A direct derivation of the exact Fisher information matrix of Gaussian vector state space models

Klein, André; Neudecker, Heinz

doi:10.1016/s0024-3795(99)00177-9

Cited by 18 publications

(18 citation statements)

References 4 publications

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“…As shown in the two examples here described, our method greatly simplifies, in terms of computation complexity, the calculation of bounds on the estimation of parameters for such a rich and physically relevant family of quantum systems, compared to both the method presented in Ref. [24] and the ones derived for general classical Gaussian systems [47][48][49][50]. It can also provide analytical results, allowing one to investigate in more detail the role played by the different physical parameters and to compare easily the efficiency of different measurement strategies.…”

Section: Discussion and Outlookmentioning

confidence: 97%

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Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

Genoni

2017

Phys. Rev. A

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We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve the numerical integration of a stochastic master equation for the corresponding density operator in a Hilbert space of infinite dimension, the formulas here derived depend only on the evolution of first and second moments of the quantum states and thus can be easily evaluated without the need of any approximation. We also present some basic but physically meaningful examples where this result is exploited, calculating analytical and numerical bounds on the estimation of the squeezing parameter for a quantum parametric amplifier and of a constant force acting on a mechanical oscillator in a standard optomechanical scenario.

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Section: Discussion and Outlookmentioning

confidence: 97%

“…As a consequence we can generalize the method to the classical case, obtaining similar equations as the ones presented in Refs. [47][48][49][50].…”

Section: Appendix C: Estimation Of a Constant Force On A Mechanical Omentioning

confidence: 99%

Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

Genoni

2017

Phys. Rev. A

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“…Our implementation is available at location http:\\homepages.ulb.ac.be\˜gmelard\rech\km12prog.zip. It is heavily based on [29] and [17], which were developed for VARMA models without exogenous variables.…”

Section: A Numerical Example and A Comparison With The E4 Toolboxmentioning

confidence: 99%

“…It is partially based on the theory in [21] and on the example limited there to the case of the γ's. As a by-product of the present paper, it appears that the formulas for the mixed blocks involving α and β are wrong.…”

Section: The Asymptotic Fisher Information Matrixmentioning

confidence: 99%

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An algorithm for the exact Fisher information matrix of vector ARMAX time series

Klein

Mélard

2014

Linear Algebra and its Applications

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In this paper an algorithm is developed for the exact Fisher information matrix of a Gaussian vector ARMAX or VARMAX process. The algorithm proposed in this paper is composed by Chandrasekhar recursion equations at a vector-matrix level, and some of these recursions consist of derivatives based on appropriate differential rules applied to a state space model for a vector process. The chosen representation is such that the recursions extracted from the state space model are given in terms of expectations of derivatives of innovations, and not the process and observation disturbances. The algorithm will be illustrated by an example. On that example, a comparison is made with results from E4, a toolbox for Matlab, and with the asymptotic information matrix.

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SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation

Kulikova

Tsyganova

Kulikov

2021

Journal of Computational and Applied Mathematics

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A direct derivation of the exact Fisher information matrix of Gaussian vector state space models

Cited by 18 publications

References 4 publications

Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems

An algorithm for the exact Fisher information matrix of vector ARMAX time series

SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation

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