Abstract: A new approach is presented by polynomial-quotient which translates colored observation noises into infinite series,and chooses the finite series,calculates the variance of dummy white observation noises.The stochastic model can be compensated with this method.An ARMA innovation model and the state optimal filter are designed by modern time series analysis method.In order to verify the validity and rationality of this method,a contrast between this method and the approach of observation-expand filter is given.The result shows that the approach can control the influences of the colored observation noises effectively.