Wavelet based approach for joint time delay and Doppler stretch measurements

A new wavelet-based algorithm for joint time delay and Doppler stretch esti mation in passive radar, sonar, and GPS applications is described. By takin g the cross wavelet transform of the noisy outputs from two spatially separ ated sensors, the wideband, cross ambiguity function (WBCAF) can be compute d. This in turn provides a direct measurement of the time difference and Do ppler stretch between the two signals. The Cramer-Rao lower bound (CRLB) is derived and the performance of the proposed algorithm is analyzed. It Is f ound that the theoretical variances of the estimates are unbiased and appro ach the CRLB at high signal-to-noise ratio (SNR). In order to improve the a ccuracy of the estimation under noisy environment, a simple denoising metho d is introduced. Simulation results are given to corroborate the analysis.