The Algorithms of Rigorous Recursive Least Square
Xuan Liu · Hainan Daxue xuebao. Ziran kexue ban · 2000
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 reference[1],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