Simultaneous estimation of array tilt and source range using broadband ship noise and a vertical array

Abstract

The array invariant, a robust approach to source-range estimation in shallow water, is based on the dispersion characteristics of broadband signals in ideal waveguides. It involves time-domain planewave beamforming using a vertical line array (VLA) to separate multiple coherent arrivals (eigenrays) in beam angle and travel time. Typically, a probe signal (i.e., a cooperating source) is required to estimate the Green’s function, but the array invariant has been recently extended to a ship of opportunity radiating random signals using a ray-based blind deconvolution. Still, one major drawback is its sensitivity to the array tilt, shifting the beam angles and adversely affecting the array invariant parameter that determines the source range. In this paper, a simple optimization algorithm for simultaneous estimation of the array tilt and the source range is presented. The method is applied to a ship of opportunity (200–900 Hz) circling around a 56-m long VLA at a speed of 3 knots (1.5 m/s) at ranges of 1.8-3.6 km in approximately 100-m deep shallow water. It is found that the standard deviation of the relative range error significantly reduces to about 4%, from 14% with no compensation of the array tilt.