Weighting statistics for estimation in a multistatic sensor radar configuration

Abstract

For the second and third topics this thesis then focuses on radar imaging with respect to two subjects related to weighting data from different receivers. The received signal is made up of a weighted sum of the signals from each individual receiver, and each individual receiver's signal is based on the sum of the transmitters' time-delayed and Doppler-shifted waveforms corrupted by additive complex white Gaussian noise. The goal is to use the weights to improve target estimation and, hence, to improve the imaging of the target. Before considering the received signal, for the second topic we investigate both certain geometric configurations of bistatic pairs of antennas and combinations of weighting values with respect to the calculation of a weighted sum of the discretized point-spread function within k-space. We show that weights, geometry, and carrier frequency all affect the overall point-spread function with respect to its delta-function-like behavior.

This thesis addresses three related topics. The first topic covers reproducing kernel Hilbert spaces and the associated techniques for estimation. There is much prior theory for RKHS techniques applied to the estimation of unknown parameters, and these techniques apply to unbiased estimators of the unknown parameters. With the existing RKHS techniques it has been possible to calculate minimum-variance unbiased estimators and their variances. It has also been possible to calculate Cramér-Rao lower bounds of unbiased estimators in the case when the covariance process of the model is parameterized by the unknown to be estimated. With respect to MVUEs one such prior example is the unbiased estimation of the time-delay parameter in the random process made up of a time-delayed transmitted signal embedded in noise. This thesis extends the applicability of these RKHS techniques, for both scalar and vector unknown parameters, to the more general case of estimators with bias. Then we can employ these new RKHS techniques to calculate minimum-variance estimators and their variances as well as CRLBs, even when we cannot assume the use of unbiased estimators.

Finally, the third topic is weighting statistics for estimating a moving target's position and velocity in a radar configuration made up of multiple transmitter and receiver antennas. We wish to optimize the CRLB values of the unbiased estimators of the target's unknown yet deterministic position and velocity via the received signal scattered from the target. Certain geometric configurations of the antennas and the target, in addition to the quantity of antennas and to the weighted signals at the individual receivers, lead to different variance bounds based on the weights. We show the consequences of poorly chosen weights on the variance bounds. And we show other cases that lead to lower variance bounds due to differently chosen weights compared to equally weighted received signals.