Performance Prediction of a Dual-Baseline Radar or Sonar Interferometer Based on a Vernier Critical Value Concept

Abstract

Determination of the angle of arrival in radar and sonar, including synthetic aperture systems, is complicated by the common problem of $2\pi$ -ambiguity in phase, which is exacerbated by noise. Use of two receiving sensors establishing a baseline can remove some ambiguity; use of additional receiving sensors can further improve the ambiguity-removal process. Here, the influence of noise on sensor phase is modeled using random variables. Upper bounds are associated with these random variables, to define a formalism adapted to the threshold effect controlling the ambiguity removal process. This threshold noise level is determined for a dual-baseline interferometer: Above it, the ambiguity cannot be removed with certainty; below it, the ambiguity can be removed with certainty. This threshold, for a particular dual-baseline, defines the Vernier critical value, which can be computed for any pair of baselines, hence mapped when the two baselines are represented parametrically. This approach based on theoretical formalism using numerical values derived from this map, allows performance prediction with high accuracy and ultimately presents, in a unique plot, a tradeoff between ambiguity removal and bathymetric accuracy. Finally the angle-of-arrival determination is improved for any dual-baseline interferometer.