Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

Bavdekar, Vinay A.; Deshpande, Anjali; Patwardhan, Sachin C.

doi:10.1016/j.jprocont.2011.01.001

Cited by 233 publications

(127 citation statements)

References 18 publications

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“…In the early 1970s, Mehra [5] classified into four categories the methods for the estimation of the KF covariances: Bayesian [6], [7], ML [8]- [10], correlation [11]- [20], and covariance matching [2], [3].…”

Section: Literature Reviewmentioning

confidence: 99%

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

Zanni

Boudec

Cherkaoui

et al. 2017

IEEE Trans. Contr. Syst. Technol.

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Abstract-In this paper, we present a new method for the estimation of the prediction-error covariances of a Kalman filter (KF), which is suitable for step-varying processes. The method uses a series of past innovations (i.e., the difference between the upcoming measurement set and the KF predicted state) to estimate the prediction-error covariance matrix by means of a constrained convex optimization problem. The latter is designed to ensure the symmetry and the positive semidefiniteness of the estimated covariance matrix, so that the KF numerical stability is guaranteed. Our proposed method is straightforward to implement and requires the setting of one parameter only, i.e., the number of past innovations to be considered. It relies on the knowledge of a linear and stationary measurement model. The ability of the method to track state step-variations is validated in ideal conditions for a random-walk process model and for the case of power-system state estimation. The proposed approach is also compared with other methods that estimate the KF stochastic parameters and with the well-known linear weighted least squares. The comparison is given in terms of both accuracy and computational time.Index Terms-Adaptive Kalman filter (AKF), covariance estimation, phasor measurement unit (PMU), power systems, state estimation, step processes.

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Section: Literature Reviewmentioning

confidence: 99%

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

Zanni

Boudec

Cherkaoui

et al. 2017

IEEE Trans. Contr. Syst. Technol.

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“…The Extended Kalman Filter is one of the most used methods for joint state and parameter estimation of nonlinear systems [38,39]. The main idea is the use of the prediction-correction principle where the non-linear model is used for the prediction (denoted by the superscript − ), and its linearized counterpart around the current estimate is exploited in the propagation of the covariance matrix P and in the subsequent correction step (denoted by the superscript + ) with the discrete system measurements.…”

Section: Extended Kalman Filtermentioning

confidence: 99%

Combined Estimation and Optimal Control of Batch Membrane Processes

et al. 2016

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Abstract:In this paper, we deal with the model-based time-optimal operation of a batch diafiltration process in the presence of membrane fouling. Membrane fouling poses one of the major problems in the field of membrane processes. We model the fouling behavior and estimate its parameters using various methods. Least-squares, least-squares with a moving horizon, recursive least-squares methods and the extended Kalman filter are applied and discussed for the estimation of the fouling behavior on-line during the process run. Model-based optimal non-linear control coupled with parameter estimation is applied in a simulation case study to show the benefits of the proposed approach.

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“…Maximum likelihood methods estimate the covariances by maximizing the likelihood function of the innovations [16], but these methods need heavy computations and they can be implemented offline. A modified one using the expectation-maximization algorithm (EM) was reported in [17].…”

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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Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter

Cited by 233 publications

References 18 publications

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

Combined Estimation and Optimal Control of Batch Membrane Processes

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

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