Kalman滤波理论的推广

A Generalization of Kalman Filtering Theory

本文利用Hilbert空间几何理论将Kalman滤波理论进行了推广,在线性最小方差准则下,解决了状态噪声一步相关及状态噪声和测量噪声在同时刻和过去相邻时刻都相关情况的滤波,并给出了递推滤波公式。

In this paper,by means of Hilbcrt space geometry theory,Kalman filter theory is generalized to the case that the system noise Correlates itself in one-step and system Correlates with the measuring noise at the present step as wall as one past step. The recursive filtering formulas with linear minimun variance are derived.