs use a color gradient green to red to show the error magnitude Figure 16 In addition the speed design uses a vertical line whose length corresponds to the difference in wind magnitude between our approximation and the M t o France data The angle design uses two lines The white line shows the wind direction approximated by our method whereas the gray line shows the direction of the M t o France wind Figure I7 shows the differences between the approximated wind and the reference wind provided by M t o France at various altitudes and for three different grid sizes The three grids at the top of Figure I7 display the automatic wind estimation without 20 Filtered Data comparison Filtered Data comparison Filtered Data comparison trajectories Angle trajectories Speed Angle trajectories Speed Angle FL 300 350 FL350 400 FL400 450 FL 250 300 Too many outliers the Ss sinus shape f does not fit x A correctly 068 deg 31
9. data with several aircraft flying in various directions In addition these aircraft should fly at similar constant airspeeds In practice we have shown that this occurs in the upper airspace where commercial aircraft with similar performances fly at similar cruising flight levels A good compro mise for the time window used to filter the input data seems to be between 1 and 2 hours To summarize our wind extraction method is most efficient when applied to the en route airspace at altitudes ranging from flight level 310 to 390 where the cruis ing commercial traffic is of highest density Conveniently such airspace volumes of high traffic density are the ones where air traffic controllers most need accurate wind estimations for their trajectory prediction purposes Some interviews with air traffic controllers confirmed the interest of our approach from an operational point of view Concerning the perspectives of operational use one could think of feeding the exist ing meteorological models with the wind approximated from radar data In our opinion though this seems a less promising approach than using the aircraft on board measure ment of the true airspeed and ground speed downlinked to ground systems via Mode S However collecting and using such data does require fully deployed Mode S datalink capabilities and also some additional data processing in order to remove some equip ment biases see 17 There are good hopes that such wind pre
10. easily recognize inconsistent wind extraction when the direction of arrows does not correspond to the neighboring ones Wind cannot drastically change direction with neighboring cells The user can then select each cell and manually adjust extracted wind i e use direct manipulation to adjust a better sinus shape applying a semi automatic procedure see section 6 1 The user can also invalidate the cell if there is not enough data or if a suitable sinus shape cannot be adjusted This data validation and adjustment is fast a few seconds for each cell that needs to be adjusted or invalidated In order to check if the software and procedure are easy enough to use we asked an air traffic controller to adjust the extracted wind param eters Within 2 minutes he corrected more than 10 cells the ones with strong wind amplitudes and those with inconsistent wind directions 6 1 Semi automatic procedure The interactive procedure allowing the user to adjust the wind in a grid cell is the following a Filtering stage filtering is performed in space and time As explained in sec tion aircraft with a vertical speed must be removed Since aircraft with similar 15 Top view Investigated area Wind estimation 4am 8am 8am 12am 4pm 8 amp pm 8 pm 12 pm Figure 11 Wind parameter extraction at flight level 350 top view The small mul tiples below show the wind in one cell at incremental times morning mid day after n
11. flights i Let us start with a simple case and imagine that all aircraft flying through A belong to a single aicraft category of mean speed V If the quality of the available data is sufficient that is if we have enough data with a correct dispersion of the 0 values the unknown variables W and V can be computed from the N measurements of the track angle and velocity considering the N corresponding instances of equation 4 In general N will be much greater than the number of unknown variables and our model eq will not fit the observed data exactly Let us introduce the differ ence between the velocity V computed from the model and the observed velocity V We now have a system of equations expressing linear relationships between the three unknown variables Wx Wy and V e Vj Wx cosb Wy sino V je 1 N 5 We can use the ordinary least squares method to determine the optimum values of Wx Wy and V minimizing the quadratic error N N E Wx Wy V 5 G So Wx cos Wy sind V j l j l This is done by solving the linear system involving the partial derivatives of the error with respect to the unknown variables OE Wx Wy V 0 OE Wx Wy V OE Wx Wy V aWx aWy av When the associated matrix is invertible this system will have solution Wx Wy V that minimizes the sum of squares error This solution is meaningful when the matrix is well conditioned Finally the wind is obta
12. is represented on the x axis and the magnitude of the ground speed on the y axis When drawing this graph we used a 40 transparency setting in order to emphasize the emergence of dense areas pixels become visible only if many plots are drawn at the same location As seen in Figure 1 some approximately sinusoidal shapes stacked one upon the other emerge from our scatterplot Apart from the sinusoidal curves this visualization also shows vertical lines which correspond to the accumulation of pixels representing aircraft with the same direction but different speed j Filtering out 2 j Filtering out vertical 9o low altitudes iiiu evolving aircraft ee of MAK i cane EP ih ia il 3 600 Kts Full Dataset 300 Kts 0 Kts o 180 360 Aircraft ground heading degree Figure 2 Wind view with one day of recorded aircraft trajectories Data filtering to highlight wind influence on aircraft trajectories The emerging sinusoidal curves give a visual clue as to how the wind globally im pacts the ground speed of flying aircraft Indeed for each sinusoidal shape the lateral distance along the x axis between the x coordinate of the maximum and minimum ground speed values is 180 degrees i e aircraft facing the wind have the minimum ground speed and those with the wind behind them have the maximum ground speed The wind magnitude can therefore be deduced by retrieving the maximum and mini mum values
13. results for altitudes ranging from flight level 300 to 350 are similar to the ones presented here FL350 400 All these numerical results confirm the conclusion of the visual comparison made in section 8 1 They show the good performances of the pro posed wind approximation method when the input data is of sufficient quantity and quality In practice the domain of application of our method is the upper airspace at altitudes ranging from flight level 300 to 400 with relatively dense traffic flying in vari ous directions At these altitudes we find commercial aircraft of similar performances flying at their cruising flight level at approximately the same true airspeed 8 3 Confidence intervals and significance testing The numerical comparisons in the previous section are relevant only if the confi dence intervals associated to the least squares estimations of the wind are of a smaller order of magnitude than the differences with the two other winds MTO and Mode S Assuming we had a very large confidence interval around the wind estimate and 25 assuming that the the M t o France and Mode S wind values fall within this interval the wind estimates and the differences between the three wind values observed in the previous section would lose their significance Let us check the size of the confidence intervals associated with the least squares approximation In the application described in the paper a QR decomposition of the design mat
14. 200 average speed aircraft flying at an average altitude FL 100 FL 200 fal n S S low speed aircraft flying at low altitude lt FL 100 Aircraft altitude z Aircraft ground speed Figure 3 The sinus shapes show the wind influence on aircraft ground speed at three different clusters of altitudes In Figure 3 the filtered view of aircraft trajectories the sinus shape shows the wind influence on aircraft ground speed at three different clusters of altitudes FL100 FL200 and FL300 High speed aircraft fly at high altitude visible in image 2 and have different sinus shape parameters compared to the two other clusters Each sinus shape corresponds to specific wind parameters direction and speed These images clearly show the wind influence on aircraft trajectories at different altitudes 3 2 Ground speed and wind model Now that we have seen how the wind characteristics emerge from the visualized data let us introduce a mathematical formulation of the wind influence on aircraft movement In this section we will show that the hypothesis of a sinusoidal curve oscillating around an average speed is not exactly true and that it requires some sim plifications and approximations in the underlying model relating the ground speed to the wind Considering a flight 2 let us denote V the ground speed along the track followed by the aircraft and 0 the track angle co
15. Kts After user nal BE High entropy value adjustment the sipate g ER enough data No valid wind estimation valid wind estimation sinus shape better fits the central points Figure 17 Wind parameter extraction and comparison with M t o France data with three different grid sizes Image 1 illustrates a manual user adjustment Image 2 shows an invalidated cell Image 3 shows a valid wind extraction 21 user adjustment Image 1 below these three grids shows how the user can adjust the sinus shape to better fit the points and ignore many outliers Image 2 shows a cell with a low entropy criteria not enough data Image 3 shows a perfect match between the extracted wind parameters and the meteorological data We can see that the best results are obtained for the altitudes ranging from flight level 300 to flight level 400 There are much fewer valid cells at very high above flight level 400 and very low altitudes below flight level 300 and a few of the remaining valid cells show marked differences with the M t o France wind Investigating our dataset we observed that very high altitudes do not contain enough data to produce accurate wind estimations Furthermore at low altitudes most aircraft are climbing or descending and there are few trajectories at a cruising altitude with a stable airspeed As the records have been filtered so as to remove climbing or descending aircraft low altitude cells do not contain enough leveled traj
16. Roeland Scheepens Niels Willems Huub van de Wetering Gennady Andrienko Natalia Andrienko and Jarke J van Wijk Composite density maps for multivari ate trajectories Visualization and Computer Graphics IEEE Transactions on 17 12 2518 2527 2011 29 9 Christophe Hurter Mathieu Serrurier Roland Alonso Gilles Tabart and Jean Luc Vinot An automatic generation of schematic maps to display flight routes for air traffic controllers structure and color optimization In Proceedings of the International Conference on Advanced Visual Interfaces pages 233 240 ACM 2010 10 Christophe Hurter Ozan Ersoy and Alexandru Telea Smooth bundling of large streaming and sequence graphs 2013 11 Natalia Andrienko and Gennady Andrienko Visual analytics of movement An overview of methods tools and procedures Information Visualization 12 1 3 24 2013 12 Gianni Giannotti Fosca Giannotti and Dino Pedreschi Mobility data mining and privacy Geographic knowledge discovery Springer 2008 13 Gennady Andrienko and Natalia Andrienko Visual exploration of the spatial dis tribution of temporal behaviors In Information Visualisation 2005 Proceedings Ninth International Conference on pages 799 806 IEEE 2005 14 Patrick Laube Progress in movement pattern analysis In BMI Book pages 43 71 2009 15 Ralf Hartmut Giiting and Markus Schneider Moving objects databases Access Online via Elsevier 2005 16 Gennady A
17. S Mode S Mode S MTO LS MTO LS Mode S Mode S MTO a 30 minute time window b J hour time window 54 Si aw E poner aw f 8 2 o i 4 4 i 504 5 oJ o o i pre S 8 f 294 29 2 i 5 S eo Eo eat oo Se En Sa So i 7 i 8 8 LS MTO LS Mode S Mode S MTO LS MTO LS Mode S Mode S MTO c 2 hour time window d 3 hour time window Figure 19 Boxplots of wind magnitude errors in Kts for a 4x4 grid at flight level 350 Of course results are better when focusing on flight levels where the input data is of sufficient quality In practice the quality of the input data depend on several factors the altitude range and geographic location and also the time window chosen when filtering the data Let us now focus on the upper airspace at flight levels ranging from These boxplots were obtained using the boxplot function of the R environment for statistical comput ing with its default settings The box itself represents the interquartile interval the bold line is the median and the whiskers represent either an extremum value or at most 1 5 times the interquartile distance 23 350 to 400 and consider the use of several time windows for the estimation of the wind at a given time 16h as in Figure I8 Figures I9 and 20 show the wind deviations in magnitude for the chosen altitude range FL 350 to 400 and for several time windows
18. Wind parameters extraction from aircraft trajectories C Hurter R Alligier D Gianazza S Puechmorel G Andrienko N Andrienko aENAC MATAA F 31055 Toulouse France Institut de Recherche en Informatique de Toulouse France Fraunhofer Institute TAIS Intelligent Analysis and Information Systems Sankt Augustin Germany 4City University London Abstract When supervising aircraft air traffic controllers need to know the current wind magnitude and direction since they impact every flying vessel The wind may accel erate or slow down an aircraft depending on its relative direction to the wind Con sidering several aircraft flying in the same geographical area one can observe how the ground speed depends on the direction followed by the aircraft If a sufficient amount of trajectory data is available approximately sinusoidal shapes emerge when plotting the ground speeds These patterns characterize the wind in the observed area After visualizing this phenomenon on recorded radar data we propose an analytical method based on a least squares approximation to retrieve the wind direction and magnitude from the trajectories of several aircraft flying in different directions After some prelim inary tests for which the use of the algorigthm is discussed we propose an interactive procedure to extract the wind from trajectory data In this procedure a human operator selects appropriate subsets of radar data performs auto
19. angle Shift The user can change its phase the Shift angle value by dragging the sinus shape across the wind view The user can change the sinus curve Amplitude with the mouse wheel When the user changes the sine wave parameters the view updates the corre sponding estimated wind speed Amplitude 2 and direction Shi ft These parame ters are displayed as text values in addition an oriented arrow shows the wind direction Figure 13 6 3 3 User assesment of the estimated wind In order to assess the validity of the sine wave parameters the user can display two estimation error metrics Figure 14 The system computes the distance to the sine curve for every aircraft plot This distance is displayed with vertical yellow lines which start from the middle of the sine wave and whose length is proportional to the computed distance In addition the quadratic error is displayed as a transparent red rectangle The user can visually assess if the sine curve fits the aircraft plots correctly by trying to reduce the size of the transparent red rectangle quadratic error and by reducing the height of the vertical yellow lines distance to the sine curve for each aircraft record 7 Wind dynamic In section 6 the illustration of the interactive procedure Fig showed the ex tracted wind at several time intervals This gave us a succint view of the wind evolution 18 Figure 14 After adjustment the yellow peaks correspond to the diff
20. ares algorithm seems inconsistent e assess the wind estimation error and if necessary change the spatio temporal data to be investigated Each of these steps is described in detail below 6 3 1 View filtering In order to extract wind parameters the user defines the temporal bounding volume to investigate We use the same interaction techniques available in 6 The user left clicks with the mouse pointer on the top view Figure 12 to define the center of the selected volume and then manipulates range sliders to define the time range the altitude range and the latitude and longitude range Figure 12 When manipulating range sliders the top and the wind view are automatically updated with the filtered aircraft 17 records The top view displays the full dataset to provide data context but with the selected aircraft shown in color and the non selected ones in gray Figure 12 6 3 2 User adjustments of the sine curve Phase adjustment Amplitude adjustment wind direction 048 deg wind direction 24 Kts wind speed Figure 13 Using direct manipulation techniques the user can adjust the sine wave curve location mouse drag and amplitude mouse wheel In the next step the user adjusts the shape of the sine curve shown in gray so that it best fits the visualized aircraft plots in the wind view The shape of the sine curve is defined by the following formula f angle Amplitude sin
21. ced by flying aircraft It is the result of a process of data assimilation and smoothing using observations from various sensors sounding balloons wind profiling radars etc Collecting and smoothing this data is a relatively long process a cycle of several hours so the resulting wind field may not be up to date and accurate at the time the user will exploit it Much can be learned however from the comparison of our results with this M t o France wind model knowing the amount of scientific and computational effort that is devoted to developing high quality meteorogical models 5 Preliminary tests and algorithm tuning The preliminary tests presented in this section give us some insights into the be havior of the least squares method when it is used to extract the wind parameters from aircraft trajectory data automatically The potential issues are illustrated by several examples We introduce two quality criteria for the wind estimation Finally we sum marize the remaining issues with the automatic extraction method and motivate the choices made when designing the interactive wind extraction procedures presented in section The preliminary tests were run on the Paris Mode C radar records because this data was readily clusterized by categories of airspeed and operating mode This clustering allowed us to assume that all radar records within a same category belonged to aircraft with approximately the same average true airspeed in the cr
22. dictions with enhanced accuracy will be made available in the future at least in the core traffic areas where Mode S radars are being deployed In the meantime our method could be used as an inexpensive alternative to this approach It could provide up to date wind estima tions in dense en route airspace areas as a complement to the meteorological wind grid which is currently refreshed every hour at best It could also be useful in geographic areas not covered by accurate meteorological models or where Mode S capabilities will not be deployed As future work we plan to try robust estimation methods instead of the ordinary least squares approximation More extensive numerical experiments could also help to tune our data quality criteria Another promising path could be to take into account 3For the Rapid Refresh RAP in the U S 28 some constraints on the wind field minimum Lz norm of the Laplacian so as to im prove our wind estimation Concerning the interactive procedure further investigations are in progress to validate the user performance when adjusting the sinus shape Fi nally we plan to design a specific system to emphasize wind dynamic perception for the air traffic controller Acknowledgements We would like to thank Christophe Baehr and M t o France for providing the m t orological data used in this study and the French Air Traffic Services provider DSNA for making the radar records available to us Many thanks
23. different for these two datasets For the one correspond ing to the Mode C radar data the grid at a given time and altitude is composed of 151 rows and 101 columns and is 587 NM wide and 625 NM high The altitude varies from isobar 1 013 25 hPa to Flight Level 340 34 000 feet above isobar 1 013 25 hPa this range being split into 10 steps The data is given every 3 hours The grid location starts from the North east and continues to the South west of France and covers the whole country However in our investigation we will only consider the area which corresponds to our multi radar coverage 11 The grid corresponding to the Mode S radar dataset is made of 42 altitude levels and refreshed every hour Horizontally the grid size is 0 1 degrees in latitude and longitude The visual and numerical comparisons made in section B use this 4D grid Note however that this precise 4D grid is not currently available in the French air traffic control centers The wind data is still updated every 3 hours 25 kts 100 kts l l Figure 6 Wind speed data provided by M t o France at low altitude below FL10 left and high altitude above FL340 right Figure 6 shows the grid of wind magnitude at low and high altitudes We can observe that at low altitude the wind shows boisterousness whereas the wind gradient is smoother at high altitude One must be aware that this wind data from M t o France is actually not the true wind experien
24. e extracted and displayed in order to help the user to select time windows when filtering the data Finally in sec tion 8 we visually compare our results with M t o France data We also discuss the confidence intervals of the least squares method and give some numerical results on the comparison with the M t o France wind data and the wind computed from downlinked aircraft data Section concludes the paper and gives some perspectives about further improvements and possible applications of our method 2 Related work 2 1 Trajectory exploration The data flow model in is widely used to perform data exploration In this paper we also use this data flow model to transform raw data i e aircraft records into visualization with a sequence of transformation steps There is a rich bibliography on trajectory analysis in information visualization in particular on direct manipulation to filter and extract relevant aircraft information 6 7 density map computation to discover boat trajectory interactions 8 aircraft trajectory schematization 9 trajectory bundling 10 Visual Analytics 11 knowledge discov ery in databases 13 geocomputations 14 moving object databases 15 and detection of landing areas 16 However none of these previous works tried to extract wind parameters from trajectories 2 2 Wind extraction De Haan and Stoffelen show that high resolution wind and temperature obser vations can be obtained using on
25. e of Aircraft Data BADA see 20 The above model can be linearized by introducing two new variables Wx W cos and Wy W sin and considering that cos 0 t cos cos 0 t sin sin 6 t Vi t V Wx cos 6 t Wy sin 6 t 4 As the 0 t are numerical values obtained from our radar records we see that Equation 4 is linear with respect to V Wx and Wy This simplification of the initial model drastically reduces the number of unknown variables With equation 2 the aircraft headings a were unknown variables We had one new unknown variable for each straight trajectory segment of each aircraft With our approximation for the drift angle we now have only 3 unknown variables Wx Wy and V when considering one category of aircraft or c 2 unknown variables Wx Wy Vi bias V when considering c categories In the following we see how the least squares approximation method can be applied to extract the wind from an over determined system of equations resulting from several measurements of 0 t Vi t from several flights i over a chosen time interval 3 3 Least squares approximation of the wind Let us now consider an airspace volume A over a time interval 1 t2 assuming the wind remains constant within this 4D volume Let us consider N measurements 9 V l7 1 N of the track angle 6 t and ground speed V t made at different times within the interval t1 t2 measured from several
26. ectories with a sufficient variety of ground speed directions Comparing the results for wind magnitude speed and wind direction angle in Figure we can observe that the displayed error in percentage is smaller in direction than in magnitude whatever the altitude From this visual comparison we can conclude that our wind approximation is clos est to M t o France data in the grid cells and at altitudes where there are many aircraft flying in different directions at their cruising flight level with a stable airspeed This was to be expected considering that the quality of the least squares approximation depends on the quality of the input data 8 2 Numerical comparison with M t o France and Mode S winds Let us now present some numerical results comparing three different wind values the wind approximated with the least squares method the M t o France wind and a wind computed from the ground speed and the true airspeed downlinked from the air craft and available in the Mode S data provided by the experimental radar in Toulouse France These three different wind values are denoted LS MTO and Mode S re spectively 100 L 50 f 0 1 0 Wind direction error deg 50 1 100 Relative wind magnitude error p c 20 10 1 L 100 1 150
27. er forecast and a stochastic error on this weather forecast The dimensionality and non linearites of the multi aircraft problem lead the authors to introduce a new particle filtering algorithm in order to estimate the error on the wind forecast discard ing standard methods such as Kalman filters The aircraft airspeeds are assumed to be known As in 4 the method is validated on simulated trajectories only All these approaches are based on specific assumptions about the trajectories e g constant turn ing rate As these assumptions cannot be ensured for radar recorded air traffic data a different approach is required 3 Wind extraction principle 600 Kts Full Dataset 300 Kts Aircraft ground speed Kts 180 Aircraft ground heading degree Figure 1 right Top view one day of recorded aircraft trajectories over Paris area Left wind view scatterplot with aircraft headings and their corresponding ground speeds Sinus shapes emerge which show the wind influence on aircraft ground speed Our idea is to take advantage of the amount of data and to consider categories of aircraft having the same speed characteristics Contrary to Delahaye et al 4 our method is validated with real aircraft trajectories instead of simulated ones and it relies on more than one or two aircraft Our system uses Information Visualization Infovis techniques including a scatterplot and the visualization of aircraft ground
28. erence between the sinus shape and the actual aircraft record The red rectangles correspond to the quadratic error The figure on the right shows incorrect sinus shape adjustment with large errors The left figure shows a better adjustment with smaller errors during the day In addition to this interactive inspection procedure we propose a more systematic way to investigate the dynamics of the wind Generally the goal is to find a compromise between the need to use as many trajectories as possible to ensure suffi cient coverage of the 3D space and the need to use the most recent data to avoid using outdated records after the wind has changed Figure 15 Wind dynamic extraction with a 4x4 grid at FL 350 Each time series shows the direction or speed evolution over time Cell 1x1 shows how the wind changed direction and speed during the day in the morning 50 15 Kts mid day 70 5 Kts in the evening 110 25 Kts The procedure starts with a user defined division of the territory into compartments One possibility is to use a regular grid either rectangular or hexagonal A more so phisticated alternative is to use a Voronoi tessellation that reflects the distribution of position records and minimizes trajectory distortions 21 Next the user divides the time range of available data into equal time intervals for example with a length of 1 hr For each cell of the territory division and each time 19 interval the automat
29. ground Interestingly enough air traffic controllers already apply this idea in their everyday work Experienced controllers can roughly estimate the wind force and direction by observing the aircraft trajectories and comparing the ground speeds of aircraft flying in different directions aircraft facing the wind have a lower ground speed than aircraft flying in the opposite direction This basic idea is at the core of the interactive process proposed in this paper which allows users to extract the wind direction and magnitude from aircraft radar tracks Air Traffic Controllers need accurate wind parameters to perform their activity ef ficiently For instance one can reduce the converging speed of two conflicting aircraft by turning one aircraft so that it will face the wind The wind impact on aircraft ground speed is also used to slow down or speed up aircraft in order to respect a paced landing sequence optimizing runway usage i e one landing every 3 minutes The wind pa rameters are also necessary to make reliable short medium term trajectory predictions so as to avoid trajectory conflicts With the emergence of new operational concepts and automated tools for air traffic management predicting aircraft trajectories with great accuracy has become more and more critical in recent years For example medium term conflict detection and resolution is very sensitive to trajectory predic tion uncertainties 3 In this context it is crucial to fo
30. he along track speed for aircraft flying at high speeds As the perfor mance disparities among flying aircraft even within a same speed category are of a greater order of magnitude than the effects of the lateral drift this approach is justified 2 ATCC Air Traffic Control Center 27 An interactive Visual Analytics system has been developed to demonstrate the re sults of our automatic approach on recorded radar tracks Users can explore validate or adjust the extracted wind parameters The wind dynamics can also be extracted from the radar tracks and displayed as time series Knowing the trends in wind evolution can help the operator in the choice of a time window when filtering the data before extract ing the wind Filtering the data is a compromise between the quantity of data required to perform the extraction and its temporal and spatial proximity to the point where the wind is approximated The extracted wind has been compared with the M t o France wind grid and with the wind computed from Mode S data ground speed and true airspeed downlinked from the aircraft For this purpose we used a dataset of radar reports from the ex perimental Mode S radar in Toulouse France As a result we have shown that the approximated wind is very close to the wind obtained from the other two sources at least in airspace volumes where sufficient data is available We have also discussed the limitations of our method it requires enough input
31. ic wind assessment procedure is applied In the result time series of wind speed and direction values are produced These time series are presented for inspection on time graphs and maps Figure I5 left shows the spatial distribution of speed dynamics at flight level 350 Similarly Figure T5 right shows the dynamics of directions In both maps cell 1x1 is highlighted We can observe in Figure 15 that the wind speed was quite stable over the whole time period with a monotonous change from direction 50 in the morning to direction 110 in the evening According to Figure 15 the wind started to blow in the morning slowed down at mid day and started again in the evening As a result it can be recom mended to apply the analytical procedures either fully automatic or interactive only to the recent data If the amount of trajectory data is sufficient this procedure can be applied sepa rately for different ranges of flight levels By inspecting outliers on the time graph it is possible to identify regions that require special attention In particular it is necessary to apply manual curve fitting to these cells 8 Wind extraction results In this section we detail our investigations to validate our wind extraction method We first compare our results with two other sources of meteorological data Then we report informal discussions with air traffic controllers The results presented here were obtained with the second dataset Mode S radar
32. iltering can be performed with range sliders Figure 12 lower right part 16 Wind view Top view Latitude E FHS A Pa Longitude 4 Filters F 0 6 0 d e g Time J i 27 Kts nma Aircraft ground heading Longitude c Figure 12 Interface layout with top view latitude longitude wind view aircraft speed aircraft direction and filters with range sliders used to define the 3D temporal volume to investigate The wind view displays the same trajectories as shown in the top view but with a different scatterplot configuration The X axis shows the aircraft direction 0 360 whereas the Y axis shows the aircraft ground speed We display transparent dots that correspond to recorded aircraft parameters In order to visualize whether dots belong to the same trajectory we connect them with a line Since the Y axis represents aircraft direction many long horizontal lines appear when aircraft direction changes around 0 In order to remove these visual artifacts and reduce cluttering we connect trajectory points only if the distance between dots is lower than one third of the scatterplot width 6 3 Interactions In the interactive procedure described at the beginning of section 6 1 the user must be able to e define the extent of spatio temporal data to be investigated view filtering e adjust a sine curve so that it best fits the filtered data when the default curve adjusted by the least squ
33. ind estimations could often and easily be spotted by a human being by visually comparing the wind estimates in neighboring grid cells In the next section we propose an interactive procedure combining the wind extraction algorithm with manual data filtering and curve adjustments 6 Interactive wind extraction In this section we describe our process to extract wind direction and speed with an interactive system In order to extract wind parameters the user can perform an initial automatic process He or she defines the number of cells to investigate and then launches the wind extraction The software then clusters the aircraft positions into 3D space and time and tries to fit a sinus shape for each cell The entropy and error criteria are used to automatically invalidate cells with insufficient angle repartition The extracted wind parameters are then displayed in small multiples with an arrow in each cell Figure I 1 shows a top view of the adjusted wind in several grid cells at flight level 350 and also the evolution of wind over time in one of the grid cells We see in this example that the wind changes orientation from North to West during the day The computation process lasts 2 seconds with a 4x4 grid and 150 000 records The soft ware provides geographical grids at 4 different altitudes FL 250 FL 450 The arrow indicating the wind direction is displayed with a length proportional to the correspond ing wind speed The user can then
34. ined using the following equations remembering that Wx W cos and Wy W sin W V We We 7 Wy 7 arctan 5 4 Available datasets For this study two datasets of aircraft trajectories were available the first one containing one day of Mode C multi radar records from the Paris area France and the second one containing one day records from the experimental Mode S radar in Toulouse South West of France The dataset details and the differences between Mode C and Mode S radar data are explained in the following section Meteorological data including wind and temperature on a fixed size 4D grid have been collected from M t o France for the corresponding days 600 kts Hjem 300 Kts Aircraft ground speed Kts 23 Kts 0 Kts o 180 360 Aircraft ground heading degree Figure 5 Radar data top view right from Toulouse Mode S experimental radar and wind view left In the wind view records are in transparent black and those of a same trajectory are connected by a colored line low altitude records are in green high altitude in blue 4 1 Trajectory datasets Aircraft positions are detected by radars dispatched all over Europe There are two technologies for aircraft position monitoring primary and secondary radars Primary radars use an emitted beam and its corresponding reflection on the aircraft body to compute an azimuth radar angle and a distance echo response ti
35. lative to airspeed capabilities and operating mode constant calibrated airspeed or constant Mach number made available by a previous post processing of this data These preliminary tests showed some of the drawbacks of the fully automatic wind extraction and motivated the semi 10 automatic procedure presented in section 6 1 When the Toulouse Mode S data became available we decided to evaluate the interactive wind extraction procedure on this new data allowing us to compare the results see section 8 with M t o France data and also with a wind computed from on board measurements of the aircraft ground speed and true airspeed The two trajectory datasets are detailed below 4 1 1 Mode C radar data Paris area Our Mode C records were made over an extended area in the Northern part of France centered on Paris see Figure p The dataset contains 3 712 trajectories com posed of 571 580 points with one point every 15 seconds for each aircraft The recorded attributes are the location X Y using a Polar Stereographic WGS84 projection cen tered on 47N 0E the altitude measured by the difference of pressure with isobar 1 013 25 hPa the ground speed and ground track angle and a unique aircraft iden tifier This unique identifier is helpful to draw lines in the visualization Distances are counted in nautical miles NM speeds in knots Kts NM hour and altitudes in feet ft The angles are in degrees counted clockwise relative t
36. licies So on one hand the actual dispersion of speeds within one such aircraft category is expected to be relatively large On the other hand for aircraft flying at high speeds the drift angle a 0 is expected to be relatively small for an aircraft flying at about T 450 Kts with a cross wind of 70 Kts the error made when considering that cos a 6 1 is about 1 percent of the aircraft speed Taking these considerations into account the exact model of equation 2 can be simplified by replacing T cos a 0 by a unique speed V for all flights 7 belonging to a same category For a flight with a velocity V t and a track angle 6 t measured at time t by radar detection we then obtain the following simplified model considering that W and remain constant over the chosen time interval Vi t V W cos 6 t 3 with V V k 1 c the average speed corresponding to the category of aircraft 7 The average speed V does not have to be known and can be considered as an un known variable like W and The only pre requisite is that every flying aircraft must be assigned to one of the existing classes 1 c that must be determined in advance considering the theoretical cruising speed of each aircraft type These the oretical cruising speeds are the results of a model 19 of the airframe and engine performances provided by the aircraft manufacturers They are available in the Euro control Bas
37. matic and or manual curve fit ting to extract the wind and validates the resulting wind estimates The operators can also assess the wind stability in time and validate or invalidate their previous choices concerning the time interval used to filter the input data The wind resulting from the least squares approximation is compared with two other sources the wind data provided by M t o France and the wind computed from on board aircraft parameters showing the good performance of our algorithm The interactive procedure received positive feedback from air traffic controllers which is reported in this paper Keywords Wind extraction least squares approximation air traffic control data exploration visual analytics Principal Corresponding Author Email addresses hurter recherche enac fr C Hurter alligier cena fr R Alligier gikanazza recherche enac fr D Gianazza puechmor recherche enac fr S Puechmorel gennady andrienko iais fraunhofer de G Andrienko natalia andrienko iais fraunhofer de N Andrienko Preprint submitted to Elsevier January 22 2014 1 Introduction Aircraft fly through the air and the air flows over the Earth s surface This simple statement highlights the crucial need to know the winds aloft when one wants to navi gate over the Earth s surface in a flying machine Alternatively one can also guess how the wind flows simply by observing the trajectories of aircraft relative to the
38. me This kind of radar is passive no data communication is required between the aircraft and the ground station Nowadays the use of primary radars is mostly limited to military applications where the aircraft are assumed to be potentially non cooperative Secondary radars widely used in Civil Aviation emit a beam which embeds a query and then compute an azimuth and a distance thanks to the response beam emit ted by the aircraft which embeds specific data There are different types of secondary radars depending on the data embedded in the aircraft response Mode C data con tains the aircraft identity and altitude reports in 100 ft intervals Elementary Mode S data contains the aircraft identity altitude reports in 25 ft intervals and some basic information flight status equipment status Enhanced Mode S contains useful addi tional information such as the aircraft velocities ground speed true airspeed indicated airspeed Mach number magnetic heading roll angle etc All of our radar records were obtained from secondary radars either from a Mode C multi radar system located in Paris France or from an experimental Enhanced Mode S radar located in Toulouse South West of France We used the Paris Mode C dataset in preliminary experiments see section 5 to test the least squares approxi mation method presented in section 3 3 This was facilitated by the presence in this data of some extra information the aircraft categories re
39. ndrienko Natalia Andrienko Christophe Hurter Salvatore Rinzivillo and Stefan Wrobel Scalable analysis of movement data for extracting and ex ploring significant places 2012 17 asi Siebren De Haan and Ad Stoffelen Assimilation of high resolution Mode S wind and temperature observations in a regional NWP model for nowcasting applica tions Weather and Forecasting 21 4 918 937 2012 18 4 Ioannis Lymperopoulos and John Lygeros Sequential monte carlo methods for multi aircraft trajectory prediction in air traffic management International Jour nal of Adaptive Control and Signal Processing 2010 19 Base of aircraft data BADA aircraft performance modelling report Technical report EUROCONTROL 2009 20 Angela Nuic User manual for base of aircarft data bada rev 3 9 Technical report EUROCONTROL 2011 21 Natalia Andrienko and Gennady Andrienko Spatial generalization and aggre gation of massive movement data Visualization and Computer Graphics IEEE Transactions on 17 2 205 219 2011 30
40. o the North reference Since we recorded the data from Paris air traffic control center the lines representing the air craft trajectories Figure I right end at the border of the image which corresponds to the limits of the multi radar coverage of this center 4 1 2 Mode S radar data Toulouse area We also investigated a second dataset from a single radar ground station located in Toulouse South of France Figure 5 We used this second dataset to validate our wind extraction algorithm since it contains additional Mode S data Thanks to the wind tri angle principle see 4 we can compute the wind measured on board the aircraft We use this wind computed from downlinked Mode S data as another source of meteoro logical data in addition to the reference wind provided by M t o France presented in the next section Geographically the dataset covers a circular area of radius 170 NM 315 km cen tered on Toulouse The dataset comprises 1 917 aircraft trajectories with 169 468 radar reports The average time span of a trajectory is 25 minutes with one point every 15 seconds 4 2 M t o France dataset The meteorological data provided by M t o France is a 4D datagrid latitude lon gitude isobar altitude time containing values of temperature wind direction and mag nitude M t o France provided us with two different meteorological datasets corre sponding to the recorded days in our two radar datasets The 4D grids are slightly
41. of each sinusoidal shape and dividing their difference by two The wind direction can be directly deduced by considering the direction for which the ground speed is at a maximum i e when the wind is pushing the aircraft The fact that several sinusoidal patterns emerge reveals several categories of air craft Since it is quite rare that a commercial aircraft flies in circles one such sinusoid cannot be caused by a single aircraft Each pattern is due to several aircraft flying in different directions belonging to a same category regarding their airspeed Therefore it does make sense to group aircraft which have similar average airspeeds In order to highlight the wind influence of aircraft ground speed we used the multi variate visualization software FromDaDy 6 Figure 2 represents one day of recorded aircraft trajectories image 1 shows the aircraft heading on the X axis and the aircraft ground speed on the Y axis In order to emphasize the sinus wave on aircraft ground speed one can filter out low altitude records which corresponds to aircraft landing or taking off in image 2 and remove aircraft with a vertical speed climbing or de scending aircraft in image 3 Low altitude or climbing descending aircraft do not have a stable airspeed magnitude therefore the ground speed evolutions cannot fit a sinus shape These records can be considered as noise and can be removed high speed aircraft flying at a hight altitude gt FL
42. oon night cruising performances tend to fly at similar altitudes see section 3 Ip it is not es sential to cluster records by aircraft category The radar position reports can simply be filtered by altitude range b Data quality check records must have various ground speed directions An entropy value above 1 7 with 20 angle bins validates the data quality c Sinus shape extraction thanks to the least squares estimation a sinus shape can be extracted from the filtered data If the quadratic error between the filtered data and the estimated sinus shape is below 0 35 the extraction is valid d User adjustment stage in order to add flexibility to our wind extraction process the user can manually adjust the sinus shape for the grid cells exhibiting inconsistent wind estimations The following three sections describe the views available to the user when adjusting the wind in a grid cell how the user interacts with the system and assesses the results of his manual adjustment 6 2 Visualization Our tool displays two main plots the top view and the wind view Figure 03 The top view displays trajectories with a top visualization the X axis shows the longi tudes the Y axis the latitudes We also use a color gradient to display aircraft altitude green shades represent low altitudes and blue shades high altitudes The top view helps users to observe the selected 2D volume which is used to extract wind parameters More f
43. recast the wind with accuracy within a prediction window of 15 to 30 minutes at any point in the airspace The cur rent meteorological forecasting models do not operate within such timeframes and the best alternative is most probably to use the current wind assuming that it will remain constant during the time interval of the prediction Estimating the current wind numerically still remains a difficult problem as wind measurements through sensors such as meteorological balloons or radar wind profil ers are sparse in both space and time These wind measurements must be processed by a numerical model and the meteorological wind pressure and temperature data is updated every N hours 3 hours usually In this paper flying aircraft are used as passive wind sensors with their positions and velocities measured through radar detection These radar measurements are cur rently used for air traffic management purposes and are easily available to ground sys tems in great quantities When plotting the ground speed magnitude as a function of ground speed direction for a number of aircraft some roughly sinusoidal patterns emerge These visual patterns are a straightforward result of the wind influence on aircraft trajectories Figure I In the following we propose an analytical method to extract the wind from these patterns using a least squares regression Instead of focusing on one or two aircraft as in 4 the idea is to take advantage of the amo
44. rix is preferred to the classic normal equations trading computational effi ciency for numerical stability One benefit of the QR solution is the ease of computa tion of the terms involved in the expression of the test statistics Denoting w Wz Wy V the vector of unknowns for each of the components W 4 1 3 of a confidence interval at level a is given by eis ON Pe ZZ i ty ey ZZ 9 where Z is the design matrix and om Ti is the value of the student test statistics for confidence level a 2 and N 3 degrees of freedom Size of confidence intervals Size of confidence intervals Rie 4 i o Wx f Avg true airspeed estimate Wy re o co o j a s ef ge J gt x a 0 4 0 2 0 2 0 1 li j lee y f Oxt 0x2 0x3 1x0 1x1 1x2 1x3 2x1 2x2 2x3 3x1 3x2 3x3 0x1 0x2 0x3 1x0 1x1 1x2 1x3 2x1 2x2 2x3 3x1 3x2 3x3 Grid cells Grid cells 0 0 0 0 Figure 22 Size of the confidence intervals for the estimated wind left and for the estimated average true airspeed for a 4x4 grid at flight level 350 On the data available for the study a very good adequation between the size of the confidence interval and the quality of the sample assessed using the entropy criterion was observed Figure 22 shows the size of the confidence interval for each cell of a 4x4 grid for W Wy left
45. speed and aircraft heading With enough data approximately sinusoidal shapes emerge one for each aircraft category or average speed category Figure hight shows recorded aircraft trajectories in 2D with their latitude and longitude We will refer to this view as the top view Figure I left shows the same dataset in a scatterplot with the X axis showing the aircraft direction relative to the ground and the Y axis showing the aircraft ground speed This view will be referred to as the wind view The emerging sinusoidal shape is due to the wind influence on aircraft ground speed The sine angle shift gives the wind direction aircraft facing the wind have the lowest ground speed the amplitude of the sine curve gives the wind speed the amplitude must be divided by two to retrieve the actual wind speed Specific units are used in the Air Traffic Control ATC community aircraft alti tudes are given in feet ft or Flight Levels FL For example FL350 means 35 000 feet above isobar 1013 25 hPa Distances are given in nautical miles NM with 1NM 1852m and speeds in Knots Kts NM h In order to assess our software with air traf fic controllers we have kept these ATC specific units in the following instead of using international units 3 1 Wind influence on aircraft velocities Figure i shows a scatterplot of the aircraft velocities for one day of recorded traffic The direction followed by the aircraft ground track angle
46. uising phase 12 5 1 Data quality issues Basically wind extraction consists in retrieving the estimated wind at a requested 3D location P x y z and at a given time t This requires the data to be filtered in time and space so as to select the radar plots in the neighborhood of P x y z t The least squares approximation is then applied to the filtered data as described in section 3 3 Fd 267 deg 267 deg 75 Kts 75 Kts Figure 8 Limited range distribution Some issues regarding the quality of the input data were encountered during the preliminary tests when applying this basic automatic procedure For example if the filtered aircraft plots are not numerous enough the automatic extraction can fit a sinus shape but the wind estimation may not be accurate Figure 7p Even if the number of aircraft plots is sufficient the wind estimation can be incor rect due to a limited angle distribution Figure 8 Figure 9 Impossibility of finding a wind estimation due to multiple solutions If the aircraft record angles have a large distribution the wind estimation can still be erroneous due to multiple possible solutions Figure The automatic wind regression tries to minimize the quadratic error taking into account every aircraft record This creates an incorrect wind estimation when a cluster of records contains outliers A few outliers can drastically change the wind estimation parameters Figure 10
47. unt of data and consider categories of aircraft with the same speed characteristics The wind magnitude and direction is then approximated by applying a least squares method to selected radar tracks considering all flights in the vicinity of the points where the wind is estimated A simplified ground speed and wind model is used neglecting the influence of lateral drift the drift angle is the angle between the longitudinal axis of an aircraft and its path relative to the ground on the along track ground speed With this approximation which is justified for aircraft flying at high speeds the number of unknown variables can be considerably reduced and the model can be linearized We also propose an interactive semi automatic process where the least squares computation is driven by the user who selects the input data and validates the results through a visual interface The remainder of the paper is organized as follows section 2 details the related works on trajectory exploration and wind extraction while section 3 introduces the principles of wind extraction from a dataset of aircraft trajectories The dataset itself is described in section 4 The issues that were raised during some preliminary tests of the automatic extraction method are detailed in section 5 The interactive extraction proce dure mixing the least squares algorithm and user filtering and adjustments is presented in section 6 Section 7 shows how the wind dynamics can b
48. unted clockwise from the north reference T will denote the true airspeed TAS and a the direction towards which the aircraft is heading i e the angle between the longitudinal axis of the airframe and the North reference Let us denote W the wind magnitude and the wind direction In the following vectors will be denoted in bold font e g W whereas vector magnitudes will be in normal font W North North Ground track Figure 4 Wind and aircraft velocity T True Airspeed V ground speed 0 track angle a aircraft heading angle W wind magnitude wind direction The relationship between the true airspeed the ground speed and the wind is illus trated in Figure 4 and simply expressed as follows using vector notations V T W 1 When projecting all vectors on the along track axis we obtain V T cos a 6 W cos 0 2 Our aim is to deduce W and from several measurements of 6 t Vi t made at different times t in a chosen time interval using several flights 7 In this work we shall assume that all flights belonging to a same category i e similar performances for the airframe structure and engines fly at the same average cruising speed Of course there will remain some disparities within a same category Even if all aircraft had the same cruising speed in theory this hypothesis could only be a statistical one as airlines may operate their flights differently depending on their cost po
49. urate but sufficient to assess approximate wind parameters Controllers also have a screen which displays estimated wind parameters provided by M t o France This data is displayed in 2 tables with four geographically specific points each South points Barcelona Montpellier Nice Ajaccio and North points C Ferrand Dijon Lyon Geneva with 5 Flight Levels 180 390 These tables are updated every 3 to 6 hours The controllers confirmed the validity and interest of our wind parameter extraction method They also explained that our tool is not designed for air traffic controllers who monitor aircraft but rather for the regulator controller the one that supervises the traffic regulation and does not have to deal in real time with aircraft The regulator controller needs to forecast traffic evolution and therefore our dynamic wind parameter extraction could provide valuable information for this operator 9 Conclusion In this paper after visualizing the sinusoidal patterns resulting from the wind in fluence on aircraft ground speeds we have proposed an analytical method to extract the wind magnitude and direction from the radar tracks of aircraft belonging to various speed categories A simplified model has been introduced allowing us to drastically re duce the number of unknown variables and to apply the ordinary least squares method to a linearized problem The proposed simplification consists in neglecting the effects of lateral drift on t
50. window influences the wind estimates Clearly a 30 minute time window is too short It seems that the best results are obtained with time windows of 2 or 3 hours However we must be aware that the boxplots are drawn from data of different sizes As shown in Table the 24 ol al H al i g i 7 Be ge i 3 3 5 o l e 50924 i se i Pe ev Sy 8 E 5 2 3 F4 EE ES Zg Zg o o TT q LS MTO LS Mode S Mode S MTO LS MTO LS Mode S Mode S MTO a 30 minute time window b J hour time window o e e aR 8 8 2 i 5 of of F ji i eines 58 58 ki da 4 R 2 Zg g 3 LS MTO LS Mode S _ Mode S MTO LS MTO LS Mode S Mode S MTO c 2 hour time window d 3 hour time window Figure 21 Boxplots of wind direction errors for a 4x4 grid at flight level 350 number of valid cells i e those satisfying our quality criteria is smaller for the shortest time windows This should mitigate the statistical interpretation of the boxplots and expecially concerning the 1h time window where the apparent bias towards higher values for the deviations of the wind direction might be explained by the small sample size Actually a time window of 1 to 2 hours size might be the best compromise if we want the estimates to be sufficiently up to date The
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