Robust Kalman Filtering of Linear System with Colored Noises

The classical robust Kalman filter is derived by the conditions of white noise, but during the dynamic data processing, the colored noises may occur. For example, the three phase differences measuring errors of GPS carrier waves are colored noises and the measuring data between the adjacent satellite almanac is correlated, and the measuring data for the non-adjacent satellite almanac is uncorrelated, the covariance matrix of observational noises is triple diagonal block matrix. For achieving the precise dynamic positioning(or navigation) by the three phase differences of GPS carrier waves, the robust Kalman filtering with dynamic colored noises and observational colored noises are derived. It may be proved that the robust Kalman filter with white noises is the special case of robust Kalman filter with colored noises, the robust Kalman filter with colored noises is the extending of robust Kalman filter with white noises