Abstract Robust Kalman estimators for systems with multiplicative and uncertain-variance linearly correlated additive white noises
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Robust Kalman estimators for systems with multiplicative and uncertain-variance linearly correlated additive white noises

机译：具有乘法和不确定方差线性相关加性白噪声的系统的鲁棒Kalman估计

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AbstractFor linear discrete-time stochastic systems with mixed uncertainties including multiplicative and uncertain-variance linearly correlated additive white noises, this paper addresses the problem of designing robust Kalman estimators. By the fictitious noise-based Lyapunov equation approach, the system under consideration is converted into one with only uncertain noise variances. Based on the worst-case system with conservative upper bounds of actual noise variances, the minimax robust time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The corresponding robust steady-state Kalman estimators are also presented. An innovation test rule and a search technique of selecting the less-conservative upper bounds of actual noise variances are presented, by which the two classes of guaranteed robust accuracy Kalman estimators are presented. One class is robust Kalman estimators with improved robust accuracy, the other class is ones with the prescribed robust accuracy index. Three modes of convergence in a realization among the time-varying and steady-state robust Kalman estimators for the time-varying and time-invariant systems are presented and proved by the dynamic error system analysis (DESA) method. Two simulation examples applied to autoregressive (AR) signal processing and uninterruptible power system (UPS) show the effectiveness of the proposed results.
机译： 摘要 对于具有混合不确定性（包括乘法和不确定性线性相关加性白噪声）的线性离散时间随机系统，本文解决了设计鲁棒Kalman估计器的问题。通过基于虚构噪声的Lyapunov方程方法，可以将所考虑的系统转换为仅具有不确定噪声方差的系统。基于实际噪声方差具有保守上限的最坏情况系统，在统一框架中给出了最小极大鲁棒时变卡尔曼估计器（预测器，滤波器和平滑器）。在一定程度上证明了它们的鲁棒性，对于所有可允许的不确定性，可以保证它们的实际估计误差方差具有相应的最小上限。还介绍了相应的鲁棒稳态卡尔曼估计器。提出了一种创新测试规则和一种选择实际噪声方差的保守性较低的上限的搜索技术，从而提出了两类保证鲁棒精度的卡尔曼估计器。一类是具有改进的鲁棒精度的鲁棒卡尔曼估计器，另一类是具有规定的鲁棒精度指标的类。提出了时变和时不变系统时变和稳态鲁棒卡尔曼估计器实现中的三种收敛模式，并通过动态误差系统分析（DESA）方法进行了证明。分别应用于自回归（AR）信号处理和不间断电源系统（UPS）的两个仿真示例证明了所提出结果的有效性。

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