Adaptive reduced-rank localization for multiple wideband acoustic sources

This paper proposes an adaptive reduced-rank algorithm, which is based on a multi-stage Wiener filter (MSWF) developed by Goldstein, to localize multiple wideband acoustic sources in the far field. In this paper, we provide two implementation schemes for this reduced rank algorithm. The samples in each sensor data are transformed to the frequency domain by the discrete Fourier transformation (DFT). In the first implementation scheme of MSWF, the received vector in the frequency domain is projected onto a lower dimensional subspace, which is formed by successively multiplying the initial steering vector with the sample covariance matrix. The reduced-rank cost function is then minimized to get the weight vector to estimate the sources´ direction of arrival (DOA). In the second implementation scheme, the received vector is projected successively into orthogonal, lower dimensional subspaces. The simulation studies of the proposed algorithm show that near full-rank performance is achieved with rank much less than the source members.