Tensor Decomposition Enhanced LRFS Multi-DOA Tracking Based on Coprime Array

This paper addresses the problem of tracking a time-varying number of multiple direction-of-arrival ( multi-DOA) by exploiting the received signals of a coprime array. The multi-DOA state is represented by a labeled random finite set (LRFS), which is further modeled using the generalized labeled multi-Bernoulli (GLMB) distribution. Therefore, the GLMB filter naturally arises as a suitable method to propagate the multi-DOA posterior, from which the multi-DOA state can be extracted. To capture the intrinsic high dimensional characteristics of the signals received by the coprime array, a tensor model is adopted, followed by the canonical polyadic decomposition (CPD) to extract the rank-1 components of the tensor, which contain the spatial information corresponding to each source. Building on such a result, we formulate the multi-DOA likelihood in the form of a von Mises–Fisher (vMF) distribution. This likelihood enables the derivation of the update equation for the GLMB filter. Furthermore, we developed a particle-based implementation of the algorithm, and its effectiveness is subsequently assessed through simulation experiments. Even under low SNR and limited snapshot conditions, the proposed algorithm can accurately track the multi-DOA of time-varying source numbers, with the generalized optimal subpattern assignment (GOSPA) error remaining within$0.5^\circ$.