The recruitment of the Low Earth Orbit (LEO) constellation is recognized as an effective way to augment Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) in the near future. Its potential to accelerate PPP convergence has been proved with simulated data. However, the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective, which hampers the understanding and exploitation of the enhancement of LEO. In this article, the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification. To show the characteristics of the ambiguities during convergence, eigenvalue decomposition is used to divide the ambiguities into orthogonal components, named geometric-related component, clock-error-related component, and independent component. The results show that the precision of geometric-related components of ambiguities, which correlates with position parameters, is low at a single epoch, while the precision can be greatly improved with the fast geometric change of LEO. On the other hand, the precision of clock-error-related components of ambiguities, which correlates with clock errors, cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry, which causes the precision of each ambiguity to be low. Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.
The recruitment of the Low Earth Orbit (LEO) constellation is recognized as an effective way to augment Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) in the near future. Its potential to accelerate PPP convergence has been proved with simulated data. However, the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective, which hampers the understanding and exploitation of the enhancement of LEO. In this article, the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification. To show the characteristics of the ambiguities during convergence, eigenvalue decomposition is used to divide the ambiguities into orthogonal components, named geometric-related component, clock-error-related component, and independent component. The results show that the precision of geometric-related components of ambiguities, which correlates with position parameters, is low at a single epoch, while the precision can be greatly improved with the fast geometric change of LEO. On the other hand, the precision of clock-error-related components of ambiguities, which correlates with clock errors, cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry, which causes the precision of each ambiguity to be low. Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.