On the best integer equivariant estimator for low-cost single-frequency multi-GNSS RTK positioning

Carrier phase integer ambiguity resolution with a high success rate is the key to precise Global Navigation Satellite System (GNSS) positioning. When the success rate is too low the user will normally prefer the float solution, whereas the alternative can be to use the Best Integer Equivariant (BIE) estimator. Low-cost receiver real-time kinematic (RTK) precise positioning has become possible through combining signals from several GNSSs, such as BDS, Galileo, QZSS, and GPS. In this contribution we will use single-frequency (SF) low-cost receiver multi-GNSS data to compare the performance of the BIE estimator and the standard method of Integer Least Squares (ILS). The GNSS data is evaluated in Dunedin, New Zealand, with short baselines so that the relative atmospheric delays can be neglected. We show, with real multi-GNSS data and when the success rate is at low to medium levels, that the positioning performance of the BIE estimator will resemble or be better than that of the float solution, and always be better in the minimum mean squared error (MMSE) sense than the ILS fixed solutions. Whereas for very high success rates we get a BIE performance similar to that of the ILS estimator and much better than the float solution.