Numerical comparison of discrete Kalman filter algorithms: Orbit Determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms, Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the UD covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the UD filter is further demonstrated by its insensitivity to variations in the a priori statistics.