Extracting fast targets from an EO sensor

Abstract

This work describes a method for measurement extraction of fast point targets leaving an extended signature in the pixelated focal plane array of an EO sensor. The extraction method and subsequent statistics are derived from a physics based model where the spatial quantization regions, or pixels, are separated by dead zones. Furthermore, the intensity in a pixel is corrupted by approximately Gaussian noise which exhibits a variance proportional to the pixel area. This noise model is based on a Poisson assumption, in reference to the number of photons that contribute to the noise intensity. The signal portion of the image is a spatially quantized version of the target’s point spread function (PSF) that is modeled as a Gaussian PSF that moves at a constant velocity, a realistic assumption during an exposure time that may have been adjusted (and lengthened) to enhance target SNR. The measurement extraction is done using a Maximum Likelihood (ML) method for which we provide an appropriate Cramer-Rao Lower Bound (CRLB) on the estimation error of the target’s 2-D starting and ending positions. We then provide a definition for the signal to noise ratio (SNR) in an image using a matched filter (MF). Next, we present Monte Carlo simulations to confirm the derived results and find that the measurement extractor is efficient for SNRs .≥ 12dB (using our SNR definition). Finally, we develop a solution to the problem of detecting fast targets in images. We present approximate distributions for the test statistic under the null (H0 — target absent) and alternative (H1 — target present) hypotheses that can be used to set a threshold for specific probabilities of detection PD and false alarm PFA. Finally, we verify these distributions with Monte Carlo simulations.