Cramer-Rao Lower Bounds of Joint Delay-Doppler Estimation for an Extended Target

TL;DR

This paper derives the Cramer-Rao Lower Bounds for joint delay-Doppler estimation of extended targets, analyzes the impact of waveform parameters, and evaluates the effectiveness of the WBAF estimator compared to the bounds.

Contribution

It provides integral and series representations of CRLBs for extended targets and assesses the suitability of the WBAF estimator for such scenarios.

Findings

CRLBs for delay and Doppler stretch are derived and approximated.

Doppler CRLB inversely proportional to waveform's effective time-bandwidth.

WBAF estimator is unsuitable for extended target parameter estimation.

Abstract

The problem on the Cramer-Rao Lower Bounds (CRLBs) for the joint time delay and Doppler stretch estimation of an extended target is considered in this paper. The integral representations of the CRLBs for both the time delay and the Doppler stretch are derived. To facilitate computation and analysis, series representations and approximations of the CRLBs are introduced. According to these series representations, the impact of several waveform parameters on the estimation accuracy is investigated, which reveals that the CRLB of the Doppler stretch is inversely proportional to the effective time-bandwidth product of the waveform. This conclusion generalizes a previous result in the narrowband case. The popular wideband ambiguity function (WBAF) based delay-Doppler estimator is evaluated and compared with the CRLBs through numerical experiments. Our results indicate that the WBAF estimator, originally derived from a single scatterer model, is not suitable for the parameter estimation of an extended target.