Multidimensional spectral estimation using iterative methods

This thesis treats the topic of multi-dimensional autoregressive (AR) spectral estimation. An iterative algorithm for the solution of toeplitz block- toeplitz matrix equations is presented. This leads to a fast solution of the two dimensional normal equation compared with direct inversion of the autocorrelation matrix. The covariance method is used to estimate the autocorrelation function. Because the resulting matrix is not toeplitz block- toeplitz, a modified iterative algorithm is presented. Quarter-plane and nonsymmetric half-plane support are used, as well as combined quadrant averaging. Results of computer simulation show that in some cases a single iteration is sufficient to produce an acceptable spectral estimate. Because the AR parameters are estimated from previous values, this suggests the possibility to estimate spectral densities of slowly varying random processes. http://archive.org/details/multidimensional1094530666 Lieutenant, United States Navy Approved for public release; distribution is unlimited.