针对石油地震勘、通讯工程、语言处理等应用领域 ,该文研究一种在更弱的噪声限制条件下带乘性噪声系统的状态最优滤波 ,就动态噪声为有色噪声及动态噪声和量测噪声在有限时间段上相关的情形 ,给出了线性最小方差意义下的状态最优滤波算法 ,并对此算法作了仿真计算 ,获得满意的结果 In the field of petroleum seismic exploration, communication engineering, language processing and other applications, this paper studies a state optimal filter of the system with multiplicative noise under weaker noise limits. The dynamic noise is colored noise and dynamic noise and measurement In the case that the noise is correlated for a limited period of time, the state optimal filtering algorithm in the sense of minimum linear variance is given, and the algorithm is simulated and the satisfactory result is obtained