A Comprehensive Kalman Filtering and Its Application to GPS-based Orbit Determination for LEOs

In applying typical Kalman filtering technique to the optimal estimation of motion state of LEOs, there are some limitations, such as divergence of filter because of inaccurate of dynamic noise and observation noise, distortion of estimation of Kalman filter caused by measurement pollution and being not positive definite of covariance matrix due to computing rounding errors. In order to cope with these limitations, a comprehensive Kalman filter is presented in this paper. This filter is a combination of adaptive UD decomposition Kalman filter with QUAD method. It applies the QUAD method to detect and correct the gross errors in observations, uses UD decomposition technique to improve computation precision and overcome the instability of filter caused by instability of values.