Supporting Linear Least Square Filter by Adding New Mathematical Conditions for Solving Ambiguity in Precise Point Positioning and Comparative Study Versus Kalman Filter

Abstract

Precise Point Positioning (PPP) suffers from (Slow Convergence Time) from the stable value, because this technique adopts the navigational solution on its non-differential form from the (Single Receiver), and because it deals with error sources in Global Navigation Satellite Systems (GNSS) individually and independently.

The convergence of the navigation solution is related to the approach of the phase ambiguity resolution to the stable value, which takes place on average after (20-40) minutes of observations within the Precise Point Positioning (PPP) technique [1], and is mainly related to the occurrence of unpredicted jumps of Phase cycle which return convergence to an inaccurate initial value.

Filters are often used to filter the observations coming to the single geodetic receiver, and the performance of this filter is the actual measure of the Convergence time of the navigation solution as a whole within the Precise Point Positioning (PPP) technique [2].

The research aims to develop a new method of using the linear least square Filter to overcome (Cycle Slips), by compensating ambiguity loss, and correcting the wrong jumps on it, with new mathematical conditions, then discussing the performance of the three filters: linear least squares filter, Kalman filter, and adaptive Least squares filter developed in this research, in Precise Point Positioning (PPP) technique.

The absolute differences between the reference network and the (PPP) measurements in the three stations, reached mean values of (3.5 cm) on the (X) axis, (2.70 cm) on the (Y) axis, and (7.70 cm) on the (Z) axis, By using new mathematical conditions in Linear Least Square Filter, we reach high accuracy level that outperform the Kalman Filter (PPP) Positioning, and Linear Least Square Filter (PPP) Positioning as well.