Robust state estimation for uncertain linear systems with random parametric uncertainties

Abstract

In this paper, we investigate state estimations of a dynamical system with random parametric uncertainties which may arbitrarily affect a plant state-space model. A robust estimator is derived based on expectation minimization of estimation errors. An analytic solution similar to that of the well-known Kalman filter is derived for this new robust estimator which can be realized recursively with a comparable computational complexity. Under some weak assumptions, it is proved that this estimator converges to a stable system, the covariance matrix of estimation errors is bounded, and the estimation is asymptotically unbiased. Numerical simulations show that the obtained robust filter has an estimation accuracy comparable to other robust estimators and can be applied in a wider range.

创新点

本文研究了存在随机参数不确定性时线性时变系统的鲁棒状态估计问题, 参数不确定性可以以任意方式影响系统模型。论文提出的算法基于卡尔曼滤波器和正则最小二乘之间的关系, 同时考虑了随机的模型误差的影响。提供了该鲁棒状态估计器的解析表达式, 可以递归实现, 其与标准卡尔曼滤波器有相似的形式和相当的计算复杂度。证明了在一定的假设条件下, 该鲁棒状态估计器收敛到一个稳定的系统, 估计误差的协方差矩阵是有界的, 且估计器是渐近无偏的(估计误差的期望以指数收敛到0)。数值仿真例说明该鲁棒状态估计器拥有与其它鲁棒估计器相近的估计性能, 且不需要设计参数的优化, 而仅仅需要离线计算若干个矩阵, 因此有更广泛的应用。