Energy-to-Peak State Estimation With Intermittent Measurement Outliers: The Single-Output Case
针对带有能量有界噪声和间歇性测量异常值的线性离散时间系统，提出一种参数依赖的状态估计策略，通过两步过程检测并移除异常值，实现能量到峰值性能约束下的状态估计。
This article is concerned with the energy-to-peak state estimation problem for a class of linear discrete-time systems with energy-bounded noises and intermittent measurement outliers (IMOs). In order to capture the intermittent nature, two sequences of step functions are introduced to model the occurrence of the IMOs. Furthermore, two special indices (i.e., minimum and maximum interval lengths) are adopted to describe the "occurrence frequency" of IMOs. Different from the considered energy-bounded noises, the outliers are assumed to have their magnitudes larger than certain thresholds. In order to achieve a satisfactory performance constraint on the energy-to-peak state estimation under the addressed kind of measurement outliers, a novel parameter-dependent (PD) state estimation strategy is developed to guarantee that the measurements contaminated by outliers would be removed in the estimation process. The proposed PD state estimation method is essentially a two-step process, where the first step is to examine the appearing and disappearing moments for each IMO by using a dedicatedly constructed outlier detection scheme, and the second step is to implement the state estimation task according to the outlier detection results. Sufficient conditions are obtained to ensure the existence of the desired estimator, and the gain matrix of the desired estimator is then derived by solving a constrained optimization problem. Finally, a simulation example is presented to illustrate the effectiveness of our developed PD state estimation strategy.