| Determination of filter length for blind deconvolution and source signal estimation is considered. N channels of received data are modeled by the convolution of two functions. One of the functions is a common source and the other function is a multipath function, also referred to as a Green's function. The latter describes the effect of the environment on the source signal that is unique to each receiver.; The first part of this dissertation shows that from the eigenspace decomposition determined from a data covariance matrix, using an algorithm based on all of the eigenvectors instead of existing eigenvalue algorithms, channel order estimates can be improved. The eigenvector method gives exact filter length estimates down to SNR 18 dB while the best eigenvalue method is not reliable under SNR 25 dB. This method does not involve principal component analysis.; Furthermore, it is shown that in a more general setting, applying tailored statistical based functions to the eigenvectors has yielded meaningful subspace partitions that neither eigenvalues nor principal components can provide.; The second part of this dissertation describes source identification in a shallow water environment using the same convolution model given above. The necessity of taking a large number of samples from each receiver in order to determine a solution for the source impedes the ability to use subspace techniques involving matrix methods. The new technique involves using the observation that the modeled multipath function has a concentrated area of large peaks in the time domain for short ranges. Using smaller blocks of time, the transient source signal can be tracked as it propagates in range, when it passes by the relatively narrow high-peaked area of the multipath function, through the dominant frequency-carrying modes. In the difficult case of a quadratic frequency modulated source signal, the new short-time tracking method estimates the signal accurately and reliably. However, the conventional approach of using the complete received signal in the transform domain, necessarily leads to phase mixing resulting in a poor and misleading estimate. |
