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

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 locally reduced-rank optimal filtering, we present a closed form solution to the problem in terms of SVD. Moreover, in a way similar to the techniques shown recently by Y. Hua et al. (see IEEE Trans. Sig. Processing, vol.49, p.457-69, 2001), we deduce a numerical algorithm converging globally and exponentially to the solution without passing any computation of the eigenvalue decomposition (or SVD). A numerical example shows that the proposed algorithm converges efficiently to the locally reduced-rank optimal filter that realizes an ideal trade-off between rank-reduction and estimation accuracy.