Theoretical accuracy of synthetic aperture sonar micronavigation using a displaced phase-center antenna

The Cramer-Rao lower bounds on the cross-track translation and rotation of a displaced phase-center antenna (DPCA) in the slant range plane between two successive pings (known as DPCA sway and yaw in what follows) are computed, assuming statistically homogeneous backscatter. These bounds are validated using experimental data from a 118-182-kHz sonar, showing an accuracy of the order of 20 microns on the ping-to-ping cross-track displacements. Next, the accuracy required on the DPCA sway and yaw in order to achieve a given synthetic aperture sonar (SAS) beampattern specification, specified by the expected 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 as P/sup -1/2/ for the DPCA sway and P/sup -3/2/ for the yaw. Finally, by combining the above results, the lower bounds on DPCA micronavigation accuracy are established. These bounds set an upper limit to the SAS length achievable in practice. The maximum gain Q in cross-range resolution achievable by a DPCA micronavigated SAS is computed as a function of the key SAS parameters. These theoretical predictions are compared with simulations and experimental results.

I. Introduction

The performance of the synthetic aperture sonar (SAS) on ocean going platforms is limited first and foremost by the accuracy with which the motion of the platform can be estimated [1]. The term “micronavigation” is used here to describe this very specific requirement for subwavelength short-term relative positioning, which is beyond the scope of instrumentation for most high-resolution imaging applications. In recent years, data driven micronavigation techniques have emerged as a possible solution. The most promising are based on the concept of the displaced phase-center antenna (DPCA) which exploits, in a unique way, the spatial and temporal coherence properties of the sea-floor backscatter [2]. DPCA is a known concept in radar space–time processing [3]. DPCA also forms the basis of correlation sonar, a subject which has recently been revisited theoretically by Doisy [4] who derived the accuracy of translational displacement estimates for volumetric arrays, as well as for attitude-stabilized planar arrays. Several experimental SAS prototypes exploit the DPCA principle for SAS micronavigation [5]–[8]. A large data set has been collected with a 100-kHz towed SAS to evaluate DPCA micronavigation for a wide range of parameters [9]. The aim of this paper is to determine the theoretical accuracy of DPCA-based SAS micronavigation.