Measurement Extraction for Two Closely-Spaced Objects Using an Imaging Sensor

Abstract

This paper considers measurement extraction for two closely-spaced objects with unknown equal intensities in an imaging sensor's focal plane array (FPA). Given a screen of FPA data, the first part of the measurement extractor, target location estimator, can extract the location estimates for two targets or one, with the corresponding accuracy given by the Cramer Rao lower bound (CRLB). The second part of the measurement extractor, target detector, selects among the hypotheses of two resolved targets and a single one using information-theoretic criteria and hypothesis tests. Simulation results have been conducted to evaluate the measurement extraction performance including the probability of resolving the two hypotheses, and the efficiency and unbiasedness of the target location estimates for the selected hypothesis using different hypothesis detection schemes. The generalized likelihood ratio test (GLRT) based on linearized observation model using second order Taylor series expansion is most appealing as it provides an explicit expression of the probability of detecting two targets as a function of the target separations, the signal-to-noise ratio at a given false resolution probability. It is shown that the simulation-based resolution performance for the GLRT using the estimated center location of the two targets matches well with the analytic performance assuming known center.