Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements
The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing...
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| Published in | Discrete dynamics in nature and society Vol. 2018; no. 2018; pp. 1 - 12 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2018
Hindawi John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1026-0226 1607-887X |
| DOI | 10.1155/2018/1516028 |
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| Abstract | The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena. |
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| AbstractList | The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena. |
| Audience | Academic |
| Author | He, Yonghui Jiang, Jibin Wu, Yanfeng Zhuo, Shufang Huang, Hischuan |
| Author_xml | – sequence: 1 fullname: Zhuo, Shufang – sequence: 2 fullname: Huang, Hischuan – sequence: 3 fullname: Jiang, Jibin – sequence: 4 fullname: He, Yonghui – sequence: 5 fullname: Wu, Yanfeng |
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| ContentType | Journal Article |
| Copyright | Copyright © 2018 Yonghui He et al. COPYRIGHT 2018 John Wiley & Sons, Inc. Copyright © 2018 Yonghui He et al.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| SubjectTerms | Algorithms Analysis Correlation analysis Covariance matrix Design Discrete time systems Economic models Error detection Euclidean space Filtration Kalman filters Mathematical models Mean square errors Nonlinearity Random variables Sensors Signal processing Tracking systems |
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| Title | Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements |
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