中文摘要：

作者详细讨论了随机离散时间动态系统中过程噪声Wk和量测噪声Vk。两步相关情况下的最优状态估计，给出了两步相关情况下的卡尔曼型滤波，然后把它推广到过程噪声Wk和量测噪声Vk多步相关的情况，给出了n步相关情况下卡尔曼型滤波的一般表达式．

英文摘要：

This paper discusses first that in the discrete time random dynamic system, what is the optimal recursive solution of the state estimation when the process noise and measurement noise are two-step correlated. A Kalman type filter for this system is present. Then,the authors extend it to the more general case of the process noise and measurement noise being n-step correlated and present a Kalman type filter in this case.