Performance Analysis of Triple Carrier Ambiguity Resolution in Precise Point Positioning with Smoothed Ionosphere Corrections

Abstract

Multi-frequency signals, broadcast by the next generation GNSS satellites, have led to the development of the Triple Carrier Ambiguity Resolution method. This method, which is based on the “gap-bridging” concept, is an extraordinarily simple approach that allows quick ambiguity resolution. Due to large ionospheric delays, Triple Carrier Ambiguity Resolution was originally developed for and applied only to double difference measurement processing in Real Time Kinematic (RTK) systems. In recent years Precise Point Positioning (PPP) has become an attractive solution for high accuracy positioning in remote areas where, for logistics or economic reasons, cannot have any nearby reference station. Unfortunately, PPP’s long convergence time (typically 20 minutes) limits the scientific and commercial applications for PPP to only open sky conditions. For this reason, an instantaneous ambiguity fixing methods such as Triple Carrier Ambiguity Resolution could represent an extraordinary asset for PPP. This paper presents an implementation of the Triple Carrier Ambiguity Resolution that makes use of a smoothed ionosphere correction to mitigate for the ionospheric delay in the pseudorange measurements and, therefore, it can be used with undifferenced observations as in case of PPP. From the statistical point of view, reliable ambiguity fix can be achieved in less than 30 seconds in a multipath-free environment, while in presence of severe multipath the narrow lane ambiguity can be fixed after 10 minutes. Results based on simulated data showed that the time required to fix the narrow lane ambiguity, with measurements affected by multipath, was much larger than the one promised by the theoretical statistical analysis. It confirmed what stated by other authors, that triple carrier ambiguity resolution works well only in absence of multipath. Finally, this paper also analyzes the positioning performance of a PPP configuration in which the narrow lane ambiguity is kept float, while the extra-wide and wide lane ambiguities are fixed. In this configuration, a triple-frequency ionosphere-free carrier phase combination, characterized by a large narrow lane wavelength, is used together with the two frequency pseudorange and carrier phase ionosphere-free combinations. Results based on simulated data show that the horizontal error converges below 10 cm in less than 3 minutes and below 5 cm in less than 10 minutes.