Sliding window test vs. single time test for Track-to-Track Association

Track-to-track association (T2TA) is very important in distributed tracking systems. When the fusion center receives multiple tracks from a local tracker, T2TA needs to be performed before track-to-track fusion (T2TF). The problem of T2TA, similar to measurement-to-track association, can be formulated and solved as an assignment problem, whose costs are based on the likelihood of assigning a local track to a central track, namely, the likelihood of the hypothesis H₀: the two tracks originated from the same target. Thus the basic hypothesis test of whether two tracks are for the same target is very important for T2TA. Compared to the measurement-to-track association, T2TA has two features: i) The local track is correlated with the central track that has the same origin with it, due to the common process noise of the target. ii) Multiple frames of data are available from both the tracks. Thus, two issues are of concern for the T2TA test, namely, the derivation of the exact test statistic needs to take into account the crosscorrelation between the tracks; and how should multiple frames of data from the tracks be utilized. In this paper, the exact algorithm for calculating the test statistic for T2TA using multiple frames of data is derived. To keep the complexity of the algorithm under control, a limit is set for the number of the frames of data used in the test, which leads to a sliding window test for the problem of T2TA. By accounting for the cross-correlations between tracks for the same target and the cross-correlations across time of the terms entering into the test statistics, the proposed test for T2TA yields false rejections of H₀ that match the theoretical values. Then the sliding window test is compared with the single time test. It is shown that the intuitive belief ldquothe longer the window, the more the power of the testrdquo is not necessarily correct. Thus, caution should be used when using multiple frames of data from the tracks - - to improve the power of the test.