A Closed-Form Formula of Weighted GDOP in Multi-GNSS Positioning

With the ongoing GNSS development and modernization, multi-GNSS receivers can track more satellites, and improve the positioning performance effectively. In multiGNSS positioning using integrated receivers, the weighted geometric dilution of precision (GDOP), namely, the WGDOP, is an important index for selecting satellites from all visible ones. However, the WGDOP calculation involves complicated transformation and inversion of matrices. In this paper, we focus on the calculation of the WGDOP for five satellites and propose a closed-form formula for the WGDOP. By calculating the inverse of a matrix of three-order instead of a high-order matrix, the closed-form formula can reduce the computation burden, and give the direct expression of WGDOP. Experimental results verify the validity of the proposed method.