Iterative Scalar Observation Update for Precise Point Positioning to Reduce Convergence Time

One of the challenging problems for the precise point positioning (PPP) is the reduction of the convergence time (CT). When the CT is defined as the time that the filter reaches a horizontal accuracy of 10 centimeters, the CT is usually about 30 minutes using the GPS satellites. The reason for this relatively long CT comes from the fact that the filter starts from the single point positioning (SPP) result, which is a meter-level, and that it is necessary for the filter to estimate many unknown parameters such as tropospheric delay and carrier phase ambiguities in addition to the receiver position and clock bias. In this paper, we investigate the impact of the iterative scalar observation update on shortening the CT. We propose the iterative scalar observation filtering based on the Joseph form (JF) of the extended Kalman filter (EKF) and show that the CT reduction can be achieved in the static PPP experiments using actual GPS carrier phases and precise ephemerides. Compared with the vector observation update of the standard EKF whose average CT was about 28 minutes, about 3-minute reduction was confirmed by using the proposed filter. We also confirmed that the proposed exception handling based on the normalized prediction residual was significant in reducing the CT. According to our experimental evaluation results, the probabilities of the convergence less than 20 and 30 minutes were about 50% and 75%, respectively, and the longest CT was about 2 hours.