Improved Lower Bounds on Signal Parameter Estimation

Chazan, Dan; Zakai, Moshe; Ziv, J.

doi:10.1109/tit.1975.1055325

Cited by 188 publications

(120 citation statements)

References 6 publications

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“…two magnitudes at least: i) the achieved MSE [7], [9], [21] like in our case (which is the most reliable because the main concern in estimation is to minimize the MSE) and ii) the probability of non-ambiguity [15], [37] (for simplicity reasons). Note that the RMSE achieved in the a priori region increases with the width of the a priori domain as can be seen from (19). This explains why the RMSE is relatively small at low SNRs (1.9 ns at dB) in our numerical example; in fact, the considered is relatively narrow ( is 3.5 times the pulse width).…”

Section: A Baseband Pulsementioning

confidence: 56%

“…Some upper bounds (UB) have also been derived like the Seidman UB [17]. It will suffice to mention here [16], [18] the Cramer-Rao, Bhattacharyya, Chapman-Robbins, Barankin and Abel deterministic LBs, the Cramer-Rao, Bhattacharyya, Bobrovsky-MayerWolf-Zakai, Bobrovsky-Zakai, and Weiss-Weinstein Bayesian LBs, the Ziv-Zakai Bayesian LB (ZZLB) [2] with its improved versions: Bellini-Tartara [4], Chazan-Ziv-Zakai [19], Weinstein [20] (approximation of Bellini-Tartara), and Bell-Steinberg-Ephraim-VanTrees [21] (generalization of Ziv-Zakai and Bellini-Tartara), and the Reuven-Messer LB [22] for problems of simultaneously deterministic and Bayesian parameters.…”

Section: )mentioning

confidence: 99%

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Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Mallat

Gezici

Dardari

et al. 2014

IEEE Trans. Signal Process.

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Abstract-In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramér-Rao lower bound at low and medium signal-to-noise ratios (SNRs) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accuracy of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.Index Terms-Nonlinear estimation, threshold and ambiguity phenomena, maximum likelihood estimator, mean-squared error, upper and lowers bounds, time-of-arrival.

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Section: A Baseband Pulsementioning

confidence: 56%

Section: )mentioning

confidence: 99%

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Mallat

Gezici

Dardari

et al. 2014

IEEE Trans. Signal Process.

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show abstract

“…Finally, it is important to point out that: a) in localization problems BCRB's often provide useful insights [9], [10], [12], but these bounds are usually loose for low SNR conditions [22], [23], i.e., when a priori information (the map in this context) plays a critical role due to the poor quality of observations; b) the BCRB analysis requires the adoption of the smoothed uniform pdf model for prior information (see Section II-A).…”

Section: A Bayesian Cramer-rao Boundsmentioning

confidence: 99%

“…These considerations motivate the search for other bounds and, in particular, for the EZZB, which is usually tighter than the BCRB at low SNRs [23]- [27] and does not require (7) to hold (so that the uniform model (1) can be employed as it is); this is further discussed in the following section.…”

Section: A Bayesian Cramer-rao Boundsmentioning

confidence: 99%

On the Performance Limits of Map-Aware Localization

Montorsi

Mazuelas

Vitetta

et al. 2013

IEEE Trans. Inform. Theory

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Abstract-Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a set of observations and, possibly, of some a priori information related to them (e.g., information about anchor positions and properties of the communication channel). In this manuscript new bounds are derived under the assumption that the localization system is map-aware, i.e., it can benefit not only from the availability of observations, but also from the a priori knowledge provided by the map of the environment where it operates. Our results show that: a) map-aware estimation accuracy can be related to some features of the map (e.g., its shape and area) even though, in general, the relation is complicated; b) maps are really useful in the presence of some combination of low signal-to-noise ratios and specific geometrical features of the map (e.g., the size of obstructions); c) in most cases, there is no need of refined maps since additional details do not improve estimation accuracy.

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“…However, the CRB is a local bound that fails to characterize performance when the ambiguity-free condition is violated, for example, when a crosscorrelation TDE incorrectly selects neighboring correlation peaks. Tighter bounds for TDE have been developed, including the ChapmanRobbins (Barankin) bound [2], and the Ziv-Zakai bound (ZZB) [3]. Though much tighter than the corresponding CRB, they are not easily manipulated into simple closed form expressions, and consequently often require numerical evaluation.…”

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

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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.

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Improved Lower Bounds on Signal Parameter Estimation

Cited by 188 publications

References 6 publications

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

On the Performance Limits of Map-Aware Localization

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

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Improved Lower Bounds on Signal Parameter Estimation

Cited by 188 publications

References 6 publications

Statistics of the MLE and Approximate Upper and Lower Bounds&#x2014;Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds&#x2014;Part I: Application to TOA Estimation

On the Performance Limits of Map-Aware Localization

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

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Product

Resources

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Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation