Bayesian Synthetic Aperture Processing for Direction Finding With a Deformed Towed Array

This article considers direction finding with a passive towed sonar array that is deformed during platform maneuver. Since uncertainties in sensor location can severely degrade the direction finding performance, joint estimation of source directions of arrival (DOAs) and sensor positions is desired. This motivates us to present a synthetic aperture algorithm here that has improved performance compared to conventional schemes regarding phase coherent limitations on the incoming signals. With certain prior knowledge of source-array geometry, the maximum likelihood estimates of DOAs and sensor positions are found from maximizing the model evidence of these parameters and the observed data. The resulting computationally expensive optimization problem is simplified by utilizing the variational Bayesian expectation–maximization framework. By representing the array observation as a hierarchical binary mask formulation with several latent variables, whose estimates are iteratively updated by approximating the posteriors thereof analytically, we gain the benefit of selecting the model order automatically. This methodology, while retaining the advantage of synthesizing an aperture with improved angular resolution, is robust to perturbations in the array manifold. In addition, several open-form Cramér–Rao bound expressions are derived as indicators of limits on array and signal parameter estimates. Numerical simulations illustrate that the proposed technique is statistically efficient in both deterministic and stochastic source scenarios.