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

The problem of the Cramer-Rao Lower Bounds (CRLBs) for the joint time delay and Doppler stretch estimation of an extended target is considered in this paper. 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 and 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, which was originally derived from a single scatterer model, is not suitable for the parameter estimation of an extended target.