有色噪声作用下的抗差卡尔曼滤波

根据用GPS载波相位三差观测量进行动态定位或精密导航的需求,推导了动态噪声、观测噪声为有色噪声的抗差卡尔曼滤波公式。白噪声的抗差卡尔曼滤波是有色噪声的抗差卡尔曼滤波的特例,有色噪声的抗差卡尔曼滤波为白噪声的抗差卡尔曼滤波的推广。

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.