A random finite set based joint probabilistic data association filter with non-homogeneous Markov chain

Abstract

We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set (RFS) theory. Specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, known as the nearest-neighbor set JPDA (NNSJPDA). The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback–Leibler divergence, with the goal of improving the accuracy of the marginalization. Next, the distribution of the target-label vector is considered. The transition matrix of the target-label vector can be obtained after the switching of the posterior density. This transition matrix varies with time, causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain. We show that the chain is inherently doubly stochastic and deduce corresponding theorems. Through examples and simulations, the effectiveness of NNSJPDA is verified. The results can be easily generalized to other data association approaches under the same RFS framework.

Keywords

Target tracking / Filtering theory / Random finite set theory / Bayes methods / Markov chain

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2021 Zhejiang University Press