Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

Ren, Chengfang; Galy, Jérôme; Chaumette, Éric; Vincent, François; Larzabal, Pascal; Renaux, Alexandre

doi:10.1109/lsp.2015.2412173

Cited by 8 publications

(17 citation statements)

References 19 publications

(38 reference statements)

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“…One way to estimate the unknown parameters is to estimate them at the same time as sequentially estimating the states, see for instance [5]. Correspondingly, the theoretical lower limits on both the unknown states and parameters in the models can be derived, and the limits are known as hybrid bounds, see for instance [12]. Another way is to assume an off-line phase, where the unknown parameters are estimated from a set of precollected training data.…”

Section: B Related Work and Contributionsmentioning

confidence: 99%

“…From (38) and (37), (40) and (39), we can easily obtain the distributions. Hence, the L-terms defined in (61) are derived as follow: L 11 k is given in (66a) and (67), L 12 k is given in (66b) and (69), L 22 k is derived as…”

Section: Posterior Filtering Crb: Casementioning

confidence: 99%

“…From previous derivations, to compute the posterior CRB in this case, the L-terms are specified as follows 1) Compute L 11 k according to (89); 2) Compute L 12 k according to (90); 3) Compute L 22 k according to (70), with M k given in (82) and the first expectation is computed using Monte Carlo integration.…”

Section: Posterior Crb For Target Tracking Example: Casementioning

confidence: 99%

See 2 more Smart Citations

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Zhao

Fritsche

Hendeby

et al. 2019

IEEE Trans. Signal Process.

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Posterior Cramér-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process-based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process-based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posterior filtering CRBs for this specific application. Finally, the theory is illustrated with a positioning problem, with experimental data from an office environment where the obtained estimation performance is compared to the derived CRBs.

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Section: B Related Work and Contributionsmentioning

confidence: 99%

Section: Posterior Filtering Crb: Casementioning

confidence: 99%

Section: Posterior Crb For Target Tracking Example: Casementioning

confidence: 99%

See 1 more Smart Citation

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Zhao

Fritsche

Hendeby

et al. 2019

IEEE Trans. Signal Process.

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“…Then, if is a set of samples of a parametric function , then subject to (4)(6), satisfies: (20) If is integrable over , then (20) is, up to a scale factor (differential element ), a numerical approximation (with rectangle rule) of the following identity: (21) where and . Moreover, subject to (21), (2) becomes: (22) where , which corresponds to [7, (18) (19)] in the case of a single function (QED).…”

Section: A New Family Of Hybrid Large Error Boundsmentioning

confidence: 99%

“…Note that the derivation is conducted in the multivariate context with multiple test points. The starting point is the result provided in[21, Sec. III] showing that the class of estimators satisfying:…”

mentioning

confidence: 99%

Hybrid Barankin–Weiss–Weinstein Bounds

Ren

Galy

Chaumette

et al. 2015

IEEE Signal Process. Lett.

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This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.Index Terms-Hybrid bounds, MAPMLE, mean-square-error bounds, parameter estimation, threshold SNR.

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Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Duan

Hanebeck

2021

IET Signal Processing

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Joint Cramér-Rao lower bound ( JCRLB) is very useful for the performance evaluation of joint state and parameter estimation ( JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

Cited by 8 publications

References 19 publications

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Hybrid Barankin–Weiss–Weinstein Bounds

Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

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