| 中心差分卡尔曼平滑器 |
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| 引用本文： | 王小旭,潘泉,程咏梅,赵春晖,杨峰. 中心差分卡尔曼平滑器[J]. 控制理论与应用, 2012, 29(3): 361-367 |
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| 作者姓名： | 王小旭 潘泉 程咏梅 赵春晖 杨峰 |
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| 作者单位： | 西北工业大学自动化学院,陕西西安,710072 |
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| 基金项目： | 国家自然科学基金重点资助项目(61135001); 国家自然科学基金资助项目(61075029, 61074179, 61074155); 中国博士后科学基金资助项目(20110491692). |
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| 摘 要： | 针对一类非线性离散系统的状态平滑问题, 本文设计了一种中心差分卡尔曼平滑器(CDKS). 文中基于最小方差估计准则, 详细推导了非线性系统的状态最优平滑递推公式, 并采用中心差分变换来近似计算状态的后验均值和协方差. 相比于传统中心差分卡尔曼滤波器(CDKF), 所设计的CDKS算法有效提高了非线性状态的估计精度, 拓展了中心差分变换的应用范围. 仿真实例验证了所提出平滑器的可行性和有效性.
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| 关 键 词： | 非线性离散系统 中心差分卡尔曼平滑器 最小方差估计 中心差分变换 |
| 收稿时间： | 2011-01-18 |
| 修稿时间： | 2011-04-25 |
Central difference Kalman smoother |
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| WANG Xiao-xu,PAN Quan,CHENG Yong-mei,ZHAO Chun-hui and YANG Feng. Central difference Kalman smoother[J]. Control Theory & Applications, 2012, 29(3): 361-367 |
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| Authors: | WANG Xiao-xu PAN Quan CHENG Yong-mei ZHAO Chun-hui YANG Feng |
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| Affiliation: | College of Automation, Northwestern Polytechnical University,College of Automation, Northwestern Polytechnical University,College of Automation, Northwestern Polytechnical University,College of Automation, Northwestern Polytechnical University,College of Automation, Northwestern Polytechnical University |
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| Abstract: | A central difference Kalman smoother (CDKS) is designed to solve the nonlinear state-smoothing problem for a class of nonlinear discrete-time systems. Optimal smoothing recursive formulas for estimating nonlinear system states are derived on the basis of minimum mean-square-error estimation; and the central difference transformation is used to calculate the posterior mean and covariance of nonlinear states. Compared with the standard central difference Kalman filter (CDKF), the proposed CDKS effectively improves the estimation precision of the nonlinear system states, and extends the applications of the central difference transformation. Simulations example shows the feasibility and effectiveness of the proposed smoother. |
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| Keywords: | nonlinear discrete-time systems central difference Kalman smoother minimum mean square error estimation central difference transformation |
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