An important problem in sonar signal processing is the two-point estimation of the velocity of a range-spread target, such as the seafloor. This thesis provides a detailed mathematical foundation for the analysis of common velocity estimation methods, and supports this analysis through simulation and experimentation. A Gaussian model is assumed for both noise and signal, and covariance functions for range-spread targets are then derived. From these covariance functions, the Cramer-Rao lower bound is determined for the coherent estimation techniques, and a detailed discussion of how to minimize this bound is provided. Three-dimensional boat motion is seen to play a large role in determining the experimental performance of the estimators. The "micro-Doppler" method is introduced as a novel approach to underwater velocity estimation, facilitating both the estimation of small phase changes caused by micro velocities, and the detection of faster targets causing larger phase changes.
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