Integer ambiguity resolution in precise point positioning: method comparison

Abstract

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 (IRCs) by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove the equivalence of the ambiguity-fixed position estimates d from these two methods by assuming that the F Bs ar hard are-dependent and only they are assimilated into the clocks and ambiguities. To ify is equivalence we implement both methods in the PANDA (Position and Navigation Data Analyst) software to process one 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 IGS weekly ons for the former method differs by below 0.1 mm on vera e for each component from that for the latter method. Therefore, considering th cogned millimeter-evel 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.

Dokładność Wyznaczania Pozycji Z Zastosowaniem Permanentnych Usług Internetowych PPP (Precise Point Positioning)

“…przedstawiono odpowiednio na (Rys. 4,6,8,10). Rodzaj zastosowanej permanentnej usługi internetowej PPP wyróżniono kolorem.…”

“…Wyznaczenie liczby pełnych cykli fazowych sygnału GNSS czyli nieoznaczoności fazy jest niezwykle trudne w pomiarach bezwzględnych. Określenie wartości tej niewiadomej wymaga długotrwałych obserwacji [7,8].…”

An assessment of the interoperability of PPP-AR network products

“…If the ambiguities could be isolated and estimated as integers, then there would be more information that could be exploited to accelerate convergence to give cm-level horizontal accuracy within an hour of data collection. Collins et al (2008) and Laurichesse et al (2009) saw improvements in hourly position estimates by 2 cm and Geng et al (2010) saw noticeable hourly improvements from 1.5, 3.8 and 2.8 cm to 0.5, 0.5, 1.4 cm for north, east and up, respectively.…”

“…One method of deriving such products is to estimate the satellite equipment delay by averaging the fractional parts of the steady-state float ambiguity estimates (Ge et al 2008), and the other is to estimate the pseudorange and carrierphase clocks independently by fixing the undifferenced ambiguities to integers in advance (Collins 2008;Laurichesse et al 2009). The initial application of ambiguity resolution to PPP was made by Ge et al (2008) using the Uncalibrated Phase Delay (UPD) model, now called Fractional Cycle Bias (FCB) model (Geng et al 2010(Geng et al , 2012. The FCB method estimates combined pseudorange/ carrier-phase satellite equipment delays removing the pseudorange satellite equipment delays from common clock estimates, such as those provided by the IGS (International GNSS Service).…”

Comparative analysis of real-time precise point positioning zenith total delay estimates

“…In the DD strategy, common errors are removed and it becomes easier to identify and fix such integer ambiguities. However, for un-differenced observations, it was not possible to fix the integer phase ambiguities until recently (Geng et al 2010). Among others, the Centre National d'Etudes Spatiales (CNES) has developed strategies to fix integer ambiguities of un-differenced phase measurements by first fixing the difference between the ambiguities on the two carrier frequencies and then fixing the remaining ambiguity in a global network solution (Loyer et al 2012).…”