Online subspace and sparse filtering for target tracking in reverberant environment

This paper proposes a class of joint subspace and sparse filtering algorithms with an example application in tracking moving targets in highly reverberant environment. Motivated by recent work in low-rank and sparse matrix decomposition, we have developed filtering algorithms that alternate between tracking the low-rank subspace and estimating the instantaneously sparse components, both of which are recursively updated as new data arrives. The algorithms are particularly suitable for online applications with streaming data or sequential processing of extremely large data sets for which matrix decomposition is computationally infeasible. In contrast to simple signal and noise subspace decomposition in traditional subspace processing, the algorithms we describe here assume a generative model consisting of a low-rank subspace, an additional sparse component and noise. This approach is well suited for tracking a sparse moving target signal in the presence of low-rank reverberations. We demonstrate the target tracking performance via a set of beam space field data.