scholarly journals A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1351
Author(s):  
Chenghao Shan ◽  
Weidong Zhou ◽  
Yefeng Yang ◽  
Hanyu Shan
Keyword(s):  
Kalman Filter ◽  
Random Variable ◽  
Loss Probability ◽  
Measurement Noise ◽  
Estimation Accuracy ◽  
Gaussian State ◽  
Time Varying ◽  
Bernoulli Random Variable ◽  
Variational Bayesian ◽  
Heavy Tailed

In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP.

A new robust Kalman filter with measurement loss based on mixing distribution

2021 ◽  
pp. 014233122110549
Author(s):  
Chenghao Shan ◽  
Weidong Zhou ◽  
Yefeng Yang ◽  
Hanyu Shan
Keyword(s):  
Kalman Filter ◽  
Likelihood Function ◽  
State Space Model ◽  
Random Variable ◽  
Superior Performance ◽  
Gaussian State ◽  
Bernoulli Random Variable ◽  
Mixing Distribution ◽  
Robust Kalman Filter ◽  
Heavy Tailed

A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student’s t-inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN.

scholarly journals Adaptive Dual Extended Kalman Filter Based on Variational Bayesian Approximation for Joint Estimation of Lithium-Ion Battery State of Charge and Model Parameters

2019 ◽  
Vol 9 (9) ◽  
pp. 1726 ◽  
Author(s):  
Jing Hou ◽  
Yan Yang ◽  
He He ◽  
Tian Gao
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Lithium Ion ◽  
Measurement Noise ◽  
Estimation Accuracy ◽  
Variational Bayesian ◽  
Soc Estimation ◽  
Bayesian Approximation ◽  
Noise Statistics ◽  
Discharge Test

An accurate state of charge (SOC) estimation is vital for the safe operation and efficient management of lithium-ion batteries. At present, the extended Kalman filter (EKF) can accurately estimate the SOC under the condition of a precise battery model and deterministic noise statistics. However, in practical applications, the battery characteristics change with different operating conditions and the measurement noise statistics may vary with time, resulting in nonoptimal and even unreliable estimation of SOC by EKF. To improve the SOC estimation accuracy under uncertain measurement noise statistics, a variational Bayesian approximation-based adaptive dual extended Kalman filter (VB-ADEKF) is proposed in this paper. The variational Bayesian inference is integrated with the dual EKF (DEKF) to jointly estimate the lithium-ion battery parameters and SOC. Meanwhile, the measurement noise variances are simultaneously estimated in the SOC estimation process to compensate for the model uncertainties, so that the adaptability of the proposed algorithm to dynamic changes in battery characteristics is greatly improved. A constant current discharge test, a pulse current discharge test, and an urban dynamometer driving schedule (UDDS) test are performed to verify the effectiveness and superiority of the proposed algorithm by comparison with the DEKF algorithm. The experimental results show that the proposed VB-ADEKF algorithm outperforms the traditional DEKF algorithm in terms of SOC estimation accuracy, convergence rate, and robustness.

scholarly journals Multi-Fading Factor and Update Monitoring Strategy Adaptive Kalman Filter Based Variational Bayesian with Inaccurate Time-Varying Process and Measure-Ment Noise Covariance Matrices

2020 ◽  
Author(s):  
Chenghao Shan ◽  
Weidong Zhou ◽  
Yefeng Yang ◽  
Zihao Jiang
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Measurement Noise ◽  
Time Varying ◽  
Monitoring Strategy ◽  
Adaptive Kalman Filter ◽  
Variational Bayesian ◽  
Measurement Noise Covariance ◽  
Noise Covariance ◽  
Fading Factor

Aiming at the problem that the performance of Adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement noise matrix are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of Multi-fading factor and update monitoring strategy adaptive Kalman filter based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model, the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the update monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

scholarly journals Multi-Fading Factor and Updated Monitoring Strategy Adaptive Kalman Filter-Based Variational Bayesian

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 198
Author(s):  
Chenghao Shan ◽  
Weidong Zhou ◽  
Yefeng Yang ◽  
Zihao Jiang
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Measurement Noise ◽  
Time Varying ◽  
Monitoring Strategy ◽  
Adaptive Kalman Filter ◽  
Variational Bayesian ◽  
Measurement Noise Covariance ◽  
Noise Covariance ◽  
Fading Factor

Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

scholarly journals A Novel Robust Kalman Filter With Non-stationary Heavy-tailed Measurement Noise

2020 ◽  
Vol 53 (2) ◽  
pp. 368-373
Author(s):  
Guangle Jia ◽  
Yulong Huang ◽  
Mingming B. Bai ◽  
Yonggang zhang
Keyword(s):  
Kalman Filter ◽  
Measurement Noise ◽  
Robust Kalman Filter ◽  
Heavy Tailed

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

scholarly journals Dynamic State Estimation for Synchronous Machines Based on Adaptive Ensemble Square Root Kalman Filter

2019 ◽  
Vol 9 (23) ◽  
pp. 5200 ◽  
Author(s):  
Dongliang Nan ◽  
Weiqing Wang ◽  
Kaike Wang ◽  
Rabea Jamil Mahfoud ◽  
Hassan Haes Alhelou ◽  
...  
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Random Noise ◽  
Measurement Noise ◽  
Dynamic State ◽  
Estimation Accuracy ◽  
Measurement Unit ◽  
Square Root ◽  
Dynamic State Estimation ◽  
And Control

Dynamic state estimation (DSE) for generators plays an important role in power system monitoring and control. Phasor measurement unit (PMU) has been widely utilized in DSE since it can acquire real-time synchronous data with high sampling frequency. However, random noise is unavoidable in PMU data, which cannot be directly used as the reference data for power grid dispatching and control. Therefore, the data measured by PMU need to be processed. In this paper, an adaptive ensemble square root Kalman filter (AEnSRF) is proposed, in which the ensemble square root filter (EnSRF) and Sage–Husa algorithm are utilized to estimate measurement noise online. Simulation results obtained by applying the proposed method show that the estimation accuracy of AEnSRF is better than that of ensemble Kalman filter (EnKF), and AEnSRF can track the measurement noise when the measurement noise changes.

scholarly journals Adaptive Unscented Kalman Filter for Target Tacking with Time-Varying Noise Covariance Based on Multi-Sensor Information Fusion

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5808
Author(s):  
Dapeng Wang ◽  
Hai Zhang ◽  
Baoshuang Ge
Keyword(s):  
Kalman Filter ◽  
Information Fusion ◽  
Stochastic Systems ◽  
Unscented Kalman Filter ◽  
Minimum Variance ◽  
Measurement Noise ◽  
Time Varying ◽  
Measurement Noise Covariance ◽  
Noise Covariance ◽  
Sensor Information

In this paper, an innovative optimal information fusion methodology based on adaptive and robust unscented Kalman filter (UKF) for multi-sensor nonlinear stochastic systems is proposed. Based on the linear minimum variance criterion, this multi-sensor information fusion method has a two-layer architecture: at the first layer, a new adaptive UKF scheme for the time-varying noise covariance is developed and serves as a local filter to improve the adaptability together with the estimated measurement noise covariance by applying the redundant measurement noise covariance estimation, which is isolated from the state estimation; the second layer is the fusion structure to calculate the optimal matrix weights and gives the final optimal state estimations. Based on the hypothesis testing theory with the Mahalanobis distance, the new adaptive UKF scheme utilizes both the innovation and the residual sequences to adapt the process noise covariance timely. The results of the target tracking simulations indicate that the proposed method is effective under the condition of time-varying process-error and measurement noise covariance.

A New Heavy-Tailed Robust Kalman Filter with Time-Varying Process Bias

2021 ◽  
Author(s):  
Zi-hao Jiang ◽  
Wei-dong Zhou ◽  
Guang-le Jia ◽  
Cheng-hao Shan ◽  
Liang Hou
Keyword(s):  
Kalman Filter ◽  
Time Varying ◽  
Robust Kalman Filter ◽  
Heavy Tailed
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