Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm
The proper selection of the model error covariance matrix and the measurement noise covariance matrix of Kalman filter is an optimization problem. Some scholars have studied this, but there is relatively little research on the selection of the two covariance matrices for Kalman filters with an unkno...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Buildings |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-5309/15/2/196 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588829593174016 |
|---|---|
| author | Lijun Liu Chang Yin Yonghui Su Yinghai Lin Ying Lei |
| author_facet | Lijun Liu Chang Yin Yonghui Su Yinghai Lin Ying Lei |
| author_sort | Lijun Liu |
| collection | DOAJ |
| description | The proper selection of the model error covariance matrix and the measurement noise covariance matrix of Kalman filter is an optimization problem. Some scholars have studied this, but there is relatively little research on the selection of the two covariance matrices for Kalman filters with an unknown input. Recently, the authors proposed a modified directed bat algorithm (MDBA) which introduces the best historical location of individuals and the elimination strategy to effectively prevent falling into local optimal solution. So, two methods are proposed in this paper to optimize the model error covariance matrix and measurement noise covariance matrix of Kalman filter with unknown inputs (KF-UI) and extended Kalman filter with unknown inputs (EKF-UI) by MDBA, respectively. The objective functions are constructed using the measurement vectors and the corresponding estimated values, and MDBA is adopted to optimize the two covariance matrices of KF-UI and EKF-UI. To validate the effectiveness of proposed methods, two simple structure examples and a benchmark example are adopted. The influence of structural parameter uncertainties on KF-UI is also considered. The result shows that the MDBA-optimized KF-UI has a strong convergence and can take into account the effect of parameter uncertainties. Then, the effectiveness of the proposed MDBA-optimized EKF-UI method is validated by comparing it with EKF-UI with empirically selected covariance values through trial-and-error. The identification results showed that the proposed methods achieved better identification accuracy and enhanced convergence compared to KF-UI and EKF-UI with empirical covariance values. |
| format | Article |
| id | doaj-art-2e7c5c7336b74bb187fcc6173d043e73 |
| institution | Kabale University |
| issn | 2075-5309 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Buildings |
| spelling | doaj-art-2e7c5c7336b74bb187fcc6173d043e732025-01-24T13:26:08ZengMDPI AGBuildings2075-53092025-01-0115219610.3390/buildings15020196Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat AlgorithmLijun Liu0Chang Yin1Yonghui Su2Yinghai Lin3Ying Lei4Department of Civil Engineering, Xiamen University, Xiamen 361005, ChinaDepartment of Civil Engineering, Xiamen University, Xiamen 361005, ChinaDepartment of Civil Engineering, Xiamen University, Xiamen 361005, ChinaDepartment of Civil Engineering, Xiamen University, Xiamen 361005, ChinaDepartment of Civil Engineering, Xiamen University, Xiamen 361005, ChinaThe proper selection of the model error covariance matrix and the measurement noise covariance matrix of Kalman filter is an optimization problem. Some scholars have studied this, but there is relatively little research on the selection of the two covariance matrices for Kalman filters with an unknown input. Recently, the authors proposed a modified directed bat algorithm (MDBA) which introduces the best historical location of individuals and the elimination strategy to effectively prevent falling into local optimal solution. So, two methods are proposed in this paper to optimize the model error covariance matrix and measurement noise covariance matrix of Kalman filter with unknown inputs (KF-UI) and extended Kalman filter with unknown inputs (EKF-UI) by MDBA, respectively. The objective functions are constructed using the measurement vectors and the corresponding estimated values, and MDBA is adopted to optimize the two covariance matrices of KF-UI and EKF-UI. To validate the effectiveness of proposed methods, two simple structure examples and a benchmark example are adopted. The influence of structural parameter uncertainties on KF-UI is also considered. The result shows that the MDBA-optimized KF-UI has a strong convergence and can take into account the effect of parameter uncertainties. Then, the effectiveness of the proposed MDBA-optimized EKF-UI method is validated by comparing it with EKF-UI with empirically selected covariance values through trial-and-error. The identification results showed that the proposed methods achieved better identification accuracy and enhanced convergence compared to KF-UI and EKF-UI with empirical covariance values.https://www.mdpi.com/2075-5309/15/2/196Kalman filter with unknown inputsextended Kalman filter with unknown inputsmodel error covariance matrixmeasurement noise covariance matrixmodified directed bat algorithm |
| spellingShingle | Lijun Liu Chang Yin Yonghui Su Yinghai Lin Ying Lei Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm Buildings Kalman filter with unknown inputs extended Kalman filter with unknown inputs model error covariance matrix measurement noise covariance matrix modified directed bat algorithm |
| title | Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm |
| title_full | Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm |
| title_fullStr | Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm |
| title_full_unstemmed | Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm |
| title_short | Optimization of Covariance Matrices of Kalman Filter with Unknown Input Using Modified Directional Bat Algorithm |
| title_sort | optimization of covariance matrices of kalman filter with unknown input using modified directional bat algorithm |
| topic | Kalman filter with unknown inputs extended Kalman filter with unknown inputs model error covariance matrix measurement noise covariance matrix modified directed bat algorithm |
| url | https://www.mdpi.com/2075-5309/15/2/196 |
| work_keys_str_mv | AT lijunliu optimizationofcovariancematricesofkalmanfilterwithunknowninputusingmodifieddirectionalbatalgorithm AT changyin optimizationofcovariancematricesofkalmanfilterwithunknowninputusingmodifieddirectionalbatalgorithm AT yonghuisu optimizationofcovariancematricesofkalmanfilterwithunknowninputusingmodifieddirectionalbatalgorithm AT yinghailin optimizationofcovariancematricesofkalmanfilterwithunknowninputusingmodifieddirectionalbatalgorithm AT yinglei optimizationofcovariancematricesofkalmanfilterwithunknowninputusingmodifieddirectionalbatalgorithm |