Measurement Extraction From a Focal Plane Array and Remote Tracking of Fast Objects Outside Line of Sight

Measurement extraction is an application of the technique in statistical inference known as parameter estimation. In this application, the parameters are defined as some characteristic of the unprocessed data that describes an observation of some underlying and unknown object/location/etc. This thesis focuses on parameter estimation problems in two ways: the first chapters use this technique within the context of measurement extraction, while in the later chapters it is used in its more traditional application of estimating motion parameters from a time-series of observations. This work’s first topic deals with measurement extraction, from an optical sensor’s Focal Plane Array (FPA), of a streaking target. We use a model that assumes pixels are separated by dead zones and model the streaking target’s point spread function (PSF) as a Gaussian PSF that moves during the optical sensor’s integration time. We make an assumption that the target has a constant velocity over the sampling interval and parametrize its motion with a starting and ending position. The noise model for a single pixel has variance proportional to its area, consistent with a Poisson model of the number of non-target originated photons. We develop a maximum likelihood (ML) method of estimating the target motion parameter vector based on the set of pixel measurements from the optical sensor. This work then derives the Cramer-Rao Lower Bound (CRLB) on the estimation error of the target motion parameter. We then present a Matched Filter (MF) based definition of the signal to noise ratio (SNR) to use as a basis for comparison of Monte-Carlo simulation based location estimates to the calculated CRLB. It is shown that the maximum likelihood estimator (MLE) for the starting and ending positions of a streak in the FPA is efficient for sufficiently high SNR targets. We then provide a test statistic for target detection and propose approximate distributions to set the detection threshold for specific detection (PD) and false alarm probabilities (PFA), which are then verified via simulations. The second topic extends previous work on location and intensity estimation for measurement extraction of targets in a FPA. Prior work has been done to extract single targets and two targets of equal intensity, while the present work explores the case where two targets have unequal and unknown intensities. We present a Maximum Likelihood method for target extraction under resolved and unresolved assumptions. In the unresolved case, we estimate the parameters of a single target that represents the centroid of the two unresolved targets. We also present the Cramer-Rao lower bound (CRLB) of the estimation variances for both cases. Our simulation results show that resolved targets have their parameter vectors estimated efficiently (i.e., the variance meets the CRLB) when the targets are sufficiently separated (by about 1.8 pixel widths). We also find that estimation of the centroid parameters is efficient for target separations below another separation threshold (about 1.3 pixel widths). Furthermore, we find that increased difference in the SNR of two targets causes the variances in the resolved scenario to be lower and, in the case of the unresolved scenario, to increase. We also derive and characterize a decision about target cardinality as a hypothesis testing problem and develop a generalized likelihood ratio test (GLRT) to perform the decision making. The performance of this test is evaluated via MC simulations and matches well to theoretical predictions. Finally, we explore the effect of separation between targets and individual target SNR on resolvability. The final chapter of this work develops an Object Extraction (OE) algorithm from a remote sensor in the presence of multipath propagation between the sensor and the object. The OE is carried out by estimating the object’s motion parameter by fusing the multipath measurements. The signals from the object are assumed to have a low SNR, i.e., the OE has to be done in the presence of numerous spurious detections. This paper also discusses a method to reduce the size of the motion parameter space by considering the object’s motion in a non-inertial frame. The object is observed using a measurement model that produces range, azimuth and range-rate using a multipath refraction model for the signal propagation through the medium. The OE accounts for the multipath environment as the model allows for multiple returns from a single object. Finally, this section shows the effectiveness of the OE by evaluating the accuracy of the estimation with MC simulation.