# Radar Signature in Multiple Target Tracking System for Driver Assistant Application

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3 accelerator has been proposed to meet the high real-time constraint due to the correlation computation. Our proposal is also based on the utilization of UWB radar to build an ORS system. As stated, the outputs of the ORS are sent to the MTT block to optimize the overall computation. The general outline of data flow processing is presented in Fig. 3. As described, the recognition system consists of two key steps: 1). Radar detection and 2). Signature identification. Fig. 3. Impulse sending Correlation Transmission channel Leakage elimination Target detection Target recognition Target identity Function : Reference signal Signature database General outline of data flow processing for signature identification 1) Radar detection The radar transmitter sends periodically an impulse signal S. The reflected signal R is modeled by a vector containing Ñ samples: R = { r0,, rñ 1 }. Similarly, the reference signal R that corresponds to the reflected wave as transmitting an impulse signal to the receiver is represented by the M-element vector R = {r 0,, r M 1 }. At the reception, a correlation between both the signals R and R is performed to determine the respective distances to the obstacles. Mathematically, the correlation function f c is expressed by Equation (1). T d = f c ( R R ) = Ñ 1 i=0 M 1 ( r i+j r j) (1) j=0 The obstacle distances are respectively calculated by checking the peak positions in the result T d. In addition, the leakage elimination in Fig. 3 is to deal with the leakage transmission between both the transmission and reception antennas. 2) Signature identification The obstacle signature is identified by comparing the obstacle to a set of candidate signatures, denoted by S = {s 0, s K 1 } where the candidate s i is itself a vector composed of M samples, as the reference signal R. Similarly, this comparison is realized by the convolution equation. Hence, for obstacle k, the relevant samples r k are successively correlated with the candidate signatures s i, as expressed in Equation (2). V i = f c (r k s i ) for k O k (2) where the symbol O k related to the k th peak position represents the sub-set of sample subscripts in the received signal R. The signature pointed by the subscript i is selected in such a way that V i = max{v }. IV. MTT SYSTEM ARCHITECTURE In this section, we first present an architecture overview of the MTT system. Secondly, we discuss in detail the obstacle signature application in the MTT system. Finally, the Munkres algorithm, i.e., the assignment solver, is briefly reviewed. A. MTT functional architecture The MTT system tracks targets by consistently processing the observation data in three iterative stages, as shown in Fig.4. 1) Observation: The distance and angle values are given during a radar scan. 2) Data Association: In the Obstacle to Track Assignment block, the observations are mapped respectively to the tracked targets. The Track Maintenance block initiates new tracks or deletes existing ones when needed. The Gate Computation block defines the gate parameters from around the predictions [11]. 3) Filtering and Prediction: The filtering block estimates the current position and predicts the next position of each target. Radar Observations Fig. 4. Observationless gate identifier Gate checker Data association Track maitenance New target identifier Obs-to-track assignment Cost matrix generator Gate computation Target Init/Del Assignment solver Filtering & Prediction Prediction (time update) Correction (measurement update) Functional block architecture of the MTT application B. MTT system modeling with signatures Estimates The signature information helps to improve the DAS accuracy performance. We propose to introduce the obstacle signature S inside the MTT computation. It is then a must to take into account the signature information in all the MTT steps. In this case, the measurement and prediction are respectively expressed by the vectors V m and V p in Equation (3): V m = D A S and V p = D V A V a S where the symbols D, A, S, V, and V a correspond to distance, angle, signature, velocity and angular velocity, respectively. (3)

4 C. Cost matrix generation Considering N tracks and N measurements during a scan, the problem that should be resolved is to establish the oneto-one relationship between the tracks and the measurements. The costs of the possible assignments are calculated in a 2D cost matrix of size N N. Mathematically, the assignment cost for the i th measurement to the j th track is expressed by Equation (4) : [ ] [ ] pjθ θ + r [ỹ ijd ỹ ijθ ] θ p jd θ ỹijd p jθ d p jd d + r d ỹ ijθ c ij = ( p jd d + r d )( p jθ θ + r θ ) p jd d p jθ θ (4) where the symbols are defined as follows: The differences between measurements and predictions in distance d and angle θ are respectively represented by ỹ d, ỹ θ. The relationship p jd θ means the covariance p between distance and angle for the j th track. The covariance progressively evolves following the tracking iteration. As indicated, each track is associated to a covariance matrix. Similarly, the representation r d, r θ is for the constant transmission variance r related to the distance and the angle, respectively. D. Munkres algorithm The Munkres algorithm is well adapted to the MTT application to resolve the assignment problem [11]. The principle is to establish the optimal association between the N measurements and the N predictions by minimizing the total cost. For this purpose, an iterative process is executed until the total assignment cost is not improved no longer. Moreover, a unique measurement can only be assigned to one track (prediction). The description of this algorithm is beyond the scope of this paper. The interested readers are referred to the article [15] for details. As an example, giving a 2D cost matrix C: C = the Munkres algorithm generates a corresponding binary mask M: M = (5) where the binary value 1 represents the coupled assignment between the relevant measurement (line) and the track (column), 0 on the contrary. The iterative researching process is stopped if the following condition is verified: { Mij = 1 i (0 N 1) Mij = 1 j (0 N 1) We obtain the minimal assignment cost of 0 with the mask given by Equation (5). A. Motivation V. GATE AND SIGNATURE CHECK The Munkres algorithm basically relies on the cost matrix. For a given line i in the matrix C, if the polynomial S, denoted by the expression : S = j (c j min(c j )), (6) is large enough. it can preliminary be determined with high probability that, the line element i is assigned to the column element j, in such a way that: m ij = 1 if c ij = min(c j ). (7) The expression (7) can be considered as stop criteria during the iterative process. In this case, it is not necessary to run through all the steps required by the Munkres algorithm. Thanks to the stop criteria, the number of iterations can be reduced, thus the execution time. In the next of this section, we investigate two approaches making possible to fulfill both the equations (6) and (7). B. Gate Check Fig. 5. panel pedestrian Gate Gate checking between 1 track (prediction) and 4 measurements. The gate check method consists in calculating the binary mask matrix, which indicates the possible assignments of measurements and tracks. Only the measurements inside a specific window around each track are candidates for the assignment. The window is defined by the following rules: { D < K r 0 + p 0 A < K r 1 + p 1 (8) where the symbol represents the difference between the measurements and the track prediction. The subscripts D and A denote respectively distance and angle. The values r i and p i correspond respectively to the noise variance and the process co-variance and K is the gate coefficient. If the inequality (8) is not verified, the cost is set to an arbitrary large value. The gate checking procedure for 4 measurements and 1 track is illustrated in Fig. 5 where possible assignments are marked by ones and others by zeros. Thanks to the gate checking, the measurement m 0 is first eliminated due to its exceeded cost outside the gate area.

5 C. Signature Check As evoked, the radar measurement signal contains the obstacle signature information such as panel,, pedestrian etc. At first, we consider only the binary signature identification, which implies that each obstacle does not have more than one signature. In other words, if the measurement m i does not have the same signature to the track t, it means that the possibility to link these two elements is equal to 0. The above assumption leads to the signature check, which consists in comparing the signature identity as performing the assignment operation. As shown in Fig. 5, the target track has the signature. In this case, only the assignment t m 2 is possible after applying the signature check, because both of them have the same identity. Similarly to the gate checking, the cost values of the non-possible assignments are equal to a large number. Again, the computational complexity is reduced because these non-possible assignments are with no needs to run the cost generation formula (see Equation (4)). VI. REAL-TIME PROFILE ANALYSIS In this section, we first perform the time profiling by running the MTT application code on a Microblaze processor. Secondly, the time impact due to the obstacle signature utilization in the MTT system is analyzed. A. Time distribution of the MTT system The time profiling of the ORS-MTT system is done through a Microblaze-based architecture. The architecture is implemented on the Xilinx ML605 kit board, on which an FPGA circuit Virtex 6 is included [16]. The relevant Xilinx embedded development tools are consequently used. MA=25.7% TM=0.7% CG = 47.9% KF=6.4% IC = 19.4% Fig. 6. Time distribution in the MTT system. The abbreviations are defined as follows: KF for Kalman Filter, IC for Innovation Computing, MA for Munkres Algorithm, TM for Track Maintenance and CG for Cost Generation. We consider the MTT application using integer values for 1000 scans and a maximum of 20 obstacles. In Fig. 6, the execution time of the Kalman Filter (KF) corresponds to the processing of only one obstacle. It is shown that the most time consumed component functions are the Cost Generation (CG) and the Munkres Algorithm (MA), of which the execution time accounts respectively for 25.7% and 47.9%. The time required by Innovation Computing (IC) accounts for 19.4%. As conclusion, the complexity of the functions CG and MA is relatively higher than the others. According to Equation (4), the complexity of cost generation is equal to N 2 operation units, i.e. O(N 2 ). The operation unit here includes multiplications, additions and division. For the Microblaze [17] processor, an addition and a multiplication needs respectively 1 and 3 clock cycles for integer values, whereas a division requires up to 34 clock cycles. On the other hand, the Munkres algorithm exposes an iterative process to obtain the optimal solution. The number of iterations might vary in function of the cost matrix. This explains that the cost generation and the Munkres algorithm need a relatively long time to execute. B. Execution Time Analysis Two key factors are to be taken into account for the execution time: the number of obstacles N and the gate coefficient K (see Equation (8)). The first factor determines the computational complexity of generating the cost matrix C. The second one defines the size of the gate area, i.e., the number of gates available for a possible assignment. With regards to the impact on the execution time, three cases are to be investigated for the overall MTT system: 1). Without gate check nor signature check, 2). With gate check only and 3). With gate and signature checks. 1) Without gate check nor signature check. As no checks are considered inside the application process, the cost matrix is to be generated with the highest complexity, i.e. O(N 2 ) operations. This is equivalent to affect an infinite value to the gate coefficient K (K = ). Hence, the application with no checks consumes the most important time. Instead of considering the total time consumed by the MTT application, it might be of interest to count merely the impacted part: the Cost Generation (CG) function and the Munkres Algorithm (MA). According to the execution times given in Fig. 7 (see K = ), where the time basis in the vertical axis is changed to the sum of MA and CG times, we obtain a time of 15 milliseconds for 20 obstacle and 1 millisecond for 5 obstacles. This time consumption increases when the matrix size N increases. 2) With gate check only. The cost generation outside the gate area can be omitted thanks to the gate check. The gate size is determined by the gate coefficient K. Thus, the parameter K jointly with the number of obstacles N plays a primordial role to reduce the time consumption. According to Fig. 7, which depicts the time profile in function of the parameters N and K, we obtain a time of 14 milliseconds for the gate coefficient K equal to 30 and N to 20. This value changes to 11 milliseconds when K is equal to 3 for the same number of obstacles. Additionally, the gate coefficient K does not have a significant impact on the execution time when the number of obstacle N is small, e.g. N = 5.

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