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Journal ArticleDOI

Fundamental limitations in passive time delay estimation--Part I: Narrow-band systems

TL;DR: A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB) to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions.
Abstract: Time delay estimation of a noise-like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar/sonar applications. A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB). This technique is shown to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions. For delay estimation using narrow-band (ambiguity-prone) signals, the fundamental result of this study is illustrated in Fig. 3. The entire domain of SNR is divided into several disjoint segments indicating several distinct modes of operation. If the available SNR does not exceed SNR 1 , signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation. As a result, the attainable mean-square error \bar{\epsilon}^{2} is bounded only by the a priori parameter domain. If SNR 1 2 , the modified ZZLB coincides with the Barankin bound. In this regime differential delay observations are subject to ambiguities. If SNR > SNR 3 the modified ZZLB coincides with the Cramer-Rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved. The transition from the ambiguity-dominated mode of operation to the ambiguity-free mode of operation starts at SNR 2 and ends at SNR 3 . This is the threshold phenomenon in time delay estimation. The various deflection points SNR i and the various segments of the bound (Fig. 3) are given as functions of such important system parameters as time-bandwidth product (WT), signal bandwidth to center frequency ratio (W/ω 0 ) and the number of half wavelengths of the signal center frequency contained in the spacing between receivers. With this information the composite bound illustrated in Fig. 3 provides the most complete characterization of the attainable system performance under any prespecified SNR conditions.
Citations
More filters
Journal ArticleDOI
01 Feb 1987
TL;DR: A derivation of the ML estimator for time delay is presented together with an interpretation of that estimator as a special member of a class of generalized cross correlators that is found to be in good agreement.
Abstract: This paper presents a tutorial review of work in coherence and time delay estimation. A review of coherence research and development is presented. A derivation of the ML estimator for time delay is presented together with an interpretation of that estimator as a special member of a class of generalized cross correlators. The performance of the estimator is given for both high and low signal-to-noise ratio cases. The proposed correlator is implemented and stimulated with synthetic data. The results are compared with performance predictions and found to be in good agreement.

1,141 citations

Journal ArticleDOI
16 Mar 2009
TL;DR: In this paper, the authors provide an overview of ranging techniques together with the primary sources of TOA error (including propagation effects, clock drift, and interference) and describe fundamental TOA bounds (such as the Cramer-Rao bound and tighter Ziv-Zakai bound) in both ideal and multipath environments.
Abstract: Over the coming decades, high-definition situationally-aware networks have the potential to create revolutionary applications in the social, scientific, commercial, and military sectors Ultrawide bandwidth (UWB) technology is a viable candidate for enabling accurate localization capabilities through time-of-arrival (TOA)-based ranging techniques These techniques exploit the fine delay resolution property of UWB signals by estimating the TOA of the first signal path Exploiting the full capabilities of UWB TOA estimation can be challenging, especially when operating in harsh propagation environments, since the direct path may not exist or it may not be the strongest In this paper, we first give an overview of ranging techniques together with the primary sources of TOA error (including propagation effects, clock drift, and interference) We then describe fundamental TOA bounds (such as the Cramer-Rao bound and the tighter Ziv-Zakai bound) in both ideal and multipath environments These bounds serve as useful benchmarks in assessing the performance of TOA estimation techniques We also explore practical low-complexity TOA estimation techniques and analyze their performance in the presence of multipath and interference using IEEE 802154a channel models as well as experimental data measured in indoor residential environments

840 citations

Journal ArticleDOI
01 Mar 1999
TL;DR: The strain filter formalism and its utility in understanding the noise performance of the elastographic process is given, as well as its use for various image improvements.
Abstract: The basic principles of using sonographic techniques for imaging the elastic properties of tissues are described, with particular emphasis on elastography. After some preliminaries that describe some basic tissue stiffness measurements and some contrast transfer limitations of strain images are presented, four types of elastograms are described, which include axial strain, lateral strain, modulus and Poisson's ratio elastograms. The strain filter formalism and its utility in understanding the noise performance of the elastographic process is then given, as well as its use for various image improvements. After discussing some main classes of elastographic artefacts, the paper concludes with recent results of tissue elastography in vitro and in vivo.

837 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extended the ultrasound speckle tracking method to allow measurement of internal displacement and strain fields over a wide dynamic range of tissue motion, which should lead to enhanced contrast resolution in strain and elasticity images.
Abstract: Previous ultrasound speckle tracking methods have been extended, permitting measurement of internal displacement and strain fields over a wide dynamic range of tissue motion. The markedly increased dynamic range of this approach should lead to enhanced contrast resolution in strain and elasticity images. Results of experiments on gelatin-based, tissue equivalent phantoms show the capabilities of the method. >

739 citations

Journal ArticleDOI
TL;DR: The estimated accuracy of the source position and velocity is shown to achieve the Crame/spl acute/r-Rao lower bound for Gaussian TDOA and FDOA noise at moderate noise level before the thresholding effect occurs.
Abstract: This paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival (TDOAs) and frequency differences of arrival (FDOAs) of a signal received at a number of receivers. The method employs several weighted least-squares minimizations only and does not require initial solution guesses to obtain a location estimate. It does not have the initialization and local convergence problem as in the conventional linear iterative method. The estimated accuracy of the source position and velocity is shown to achieve the Crame/spl acute/r-Rao lower bound for Gaussian TDOA and FDOA noise at moderate noise level before the thresholding effect occurs. Simulations are included to examine the algorithm's performance and compare it with the Taylor-series iterative method.

543 citations

References
More filters
Journal ArticleDOI
TL;DR: In this paper, a maximum likelihood estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise, where the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and suppress the noise power.
Abstract: A maximum likelihood (ML) estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise. This ML estimator can be realized as a pair of receiver prefilters followed by a cross correlator. The time argument at which the correlator achieves a maximum is the delay estimate. The ML estimator is compared with several other proposed processors of similar form. Under certain conditions the ML estimator is shown to be identical to one proposed by Hannan and Thomson [10] and MacDonald and Schultheiss [21]. Qualitatively, the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and, simultaneously, to suppress the noise power. The same type of prefiltering is provided by the generalized Eckart filter, which maximizes the S/N ratio of the correlator output. For low S/N ratio, the ML estimator is shown to be equivalent to Eckart prefiltering.

4,317 citations

Journal ArticleDOI
TL;DR: In this article, an overview of applied research in passive sonar signal processing estimation techniques for naval systems is presented, where the authors present a discussion of this problem in terms of estimating the position and velocity of a moving acoustic source.
Abstract: An overview of applied research in passive sonar signal processing estimation techniques for naval systems is presented. The naval problem that motivates time delay estimation is the source state estimation problem. A discussion of this problem in terms of estimating the position and velocity of a moving acoustic source is presented. Optimum bearing and range estimators are presented for the planar problem and related to the optimum time delay vector estimator. Suboptimum realizations are considered together with the effects of source motion and receiver positional uncertainty.

497 citations

Journal ArticleDOI
TL;DR: The Cramer-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates.
Abstract: For the purpose of localizing a distant noisy target, or, conversely, calibrating a receiving array, the time delays defined by the propagation across the array of the target-generated signal wavefronts are estimated in the presence of sensor-to-sensor-independent array self-noise. The Cramer-Rao matrix bound for the vector delay estimate is derived, and used to show that either properly filtered beamformers or properly filtered systems of multiplier-correlators can be used to provide efficient estimates. The effect of suboptimally filtering the array outputs is discussed.

261 citations

Journal ArticleDOI
TL;DR: An improved technique for bounding the mean-square error of signal parameter estimates is presented and the resulting bounds are independent of the bias and stronger than previously known bounds.
Abstract: An improved technique for bounding the mean-square error of signal parameter estimates is presented. The resulting bounds are independent of the bias and stronger than previously known bounds.

213 citations

Journal ArticleDOI
TL;DR: In this paper, the Cramer-Rao bound is used to determine an optimum signal processor for passive sonar target range and bearing estimation, where the sonar array consists of an M • element linear array of hydrophone point detectors.
Abstract: Optimum signal processing for passive sonar target range and bearing estimation is discussed for the case where the sonar array consists of an M‐element linear array of hydrophone point detectors whole individual outputs are corrupted by sensor‐to‐sensor‐independent self‐noises of arbitrary power spectra. By comparing the measurement error covariance matrix to the Cramer–Rao matrix bound the system performance, relative to the theoretical optimum, is determined. Further, the Cramer–Rao bound is used to determine an optimum signal processor. The optimum processor is configured as a set of M (M‐1)/2 cross‐correlator delay estimators (one for each hydrophone pair), followed by a Gauss–Markov estimation of the array delay vector (target steering vector), which in turn is followed by a linear weighting of the estimated delay vector elements to determine a bearing estimate and a range estimate. The processor is shown to have the Cramer–Rao matrix bound for its measurement error covariance matrix.Subject Classif...

202 citations