TRACKING PERFORMANCE EVALUATION - Prediction of Track Purity -

This paper is concerned with the performance evaluation of multiple-target tracking systems, in particular, with evaluating the quality of tracks as the outputs of such systems. Very simple analytic functions are developed to relate key tracking environment parameters to a selected tracking performance measure, i.e., track purity, which is an important quantification of the tracking output quality when single-frame based target classification is not possible. The method for predicting track purity is based on a simple mathematical model for data correlation performance within a single data set. Several Monte Carlo simulations are performed to verify the applicability of the analytic functions. Non-linear estimation theory provides some analytic methods, notably Cramer-Rao bound calculation, for pre­ dicting estimation performance, in terms of certain bounds on performance of optimal estimates. In parallel to development of multi-target tracking algorithms, several efforts have been made to develop analytic methods of a similar kind for predicting performance (or a bound on it) of multi-target tracking systems. Combinatorics aspects introduced by unknown track-to-measurement association in multiple-target tracking, however, makes any straight­ forward application of Cramer-Rao-like techniques extremely difficult. A class of general multi-target tracking prob­ lems has been formulated and the optimal solutions to them have been developed (See, e.g. (l)) 2. Unfortunately analytic performance evaluation of such optimal solutions is formidably difficult even for a relatively restrictive class of Gaussian-Poisson cases. A pioneer work on tracking performance evaluation is (2) which includes the prediction of association performance of a nearest-neighbor-type correlation algorithm. In this paper, however, are are primarily concerned with the performance of an optimal correlation algorithm. Recent works on this topic include (3), (4) and (5), which are mostly concerned with the statistics of missing targets and false tracks (in parallel to detection probability/false alarm statistics of sensors). Analytical results are obtained from Markov chain models which approximately describe the detection history of each track in track-oriented tracking algorithms. Therefore, we may say that in these works the emphasis is placed on track initiation aspects, and hence, track-to-measurement correlation performance in track continuation phases is not of primary concern. In this paper, our emphasis is rather on track continuation aspects of tracking systems (i.e., after tracks are more or less properly screened and established), and hence, on predicting the quality of tracks measured by track purity. Track purity is defined as the percentage of correctly associated measurements contained in a given track. Track purity is an important tracking performance measure when target classification can be performed only on time-series of data, i.e., tracks (not on frame-by-frame base). For some tracking systems, with very high target density but relatively high detection probabilities and low false alarm rates, track purity is of primary concern. In general, track purity is intimately related to track accuracy usually measured in terms of target state estimation errors. Our objective in this paper is to obtain a simple analytic function which can relate tracking performance, measured by track purity, to key tracking parameters. We wish such a function to be simple enough to produce tracking performance prediction with various parameters in a reasonably short time, without assuming any particular tracking algorithm or performing any Monte Carlo simulations. At the same time, we want the prediction produced by such a function to be accurate enough so that such prediction is useful in providing a simple but reliable functional model for a tracking system or a reference performance level to guide tracking system design.