Optimum Passive Bearing Estimation in a Spatially Incoherent Noise Environment

MacDonald, Verne H.; Schultheiss, P.M.

doi:10.1121/1.1911659

Cited by 165 publications

(41 citation statements)

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“…In derivations of (8) and (15) a shaping filter was utilized before correlation to obtain the CramBr-Rao lower bound of the variance of the time delay estimate; but in the case of (18), the shaping fdter was not utilized to obtain the variance of the time delay estimate. However, if the shaping fdter is utilized to obtain the minimun variance, then (18) will yield the same result shown in (13) or (20) [8].…”

Section: ) Effects Of Signal and Noise Autospectral Falloff On Timementioning

confidence: 59%

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

Quazi¹

1981

IEEE Trans. Acoust., Speech, Signal Process.

342

137

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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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Section: ) Effects Of Signal and Noise Autospectral Falloff On Timementioning

confidence: 59%

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

Quazi¹

1981

IEEE Trans. Acoust., Speech, Signal Process.

342

137

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“…We first notice that the solution for the constrained optimization problem in (11) and (12) [21], [22] to multiple parameter estimation, the variances ofx cw andŷ cw , when they are located in a reasonable proximity to (x; y), are given by (see Appendix C) (24) and (25), shown at the bottom of the page. In Appendix C, we show that (24) and (25) are equivalent to the CRLB in (4) and (5), respectively, and this indicates that the CWLS algorithm is optimal under sufficiently high SNR conditions.…”

Section: Performance Analysismentioning

confidence: 99%

Least Squares Algorithms for Time-of-Arrival-Based Mobile Location

Cheung

et al. 2004

IEEE Trans. Signal Process.

482

247

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“…The vector 9 represents possibly unknown spectral parameters such as signal 2 bandwidth, center frequency, noise spectral levels, etc.…”

Section: A Problem Formulation and Existing Resultsmentioning

confidence: 99%

“…If the signal and noise processes are not stationary over the observation interval, the delay estimation problem is significantly more complicated, and most of the analyses (e.g., [2]- [6]) cannot be applied. In a recent paper [7], Stuller derives the log-likelihood function under the conditions of time-varying delay and possibly non-stationary source signal contaminated by additive white G aussian noises.…”

Section: Introductionmentioning

confidence: 99%

“…see [1 ]). Assuming that the source signal and the additive receiver noises are mutually independent wide sense stationary Gaussian processes with known spectra, and that the observation interval is long compared with the correlation time (inverse bandwidth) of the signal and the noises, the Maximum Likelihood (ML) estimate of the pairwise differential delay is obtained by pre-filtering and cross-correlating the received signals, and searching for the peak of the cross-correlator output [2] [3]. Under the stated assumptions, the ML delay estimate is optimal in the sense that it is asymptotically unbiased and its error variance approaches the Cramer-Rao lower bound.…”

Section: Introductionmentioning

confidence: 99%

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