Tracking and Localizing Moving Targets in the Presence of Phase Measurement Ambiguities

When tracking a target using phase-only signal returns, range ambiguities due to the modulo 2π in measured signal phases are a major issue. Standard approaches to such problems would typically involve the use of Diophantine equations. In this paper, a simpler and robust solution is examined which uses look-up tables defined between the phase measurement and target location spaces to determine the phase measurement mapping. We show, first, that when the target motion is significant between data sampling intervals the location ambiguity can be resolved over time via known target-in-cluster tracking techniques. This method determines the optimal allocation of location with respect to phase measurements relative to the quantization of look up table values. Second, when the target is undergoing micromotions (jitter) which results in the same collection of candidate locations from phase measurements over time, the location ambiguity can be resolved using a novel phase distribution discrimination method. In this method a probability density function of the ambiguous phase-only measurement is derived that takes both sensor noise and target motion distributions into account based on directional statistics. Optimal locations are inferred from such distributions. Examples are given to demonstrate the effectiveness of these proposed methods.