Gaussian Sum Filters and its Applications to GNSS Positioning

In this paper, the methods to analyze the measurement noise (error) distributions of the GNSS observables in the point positioning, and relative positioning are derived. And we show that the measurement noises can be modeled by the weighted sum of Gaussian distributions better than ordinary single Gaussian distribution. Then we also derive a filtering method for a discrete time system with Gaussian sum distributed measurement noise by extending and modifying the Gaussian Sum filter proposed by Alspach and Sorenson [1]. The proposed filter can be implemented based on more accurate model of the measurement noise. Its applications to the relative positioning based on the double differenced C/A code pseudoranges are demonstrated, and the accuracy of positioning and variance-covariance information of the estimates are also investigated.