Improvements in PPP by Integrating GNSS with LEO Satellites: A Geometric Simulation

The precise point positioning (PPP) method in GNSS is based on the processing of undifferenced phase observations. For long static sessions, this method provides results characterized by accuracies better than one centimeter, and has become a standard practice in the processing of geodetic permanent stations data. However, a drawback of the PPP method is its slow convergence, which results from the necessity of jointly estimating the coordinates and the initial phase ambiguities. This poses a challenge for very short sessions or kinematic applications. The introduction of new satellites in Low Earth Orbits (LEO) that provide phase observations for positioning, such as those currently provided by GNSS constellations, has the potential to radically improve this scenario. In this work, a preliminary case study is discussed. For a given day, two configurations are analyzed: the first considers only the GNSS satellites currently in operation, while the second includes a simulated constellation of LEO satellites. For both configurations, the geometric quality of a PPP solution is evaluated over different session lengths throughout the day. The adopted quality index is the trace of the cofactor matrix of the estimated coordinates, commonly referred to as the position dilution of precision (PDOP). The simulated LEO constellation demonstrates the capability to enhance positioning performance, particularly under conditions of good sky visibility, where the time needed to obtain a reliable solution decreases significantly. Furthermore, even in scenarios with limited satellite visibility, the inclusion of LEO satellites helps to reduce PDOP values and overall convergence time.