Estimating Resonances in Low-SNR Late-Time Radar Returns With Sampling Jitter

The frequency and attenuation rate of a resonance in the late-time return of a radar signal are indicative of a target's geometry and conductivity, and hence they can be used as features in a variety of filtering and classification applications. However, late-time returns are typically observed over short windows at low signal-to-noise ratios (SNRs, averaged over the window), and often in the presence of sampling jitter. This can make the estimation of these parameters difficult, even when multiple measurement shots are available. In this article, we develop a new multi-shot estimation method that is based on models for the distribution of the roots of the z-transform of the received signal. Under an additive-Gaussian-noise model, we have a closed-form expression for the root distribution in terms of the resonance parameters, and the parameters are estimated by matching the model distribution to the empirical distribution. The root distribution has a strong dependence on the frequency and attenuation rate, and leads to significantly better estimates than existing techniques at low SNRs. By developing approximate models, we extend these performance advantages to scenarios with significant sampling jitter and synchronization offsets.