具有多步随机延迟和参数不确定动态系统的滤波器设计

摘要

A robust filter that is optimal by the minimax criterion is proposed for discrete dynamic systems whose sensors have random multi⁃step delays and whose state transition matrices have norm⁃bounded uncertainty. It is different from the existing methods in that the available upper bound of the estimation error covariance is minimized and an appropriate scaling parameter must be determined in each recursive step. The proposed filter can be executed in practical applications more conveniently. Numerical simulations, including comparisons with existing algorithms for dealing with one⁃step sensor delay, are provided to show the performance of the proposed filter.%针对一类传感器观测具有多步随机延迟、状态转移矩阵具有范数界不确定的离散动态系统，在Minmax准则下设计了一种最优的滤波器。对于这类问题，已有的方法主要限于一步随机延迟的情况，通过最小化估计误差协方差矩阵的某种上界来设计滤波器，在递推算法中每一步都需要给定一个尺度参数；而改进滤波算法在实际应用中更加方便。通过数值例子表明，对于具有一步延迟的传感器观测，与已有方法相比该方法具有更小的平均估计误差；同时，对于两步随机延迟的动态系统也具有较好的滤波效果。