Predicting the Success Rate of Long-baseline GPS+Galileo (Partial) Ambiguity Resolution

Abstract

This contribution covers precise (cm-level) relative Global Navigation Satellite System (GNSS) positioning for which the baseline length can reach up to a few hundred km. Carrierphase ambiguity resolution is required to obtain this high positioning accuracy within manageable observation time spans. However, for such long baselines, the differential ionospheric delays hamper fast ambiguity resolution as based on current dual-frequency Global Positioning System (GPS). It is expected that the modernization of GPS towards a triple-frequency system, as well as the development of Galileo towards a full constellation will be beneficial in speeding up long-baseline ambiguity resolution. In this article we will predict ambiguity resolution success rates for GPS + Galileo for a 250 km baseline based on the ambiguity variance matrix, where the Galileo constellation is simulated by means of Yuma almanac data. From our studies it can be concluded that ambiguity resolution will likely become faster (less than ten minutes) in the case of GPS + Galileo when based on triplefrequency data of both systems, however much shorter times to fix the ambiguities (one-two minutes) can be expected when only a subset of ambiguities is fixed instead of the complete vector (partial ambiguity resolution).

An analytical study of PPP-RTK corrections: precision, correlation and user-impact

“…2.3.1, one can improve user ambiguity resolution performance significantly if the PPP-RTK corrections would be extended with an ionospheric component, thus enabling the user to make use of the stronger ionosphereweighted model. In that case, network ambiguity resolution would improve the provided ionospheric information (Odijk 2002;Grejner-Brzezinska et al 2004;Mervart et al 2013;Odijk et al 2014).…”

Precise positioning in Europe using the Galileo and GPS combination

“…These common signals allow the combination of both systems and use that combination for positioning purposes. However, for this solution the time and coordinate system differences must be taken into account, and also the difference between the receiver hardware delays affecting the signals from different systems (Montenbruck et al 2011;Odijk et al 2013). This bias is termed inter-system bias (ISB).…”

Optimal Estimation of a Subset of Integers with Application to GNSS

“…The analysis in Verhagen et al (2013) shows that the success rates of integer BS are a tight lower bound for the ILS success rates if a prior decorrelation function is used. The idea of using BS success rates for selecting the subset I with a given reliability constraint was introduced in Teunissen et al (1999) and used for PAR in, e.g., Khanafseh and Pervan (2010), Verhagen et al (2011), Odijk et al (2014, and Nardo et al (2016). Generally, the subset selection process includes the evaluation of success rate and/or precision (30) for different subsets I, before one of them is selected.…”

“…In GNSS positioning with short observation time spans, ambiguity resolution can improve the position accuracy by roughly two orders of magnitude compared to the float solution, depending on the chosen subset of ambiguities and given that the estimated integers are correct. The performance analyses of partial ambiguity resolution (PAR) techniques in, e.g., Verhagen et al (2011), Odijk et al (2014, Nardo et al (2016), andBrack (2016) show that PAR can be very beneficial for obtaining both fast and reliable positioning results.…”