On the statistical convergence of bias in mode-based Kalman filter for switched systems
Abstract Many physical and engineered systems (e.g., smart grid, autonomous vehicles, and robotic systems) that are observed and controlled over a communication/cyber infrastructure can be efficiently modeled as stochastic hybrid systems (SHS). This paper quantifies the bias of a mode-based Kalman f...
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-11-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13634-018-0594-0 |
| _version_ | 1818217149305454592 |
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| author | Wenji Zhang Balasubramaniam Natarajan |
| author_facet | Wenji Zhang Balasubramaniam Natarajan |
| author_sort | Wenji Zhang |
| collection | DOAJ |
| description | Abstract Many physical and engineered systems (e.g., smart grid, autonomous vehicles, and robotic systems) that are observed and controlled over a communication/cyber infrastructure can be efficiently modeled as stochastic hybrid systems (SHS). This paper quantifies the bias of a mode-based Kalman filter commonly used for state estimation in SHS. The main approach involves modeling the bias dynamics as a transformed switched system and the transitions across modes are abstracted via arbitrary switching signals. This general model effectively captures a wide range of SHS systems where the modes may follow deterministic, Markovian, or guard condition based transitions. By leveraging techniques developed to analyze the stability of switched systems, we derive conditions for statistical convergence of the bias in a mode-based Kalman filter in the presence of mode mismatch errors. Developed upon the foundations of Lyapunov theory, we demonstrate a linear matrix inequality condition that guarantees asymptotic stability of the corresponding autonomous switched system irrespective of the choice of mode mismatch probability. Furthermore, we obtain the range of mode mismatch probabilities that assures bounded input bounded output stability of the bias dynamics for both stable and unstable SHS. Using numerical simulations of a smart grid with network topology errors, we verify and validate the theoretical results and demonstrate the potency of using the analysis in critical infrastructures. |
| first_indexed | 2024-12-12T07:03:16Z |
| format | Article |
| id | doaj.art-8c5f7994d3f946b98f15d9816704c823 |
| institution | Directory Open Access Journal |
| issn | 1687-6180 |
| language | English |
| last_indexed | 2024-12-12T07:03:16Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-8c5f7994d3f946b98f15d9816704c8232022-12-22T00:33:48ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61802018-11-012018111510.1186/s13634-018-0594-0On the statistical convergence of bias in mode-based Kalman filter for switched systemsWenji Zhang0Balasubramaniam Natarajan1Department of Electrical and Computer Engineering, Kansas State UniversityDepartment of Electrical and Computer Engineering, Kansas State UniversityAbstract Many physical and engineered systems (e.g., smart grid, autonomous vehicles, and robotic systems) that are observed and controlled over a communication/cyber infrastructure can be efficiently modeled as stochastic hybrid systems (SHS). This paper quantifies the bias of a mode-based Kalman filter commonly used for state estimation in SHS. The main approach involves modeling the bias dynamics as a transformed switched system and the transitions across modes are abstracted via arbitrary switching signals. This general model effectively captures a wide range of SHS systems where the modes may follow deterministic, Markovian, or guard condition based transitions. By leveraging techniques developed to analyze the stability of switched systems, we derive conditions for statistical convergence of the bias in a mode-based Kalman filter in the presence of mode mismatch errors. Developed upon the foundations of Lyapunov theory, we demonstrate a linear matrix inequality condition that guarantees asymptotic stability of the corresponding autonomous switched system irrespective of the choice of mode mismatch probability. Furthermore, we obtain the range of mode mismatch probabilities that assures bounded input bounded output stability of the bias dynamics for both stable and unstable SHS. Using numerical simulations of a smart grid with network topology errors, we verify and validate the theoretical results and demonstrate the potency of using the analysis in critical infrastructures.http://link.springer.com/article/10.1186/s13634-018-0594-0Kalman filterStochastic hybrid systemError analysis |
| spellingShingle | Wenji Zhang Balasubramaniam Natarajan On the statistical convergence of bias in mode-based Kalman filter for switched systems EURASIP Journal on Advances in Signal Processing Kalman filter Stochastic hybrid system Error analysis |
| title | On the statistical convergence of bias in mode-based Kalman filter for switched systems |
| title_full | On the statistical convergence of bias in mode-based Kalman filter for switched systems |
| title_fullStr | On the statistical convergence of bias in mode-based Kalman filter for switched systems |
| title_full_unstemmed | On the statistical convergence of bias in mode-based Kalman filter for switched systems |
| title_short | On the statistical convergence of bias in mode-based Kalman filter for switched systems |
| title_sort | on the statistical convergence of bias in mode based kalman filter for switched systems |
| topic | Kalman filter Stochastic hybrid system Error analysis |
| url | http://link.springer.com/article/10.1186/s13634-018-0594-0 |
| work_keys_str_mv | AT wenjizhang onthestatisticalconvergenceofbiasinmodebasedkalmanfilterforswitchedsystems AT balasubramaniamnatarajan onthestatisticalconvergenceofbiasinmodebasedkalmanfilterforswitchedsystems |