Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation
For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/9/1715 |
| _version_ | 1797517175581310976 |
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| author | Lijuan Chen Zihao Zhang Yapeng Zhang Xiaoshuang Xiong Fei Fan Shuangbao Ma |
| author_facet | Lijuan Chen Zihao Zhang Yapeng Zhang Xiaoshuang Xiong Fei Fan Shuangbao Ma |
| author_sort | Lijuan Chen |
| collection | DOAJ |
| description | For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm. |
| first_indexed | 2024-03-10T07:11:08Z |
| format | Article |
| id | doaj.art-fbb90b30545b4f79a4a9e54a375d009e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T07:11:08Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fbb90b30545b4f79a4a9e54a375d009e2023-11-22T15:28:55ZengMDPI AGSymmetry2073-89942021-09-01139171510.3390/sym13091715Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater NavigationLijuan Chen0Zihao Zhang1Yapeng Zhang2Xiaoshuang Xiong3Fei Fan4Shuangbao Ma5Hubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430200, ChinaSchool of Mechanical Engineering & Automation, Wuhan Textile University, Wuhan 430200, ChinaHubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430200, ChinaHubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430200, ChinaHubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430200, ChinaHubei Key Laboratory of Digital Textile Equipment, Wuhan Textile University, Wuhan 430200, ChinaFor non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.https://www.mdpi.com/2073-8994/13/9/1715projection filter methodnon-linear systemsstate estimationFokker–Planck equation |
| spellingShingle | Lijuan Chen Zihao Zhang Yapeng Zhang Xiaoshuang Xiong Fei Fan Shuangbao Ma Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation Symmetry projection filter method non-linear systems state estimation Fokker–Planck equation |
| title | Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation |
| title_full | Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation |
| title_fullStr | Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation |
| title_full_unstemmed | Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation |
| title_short | Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation |
| title_sort | research on projection filtering method based on projection symmetric interval and its application in underwater navigation |
| topic | projection filter method non-linear systems state estimation Fokker–Planck equation |
| url | https://www.mdpi.com/2073-8994/13/9/1715 |
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