Estimation of Noise Covariance Matrices for a Linear Time-Varying Stochastic Process

Bélanger, Pierre

doi:10.1016/s1474-6670(17)68341-1

Cited by 21 publications

(46 citation statements)

References 3 publications

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“…We parameterized the model error covariance in the form suggested by Belanger (1974): functions of Q only that many parameters can be identified:…”

Section: Analysis Of the Mt Methods With A Two-dof Modelmentioning

confidence: 99%

“…It is directly related to the covariance-matching with innovations algorithms, (e.g. Shellenbarger, 1967;Belanger, 1974).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

“…Matching sample lag covariances to their respective theoretical expectations has been first proposed in the context of Kalman filtering, Shellenbarger (1967) and Belanger (1974).…”

Section: Covariance Matching With Innovations Approach (Cmia)mentioning

confidence: 99%

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Adaptive error estimation in linearized ocean general circulation models

Chechelnitsky¹

1999

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“…We parameterized the model error covariance in the form suggested by Belanger (1974): functions of Q only that many parameters can be identified:…”

Section: Analysis Of the Mt Methods With A Two-dof Modelmentioning

confidence: 99%

“…It is directly related to the covariance-matching with innovations algorithms, (e.g. Shellenbarger, 1967;Belanger, 1974).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

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Adaptive error estimation in linearized ocean general circulation models

Chechelnitsky¹

1999

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“…In the same way, R is computed, but using the sample covariance of the KF innovation [7][8][9][10]. In the correlation techniques, the covariance matrices are estimated based on the sample autocorrelations between the innovations by exploiting the relations between the estimation error covariance and the innovation covariance [11][12][13][14]. The drawbacks of this method are that it does not guarantee the positive definiteness of the matrices, the estimated covariances are biased [15], and the above techniques require a large window of data, which makes them impractical.…”

Section: Introductionmentioning

confidence: 99%

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

Hashlamon¹,

Erbatur²

2016

Turk J Elec Eng & Comp Sci

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Abstract:The Kalman filter (KF) is used extensively for state estimation. Among its requirements are the process and observation noise covariances, which are unknown or partially known in real-life applications. Uncertain and biased values of the covariances result in KF performance degradation or divergence. Unlike previous methods, we are using the idea of the recursive estimation of the KF to develop two recursive updating rules for the process and observation covariances, respectively designed based on the covariance matching principles. Each rule has a tuning parameter that enhances its flexibility for noise adaptation. The proposed adaptive Kalman filter (AKF) proves itself to have an improved performance over the conventional KF and, in the worst case, it converges to the KF. The results show that the AKF estimates are more accurate, have less noise, and are more stable against biased covariances.

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“…The inaccuracy in the assumed noise covariances could disqualify any optimality claims of the EKF. Although one could estimate those noise covariances directly from data, which is a well-studied topic and dates back to early 70s, see, for instance Mehra [Meh70][Meh72], Jazwinski [Jaz70] and Belanger [Bel74], and more recently, Bunn [Bun81], the number of unknowns in the process noise covariance that can be estimated is found to be limited [Meh72].…”

Section: Introductionmentioning

confidence: 99%

Estimation and tracking of rapidly time-varying broadband acoustic communication channels

Li¹

2006

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This thesis develops methods for estimating wideband shallow-water acoustic communication channels. The very shallow water wideband channel has three distinct features: large dimension caused by extensive delay spread; limited number of degrees of freedom (DOF) due to resolvable paths and inter-path correlations; and rapid fluctuations induced by scattering from the moving sea surface. Traditional LS estimation techniques often fail to reconcile the rapid fluctuations with the large dimensionality. Subspace based approaches with DOF reduction are confronted with unstable subspace structure subject to significant changes over a short period of time.Based on state-space channel modeling, the first part of this thesis develops algorithms that jointly estimate the channel as well as its dynamics. Algorithms based on the Extended Kalman Filter (EKF) and the Expectation Maximization (EM) approach respectively are developed. Analysis shows conceptual parallels, including an identical second-order innovation form shared by the EKF modification and the suboptimal EM, and the shared issue of parameter identifiability due to channel structure, reflected as parameter unobservability in EKF and insufficient excitation in EM. Modifications of both algorithms, including a two-model based EKF and a subspace EM algorithm which selectively track dominant taps and reduce prediction error, are proposed to overcome the identifiability issue. The second part of the thesis develops algorithms that explicitly find the sparse estimate of the delay-Doppler spread function.The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.

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Estimation of Noise Covariance Matrices for a Linear Time-Varying Stochastic Process

Cited by 21 publications

References 3 publications

Adaptive error estimation in linearized ocean general circulation models

Adaptive error estimation in linearized ocean general circulation models

An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

Estimation and tracking of rapidly time-varying broadband acoustic communication channels

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