过程噪声未知但有界情况下不稳定线性离散时间系统最优滤波器设计研究

本文首先研究了不稳定线性离散时间系统的最优线性滤波器设计问题,利用状态观测器结合互质分解方法,将不稳定系统的最优线性滤波问题转化成可解的模型匹配问题,从而可利用已有的逐点优化算法进行求解,推广了线性滤波器的逐点优化设计方法.然后,本文还进一步研究了线性离散时间系统线性滤波器的最优性问题,从理论上证明了线性离散系统的线性滤波器能与非线性滤波器达到相同的最优性.

Optimal Filter Design for Unstable Linear Discrete-Time Systems with Unknown but Bounded Process Noises

The problem of designing an optimal filter for unstable linear discrete-time systems is firstly investigated.By use of state-observer and coprim-factorization,the problem of the optimal filter design for unstable system is converted to a solvable model matching problem,which can be solved by point to point optimization approach.A simulation example shows the effectiveness and feasibility of the proposed results.Thus the point-to-point optimization approach is extended to unstable systems.Furthermore,this paper considers the optimality of linear filter for linear discrete-time systems.It is shown that for linear discrete-time systems using nonlinear filter instead of linear filter does not improve the optimality of filter.