A method for separating unmodeled errors in GNSS based on the constraint of the prior variance of unit weight

Abstract

In global navigation satellite system (GNSS), unmodeled errors critically affect the accuracy and reliability of positioning solutions. When the unmodeled errors are significant in the mathematical model, they are mainly processed by choosing adjustment models with additional systematic error parameters or semiparametric estimation. However, many existing methods require knowledge of prior information on unmodeled errors; otherwise, achieving better processing results is difficult. To address this problem, this study proposes a GNSS unmodeled error separation method that does not rely on prior information on unmodeled errors. This method is based on the constraint of prior variance of unit weight. First, the method effectively separates the effect of unmodeled errors in the residuals under this constraint. Second, the initial estimate of the unmodeled errors in the observation domain is used as a virtual observation. Thus, the optimal estimate and variance of the unmodeled errors are obtained. Finally, the observations are effectively corrected by combining the concepts of mean shift and variance inflation. Multiple experiments were performed in this study. The results show that the proposed method can effectively weaken the impact of unmodeled errors on the float and fixed solutions of GNSS positioning, regardless of whether unmodeled errors exist in a single observation or multiple observations.