A novel robust Kalman filter with unknown non-stationary heavy-tailed noise

Automatica ◽  
2021 ◽  
Vol 127 ◽  
pp. 109511
Author(s):  
Hao Zhu ◽  
Guorui Zhang ◽  
Yongfu Li ◽  
Henry Leung
Keyword(s):  
Kalman Filter ◽  
Robust Kalman Filter ◽  
Heavy Tailed

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

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.

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

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

Online Dynamic Response Reconstruction in the Presence of Observation Outliers

2021 ◽  
Author(s):  
Chaodong Zhang ◽  
Jian’an Li ◽  
Youlin Xu
Keyword(s):  
Kalman Filter ◽  
Dynamic Response ◽  
Numerical Study ◽  
Frame Structure ◽  
System Model ◽  
Measurement Information ◽  
Model Errors ◽  
Process Noise ◽  
Robust Kalman Filter ◽  
Response Reconstruction

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

scholarly journals Finite-horizon robust Kalman filter design

2001 ◽  
Vol 49 (9) ◽  
pp. 2103-2112 ◽  
Author(s):  
Minyue Fu ◽  
C.E. de Souza ◽  
Zhi-Quan Luo
Keyword(s):  
Kalman Filter ◽  
Filter Design ◽  
Finite Horizon ◽  
Robust Kalman Filter
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