Integer ambiguity resolution in precise point positioning: method comparison

By Jianghui Geng, Xiaolin Meng, Alan H. Dodson, Felix Norman Teferle. 2010

279 citations recorded by the source corpus.

Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively. Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below 0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better positioning quality.

Subfields: Aerospace Engineering, Atomic and Molecular Physics, and Optics, Oceanography

View Paper: https://www.semanticscholar.org/paper/5a3619fa10fea745b4377e9fe7294d3300dc14be

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Citations in the corpus

Review and principles of PPP-RTK methods (2015, methodology): “However, as the UPD/FCB estimation method itself differs from the methods of estimation of the previous sections, see e.g., (Ge et al. 2008; Geng et al. 2010, 2011, 2012; Geng and Bock 2013), it is of interest to identify and understand what those differences are.”
Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP (2017, background): “Geng et al. (2010b) predicted the ionospheric and tropospheric delays to achieve rapid ambiguity fixing after data gaps, avoiding the problem of reinitialization in the ambiguity-fixed PPP.”
Initial results of precise orbit and clock determination for COMPASS navigation satellite system (2013, methodology): “The software was later extended to POD for Low Earth Orbits (Zhao 2004), GLONASS orbit and clock determination, PPP and network adjustment (Shi et al. 2008, 2010), PPP-RTK (Geng et al. 2010), as well as gravity field modeling using satellite-to-satellite tracking data (Zhao et al. 2011).”
Single-frequency precise point positioning: an analytical approach (2015, background): “Improvement of ambiguity fixed PPP is seen in the precision and repeatability of estimated stations’ coordinates (Geng et al. 2010), in orbit precision of low Earth orbiting satellites (Laurichesse et al. 2009) as well as in convergence time (Collins et al. 2010).”