Track-to-Track Fusion Configurations and Association in a Sliding Window

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1 December 2009
Xin Tian, Yaakov Bar-Shalom

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Track-to-track fusion (T2TF) is very important in distributed tracking systems. Compared to the centralized measurement fusion (CMF), T2TF can be done at a lower rate and thus has potentially lower communication requirements. In this paper we investigate the optimal T2TF algorithms under linear Gaussian (LG) assumption, which can operate at an arbitrary rate for various information con-figurations. It is also assumed that the tracking system is synchronized. Namely, all the trackers obtain measurements and do track updates simultaneously and there are no communication delays be-tween local trackers and the fusion center (FC). The algorithms presented in this paper can be generalized to asynchronous scenarios. First, the algorithms for T2TF without memory (T2TFwoM) are presented for three information configurations: with no, partial and full information feedback from the FC to the local trackers. As one major contribution of this paper, the impact of information feedback on fusion accuracy is investigated. It is shown that using only the track estimates at the fusion time (T2TFwoM), information feedback will have a negative impact on the fusion accuracy. Then, the algorithms for T2TF with memory (T2TFwM), which are optimal at an arbitrary rate, are derived for configurations with no, partial and full information feedback. It is shown that, operating at full rate, T2TFwM is equivalent to the CMF regardless of in-formation feedback. However, at a reduced rate, a certain amount of degradation in fusion accuracy is unavoidable. In contrast to T2TFwoM, T2TFwM benefits from information feedback.

For nonlinear distributed tracking systems, an approximate implementation of the T2TF algorithms is proposed. It requires less communications between the FC and the local trackers, which allows the algorithms to be implemented in distributed tracking systems with low communication capacity. Simulation results show that the proposed approximate implementation is consistent and has practically no loss in fusion accuracy due to the approximation. For the sensors-target geometry considered, it can meet the performance bound of the CMF at the fusion times.

The problem of track-to-track association (T2TA) is also investigated. The sliding window test for T2TA, which uses track estimates within a time window, is derived. It accounts exactly for the cross-covariances among the track estimates and yields false alarm rates that match the theoretical values. To evaluate the test power when using more data frames, a comparison between the single time association test and the sliding window test is performed. Counter-intuitively, it is shown that the belief “the longer the window, the greater the test power” is not always correct.