Source separation and tracking for time varying systems

Many situations arise when it is desired to recover from a noisy mixture of data both an estimate of a propagating source signal as well as its angular position. Accordingly, this thesis studies the problem of source separation and tracking for time-varying systems of moving sources. This problem is approached by dividing it into the three areas of modeling, processing, and evaluation.; In modeling, the goal is to provide a framework for the problem that provides insight into the underlying physics but is adaptable enough to also consider other extensions. Mixing is posed as a linear operator acting on a Hilbert space. Using Green's functions as a model to describe the propagation of point sources to sensor elements, this model is shown to simplify to a standard array processing result. Then by assuming a bounded and compact mixing operator, the singular value expansion and pseudoinverse are used to show the existence of the unmixing solution. This is related to the concept of separability in blind source separation literature. Since the proposed system is time-varying, the preceding results are carried to the time-varying domain by use of perturbation theory. This approach gives insight into the potential problems with unmixing in a time-varying system.; Using techniques borrowed from independent component analysis (ICA) and numerical linear algebra, a processing solution is formulated. Complete orthogonal decompositions (CODs) are used to normalize and decorrelate the data. Since CODs are known to stably update and downdate with time-varying data, this step is named COD adaptive whitening. COD adaptive whitening has the advantage of providing both an estimate of the number of sources from their rank revealing structure, but also estimates of the signal and noise subspaces. A further advantage is the reduction of the dimension of the data; a necessary step in overdetermined source separation, and one which decreases the effect of the noise subspace and the overall processing time. The ICA-based natural gradient algorithm (NGA) and the EASI (equivariant adaptive separation based on independence) algorithm are both adapted to provide not only separated sources but direction of arrival (DOA) estimates. Both make use of COD adaptive whitening as well as complex nonlinearities and adaptive step sizes and are thus renamed COD-NGA and COD-EASI. (Abstract shortened by UMI.)...