A DYNAMIC CONTROLLING SCHEME FOR A TRACKING SYSTEM. Received February 2009; accepted April 2009

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1 ICIC Express Letters ICIC International c 2009 ISSN X Volume 3, Number 2, June 2009 pp A DYNAMIC CONTROLLING SCHEME FOR A TRACKING SYSTEM Ming-Liang Li 1,Yu-KueiChiu 1, Yi-Nung Chung 2 and Chao-Hsing Hsu 3 1 Department of Electrical Engineering Da-Yeh University Changhua 515, Taiwan pato@nkut.edu.tw 2 Department of Electrical Engineering National Changhua University of Education Changhua 500, Taiwan ynchung@cc.ncue.edu.tw 3 Department of Electronic Engineering Chienkuo Technology University Changhua 500, Taiwan chaohsinghsu@yahoo.com Received February 2009; accepted April 2009 Abstract. The surveillance area of a radar system is usually very huge and the observations are usually more than the real targets. Moreover, both non-maneuvering and maneuvering conditions are usually existed during the tracking process. The computation burden of a radar system is heavy to track multiple maneuvering targets in real time because of the complicated tracking environment. In order to reduce the computation burden and assure the tracking accuracy in a tracking procedure simultaneously, a dynamic controllingschemeforatrackingsystemisdevelopedinthispaper. Themajorconceptof this approach is that the system will choose a suitable gating sizebased on target situations in real time. In this paper, we also apply an adaptive estimator to track maneuvering targets. Keywords: Dynamic controlling scheme, Gating size, Adaptive estimator 1. Introduction. Both non-maneuvering and maneuvering conditions are usually existed in a radar tracking system. The related techniques of radar tracking system have been explored by some papers. An acceleration estimation algorithm based on the range rate measurement was developed in [1]. The interacting multiple model methods [2] in target tracking applied two or more maneuver modes where the modes will be changed during tracking procedure according to target situations. Moreover, the surveillance area of a radar system is usually very huge and the number of observations detected by radar is usually much more than real targets. One technique denoted data association is used to calculate the relations and to provide a proper correlation between observations with the existing targets. The related techniques have been addressed by several papers. For example, Joint Probabilistic Data Association method [3] was developed for a high false target density environment. An approach using Competitive Hopfield Neural Networkbased data association algorithm for radar multiple target tracking is also proposed in [4]. However, if the tracking system concerns whole surveillance area, the computation burden will be too heavy to track targets in real time. One technique denoted gating logic [5] is used to eliminate some impossible observations to save the computation time. Some other predictive control methods were addressed in [6]. If the target is in constant velocity, then the gating size can be chosen smaller to avoid many unnecessary observations. However, if the target with maneuvering situation, we need choose larger gating size to assure the 219

2 220 M.-L. LI, Y.-K. CHIU, Y.-N. CHUNG AND C.-H. HSU correlated observations inside the gate. Currently, radar tracking system is usually accomplished by a fixed gating size. In this paper, we develop a dynamic control scheme to choose a suitable gating size based on the target situations for a tracking system in real time. The major advantage of this approach is that the tracking system will reduce the computation burden and keep the tracking accuracy also. In the system, we also apply an adaptive procedure to improve the estimation for a multiple target tracking algorithm. Based on the simulation results, the proposed approach can efficiently to obtain the more accurate tracking results. 2. Data Association Technique. In this paper, an approach denoted 1-step Conditional Maximum Likelihood is applied to obtain the solution of the multiple target tracking (MTT) problems. The mathematic model for a target tracking system is defined as: X(k +1)=F (k)x(k)+g(k)w(k) (1) Y (k) =H(k)X(k)+V (k) (2) For each step k, once a observation vector is received, the corresponding likelihood denoted as a weighting coefficient for each hypothesis can be obtained from one formula derived as follows. Let Y k = {Y (0),Y(1),,Y(k)} (3) β k = {β(0), β(1),, β(k)} (4) The conditional probability density function of Y (k) based on β k 1, Y k 1 is ½ ¾ p(y (k) βk 1,Y k )= exp (2π) m 2 S(k) τ T (k)s 1 (k)τ(k) where m is the dimension of the measurement vector, and τ(k) =Y (k) Ŷ (k) (6) S(k) =H(k)P (k k 1)H T (k)+r(k) (7) Ŷ (k) =H(k) ˆX(k k 1) (8) These quantities can be obtained from the Kalman filter equations. Suboptimal estimate can be computed, with weights given by the corresponding likelihood functions, from ˆX(k k) = X p(y (k) βkj (k), β k 1,Y k 1 ) ˆX(k k,β kj (k)) (9) j (5) 3. Dynamic Controlling Scheme. Gating logic is a technique for eliminating unlikely observation-to-track pairings, where a gating diagram shown as Figure 1 is formed around each predicted track position. Assume that the dimension of measurement vector is m, d 2 k = τ T (k)s 1 (k)τ(k), and the m-dimensional Gaussian probability density for the residual is f(τ(k)) = e d2 k 2 (2π) m 2 p Sk (10) S k =DeterminantofS(k). An observation satisfies the gates of a given track if all the elements, τ(k) of the residual vector satisfy the relationship: Y (k) Ŷ (k) = τ(k) KG σ g (11)

3 ICIC EXPRESS LETTERS, VOL.3, NO.2, Figure 1. Gating diagram K G is a constant and σ g is the residual standard deviation as definedintermsofthe measurement (σr) 2 and the prediction (σp)variances: 2 q σ g = σr 2 + σp 2 (12) In this paper, we develop a dynamic control scheme to choose a suitable gating size based on the target situations for a tracking system in real time. Such a dynamic procedure which modifies the Kalman filter equations is described as follows. Let I(k) =H(k)P (k k 1)H T (k) (13) If the target has a sudden maneuver, then this algorithm will detect this situation based on statistical calculations. In this algorithm, the components which have jumps are first detected using the following test τ i (k) K p S ii (k), for all i (14) The variance of the rejected innovation can be modified as K 2 = τi 2 (k){a i (k)i ii (k)+r ii (k)} 1 (15) so that τ(k) exists on the boundaries of the acceptable region defined by Equation (15). Thus, the parameter a i (k) can be computed as follows: a i (k) = [τ i(k)/k] 2 R ii (k) (16) I ii (k) We define the a m (k) which is the largest value of all the a i (k). With this approach, the gating size is adjusted based on the following equation in real time. Y (k) Ŷ (k) = τ(k) am (k)k G σ g (17) 4. Maneuvering Estimation Procedure. If target maneuvers occur, the maneuver detection and acceleration estimation algorithms are applied to modify the parameters of the tracking filter to allow the maneuvers to be tracked without diverging or severely distorting the estimate. In this paper, we apply a maneuvering estimation algorithm denoted adaptive procedure [4]. The algorithm will detect the target s acceleration if the situation of maneuvering is occurred. After the acceleration has been detected, an adaptive procedure is applied to modify the parameters of the tracking filter to obtain more quickly response for tracking. With this approach, the filtering estimation will have faster responses for the sudden maneuvering situations.

4 222 M.-L. LI, Y.-K. CHIU, Y.-N. CHUNG AND C.-H. HSU Table 1. Initial conditions of the simulation example Two crossing targets x Vx y Vy Target Target Table 2. Maneuvering situations of the simulation example Two crossing targets Step Target Target Simulation Results. In the simulation example, two crossing targets were chosen with the initial conditions listed in Table 1. The maneuvering situations for the targets were shown in Table 2. In the simulation, we assumed that there were five radar observations for each target in each step. We applied two different tracking techniques namely, the general tracking filter (method 1) and the proposed algorithm in this paper (method 2) for comparison. The diagram of simulation result for tracking two crossed maneuvering targets was shown in Figure 2. The diagrams of radius of gating area were shown in Figure 3. After fifty runs, their tracking RMS errors of positions and velocities were shown in Table 3. The computation time is shown in Table 4. According to the Figure 3, we knew that the radius of gating area would be changed adaptively based on the target maneuvering situations. From Table 3, we can see that the proposed algorithm has better performance, with smaller averaged position errors and velocity errors. Figure 2. Tracking result of the simulation example Table 3. Tracking errors of the second simulation example Tracking two crossing targets Target1 Target2 Method Method

5 ICIC EXPRESS LETTERS, VOL.3, NO.2, Figure 3. Radius of gating area for the simulation example Table 4. The computation time for tracking two targets Example 1 Example 2 Method s 0.638s Method s 0.383s 6. Conclusions. An improved algorithm for tracking multiple maneuvering targets was accomplished in this paper. This approach is implemented with a dynamic controlling scheme to control the radius of gating area for radar surveillance systems. The major contribution of this approach is that the system will choose a suitable gating size based on target situations in real time. By using the dynamic controlling scheme, the system can reduce the computation burden and assure the tracking accuracy simultaneously. According to the simulation results, it shows that the proposed algorithm was capable of tracking multiple targets in various situations, and has good performance also. Acknowledgment. The work was supported by the National Science Council (Taiwan) under Grant NSC E CC3. REFERENCES [1] D. F. Bizup and D. E. Brown, Maneuver detection using the radar range rate measurement, IEEE Trans. Aerosp. Electron. Syst. vol.aes-40, no.1, pp , [2] E. Mazor, A. Averbuch, Y. Bar-Shalom and J. Dayan, Interacting multiple model methods in target tracking: A survey, IEEE Trans. Aerosp. Electron. Syst., vol.aes-34, pp , [3] K. C. Chang, C. Y. Chong and Y. Bar-Shalom, Joint probabilistic data association distributed sensor networks, IEEE Trans. Automa. Contr., vol.ac-31, pp , [4] Y.-N. Chung, P.-H. Chou, M.-R. Yang and H.-T. Chen, Multiple-target tracking with competitive hopfield neural network-based data association, IEEE Trans. Aerosp. Electron. Syst., vol.aes-43, no.3, pp , [5] V. Khandelwal and A. Srivastava, Variability-driven formulation for simultaneous gate sizing and postsilicon tunability allocation, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.27, no.4, pp , [6]C.J.Lin,Y.C.LiuandC.Y.Lee,Anefficient neural fuzzy network based on immune particle swarm optimization for prediction and control applications, International Journal of Innovative Computing, Information and Control, vol.4, no.7, pp , 2008.