Maximum Likelihood Delay and Doppler Estimation for Passive Sensing

Abstract

We consider the problem of delay and Doppler frequency estimation of a moving target in passive radar using a non-cooperative illuminator of opportunity (IO). The passive radar consists of a reference channel (RC), i.e., an antenna steered to the IO, and a surveillance channel (SC) that collects target echoes. We examine the maximum-likelihood estimator (MLE) for the passive estimation problem by modeling the unknown IO waveform as a deterministic process. Under this condition, the passive MLE is shown to reduce to a cross-correlation and search process using the surveillance signal and a delay-Doppler compensated version of the reference signal. We present two implementations for the passive MLE, including a direct and, respectively, a fast implementation based on a two-dimensional Fast Fourier Transform. In addition, the Cramer-Rao Bound is derived to benchmark the passive estimation performance. The passive MLE is compared via numerical simulation with its active counterpart, which has the exact knowledge of the waveform and uses it for cross-correlation. Our results show that the signal-to-noise ratio (SNR) in the RC relative to the SNR in the SC has a significant impact on the passive MLE. Specifically, if the former is notably higher than the latter (by, e.g., 5 dB), there is a minor difference between the passive and active MLEs for the delay and Doppler estimation; otherwise, the difference is non-negligible and increases with the SNR.