Ambiguity Resolution in Interferometry

Abstract

A comprehensive theory of interferometry from a system viewpoint with particular emphasis on the ambiguity resolution problem is developed. The derived error equations include contributions from all system uncertainties, i.e., phase measurement, frequency, and element phase center position errors in three dimensions. The direction-of-arrival errors are inversely proportional to the interferometer baseline and it is customary to make the baseline large enough to meet the accuracy requirements. A system with a baseline greater than a half-wavelength results in the well known direction-of-arrival ambiguity problem with the addition of a third element to each baseline being a common method for resolving the ambiguity. It is shown that contrary to previous thinking there are many equally optimal positions for adding the third element to resolve the ambiguity. In addition, it is shown how the measurement made to resolve the ambiguity can also be applied to increase the accuracy of the angle-of-arrival measurement. A central result is the derivation of expressions specifying the probability of correct resolution of ambiguities as a function of system parameters and system errors. Moreover the concept of an acceptance criterion designed to reduce processing of erroneous measurements is developed. Narrowing the criterion reduces the percentage of data accepted for processing, but increases the probability of correct ambiguity resolution. This is analogous to the relationship between the probability of detection and the probability of false alarm in radar theory.