无需初始状态先验统计知识的最优状态估计

为获得系统状态的最优线性无偏估计（ＢＬＵＥ），Ｋａｌｍａｎ滤波算法要求事先知道系统状态的均值与方差，但此要求往往难以满足．今放弃这一要求而考虑离散线性时变多输入多输出（ＭＩＭＯ）随机系统的状态估计问题．若系统是完全可重构的，则本文所给新的滤波算法便将给出系统状态的ＢＬＵＥ．对于即使不可观测的完全可重构确定性系统，该新算法也能给出其无差估计．

Optimal State Estimation without the Requirement of a Prior Statistics Information of the Initial State

The result given by Kalman filtering algorithm is the BLUE(best linear unbiased estimate) provided the mean and variance of the initial state are available. But this requirement is difficult to meet in most practical situations. We now abandon this requirement and consider the state estimation problem for stochastic MIMO discrete linear time varying systems. The new filtering algorithm presented in this paper gives the BLUE of state if the system is completely reconstructible. Even for a completely reconstructible deterministic system unobservable, the proposed algorithm can be also give a deadbeat estimation.