Some lower bounds on signal parameter estimation

Ziv, J.; Zakai, Moshe

doi:10.1109/tit.1969.1054301

Cited by 281 publications

(182 citation statements)

References 8 publications

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“…(10), it is clear that the knowledge of η (α, β, u, v) for a particular problem leads to the Weiss-Weinstein bound (without the maximization procedure over the test-points and over the parameters s i ). Surprisingly, this simple expression is given in [40] only for s i = 1 2 , ∀i and not for the general case.…”

Section: B a General Results On The Weiss-weinstein Bound And Its Appmentioning

confidence: 99%

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Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Renaux

Boyer

et al. 2014

Signal Processing

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In this paper, the Weiss-Weinstein bound is analyzed in the context of sources localization with a planar array of sensors. Both conditional and unconditional source signal models are studied. First, some results are given in the multiple sources context without specifying the structure of the steering matrix and of the noise covariance matrix.Moreover, the case of an uniform or Gaussian prior are analyzed. Second, these results are applied to the particular case of a single source for two kinds of array geometries: a non-uniform linear array (elevation only) and an arbitrary planar (azimuth and elevation) array.

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Section: B a General Results On The Weiss-weinstein Bound And Its Appmentioning

confidence: 99%

“…Ziv-Zakai family [10] [11] [12] and the Weiss-Weinstein family [13] [14] [15] [16]. Finally, when the parameter vector is made from both deterministic and random parameters, the so-called hybrid bounds have been developed [17] [18] [19] [20].…”

mentioning

confidence: 99%

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Renaux

Boyer

et al. 2014

Signal Processing

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“…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

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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.

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“…Another interesting family of nonclassical states with the same fixed mean numbern is 26) where |n/ν denote number states, assuming thatn/ν is always an integer. In this case,…”

Section: Nonclassical States With Fixed Mean Numbermentioning

confidence: 99%

Contradictions between different measures of quantum uncertainty

Matía-Hernando

Luis

2012

Phys. Rev. A

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We show that variance and Shannon entropy provide contradictory conclusions for the uncertainty associated with the number operator for some families of states of harmonic oscillator systems with fixed mean number, and for the uncertainty of a spin component for states with and without fixed mean. We analyze this behavior in terms of the properties of these uncertainty measures. We explore their impact on quantum metrology, examining the limits to resolution caused by number fluctuations in diverse scenarios of phase-shift detection.

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Some lower bounds on signal parameter estimation

Cited by 281 publications

References 8 publications

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

Frequentist and Bayesian Quantum Phase Estimation

Contradictions between different measures of quantum uncertainty

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