An improved adaptive Sage filter with applications in GEO orbit determination and GPS kinematic positioning

Abstract

The shortcomings of an adaptive Sage filter are analyzed in this paper. An improved adaptive Sage filter is developed by using a weighted average quadratic form of the historical residuals of observations and predicted states to evaluate the covariance matrices of observations and dynamic model errors at the present epoch. The weight function is constructed based on the variances of observational residuals or predicted state residuals and the space distance between the previous and the present epoch. In order to balance the contributions of the measurements and the dynamic model information, an adaptive factor is applied by using a two-segment function and predicted state discrepancy statistics. Two applications, orbit determination of a maneuvered GEO satellite and GPS kinematic positioning, are conducted to verify the performance of the proposed method.