Long Term Accuracy of Synthetic Aperture Sonar Micronavigation using a Displaced Phase Centre Antenna

The long term accuracy (i.e., bias) of Synthetic Aperture Sonar micronavigation using a Displaced Phase-Center Antenna (DPCA) is studied theoretically. We consider a linear array in an isovelocity medium, in uniform translation with relative trim over a locally planar and homogeneous seabed. For a given range, assuming a narrow field of view, it is shown that the trim introduces a bias on the cross-range displacement in the seabed plane, due to a frequency-independent projection error. It is also shown that the bias on the line of sight displacement depends on the two components of displacement in plane of sight (defined as the plane normal to the seabed containing the line of sight), the grazing angle, the trim and the square of the rms transmit-receive beamwidth of the DPCA element. This last bias is shown to result from a Fresnel diffraction effect due to a depth of field problem. The impact of these biases on SAS image quality is assessed. It is shown that image degradation results solely from the line-of-sight bias but that the effect is generally very small. Finally, it is shown that, using an Interferometric Synthetic Aperture Sonar, both the grazing angle and the relative trim angle can be estimated, and all DCPA displacements referred to a vehicle-fixed frame. By combining port and starboard DPCA estimates, the Cartesian velocity vector can be reconstructed, ready for integration in an aided inertial navigation system.