Filtering, predictive, and smoothing Cramér–Rao bounds for discrete-time nonlinear dynamic systems

Šimandl, Miroslav; Královec, Jakub; Tichavský, Petr

doi:10.1016/s0005-1098(01)00136-4

Cited by 110 publications

(44 citation statements)

References 13 publications

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“…The is given by (6) where is found by solving the RDE (7) Note that in the linear case, the Kalman filter produces the smallest [1, Th. 2.1], and the corresponding Cramér-Rao bound is identical to the Kalman filter error covariance [10].…”

Section: A Fake Algebraic Riccati Equation Techniquementioning

confidence: 99%

The use of fake algebraic riccati equations for co-channel demodulation

Einicke¹,

White

Bitmead

2003

IEEE Trans. Signal Process.

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Abstract-This paper describes a method for nonlinear filtering based on an adaptive observer, which guarantees the local stability of the linearized error system. A fake algebraic Riccati equation is employed in the calculation of the filter gain. The design procedure attempts to produce a stable filter at the expense of optimality. This contrasts with the extended Kalman filter (EKF), which attempts to preserve optimality via its linearization procedure, at the expense of stability. A passivity approach is applied to deduce stability conditions for the filter error system. The performance is compared with an EKF for a co-channel frequency demodulation application.

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Section: A Fake Algebraic Riccati Equation Techniquementioning

confidence: 99%

The use of fake algebraic riccati equations for co-channel demodulation

Einicke¹,

White

Bitmead

2003

IEEE Trans. Signal Process.

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“…Obtaining the required first or second derivatives of the log-likelihood function may be a formidable task in some applications, and computing the required expectation of the generally nonlinear multivariate function is often impossible in problems of practical interest. For example, in the context of dynamic models, Simandl, Královec, and Tichavský (2001) illustrate the difficulty in nonlinear state estimation problems and Levy (1995) shows how the information matrix may be very complex in even relatively benign parameter estimation problems (i.e., for the estimation of parameters in a linear state-space model, the information matrix contains 35 distinct sub-blocks and fills up a full page).…”

Section: Resampling-based Calculation Of the Information Matrixmentioning

confidence: 99%

Monte Carlo Computation of the Fisher Information Matrix in Nonstandard Settings

Spall

2005

Journal of Computational and Graphical Statistics

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The Fisher information matrix summarizes the amount of information in the data relative to the quantities of interest. There are many applications of the information matrix in modeling, systems analysis, and estimation, including confidence region calculation, input design, prediction bounds, and "noninformative" priors for Bayesian analysis. This article reviews some basic principles associated with the information matrix, presents a resamplingbased method for computing the information matrix together with some new theory related to efficient implementation, and presents some numerical results. The resampling-based method relies on an efficient technique for estimating the Hessian matrix, introduced as part of the adaptive ("second-order") form of the simultaneous perturbation stochastic approximation (SPSA) optimization algorithm.

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“…In time invariant statistical models, a commonly used lower bound is the Cramer-Rao bound (CRB), given by the inverse of the Fisher information matrix [23]- [26]. This places a lower bound on the variance of any unbiased parameter estimator.…”

Section: Introductionmentioning

confidence: 99%

Multisource Spatiotemporal Tracking Using Sparse Large Aperture Arrays

Kamil

Manikas

2017

IEEE Trans. Aerosp. Electron. Syst.

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Abstract-In this paper, a multi-source tracking technique is proposed using a sparse large aperture array of passive sensors of known geometry. Firstly a novel spherical-spatiotemporal-statespace model is introduced incorporating target ranges, directions and Doppler effects in conjunction with the array geometry. Subsequently, this array of sensors is integrated with an Extended Kalman Filter (EKF), defined as the Arrayed EKF, to track the trajectory of multiple mobile sources. In addition, a recursive lower bound on the performance of the proposed tracking method is obtained based on the Posterior Cramer-Rao Bound (Posterior CRB). Computer simulation studies show that the proposed approach can track the locations of sources, as these move in space, with a very high accuracy.

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Filtering, predictive, and smoothing Cramér–Rao bounds for discrete-time nonlinear dynamic systems

Cited by 110 publications

References 13 publications

The use of fake algebraic riccati equations for co-channel demodulation

The use of fake algebraic riccati equations for co-channel demodulation

Monte Carlo Computation of the Fisher Information Matrix in Nonstandard Settings

Multisource Spatiotemporal Tracking Using Sparse Large Aperture Arrays

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