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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。
Aiming at the discrete dynamic system with multi-step random delay and the state transition matrix with uncertain norm bound for a class of sensor observations, an optimal filter is designed under Minmax criterion. For this kind of problem, the existing methods are mainly limited to the one-step random delay case. The filter is designed by minimizing some upper bound of the estimation error covariance matrix. Each step in the recursive algorithm needs to be given a scale parameter. The improved filtering algorithm in practical applications more convenient. Numerical examples show that this method has smaller average estimation error than the existing methods for sensor observations with one-step delay, and also has better filtering performance for dynamic systems with two-step random delays.