Performance analysis of time-delay estimation systems
Ehud Weinstein · Woods Hole Oceanographic Institution eBooks · 1984
This is the second part of a study which deals with the problem of passive time delay estimation. The focus here is on systems employing wideband signals and/or arrays of very widely separated receivers. A modified (improved) version of the Ziv-Zakai lower bound (ZZLB) is used to analyze the effect of additive noise and signal ambiguities on the attainable mean square estimation errors. When the lower bound is plotted as a function of signal-to-noise ratio (SNR) one observes two distinct threshold phenomena dividing the SNR domain into three disjointed segments: at high SNR the lower bound coincides with the Cramer-Rae lower bound (CRLB). This is the ambiguity-free mode of operation where differential delay estimation is subject only to local errors. At moderate SNR (between the two thresholds), the lower bound exceeds the CRLB by a factor of 12(ω0/W)2 where ω0 and W are, respectively, the center frequency and signal bandwidth. In this region the ambiguities in the received signal phases cannot be resolved, however a useful estimate of the differential delay can still be obtained using the received signal envelopes. At low SNR, the lower bound approaches a constant level depending only on the variance of the a-priori search domain of the unknown delay parameter. In this region signal observations are subject to envelope ambiguities as well, thus essentially useless for the delay estimation.