HYPOTHESES PRUNING IN JPDA ALGORITHM FOR MULTIPLE TARGET TRACKING IN CLUTTER * * K. M. Alexiev, P. D. Konstantinova 25A acad. "G.Bonchev" str., Sofia, Bulgaria, alexiev@bas.bg Multiple target tracking in heavy clutter is a challenging task. Many algorithms have been proposed in recent years to solve this problem. One of the most effective and practical algorithms is Joint Probability Data Association (JPDA) algorithm. This paper comments several aspects of this algorithm. The most time consuming (combinatorial) part of this algorithm is hypotheses generation and hypotheses score calculation. Most of hypotheses are without significance, with negligible effect over final result – the choice of the best hypothesis. In this case it is useful to reduce the number of generated hypotheses. The paper comments how to do this. The received results are applicable in all real time JPDA algorithms and their modification (IMM JPDA). Keywords: multiple target tracking, JPDA * The research reported in this paper is partially supported by the Bulgarian Ministry of Education and Science under grants I-1205/2002 and I-1202/2002 and by Center of Excellence BIS21 grant ICA1-2000-70016. 1. Introduction Multiple target tracking in heavy clutter is a challenging task. This task differs from standard state estimation problem by the fact that the measurement origin is also uncertain. When new measurements are obtained, the association between the measurement list and the track list requires the estimation algorithm to test which measurement-to- track correspondence is correct, while simultaneously estimating the target states. Some times, when there are closely spaced targets, multiple tracks may share the same measurement(s). Joint events are formed by creating all possible combinations of track-measurement assignments. The probabilities for these joint events are calculated. The expressions for the joint events incorporate the probabilities of track existence of individual tracks, as well as an efficient approximation for the cluster volume and an a-priori probability of the number of clutter measurements in each cluster. From these probabilities the data association and track existence probabilities of individual tracks are obtained. Several approaches were proposed to solve described data association problem [5]. The simplest method is the so-called nearest neighbor (NN) approach. The NN approach associates one from gated measurements with minimum distance with the track file under consideration. The strongest neighbor method can be regarded as a modification of NN method. The JPDA algorithm is an extension of the Probabilistic Data Association method, which allows the possibility that a measurement may have originated by one of a number of candidate tracks or by clutter. In each scan JPDA partitions tracks into clusters, where tracks in each cluster have common measurements. It generates all possible joint measurement to track assignments and calculates the a-posteriori probability of each joint event. From these probabilities, the data association coefficients of each track are calculated and then used to update the track estimates. The multiple hypotheses tracking (MHT) method exhaustively enumerates all possible hypotheses over a number of most recent frames and chooses the most likely one. Joint Probability Data Association (JPDA) algorithm is the most effective from described above approaches and it can be implemented successfully for multiple closely spaced targets even in the presence of heavy clutter. But JPDA is rather complex because it creates a joint event for each possible combination of measurement origin. The number of joint events can grow very rapidly in a dense clutter situation. In this case JPDA requires a fairly large amount of computation to evaluate the weighting probabilities. To improve this situation, the paper studies the problem of hypotheses generation. An extension of the algorithm in previous our work [1] is proposed. Instead of enumeration of all feasible hypotheses we propose to use ranked assignment approach to find the first K-best hypotheses only. The problem is how many hypotheses K to be found out. The value of threshold K has to be optimal regarding a criterion. In this paper a probabilistic approximate measure of necessary number of hypotheses is given. The paper is organized as follows. Next section describes briefly the common JPDA algorithm. In the 3 rd section the motivation of choice of probabilistic threshold is given. The 4 th section presents simulation results. 2. JPDA algorithm and K-best hypotheses When several closely spaced targets form a cluster, the standard JPDA algorithm [5] generates all feasible hypotheses and computes their scores. Every hypothesis meets two important constraints: