Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation
This paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of the Bayes–Sard quadrature transformation, we first established a Bayesian estimator on matrix Lie grou...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/10/4/265 |
| _version_ | 1797410328459345920 |
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| author | Huijuan Guo Yan Zhou Huiying Liu Xiaoxiang Hu |
| author_facet | Huijuan Guo Yan Zhou Huiying Liu Xiaoxiang Hu |
| author_sort | Huijuan Guo |
| collection | DOAJ |
| description | This paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of the Bayes–Sard quadrature transformation, we first established a Bayesian estimator on matrix Lie groups for system measurements in Euclidean spaces or Lie groups. The estimator was then employed to develop a generalized Bayes–Sard cubature Kalman filter on matrix Lie groups that considers additional uncertainties brought by integration errors and contains two variants. We also built on the maximum likelihood principle, and an adaptive version of the proposed filter was derived for better algorithm flexibility and more precise filtering results. The proposed filters were applied to the quaternion attitude estimation problem. Monte Carlo numerical simulations supported that the proposed filters achieved better estimation quality than that of other Lie group filters in the mentioned studies. |
| first_indexed | 2024-03-09T04:27:55Z |
| format | Article |
| id | doaj.art-91898800d8154c379d7c6b77f3acfb77 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-09T04:27:55Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-91898800d8154c379d7c6b77f3acfb772023-12-03T13:38:38ZengMDPI AGMachines2075-17022022-04-0110426510.3390/machines10040265Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude EstimationHuijuan Guo0Yan Zhou1Huiying Liu2Xiaoxiang Hu3School of Automation, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Automation, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Automation, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Automation, Northwestern Polytechnical University, Xi’an 710129, ChinaThis paper investigates the numerical integration error calibration problem in Lie group sigma point filters to obtain more accurate estimation results. On the basis of the theoretical framework of the Bayes–Sard quadrature transformation, we first established a Bayesian estimator on matrix Lie groups for system measurements in Euclidean spaces or Lie groups. The estimator was then employed to develop a generalized Bayes–Sard cubature Kalman filter on matrix Lie groups that considers additional uncertainties brought by integration errors and contains two variants. We also built on the maximum likelihood principle, and an adaptive version of the proposed filter was derived for better algorithm flexibility and more precise filtering results. The proposed filters were applied to the quaternion attitude estimation problem. Monte Carlo numerical simulations supported that the proposed filters achieved better estimation quality than that of other Lie group filters in the mentioned studies.https://www.mdpi.com/2075-1702/10/4/265Bayes–Sard quadrature moment transformationcubature Kalman filterLie groupsattitude estimation |
| spellingShingle | Huijuan Guo Yan Zhou Huiying Liu Xiaoxiang Hu Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation Machines Bayes–Sard quadrature moment transformation cubature Kalman filter Lie groups attitude estimation |
| title | Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation |
| title_full | Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation |
| title_fullStr | Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation |
| title_full_unstemmed | Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation |
| title_short | Improved Cubature Kalman Filtering on Matrix Lie Groups Based on Intrinsic Numerical Integration Error Calibration with Application to Attitude Estimation |
| title_sort | improved cubature kalman filtering on matrix lie groups based on intrinsic numerical integration error calibration with application to attitude estimation |
| topic | Bayes–Sard quadrature moment transformation cubature Kalman filter Lie groups attitude estimation |
| url | https://www.mdpi.com/2075-1702/10/4/265 |
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