Synthetic aperture sonar (SAS) has become a well developed imaging technique for imaging shallow water environments. Aperture synthesis provides high along-track resolution imagery, with range independent resolution. However, mapping of the seafloor using traditional SAS is limited to a two-dimensional surface. To provide the third dimension (height), an interferometric synthetic aperture sonar (InSAS) is formed, comprising of two or more vertically displaced hydrophone arrays. Each of the interferometric receiver datasets are processed using standard SAS algorithms, with motion compensation and corrective processing applied equally to each channel, preserving the underlying interferometric time delays. By then estimating the time delay of the incoming wavefronts across the interferometric receiver array, the height of the seafloor can be inferred from the side-scan geometry of the system. The InSAS approach is similar to the radar equivalent (InSAR), however, significant differences in geometry and medium properties limit the applicability of InSAR algorithms to the sonar equivalent. A height estimate from interferometric data is formed by estimating the time difference between the receiver elements of the interferometric array. Therefore, for an accurate estimate of the time-delay, the signals of the receivers must contain significant 'common' information. Presented in this thesis is an analysis of coherence as applicable to an InSAS system. The coherence of an InSAS system can be decomposed into five 'coherence components': additive acoustic noise, footprint misalignment, baseline decorrelation, temporal decorrelation, and processing noise. Of these, it is shown footprint misalignment has the greatest effect for an InSAS system if it is not corrected for. The importance of maintaining high coherence between the receiver channels is presented; small losses in coherence from the ideal of unity will have a significant impact of the accuracy of the resulting height estimate. To reduce the sensitivity of the height accuracy losses, multiple estimates of the height can be formed from independent 'looks' of the scene. Combining all these estimates into one height estimate is shown to significantly improve the height estimate. The design and signal processing of an InSAS system is of high importance to the generation of high accuracy height estimates of the seafloor. Several parameters of design are explored, in particular the effect of aperture sampling. Low along-track aperture sampling rates are shown to cause a significant decrease in signal coherence, caused by the generating of 'grating lobes' from the synthetic aperture processing. Substantial improvements can be made by careful selection of transmitter and receiver element sizes, relaxing the requirements of a highly sampled aperture. An analysis of interpolation schemes on interferometric quality is also presented. The effect of footprint misalignment can be reduced by first resampling the data from each receiver onto a common ground-plane. However, this requires prior knowledge of the seafloor height, an unknown parameter before an interferometric height estimate is made. One possible method to form an initial height estimate is through the use of belief propagation, a technique applied from the field of stereo imaging. Belief propagation is used to estimate an initial height surface, albeit at discrete height intervals. This initial low resolution height surface can then be used to remap the data, partially eliminating the detrimental effects of footprint misalignment. The combination of all the independent estimates of the scene can be combined using maximum likelihood estimation. This framework allows the individual estimates to be combined into one overall cost function. Searching of the cost function for minimum cost yields a single interferometric time-delay estimate, from which a single height estimate can be inferred. This framework allows looks formed from many different sources to be combined, including multiple imaging frequency bands, and the use of more than one interferometric pair of receivers.

The goal of the research was to develop best practices for image signal processing method for InSAS systems for bathymetric height determination. Improvements over existing techniques comes from the fusion of Chirp-Scaling a phase preserving beamforming techniques to form a SAS image, an interferometric Vernier method to unwrap the phase; and confirming the direction of arrival with the MUltiple SIgnal Channel (MUSIC) estimation technique. The fusion of Chirp-Scaling, Vernier, and MUSIC lead to the stability in the bathymetric height measurement, and improvements in resolution. This method is computationally faster, and used less memory then existing techniques.