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 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 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

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.

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

scholarly journals An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Machines ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 182
Author(s):  
Jiaolong Wang ◽  
Chengxi Zhang ◽  
Jin Wu ◽  
Ming Liu
Keyword(s):  
Kalman Filter ◽  
Lie Groups ◽  
State Space Model ◽  
Attitude Estimation ◽  
Spacecraft Attitude ◽  
Attitude Dynamics ◽  
Process Noise ◽  
Space Model ◽  
Heavy Tailed ◽  
Scale Matrix

Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF’s performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student’s t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty.

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