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中文摘要：
控制有色状态噪声影响除了通过状态向量扩展的方法外，也可以通过修正随机模型。提出采用多项式长除法将有色状态噪声模型展开成无穷级数，截断取其有限项，进而求取有色状态噪声方差。利用该方差对随机模型进行修正，再结合现代时间序列分析方法，构造出新的ARMA新息模型，并根据该新息模型设计状态最优滤波器。为了说明该方法的正确性和合理性，将它与标准的Kalman滤波和状态向量扩展法进行分析和比较。结果证明利用该方法能有效地控制有色状态噪声的影响。
英文摘要：
There are many theories and models which can control the influence of the colored state noises, for example state-vector-expand filter and in random model compensation filter etc. A new approach is presented by polynomial-quotient which translates colored state noises into infinite series, and chooses the finite series, calculates the variance of colored state noises. The random model can be corrected with this method. The ARMA innovation model and the state optimal filter are designed by combining the modern time series analysis method. In order to verify the validity and rationality of this method, comparisons between this method and the approach of classic Kalman filter and state-vector-expand filter are given. The result shows that the approach can control the influences of the colored state noises effectively.
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