严格的最小二乘递推算法

当缺乏待估计量的初始统计知识时，最小二乘递推（ＲＬＳ）算法不能给出严格意义下的最小二乘估计．本文继文献［１］之后，应用广义逆的理论，分别就一般加权情形、最优加权情形和指数加权情形给出了严格的最小二乘速推算法（简称Ｒ２ＬＳ算法）．该算法无需事先提供待估计量的任何统计知识而能获得严格意义下的最小二乘估计，且证明了该算法分别为时变与定常系统提供了最短时间无偏状态估计算法与无差状态观测器．

The Algorithms of Rigorous Recursive Least Square

If the prior statistical knowledge of the parameters and the initial state to be estimated is not available,the RLS and Kalman filtering algorithms can not give least squares estimators or minimum variance estimators in the rigorous sense.Following the reference1],the rigorous recursive least square algorithms(be called R 2LS algorithms for short)are derived by applying the theory of generalized inverse.The R 2LS algorithms give the least square estimators not requiring any prior statistical knowledge of parameters or the initial state to be estimated .Further discussion in this paper show that R 2LS algorithms provide the minimum time unbiased filters for linear stochastic systems and minimum time deadbeat observers for linear deterministic systems