An overview on the time delay estimate in active and passive systems for target localization

Abstract

Abstract-Sonar and radar systems not only detect targets but also localize them. The process of localization involves bearing and range estimation. These objectives of bearing and range estimation can be accomplished actively or passively, depending on the situation. In active sonar or radar systems, a pulsed signal is transmitted to the target and the echo is received at the receiver. The range of the target is determined from the time delay obtained from the echo. In passive sonar systems, the target is detected from acoustic signals emitted by the target, and it is localized using time delays obtained from received signals at spacially separated points. Several authors have calculated the variance of the time deZay estimate in the neighborhood of true time delays and have presented their results in terms of coherence function and signaZ and noise autospectra. Here we analyze these derivations and show that they are the same for the case of low signalto-noise ratio (SNR). We also address a practical problem with a target-generated wide-band signal and present the Cram6r-Rao lower bound on the variance of the time delay estimate as a function of commonly understood terms such as SNR, bandwidth, observation time, and center frequency of the band. The analysis shows that in the case of low SNR and when signal and noise autospectra are constants over the band or signal and noise autospectra fall off at the same rate, the minimum standard deviation of the time delay estimate varies inversely to the SNR, to the square root of the product of observation time and bandwidth, and to the center frequency (provided W2/12f; << 1, where W = bandwidth andfo = center frequency of the band). The only difference in the case of a high SNR is that the stanManuscript received April 4, 1980; revised October 9, 1980. This work was supported by the Naval Underwater Systems Center's Wide Aperture Array Electronics Project.The author is with the Naval Underwater Systems Center, New London Laboratory, New London, CT 06320. dard deviation varies inversely to the square root of the SNR, and all other parameter relationships are the same. We also address the effects of different signal and noise autospectral slopes on the variance of the time delay estimate in passive localization. S I. INTRODUCTIONONAR and radar systems not only detect the targets but also find the location and velocity of the target. To locate a target using an active system, a pulse is transmitted to the target and the echo is received. The range of a target is determined using the time delay between the transmission of a pulse and the reception of its echo. To estimate this time delay, the system must determine the instant when the echo arrives. Generally, this is accomplished by matched fdter or correlation where the "clean" reference signal, i.e., transmitted signal, is available. The time delay is estimated by measuring the peak of the output processor (matched filter or correlator), but exactly when this peak occurs is uncertain owing to the noise added to the echo...

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