GNSS best integer equivariant estimation using multivariant t-distribution: a case study for precise point positioning

Abstract

A key prerequisite for fast and reliable solution convergence time in precise point positioning with ambiguity resolution is the successful determination of the initial integer ambiguity parameters. In this contribution, a reliable approach of partial ambiguity resolution based on the BIE using the t-distribution (BIE-td) is proposed and compared against existing algorithms, such as the partial ambiguity resolution-based LAMBDA method (PAR-Ps) and the iFlex method proposed by the Trimble Navigation company. A 31-day set of GNSS measurements, collected in 2018 from 17 globally distributed GNSS continuously operating reference stations (CORS), were processed to determine the best-fit distribution for the GNSS measurements. It is found that the t-distribution with three degrees of freedoms provides a better fit compared to the Gaussian distribution. The authors then propose a method for selecting the integer ambiguity candidates when using the BIE-td approach. This method is based on the differences of unknown parameters of interest (i.e. receiver’s coordinates) determined at two consecutive processing steps. Finally, another 30-day set of GNSS measurements, collected in 2019 from the same CORS, confirm that the iFlex method outperforms the PAR-Ps method in the sense of minimizing the position errors of a simulated kinematic test. In particular, compared to the PAR-Ps method for 99th percentile of errors, the iFlex method has an improved convergence time of about 10 min. In addition, the positioning performance using the BIE-td and iFlex methods is comparable, with a similar positioning accuracy for both horizontal and vertical coordinate components.