RESONANCE-BASED TARGET IDENTIFICATION USING LATE-TIME RADAR RETURNS

Abstract

In time-domain radar, the resonant features of a target are contained in its late-time response (LTR). The frequencies and attenuation rates (i.e., complex frequencies) of these resonances can be viewed as inherent features of the target. Thus, they could, at least in principle, be used to describe and identify it. Unfortunately, methods for estimating these complex frequencies from a single observation window of the LTR are not robust to noise. That is a concern because the LTR is an attenuating phenomenon that is quite weak to begin with, and hence, the effective signal-to-noise ratio (SNR) over an LTR observation window is low. As a result, the potential for target identification using the resonances in the LTR has yet to be robustly realized in practice in the nearly 35 years since it was identified. This thesis suggests new approaches to processing the LTR that provide more robust realizations of the underlying principles, and demonstrates their performance in physical experiments on an indoor ultra-wideband radar.

The premise for the thesis begins with the observation that it is now possible to design time-domain radars that have a rather high pulse repetition rate, allowing them to quickly capture many measurement shots. Averaging to improve the effective SNR can be employed, but this alone is insufficient for robustness. Statistical analysis of the estimates of the complex frequencies is more effective, but it is hampered because there is no known expression for the distribution of these frequencies.

In Chapter 2, a technique is developed for estimating the complex frequencies via a related distribution of the z-transform roots of the observed LTRs, which has a known expression when the noise is Gaussian. The technique is demonstrated to be effective in Gaussian noise and in the presence of non-Gaussian uncertainties such as sampling jitter, provided the uncertainty is “approximately Gaussian.”

In has been shown that, for Gaussian noise, the maximum-likelihood estimator for the complex frequencies requires the solution of a nonlinear least-squares problem. Since finding the globally optimal solution to that problem is inherently difficult, Chapter 3 presents an efficient method for finding good estimates of the complex frequencies that is based on their empirical distribution. The method is applied to measurements of handheld weapons in the presence of environmental clutter.

Chapter 4 tackles the problem of using LTR measurements to classify targets. The proposed method employs empirical distributions of the estimates of the targets’ complex frequencies, rather than employing specific estimates. The method is again applied to measurements of handheld weapons in the presence of environmental clutter and shown to be highly effective.