A Kalman filtering approach to code positioning for GNSS using Cayley-Menger determinants in distance geometry

摘要

The common approach for code-based point positioning using GNSS involves linearizing the observation equations about an estimated position and solving the equations iteratively in a least squares fashion. The solution provides estimates for the receiver coordinates and clock error. In this paper, a method based on distance geometry and Kalman filtering is presented. Distance geometry is used to provide a closed form solution for the receiver clock bias which is then used to correct the pseudorange observations before proceeding to locate the receiver coordinates. This two step method guarantees a solution for when a minimum of four satellites are available and facilitates direct utilization of a simple Kalman filter without any need for linearization. Results indicate that the method presented can provide improved estimates under poor satellite coverage as compared to the conventional iterative methods while performing similar to the conventional methods when there is good coverage.