Locally reduced-rank optimal filtering and its approximation by successive alternating minimization

In this paper, we introduce a locally reduced-rank optimal filtering that is a generalization of the globally reduced-rank optimal filtering studied extensively as a fundamental tool in signal processing applications. After formulating the problem of the locally reduced-rank optimal filtering, we present a closed form solution to the problem in terms of the SVD. Moreover, in a way similar to the techniques shown recently by Hua et al, we deduce a numerical algorithm converging globally and exponentially to the solution without passing any computation of the eigen value decomposition (or SVD). Numerical example shows that the proposed algorithm converges efficiently to the locally reduced-rank optimal filter that realizes ideal trade-off between the rank-reduction and the estimation accuracy.