Modified Robust Covariance Intersection Fusion Steady-state Kalman Predictor for Uncertain Systems
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摘要: 针对带随机参数和噪声方差两者不确定性的线性离散多传感器系统，利用虚拟噪声补偿随机参数不确定性，原系统可转化为仅带不确定噪声方差的系统.根据极大极小鲁棒估值原理，用Lyapunov方程方法提出局部鲁棒稳态Kalman预报器及其误差方差最小上界，并利用保守的局部预报误差互协方差，提出改进的鲁棒协方差交叉（Covariance intersection，CI）融合稳态Kalman预报器及其误差方差最小上界.克服了原始CI融合方法要求假设已知局部估值及它们的保守误差方差的缺点和融合误差方差上界具有较大保守性的缺点.证明了鲁棒局部和融合预报器的鲁棒性，并证明了改进的CI融合器鲁棒精度高于原始CI融合器鲁棒精度，且高于每个局部预报器的鲁棒精度.一个仿真例子验证了所提出结果的正确性和有效性.
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关键词:
- 不确定系统 /
- 协方差交叉融合 /
- 极大极小鲁棒Kalman预报器 /
- 虚拟噪声 /
- Lyapunov方程方法
Abstract: For linear discrete time multisensor systems with both stochastic parameter and noise variance uncertainties, the stochastic parametric uncertainty can be compensated by a fictitious noise, so the original system can be converted into the one with only uncertain noise variances. Based on the minimax robust estimation principle, the local robust steady-state Kalman predictors and the minimal upper bounds of their error variances are presented using the Lyapunov equation approach, and a modified robust covariance intersection (CI) fusion steady-state Kalman predictor and the minimal upper bound of its error variances are presented using the cross-covariances of the conservative local prediction errors. They overcome the disadvantages of the original CI fuser that the local estimates and their conservative error variances are assumed to be known, and the upper bound of fused estimation error variances has large conservativeness. The robustness of the robust local and fused predictors is proved, and it is proved that the robust accuracy of the modified CI fuser is higher than that of the original CI fuser and that of each local predictor. A simulation example shows the correctness and effectiveness of the proposed results. -
图 1 基于协方差椭圆的局部和CI融合鲁棒Kalman预报器的矩阵不等式精度比较
Fig. 1 The comparison of matrix inequality accuracies of the local and CI fused robust Kalman predictors based on covariance ellipses
图 2 基于协方差椭圆原始的和改进的鲁棒CI融合Kalman预报器的矩阵不等式精度比较
Fig. 2 The comparison of matrix inequality accuracies of the original and modified CI fused robust Kalman predictors based on covariance ellipses
图 3 局部和CI融合鲁棒Kalman预报器的MSE曲线
Fig. 3 The MSE curves of the local and CI fused robust Kalman predictors
图 4 位置预报误差曲线和 $\pm 3\sigma _1$ 界
Fig. 4 The position prediction error curve and $\pm 3\sigma_1 $ bounds
图 5 速度预报误差曲线和 $\pm 3\sigma _2$ 界
Fig. 5 The velocity prediction error curve and $\pm 3\sigma _2 $ bounds
表 1 鲁棒Kalman预报器的鲁棒和实际精度比较
Table 1 The comparison of robust and actual accuracies of robust Kalman predictors
${\mathop{\rm tr}\nolimits} {\bar \Sigma _1}$ ${\mathop{\rm tr}\nolimits} {\Sigma _1}$ ${\mathop{\rm tr}\nolimits} {\bar \Sigma _2}$ ${\mathop{\rm tr}\nolimits} {\Sigma _2}$ ${\mathop{\rm tr}\nolimits} {\bar \Sigma _{{CI}}}$ ${\mathop{\rm tr}\nolimits} {\Sigma _{{CI}}}$ ${\mathop{\rm tr}\nolimits} \Sigma _{{CI}}^*$ 1.6267 2.1690 1.4425 2.3544 0.8158 1.1437 1.8751 
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