Extended Ziv-Zakai lower bound for vector parameter estimation

Bell, Kristine L.; Steinberg, Yossef; Ephraim, Yariv; Trees, Harry L. Van

doi:10.1109/18.556118

Cited by 193 publications

(178 citation statements)

References 33 publications

(72 reference statements)

Supporting

Mentioning

175

Contrasting

Order By: Relevance

“…A detailed derivation of the Ziv-Zakai bound [24,58,59] is provided in Appendix B. The final result reads MSE(θ est ) µ,θ 0 ≥ ∆ 2 θ ZZB , where…”

Section: Ziv-zakai Boundmentioning

confidence: 99%

See 1 more Smart Citation

Frequentist and Bayesian Quantum Phase Estimation

Pezzé

Gessner

et al. 2018

Entropy

View full text Add to dashboard Cite

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér-Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér-Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.

show abstract

“…A detailed derivation of the Ziv-Zakai bound [24,58,59] is provided in Appendix B. The final result reads MSE(θ est ) µ,θ 0 ≥ ∆ 2 θ ZZB , where…”

Section: Ziv-zakai Boundmentioning

confidence: 99%

“…[24,58,59]). This Appendix follows these derivations closely and provides additional background, which may be useful for readers less familiar with the field of hypothesis testing.…”

Section: Appendix B Derivation Of the Ziv-zakai Boundmentioning

confidence: 99%

Frequentist and Bayesian Quantum Phase Estimation

Pezzé

Gessner

et al. 2018

Entropy

View full text Add to dashboard Cite

show abstract

“…Once again, the GML solution is an affine transformation of the sample covariance matrix that, omitting constant terms, is given by Tr (10) with (11) which is the covariance matrix of . Therefore, bearing in mind that Tr , it is found that Tr (12) are the independent term and the kernel of the GML likelihood function (10), respectively.…”

Section: Gaussian Maximum Likelihood (Gml)mentioning

confidence: 99%

Second-order parameter estimation

Villares

Vazquez

2005

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-This work provides a general framework for the design of second-order blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias. The resulting optimal estimator is found to depend on the observation fourth-order moments that can be calculated analytically from the known signal model. Unfortunately, in most cases, the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems. To overcome this limitation, the second-order minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters. This small-error approximation is adopted to design iterative estimators or trackers. It is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival (AoA) of multiple digitally-modulated sources by means of a uniform linear array. The optimal second-order tracker is compared with the classical maximum likelihood (ML) blind methods that are shown to be quadratic in the observed data as well. Simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in medium-to-high SNR scenarios.

show abstract

“…Further improvements have been made by Bellini & Tartara [4], and Weiss & Weinstein [5], [6]. Extension to the vector case has also been developed [7]. The improved ZZBs in [5], [6] are applicable to either narrowband or wideband waveforms because of explicit assumptions made throughout the derivations.…”

Section: Introductionmentioning

confidence: 99%

Ziv-Zakai Time Delay Estimation Bound for Ultra-Wideband Signals

Sadler

Huang

2007

2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07

View full text Add to dashboard Cite

The Ziv-Zakai bound (ZZB) provides a general mean-square error analytical baseline to evaluate time delay estimation (TDE) techniques for a wide range of time-bandwidth products and signal-tonoise ratios, but generally can only be numerically evaluated. The Weiss-Weinstein bound (WWB) further improves characterization of the attainable system performance, for narrowband and wideband signals with small to moderate fractional bandwidth. Similar to the WWB, here we nd a simpli ed closed-form ZZB for TDE with ultra-wideband (UWB) signals. The resulting simpli ed bound is found over disjoint segments, separated by thresholds that characterize different regions of ambiguity. The closed-form simpli ed bound can be analytically studied, and approaches both the ZZB and the TDE performance of a maximum likelihood estimator. INDEX TERMSUltra-wideband, time delay estimation, Ziv-Zakai bound, WeissWeinstein bound.

show abstract

Extended Ziv-Zakai lower bound for vector parameter estimation

Cited by 193 publications

References 33 publications

Frequentist and Bayesian Quantum Phase Estimation

Frequentist and Bayesian Quantum Phase Estimation

Second-order parameter estimation

Ziv-Zakai Time Delay Estimation Bound for Ultra-Wideband Signals

Contact Info

Product

Resources

About