the deducing of the algorithms has very practical value in state estimation for systems under the complex environments . in the instance of complicated multi-channel system with multiplicative noise, the dissertation discusses the optimal estimation of state filtering and smoothing and the stochastic input signal with the technique of innovation and projection theorem of hilbert space . the main study of the dissertation is introduced as follows : 1 according to the practical requirement of complicated multi-channel system with multiplicative noise, the dissertation broadens rajasekaran filtering algorithm 本文針對復雜多通道帶乘性噪聲系統(tǒng),應用新息的方法和hilbert空間的投影定理,對狀態(tài)最優(yōu)濾波和平滑估計、隨機輸入信號的最優(yōu)估計等理論與應用方面的問題,進行了進一步的探討,著重完成了以下工作:第一,根據(jù)復雜多通道乘性噪聲系統(tǒng)問題的實際需要,推廣了rajasekaran濾波算法。