Plot-to-track correlation in A-SMGCS using the target images from a Surface Movement Radar

Transcription

1 Plot-to-trak orrelation in A-SMGCS using the target images from a Surfae Movement Radar G. Golino Radar & ehnology Division AMS, Italy ggolino@amsjv.it Abstrat he main topi of this paper is the formulation and performane evaluation of a novel plot-to-trak orrelation logi for the A-SMGCS (Advaned Surfae Movement Guidane and Control System). he onventional plot-trak logi exploits the kinematis information only. his logi might fail when more targets move in lose proximity. Currently, high resolution radars - integrated in the A-SMGCS - are able to provide the eletromagneti image of the deteted targets. hus, the idea is to exploit also this target feature to improve the plot-trak logi. he performane of the new algorithm is evaluated by Monte Carlo simulation using a realisti senario orresponding to an airport where two targets move in lose proximity on the airport surfae. Keywords: Advaned Surfae Movement Guidane and Control System (A-SMGCS), Surfae Movement Radar (SMR), Imaging. 1 Introdution he Advaned Surfae Movement Guidane and Control System (A-SMGCS) is an integrated airport management system onsisting of dferent funtions (surveillane, ontrol, guidane and routing) to support the safe, orderly and expeditious movement of airraft and vehiles on aerodromes under all irumstanes with respet to visibility onditions, traffi density and omplexity of the aerodrome layout [1]. he main sensor of the A-SMGCS is the Surfae Movement Radar (SMR), whose high resolution in range and azimuth provides an image of the target. he traker of the A-SMGCS should manage the presene of numerous targets with very small spatial separation. he plot-to-trak assoiation algorithm of a onventional traker is based on the distane between the predited measurement and the measured plot. he loseness of the targets on the airport surfae and the presene of heavy lutter an easily degrade performane ausing lost, swapped or ollapsed traks. he target images from the SMR an be used, jointly to the information on distane, in the plot-to-trak orrelation algorithm to improve the probability of orret assoiation. Beause distane and eletromagneti image are not homogeneous harateristis, the orrelation test must be deomposed in two separated tests, one using the A. Farina Chief ehnial Offie AMS, Italy afarina@amsjv.it distane information and the other exploiting the image information; these are suessively fused by a ombination logi. his two-step test (ombined test) uses jointly both information to improve the orret plot-to-trak assoiation. In this paper the advantage of using an algorithm ombining the information on distane between plot and trak and data from a high resolution image of the target to help the orret assoiation has been proven. A ombined test is able to provide target enhaned disrimination apability with small dependeny on target distane and it an be used to avoid traking errors when two traks are lose to eah other. We used in our analysis detetion probability (P d )=1 and zero false alarm density. 2 Integration of an image-based test in the plot-to-trak orrelation algorithm In a multi target senario, there an be traking errors aused by the mixing of plots belonging to dferent targets. his event an happen when the orrelation gates of two or more traks overlap [2]. In this paper the analysis is limited to the ase of two traks (see Figure 1). In low resolution radar the plot-to-trak assoiation is based only on the information on the distane between the predited position of the target and the measured one [2]. On the other hand high resolution radar an also provide either the information on the target range profile (e.g. Radar Cross Setion - RCS - along range) or target eletromagneti image (e.g. RCS along range and along azimuth). he target range profile or target image an be used jointly to the information on distane in the plot-totrak assoiation problem to improve the probability of orret assoiation. Beause distane and eletromagneti range profile or image are not homogeneous harateristis, the orrelation test must be deomposed in two separated tests, one using the distane information and the other exploiting the range profile or image information. these are suessively fused by a ombination logi (see Figure 2). In the figure the letters and P represent respetively the trak and the plot, while IMAGE_ and IMAGE_P represent respetively the image assoiated with the trak plot P. he image of the trak is the image orresponding to the last plot orrelated with the trak. he output of the tests on distane and on

2 image an be either binary ( or 1) or it an vary in the interval (,1). he plot-to-trak assoiation logi blok diagram is shown in Figure 3 for the simplest ase of two traks and two plots. he inputs are two traks 1, 2, with their relative images IMAGE_ 1 and IMAGE_ 2, and two plots P 1, P 2, qualied by the target position measurements, with their relative images IMAGE_P 1 and IMAGE_P 2 ; the outputs are all the ombinations of plot-to-trak assoiations. he assoiation logi uses four ombined tests as shown in Figure 3. he results of the ombined tests are then proessed by a suitable seletion logi. IMAGE_ 1 P 1 IMAGE_P 1 IMAGE_P 2 IMAGE_ 2 P 2 1 test 1,P 1,P 2 test test 2,P 1,P 2 2 test Seletion logi Figure 3. Blok diagram of the plot-to-trak assoiation logi using kinematis data and the target images; the sheme is limited to the ase of 2 traks and 2 plots. he blok ombined test is the one in Figure 2. Figure 1. An example of overlapping of orrelation gates. 3 Example of plot-to-trak orrelation algorithm using both distane and image In this setion an example of plot-to-trak orrelation algorithm using both distane and eletromagneti images is desribed. he simulation results reported in the following setions are obtained by using this algorithm. he test on distane is based on the unertainty ellipsoid of the onsidered trak; it is defined as: e 1 z k H sk H Pk H Rk z k H s k h 2 (1) P IMAGE_ IMAGE_P est on distane est on image test d P Combination logi r P P where: - k z is the vetor ontaining the target position measured by the radar and Rk is its ovariane matrix; - s k is the vetor ontaining the target state predited by the traking algorithm and P k is its ovariane matrix; Figure 2. Blok diagram of the test that ombines the information on the distane and eletromagneti image of the target. Label and P in figure: : rak, P: Plot. - H is the matrix whih relates the target state to the target position; - h is a quantity related to the desired probability of finding the plot that should be assoiated to the trak inside the unertainty ellipsoid (in the simulations we set h 3). he test on distane has a binary output; it is one the plot P is within the onsidered unertainty ellipsoid, otherwise it is zero: d P 1 P e P e (2)

3 he output of the test on image is the orrelation oeffiient of the two onsidered images: r P IMAGE _ IMAGE _ P IMAGE _ IMAGE _ IMAGE _ P IMAGE _ P (3) where denotes the orrelation operator. he ombination logi of the ombined test performs the multipliation of the outputs of the test on distane and the test on images: P d r (4) P Finally, the seletion logi does not assoiate any plot both the outputs of the ombined tests are zero; otherwise it assoiates to the trak the plot relative to the test with the higher output: P1 P2 P P1 P1 P2 P2 P2 P1 4 Senario for testing the plot-to-trak assoiation algorithm he following senario has been onsidered: an airraft (similar to a Boeing 747) lands on a runway and goes to the apron; while a ar moves in the same diretion along a taxiway lose to the runway. Figure 4 shows the trajetories of the airraft and of the ar. A setion of a generi airport has been onsidered. he trajetories are sampled by an SMR with san period equal to 1 s. he two trajetories are very lose for some seonds and the distane between the airraft and the ar reahes a minimum of about 5 metres (see Figure 5). he standard deviations of the radar measurements have been set to 15 m in range and to.45 in azimuth for the plots oming from the airplane; it is 5 m in range and.15 in azimuth for the plots oming from the ar. he standard deviation of the radar measurement onerning the airplane is assumed to be larger beause of the stronger glint phenomenon due to the larger size of the airplane. he orrelation gates of the two traks are overlapped for the first thirty sans and this auses either swapping or ollapsing of the traks. Figure 6 and Figure 7 show an example of ollapsing traks obtained during a Monte Carlo simulation of the traking algorithm [1]; Figure 8 shows instead an example of swapped traks. o alulate the eletromagneti images of the airraft and of the ar a simple hot spots model has been onsidered (see [3]); speially on the geometrial (5) struture of the target some hot spots have been loated and set as soure of the baksattered power (due to geometrial disontinuities). he eletromagneti images of the airraft and of the ar have been omputed oherently summing the ontributions of the single soures whih an interfere either positively or negatively depending on the transmitted frequeny and on the angle of view of the target. Figure 9 shows a CAD model of the Boeing 747; 48 hot spots are highlighted on it. An RCS of.1 m 2 has been assigned to eah hot spot. Figure 1 shows a CAD model of the ar, a Volkswagen Beetle; 22 hot spots are seleted and highlighted on it. An RCS of.2 m 2 has been assigned to eah hot spot. he onsidered transmitted frequeny of the radar is 9 GHz, while the resolution has been fixed to 6 m in range and.5 in azimuth. hese are typial values of an SMR. he SNR with respet to an RCS target of 1 m 2 has been fixed to 4 db along the trajetory. Figure 11 shows some example of the airraft eletromagneti images along the trajetory of Figure 4. he x-oordinate represents the aross-range dimension, while y-oordinate represents the along range dimension. It an be noted that the image of the airraft hanges onsiderably during the trajetory due to the hanging of angle of view. However the images onerning onseutive sans are strongly orrelated beause of the very small variation of the angle of view; this feature is exploited by the plot-to-trak assoiation logi using images to improve the traking algorithm performane. Figure 12 shows some example of the ar eletromagneti images along the trajetory of Figure 4. It an be noted that, beause of the limited dimensions and the limited hanging of the angle of view, the eletromagneti image does not vary sensibly along the trajetory. Figure 4. Samples of the trajetory of an airraft (blue rosses) and a ar (red points) on a generi aerodrome; sampling time equal to the SMR san time = 1 s.

4 15 1 distane san Figure 5. Distane between the airraft and the ar as a funtion of the radar san number. Figure 8. Estimated traks of the airraft (blue rosses) and the ar (red points); example in whih the overlapping of the orrelation gates has aused a trak swapping. 7.7 m 64.4 m Figure 6. Estimated traks of the airraft (blue rosses) and the vehile (red points); example in whih the overlapping of the orrelation gates has aused a trak ollapsing. Figure 9. CAD model of a Boeing 747; the hot spots are shown on the model. 4.1 m 1.7 m Figure 7. Estimated traks of the airraft (blue rosses) and the vehile (red points); example in whih the overlapping of the orrelation gates has aused a trak ollapsing. Figure 1. CAD model of a Volkswagen Beetle; the hot spots are shown on the model.

5 5 san n 1 5 san n san n san n Figure 11. Example of Boeing 747 eletromagneti images along the trajetory of Figure 4 (sans n 1, 5, 9 and 13). 5 san n 1 5 san n san n san n Figure 12. Example of ar eletromagneti images along the trajetory of Figure 4 (sans n 1, 5, 9 and 13). 5 Simulation results without using the eletromagneti images In this setion the results obtained by a simple Nearest Neighbour (NN) plot-to-trak assoiation logi [2] whih uses just kinematis information are reported. wo dferent filtering algorithms have been onsidered: an Extended Kalman Filter (EKF) and a Variable Struture - Interative Multiple Model (VS-IMM) whih uses kinematis onstraints to improve the auray (for details, see [1]). able 1 and able 2 show the results obtained respetively for the airraft and the ar in terms of number of orret, lost and swapped traks. he results have been averaged over 1 Monte Carlo trials. Consider the EKF algorithm. he overlapping of the orrelation gates of the two traks in the first thirty sans auses frequent traking errors. he airraft is orretly traked in only the 59% of the trials; in the 27.4% of the ases the algorithm loses the traking, while in the 13.6% of the trials the algorithm, after traking for some plots the airraft, erroneously follows the ar. he ar is orretly traked in only the 76.1% of the ases; in the 8.1% of the trials the algorithm loses the traking; while in the 15.8 % of the ases the algorithm, after traking for some plots the ar, erroneously traks the airraft. he performane is better for the ar beause it goes straight while the airraft is manoeuvring. Consider the VS-IMM. he use of onstraints to the motion of the two targets sensibly improves the traking performane. he ase in whih the algorithm loses the airraft are redued of the 87%, while the one in whih it loses the ar are redued of the 47%. he ases in whih the algorithm follows the ar, after traking the airraft, are redued of the 12% while the ones in whih it follows the airraft, after traking the ar, are redued of 64%. able 1. Corret, lost and swapped traks of the airraft for two traking algorithms using the NN plot-to-trak EKF 59.% 27.4% 13.6% VS-IMM 84.3% 3.6% 12.% able 2. Corret, lost and swapped traks of the ar for two traking algorithms using the NN plot-to-trak EKF 76.1% 8.1% 15.8% VS-IMM 9.% 4.3% 5.7% 6 Simulation results using the eletromagneti images In this setion we report the results obtained by using the target eletromagneti image provided by the SMR in the plot-to-trak orrelation logi as indiated in the setions 2 and 3. able 3 and able 4 show the results obtained respetively for the airraft and the ar in terms of number of orret, lost and swapped traks. Also in this analysis the results have been averaged over 1 Monte Carlo trials. It an be seen that with respet to the ase of the plotto-trak orrelation algorithm based on the NN assoiation logi and kinematis measurements, the number of lost and swapped traks is drastially redued. Consider the EKF algorithm. By using the eletromagneti images the number of lost traks is redued of the 77% in the ase of the airraft and of the 93% in the ase of the ar. he number of traks in whih the algorithm follows the ar, after traking for some plots the airraft, is redued of the 82%; the number of traks in

6 whih the algorithm follows the airraft, after traking the ar, is redued of 1%. Consider the VS-IMM algorithm. By using the eletromagneti images the number of lost traks is redued of the 8% in the ase of the airraft and of the 95% in the ase of the ar. he number of traks in whih the algorithm follows the ar, after traking for some plots the airraft, is redued of the 75%; the number of traks in whih the algorithm follows the airraft, after traking the ar, is redued of 1%. able 3. Corret, lost and swapped traks of the airraft for two traking algorithms using the plot-to-trak assoiation logi desribed in setions 2 and 3. EKF 91.2% 6.3% 2.5% VS-IMM 94.9% 2.8% 2.3% able 4. Corret, lost and swapped traks of the ar for two traking algorithms using the plot-to-trak assoiation logi desribed in setions 2 and 3. EKF 99.5%.5%.% VS-IMM 99.8%.2%.% 7 Simulation results using the eletromagneti images (senario with two similar targets) Here we illustrate the results obtained by onsidering a seond airraft instead of a ar. he sope of this simulation is to test the disrimination apability of the plot-to-trak assoiation algorithm in the worst ase: two similar target moving in the same diretion. he results onerning the NN plot-to-trak logi are reported in able 5 and able 6 (airraft 1 is the manoeuvring one while airraft 2 is the one going straight). he performane are worse than the ones of the ase with the ar beause the measurement of the seond airraft is noisier due to the greater glint phenomenon. he use of VS-IMM still improves the traking performane: the ases in whih the algorithm loses the manoeuvring airraft are redued of the 82%, while the ones in whih it loses the airraft going straight are redued of the 57%; the ases in whih the algorithm follows the airraft going straight, after traking the manoeuvring airraft, are redued of the 61%, while the ones in whih it follows the manoeuvring airraft, after traking the airraft going straight, are redued of the 52%. able 5. Corret, lost and swapped traks of the airraft 1 for two traking algorithms using the NN plot-to-trak EKF 4.% 33.2% 26.8% VS-IMM 83.6% 5.9% 1.5% able 6 Corret, lost and swapped traks of the airraft 2 for two traking algorithms using the NN plot-to-trak EKF 29.5% 26.8% 43.7% VS-IMM 67.4% 11.5% 21.1% he results onerning the plot-to-trak assoiation logi using both kinematis data and the eletromagneti images are reported in able 7 and able 8. Consider the EKF algorithm. By using the eletromagneti images the number of lost traks are redued of the 78% in the ase of the manoeuvring airraft and of the 51% in the ase of the airraft going straight. he number of traks in whih the algorithm follows the airraft going straight, after traking for some plots the manoeuvring airraft, is redued of the 71%; the number of traks in whih the algorithm follows the manoeuvring airraft, after traking the airraft going straight, is redued of 51%. Consider the VS-IMM algorithm. By using the eletromagneti images the number of lost traks are redued of the 54 % in the ase of the manoeuvring airraft and of 16% in the ase of the airraft going straight. he number of traks in whih the algorithm follows the airraft going straight, after traking for some plots the manoeuvring airraft, is redued of the 84%; the number of traks in whih the algorithm follows the manoeuvring airraft, after traking the airraft going straight, is redued of 66%. It an be noted that the results are worse than the ones reported in the previous setion, but the improvement obtained by using images is still appreiable. he algorithm is in fat able to disriminate the two targets thanks to the dferent angles of view (between 2 and 6 degrees in the first thirty sans, see Figure 13) and the performane remains muh higher than the one obtained by the simple NN algorithm and kinematis measurements. he dferent viewing angle in fat gives rise to dferent eletromagneti images of the two targets.

7 able 7. Corret, lost and swapped traks of the airraft 1 for two traking algorithms using the plot-to-trak assoiation logi desribed in setions 2 and 3. EKF 84.9% 7.4% 7.7% VS-IMM 95.1% 3.2% 1.7% able 8. Corret, lost and swapped traks of the airraft 2 for two traking algorithms using the plot-to-trak assoiation logi desribed in setions 2 and 3. EKF 65.6% 13.2% 21.2% VS-IMM 83.3% 9.6% 7.1% 6 5 Dferene of the angle of view of the two targets tools (e.g.: based on the ray traing method) to alulate the eletromagneti sattering, thus allowing us to haraterize aurately the multipath phenomenon. Another investigation area will be the performane analysis when the detetion probability, P d, of the radar is < 1 and the false alarm probability is >. Finally the role of the SMR resolution on the traking performane should be investigated too. Referenes [1] A. Farina, L. Ferranti, G. Golino. Constrained traking filters for A-SMGCS. Pro. Sixth Int. Conf. Information Fusion, Cairns, Queensland, Australia, 8 11 July 23. [2] A. Farina, F.A. Studer. Radar Data Proessing. Introdution and raking (vol. I). Researh Studies Press (England), John Wiley & Sons (USA), May ( ) 4 3 [3] D. R. Wehner. High Resolution Radar. Arteh House, san Figure 13. Dferene of the angle of view of the two targets relative to the trajetories shown in Figure 4. 8 Conlusions his paper has shown the great advantage of inorporating the eletromagneti target image in the plot-to-trak orrelation logi in addition to the lassial position measurements. he probabilities of either trak swapping or trak oalesing are greatly redued. he next investigation step is to determine whih is the effet of multipath in the formation of the eletromagneti image of target and the orresponding impat on performane of the plot-to-trak orrelation logi. In fat, one of the most severe phenomenon affeting the A-SMGCS performane is the presene of multiple unwanted sattering from the many buildings and infrastrutures present in the aerodrome; the multipath phenomenon ultimately set the limit to the traking system performane. he multipath phenomenon needs to be modeled via an aurate eletromagneti reprodution of the sattering from the aerodrome buildings: a task that requires the threedimensional modeling of the aerodrome infrastrutures and the availability of powerful eletromagneti software