Updating Noise Parameters of Kalman Filter Using Bayesian Approach

Abstract. Ever since its inception, the ensemble Kalman filter (EnKF) has elicited many heuristic approaches that sought to improve it. One such method is covariance localization, which alleviates spurious correlations due to finite ensemble sizes by using relevant spatial correlation information. Adaptive localization techniques account for how correlations change in time and space, in order to obtain improved covariance estimates. This work develops a Bayesian approach to adaptive Schur-product localization for the deterministic ensemble Kalman filter (DEnKF) and extends it to support multiple radii of influence. We test the proposed adaptive localization using the toy Lorenz'96 problem and a more realistic 1.5-layer quasi-geostrophic model. Results with the toy problem show that the multivariate approach informs us that strongly observed variables can tolerate larger localization radii. The univariate approach leads to markedly improved filter performance for the realistic geophysical model, with a reduction in error by as much as 33 %.

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Innovation-based fractional order adaptive Kalman filter

Journal of Electrical Engineering ◽

10.2478/jee-2020-0009 ◽

2020 ◽

Vol 71 (1) ◽

pp. 60-64

Author(s):

Ravi Pratap Tripathi ◽

Ashutosh Kumar Singh ◽

Pavan Gangwar

Keyword(s):

Kalman Filter ◽

Fractional Order ◽

Adaptive Estimation ◽

Lyapunov Theory ◽

Measurement Noise ◽

Position Tracking ◽

Practical Application ◽

Adaptive Kalman Filter ◽

Noise Parameters ◽

The Stability

AbstractKalman Filter (KF) is the most widely used estimator to estimate and track the states of target. It works well when noise parameters and system models are well defined in advance. Its performance degrades and starts diverging when noise parameters (mainly measurement noise) changes. In the open literature available researchers has used the concept of Fractional Order Kalman Filter (FOKF) to stabilize the KF. However in the practical application there is a variation in the measurement noise, which will leads to divergence and degradation in the FOKF approach. An Innovation Adaptive Estimation (IAE) based FOKF algorithm is presented in this paper. In order to check the stability of the proposed method, Lyapunov theory is used. Position tracking simulation has been performed for performance evaluation, which shows the better result and robustness.

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A Bayesian optimized framework for successful application of unscented Kalman filter in parameter identification of MDOF structures

Journal of Low Frequency Noise Vibration and Active Control ◽

10.1177/14613484211014316 ◽

2021 ◽

pp. 146134842110143

Author(s):

Mohamadreza Sheibani ◽

Ge Ou

Keyword(s):

Kalman Filter ◽

Parameter Identification ◽

Unscented Kalman Filter ◽

Initial Conditions ◽

Coupling Effect ◽

Experimental Tests ◽

Optimization Method ◽

Bayesian Optimization ◽

Noise Parameters ◽

Inclusive Approach

The success of the unscented Kalman filter can be jeopardized if the required initial parameters are not identified carefully. These parameters include the initial guesses and the levels of uncertainty in the target parameters and the process and measurement noise parameters. While a set of appropriate initial target parameters give the unscented Kalman filter a head start, the uncertainty levels and noise parameters set the rate of convergence in the process. Therefore, due to the coupling effect of these parameters, an inclusive approach is desired to maintain the chance of convergence for expensive experimental tests. In this paper, a framework is proposed that, via a virtual emulation prior to the experiment, determines a set of initial conditions to ensure a successful application of the online parameter identification. A Bayesian optimization method is proposed, which considers the level of confidence in the initial guesses for the target parameters to suggest the appropriate noise covariance matrices. The methodology is validated on a five-story shear frame tested on a shake table. The results indicate that, indeed, a trade-off can be made between the robustness of the online updating and the final parameter accuracy.

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A Novel Distributed Adaptive Cubature Kalman Filter with Variational Bayesian Approach

10.1109/iccais52680.2021.9624527 ◽

2021 ◽

Author(s):

Feng Yang ◽

Yuwei Ying ◽

Litao Zheng

Keyword(s):

Kalman Filter ◽

Bayesian Approach ◽

Variational Bayesian ◽

Cubature Kalman Filter

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Optimizing the performance of Kalman filter based statistical time-varying air quality models

Global NEST Journal ◽

10.30955/gnj.000685 ◽

2013 ◽

Vol 12 (1) ◽

pp. 27-39

Keyword(s):

Kalman Filter ◽

Bayesian Approach ◽

Autoregressive Model ◽

Prediction Models ◽

Mean Squared Error ◽

Model Performance ◽

Time Varying ◽

Squared Prediction Error ◽

Statistical Time ◽

The Bayesian Approach

In this study, the Bayesian approach is proposed to estimate the noise variances of Kalman filter based statistical models for predicting the daily averaged PM10 concentrations of a typical coastal city, Macau, with Latitude 22°10’N and Longitude 113°34’E. By using the measurements in 2001 and 2002, the Bayesian approach is capable to estimate the most probable values of the noise variances in the Kalman filter based prediction models. It turns out that the estimated process noise variance of the time-varying autoregressive model with exogenous inputs, TVAREX, is significantly (~76%) less than that of the time-varying autoregressive model of order 1, TVAR(1), since the TVAREX model incorporates important mechanisms which govern the daily averaged PM10 concentrations in Macau. By further using data between 2003 and 2005, the choice of the noise variances is shown to affect the model performance, measured by the root-mean-squared error, of the TVAR(p) model and the TVAREX model. In addition, the optimal estimates of noise variances obtained by Bayesian approach for both models are located in the region where the model performance is insensitive to the choice of noise variances. Furthermore, the Bayesian approach will be demonstrated to provide more reasonable estimates of noise variances compared to the noise variances found by simply minimizing the root-mean-squared prediction error of the model. By comparing the optimized TVAREX model and the TVAR(p) models in predicting the daily averaged PM10 concentrations between 2003 and 2005, it is found that the TVAREX model outperforms the TVAR(p) models in terms of the general performance and the episode capturing capability.

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Adaptive Kalman Filter for Linear Systems with Additive and Multiplicative Noises

10.36227/techrxiv.14576289.v1 ◽

2021 ◽

Author(s):

Xingkai Yu

Keyword(s):

Kalman Filter ◽

Linear Systems ◽

Bayesian Approach ◽

Multiplicative Noise ◽

Measurement Noise ◽

Time Varying ◽

Projection Formula ◽

Adaptive Kalman Filter ◽

Technical Issue ◽

Multiplicative Noises

This manuscript investigates adaptive Kalman filter problem of of linear systems with multiplicative and additive noises. The main contributions are stated in two aspects. Firstly, compared with the estimation problem of linear systems with additive noises, we propose an algorithm that is applicable to the linear systems with both additive and multiplicative noises. To solve the technical issue raised by the multiplicative noise, a variational Bayesian approach is proposed. Moreover, the proposed approach is capable of estimating the multiplicative and additive measurement noise covariances as a whole, while the existing algorithms often operate in a separate way. Secondly, in contrast with existing literature, where the covariance of the multiplicative noise is assumed to be fixed and known, we focus on the situation that the covariances of both additive and multiplicative noises are time-varying and unknown. Towards this end, a novel adaptive Kalman filter is proposed to jointly estimate the covariances of multiplicative and additive noises based on projection formula and a VB approach.

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