BIE using multivariant t-distribution and the iFlex method for GNSS PPP

Reliable ambiguity resolution is the key to obtaining centimetre-level accuracy in high precision GNSS positioning techniques such as Real-Time Kinematic (RTK) and Precise Point Positioning (PPP). In this contribution, an approach for partial ambiguity resolution based on the best integer equivariant estimator using the multivariant t-distribution (BIE-td) is proposed and compared against 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 freedom provides a better fit compared to the Gaussian distribution. Finally, an additional 7-day set of GNSS measurements, collected in 2019 from the same CORS, confirms that the positioning performance using the BIE-td and iFlex method using Laplace and Maxmin function is comparable, with a similar positioning accuracy for both the horizontal and vertical coordinate components. Significantly, both the BIE-td and iFlex methods using Laplace (or Maxmin) outperform the BIE using the Gaussian function. Although the iFlex method reduces computational burden compared to the BIE-td, its function such as Laplace or Maxmin is not mathematically rigorous, and hence the BIE-td method is recommended.