Accuracy of synthetic aperture sonar micronavigation using a displaced phase centre antenna

Abstract

This work evaluates the accuracy of multi-element synthetic aperture sonar (SAS) micronavigation based on the concept of displaced phase centre antenna (DPCA). The Cramér-Rao lower bound (CRLB) for the joint estimation of the ping-to-ping, translational and rotational displacement in the slant range plane (referred to as sway and yaw) is established. The CRLB on sway is shown to be proportional to the half-wavelength at the centre frequency and that on yaw to the angular resolution of the DPCA. Both CRLBs are also inversely proportional to the square root of an effective signal-to-noise ratio Peff the which is the product of the physical reverberation-to-noise ratio number K of independent elements in the DPCA and the number BT of independent temporal samples used in the estimation (where B is the bandwidth and T the duration of the temporal estimation window). The accuracy required on the sway and yaw to achieve a given SAS beampattern specification, determined by the expected loss DeltaG in the SAS array gain, is computed as a function of the number P of pings in the SAS. Higher accuracy is required when P increases to counter the accumulation of errors during the integration of the elementary ping-to-ping estimates: the standard deviation must decrease like P^(-1/2) for the sway and P^(-3/2) for the yaw. The CRLBs are extended to include the effect of residual calibration errors of the physical reception array. It is shown that these errors set a lower bound on the achievable micronavigation accuracy. The accuracy with which the physical array has to be calibrated to achieve a given SAS performance is computed as a function of the relevant SAS parameters.