【摘要】 利用Hilbert空间的几何理论求出了噪声相关系统的卡尔曼滤波公式。在线性最小方差准则下 ,解决了状态噪声一步相关 ,相同时刻的测量噪声和状态噪声相关 ,以及测量噪声和状态噪声在相邻时刻 (无论测量噪声时刻在前还是状态噪声时刻在前 )均相关的情况下的滤波问题 ,并给出了递推滤波公式更多还原

【Abstract】 In this literature, the formulae of Kalman filtering of system with re lated noise are find out. Under the criterion of linear minimum variance, the fi ltering problem of system with one step related state noise ,the related measure noise and state noise both at the same time and the neighboring time (no matter whose time is earlier) are solved. At the same time , the recursive filtering f ormulae are given out.更多还原