Polynomial Singular Values for Number of Wideband Sources Estimation and Principal Component Analysis

A multipath enabled singular value decomposition (SVD) algorithm is presented, which will allow computation of wideband (polynomial) singular values, and hence, the signal+noise and noise subspaces. Polynomial singular values are ordered according to total energy. The number of sources can be estimated using the scalar total energy values. Results using both simulated data on the computer and actual speech recorded in a noisy multipath environment are given to demonstrate the usefulness of the techniques shown. After number of sources estimation, only the signal+noise subspace is used to create virtual sensors which have made optimal use of all the sensors. As a final signal copy step, standard blind independent component analysis (ICA) or blind source separation algorithms can be used to recover the original data from the virtual sensors. The number of estimated sources could also be given to a blind algorithm capable of using overdetermined sources and the algorithm can adaptively make use of all sensor data.