Kalman filter algorithm based on singular value decomposition

Wang, L.; Libert, G.; Manneback, Pierre

doi:10.1109/cdc.1992.371522

Cited by 31 publications

(45 citation statements)

References 15 publications

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“…The DLM was then filtered to infer the latent state from the observed state of the modelled polynomial and periodic systems in order to identify their random components. The model filtering algorithm of the dlm package is based on Kalman filtering using single value decomposition (SVD) (Wang et al, 1992). The filtered model was then used to recursively estimate the latent states of the two models in retrospection (smoothing).…”

Section: Qualitative Prediction Of Parturition Onsetmentioning

confidence: 99%

Towards qualitative and quantitative prediction and detection of parturition onset in sows using light barriers

Manteuffel

Hartung

Schmidt

et al. 2015

Computers and Electronics in Agriculture

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Section: Qualitative Prediction Of Parturition Onsetmentioning

confidence: 99%

Towards qualitative and quantitative prediction and detection of parturition onset in sows using light barriers

Manteuffel

Hartung

Schmidt

et al. 2015

Computers and Electronics in Agriculture

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“…To the best of our knowledge, the first SVD-based KF was by Wang et al and appeared in 1992; see Eqs (17), (22), (23) in [23, pp. 1225-1226].…”

Section: Svd Factorization-based Kalman Filteringmentioning

confidence: 99%

SVD-Based Kalman Filter Derivative Computation

Tsyganova

Kulikova

2017

IEEE Trans. Automat. Contr.

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Recursive adaptive filtering methods are often used for solving the problem of simultaneous state and parameters estimation arising in many areas of research. The gradient-based schemes for adaptive Kalman filtering (KF) require the corresponding filter sensitivity computations. The standard approach is based on the direct differentiation of the KF equations. The shortcoming of this strategy is a numerical instability of the conventional KF (and its derivatives) with respect to roundoff errors. For decades, special attention has been paid in the KF community for designing efficient filter implementations that improve robustness of the estimator against roundoff. The most popular and beneficial techniques are found in the class of square-root (SR) or UD factorization-based methods. They imply the Cholesky decomposition of the corresponding error covariance matrix. Another important matrix factorization method is the singular value decomposition (SVD) and, hence, further encouraging KF algorithms might be found under this approach. Meanwhile, the filter sensitivity computation heavily relies on the use of matrix differential calculus. Previous works on the robust KF derivative computation have produced the SR-and UD-based methodologies. Alternatively, in this paper we design the SVD-based approach. The solution is expressed in terms of the SVD-based KF covariance quantities and their derivatives (with respect to unknown system parameters). The results of numerical experiments illustrate that although the newly-developed SVD-based method is algebraically equivalent to the conventional approach and the previously derived SRand UD-based strategies, it outperforms the mentioned techniques for estimation accuracy in ill-conditioned situations.

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“…S contains the square roots of the eigenvalues obtained from A or B in descending order. To learn more about the SVD see Wang et al 15 and Zhang and Li 14 . In this paper, we use the SVD algorithm to estimate the sample covariance matrix for Stuart score test statistic.…”

Section: A Stuartmentioning

confidence: 99%

New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II

Kamranrad

Amiri

Niaki

2016

Quality & Reliability Eng

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In some statistical process control (SPC) applications, quality of a process or product is characterized by contingency table. Contingency tables describe the relation between two or more categorical quality characteristics. In this paper, two new control charts based on the WALD and Stuart score test statistics are designed for monitoring of contingency table‐based processes in Phase‐II. The performances of the proposed control charts are compared with the generalized linear test (GLT) control chart proposed in the literature. The results show the better performance of the proposed control charts under small and moderate shifts. Moreover, new schemes are proposed to diagnose which cell corresponding to different levels of categorical variables is responsible for out‐of‐control signal. In addition, we propose EWMA–WALD and EWMA–Stuart score test control charts to improve the performance of Shewhart‐based control charts in detecting small and moderate shifts in contingency table parameters. Meanwhile, we compare the performances of two proposed EWMA‐based control charts with the ones of three existing control charts called EWMA–GLT, EWMA–GLRT and an EWMA‐type control chart for multivariate binomial/multinomial processes along with the ones of the corresponding Shewhart‐based control charts. A numerical example is given to show the efficiency of the proposed methods. Finally, the effect of parameter estimation in Phase I based on m historical contingency table on the performance of the Shewhart‐based control charts is studied. Copyright © 2016 John Wiley & Sons, Ltd.

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Kalman filter algorithm based on singular value decomposition

Cited by 31 publications

References 15 publications

Towards qualitative and quantitative prediction and detection of parturition onset in sows using light barriers

Towards qualitative and quantitative prediction and detection of parturition onset in sows using light barriers

SVD-Based Kalman Filter Derivative Computation

New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II

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