Measurement Extraction for a Point Target From an Optical Sensor

Abstract

This paper considers the measurement extraction for a point target from an optical sensor's focal plane array (FPA) with a dead zone separating neighboring pixels. Assuming that the energy density of the target deposited in the FPA conforms to a Gaussian point spread function and that the noise mean and variance in each pixel are proportional to the pixel area (i.e., according to a Poisson noise model), we derive the Cramer–Rao lower bound (CRLB) for the covariance of the estimated target location. It is observed that that there is an optimal pixel size that minimizes the CRLB for a given dead-zone width, and the maximum likelihood estimator is shown to be efficient via Monte Carlo runs for moderate-to-large signal-to-noise ratios. The test statistic for target detection is derived and it is shown to be a matched filter at the estimated location. The distributions of the test statistic under both hypotheses are derived using some approximations. The detection probability is then obtained.