Time delay estimation with nuisance parameters: Performance approximation and coarse acquisition.
Joong Kyu Kim · Deep Blue (University of Michigan) · 1989
This thesis concentrates on two topics which are related to time delay estimation. The first is a model useful for approximating the error performance of maximum likelihood type estimators of multiple unknown parameters; this is the error intensity model. The second is a methodology for joint detection and coarse estimation of signal parameters; this is the coarse acquisition method. These are important in both single parameter and multiple parameter estimation in the presence of unknown "nuisance" parameters. Three specific examples are considered. We consider the effect of coherent interference on an estimate of the time delay of a coherent signal when the receiver uses a directional array. The cases where the time delay of the interference is known or unknown are compared using both error probability and mean squared error approximation. The second example considers the effect of a known or an unknown doppler component on an estimate of time delay of a deterministic signal. This models the moving-target target tracking problem; error probability and mean squared error approximations of the time delay estimate are the basis for comparing the performances. The third major example is coarse acquisition of time delay; this is relevant to radar and sonar target range and bearing estimation. Coarse acquisition is the first stage in a two step algorithm signal detection and rough classification followed by fine acquisition of the coarsely acquired signal. This problem was attacked with the following simple objective: based on a correlator statistic, classify the time delay into one of M intervals subject to an upper bound on the probability of falsely deciding signal presence. Methods of decision theory and invariance applied to this problem took the form of a constrained min-max invariant multiple hypotheses test. The principal significance of this work is: (1) it can yield insight into poorly understood empirical behavior of delay estimators in the presence of unknown coherent interferers or doppler; and (2) it establishes an optimality property of the correlator peak comparison scheme for coarse acquisition of delayed signals.