Error Analysis on Bearing Estimation of a Towed Array to a Far-Field Source in Deep Water

Multipath arrivals received by a towed array with different arrival angles result in a bearing estimation error (BEE) when conventional beamforming is used in the real ocean waveguide. This paper investigates the errors based on simulated data, focusing on their dependence on the range and bearing of a far-field broadband source. The BEE varies periodically with range, reaching local minima and local maxima at the edges of convergence zones (CZs). The estimated source bearing always lies between the true source bearing and the broadside direction of the towed array. The physical mechanism is analyzed by using normal-mode theory for theoretical interpretation and the ray method for perceptual analysis. Based on conventional beamforming, the approximate analytical solution of the beam-forming output is derived in terms of normal modes and can predict the BEE quantitatively. The ray trace is used to illustrate the range dependence. The BEEs for different ocean depths are also discussed and the results can be used as auxiliary information for source localization.