Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups
Motivated by the rapid progress of aerospace and robotics engineering, the navigation and control systems on matrix Lie groups have been actively studied in recent years. For rigid targets, the attitude estimation problem is a benchmark one with its states defined as rotation matrices on Lie groups....
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| Format: | Article |
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MDPI AG
2021-09-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/8/9/246 |
| _version_ | 1797520671956271104 |
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| author | Jiaolong Wang Zeyang Chen |
| author_facet | Jiaolong Wang Zeyang Chen |
| author_sort | Jiaolong Wang |
| collection | DOAJ |
| description | Motivated by the rapid progress of aerospace and robotics engineering, the navigation and control systems on matrix Lie groups have been actively studied in recent years. For rigid targets, the attitude estimation problem is a benchmark one with its states defined as rotation matrices on Lie groups. Based on the invariance properties of symmetry groups, the invariant Kalman filter (IKF) has been developed by researchers for matrix Lie group systems; however, the limitation of the IKF is that its estimation performance is prone to be degraded if the given knowledge of the noise statistics is not accurate. For the symmetry Lie group attitude estimation problem, this paper proposes a new variational Bayesian iteration-based adaptive invariant Kalman filter (VBIKF). In the proposed VBIKF, the a priori error covariance is not propagated by the conventional steps but directly calibrated in an iterative manner based on the posterior sequences. The main advantage of the VBIKF is that the statistics parameter of the system process noise is no longer required and so the IKF’s hard dependency on accurate process noise statistics can be reduced significantly. The mathematical foundation for the new VBIKF is presented and its superior performance in adaptability and simplicity is further demonstrated by numerical simulations. |
| first_indexed | 2024-03-10T07:59:56Z |
| format | Article |
| id | doaj.art-42200cc6a5a44fb0bb9c4d646742f1b3 |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-10T07:59:56Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-42200cc6a5a44fb0bb9c4d646742f1b32023-11-22T11:34:23ZengMDPI AGAerospace2226-43102021-09-018924610.3390/aerospace8090246Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie GroupsJiaolong Wang0Zeyang Chen1Key Laboratory of Advanced Process Control for Light Industry, Institute of Automation, Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry, Institute of Automation, Jiangnan University, Wuxi 214122, ChinaMotivated by the rapid progress of aerospace and robotics engineering, the navigation and control systems on matrix Lie groups have been actively studied in recent years. For rigid targets, the attitude estimation problem is a benchmark one with its states defined as rotation matrices on Lie groups. Based on the invariance properties of symmetry groups, the invariant Kalman filter (IKF) has been developed by researchers for matrix Lie group systems; however, the limitation of the IKF is that its estimation performance is prone to be degraded if the given knowledge of the noise statistics is not accurate. For the symmetry Lie group attitude estimation problem, this paper proposes a new variational Bayesian iteration-based adaptive invariant Kalman filter (VBIKF). In the proposed VBIKF, the a priori error covariance is not propagated by the conventional steps but directly calibrated in an iterative manner based on the posterior sequences. The main advantage of the VBIKF is that the statistics parameter of the system process noise is no longer required and so the IKF’s hard dependency on accurate process noise statistics can be reduced significantly. The mathematical foundation for the new VBIKF is presented and its superior performance in adaptability and simplicity is further demonstrated by numerical simulations.https://www.mdpi.com/2226-4310/8/9/246attitude estimationvariational Bayesian inferencefixed-point iterationposterior stochastic sequencesinvariant Kalman filtermatrix Lie groups |
| spellingShingle | Jiaolong Wang Zeyang Chen Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups Aerospace attitude estimation variational Bayesian inference fixed-point iteration posterior stochastic sequences invariant Kalman filter matrix Lie groups |
| title | Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups |
| title_full | Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups |
| title_fullStr | Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups |
| title_full_unstemmed | Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups |
| title_short | Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups |
| title_sort | variational bayesian iteration based invariant kalman filter for attitude estimation on matrix lie groups |
| topic | attitude estimation variational Bayesian inference fixed-point iteration posterior stochastic sequences invariant Kalman filter matrix Lie groups |
| url | https://www.mdpi.com/2226-4310/8/9/246 |
| work_keys_str_mv | AT jiaolongwang variationalbayesianiterationbasedinvariantkalmanfilterforattitudeestimationonmatrixliegroups AT zeyangchen variationalbayesianiterationbasedinvariantkalmanfilterforattitudeestimationonmatrixliegroups |