A Comparison of Two Methods for Simulating Spatial Coherence-Based Motion Estimation

Sonar systems, such as correlation velocity logs and synthetic aperture sonars, may exploit the spatial coherence of seafloor scattering for navigation. Motion estimation algorithms find the ping-to-ping displacement within the plane of an array using the magnitude of the complex correlation coefficient as an estimator of spatial coherence. Simulation of these systems requires large amounts of spatially coherent data. Therefore, methods used to simulate spatially coherent data for evaluating these algorithms should accurately describe the probability density function of the spatial coherence estimator. Several methods have been proposed for modeling and simulation of the spatial coherence of seafloor scattering. One method uses discretized time series models, such as point or facet-based models, to describe the seafloor as an ensemble of scattering elements and generate synthetic data in the time domain. The simulated time series data is used to compute the sample correlation coefficients required by the motion estimation algorithms. Such models, however, are often computationally burdensome. An alternative method directly simulates the sample covariance using Monte Carlo draws from a complex Wishart distribution. Sample correlation coefficients are computed from the random covariance matrices. The two types of methods are compared for the simulation of 200 kHz sonar array oriented at normal incidence to the seafloor. The simulated data are shown to be equivalent for the purposes of motion estimation. There are significant computational advantages, however, to using the complex Wishart-based Monte Carlo approach.