过程噪声未知但有界情况下系统最优滤波器设计方法

本文基于模型匹配方法提出了一种极小化误差幅值的线性系统的最优滤波器的设计方法,所考虑的过程噪声和量测噪声均为未知但幅值有界信号.该方法的特点是能够处理无穷观测数据量的最优滤波问题.当系统的初始条件已知时,将滤波器设计问题化为一个标准二块₁优化问题;当系统含有未知但有界初始条件时该问题归结为有限个标准₁优化问题,而标准₁优化问题已有成熟算法求解.仿真实例子说明了所提出方法的有效性和可行性.

Optimal Filter Design for Systems with Unknown But Bounded Process Noises

Based on model matching approach,this paper presents an algorithm for designing optimal filter that minimizes the magnitude of the filter error,in the case of linear discrete-time system in which the process noise and measurement noise are unknown but magnitude bounded.The presented algorithm can be used to optimal infinite-horizon filter design.When the initial condition of the system is a priori known,the optimal filter is converted into a standard tow-block ₁ optimization.When the system contains unknown but bounded initial condition,the optimal filter can be obtained by solving finite standard ₁ optimization problems that can be solved by existed techniques.A simulation example shows the effectiveness and feasibility of the proposed results.