| 引用本文: | 杨智博,杨春山,邓自立.不确定噪声方差定常系统保性能鲁棒Kalman滤波器[J].控制理论与应用,2016,33(4):446~452.[点击复制] |
| YANG Zhi-bo,YANG Chun-shan,DENG Zi-li.Guaranteed-cost robust Kalman filters for time-invariant systems with uncertain noise variances[J].Control Theory and Technology,2016,33(4):446~452.[点击复制] |
|
| 不确定噪声方差定常系统保性能鲁棒Kalman滤波器 |
| Guaranteed-cost robust Kalman filters for time-invariant systems with uncertain noise variances |
| 摘要点击 3434 全文点击 2078 投稿时间：2015-05-06 修订日期：2015-10-29 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2016.50365 |
| 2016,33(4):446-452 |
| 中文关键词 不确定噪声方差 极大极小鲁棒Kalman滤波器 保性能鲁棒性 Lyapunov方程方法 |
| 英文关键词 uncertain noise variance min-max robust Kalman filter guaranteed cost robustness Lyapunov equation approach |
| 基金项目 国家自然科学基金项目(60874063, 60374026)资助. |
|
| 中文摘要 |
| 对带不确定噪声方差线性定常系统鲁棒Kalman滤波, 提出一般的统一的保性能鲁棒性概念.用Lyapunov方程方法, 提出两类保性能极大极小鲁棒稳态Kalman滤波器.一类是寻求不确定噪声方差最大扰动域（鲁棒域）, 使得对于扰动域内的所有扰动, 确保系统滤波精度偏差的最大下界是零, 最小上界是所预置的精度偏差指标; 另一类是在预置噪声方差有界扰动域内, 寻求滤波精度偏差的最大下界和最小上界.通过引入不确定噪声方差扰动的参数化表示,问题转化为相应的非线性与线性最优化问题, 可分别用Lagrange乘数法和线性规划（LP）方法求解. 应用于跟踪系统的仿真例子验证了所提结果的正确性和有效性. |
| 英文摘要 |
| For the robust Kalman filtering of linear time-invariant systems with uncertain noise variances, the concept
of general and unified guaranteed-cost robustness of Kalman filtering is presented, and two classes of guaranteed cost
mini-max robust steady-state Kalman filters are presented by using the Lyapunov equation approach. One class is to find
the maximal perturbation region (robust region) of uncertain noise variances such that for all admissible perturbations in
this region the accuracy deviations are guaranteed to have zero as the maximal lower bound and the prescribed accuracy
deviation index as the minimal upper bound. The other class is to find the maximal lower bound and the minimal upper
bound of the accuracy deviations over the prescribed bounded perturbation region of noise variances. The problems are
converted into corresponding nonlinear and linear optimization problems by introducing the parameterized representation
of noise variances perturbations. They are solved by Lagrange multiplier method and linear programming (LP) approach,
respectively. A simulation example applied to tracking system validates the correctness and effectiveness of the proposed
method. |