Improvement of PPP-inferred Troposphere Estimates by Integer Ambiguity Resolution
December 16, 2011 By: Junbo ShiJ. Shi and Y. Gao
Department of Geomatics Engineering, University of Calgary, Canada, T2N 1N4
Introduction
GPS precise point positioning (PPP) ambiguity resolution (AR) is a challenging task for ambiguity-resolved PPP. So far, two PPP AR methods, i.e. un-differenced decoupled clock model and single-differenced between satellites model, have been proposed. Various publications have demonstrated that the integer property of the carrier phase ambiguities in the PPP positioning model can be theoretically retained and thus PPP AR is feasible if other bias sources can be eliminated by applying necessary corrections. The improvement of PPP AR on the coordinate estimates has also been investigated. In this paper, the improvement on the PPP-inferred troposphere estimates by ambiguity resolution based on the decoupled clock model will be discussed.
Overview
The decoupled clock model includes the following three observation equations:
(1)
in which the integer property of the un-differenced ambiguity terms can be recovered which makes the integer ambiguity resolution feasible. The clock-like terms related to the user receiver, namely dtrP3 , dtrL3 , and brA4 in Equation (1), are to be estimated together with other parameters including position coordinates, troposphere delay T as well as ambiguity terms. Usually the approximate zenith hydrostatic and wet delays are first calculated using a correction model with input of real pressure and temperature data. The residual zenith wet delay is then estimated. The variance-covariance matrix for the decoupled clock model is
(2)
where 
.
Equations (1) and (2) are the functional and stochastic models based on the decoupled clocks for PPP.
Experimental Result and Analysis
In order to analyze the improvement of PPP-inferred troposphere estimates by ambiguity resolution, the data from the IGS network during the Day of Year (DOY) 062 ~ 066 2008 are used. A total of ten GPS data samples from the IGS network have been identified during the period. Two external references including IGS troposphere products and COSMIC radio occultation events are also applied for the purpose of comparison. All PPP troposphere estimations are conducted based on IGS hourly data sets which are intended to support near real-time meteorological applications.
The results for the ten co-located troposphere delay estimates with float and fixed ambiguities are listed in Table 1 along with the solutions from the IGS troposphere products and the COSMIC RO events. First, the mean value of the difference between the IGS products and the COSMIC RO events are 0.0001 m. This means that these two external references match each other quite well. Second, for the case of using the IGS product as the reference, the bias of the troposphere zenith path delay estimates with the fixed ambiguities have been improved from -0.0037 to 0.0010 m compared to that with float ambiguities. This improvement implies that the bias with the float ambiguities has been mostly removed by the integer ambiguity resolution. The same can be found for the case of using the COSMIC RO reference which has been improved from -0.0038 to 0.0009 m. Third, the accuracies of the troposphere zenith path delay estimates as shown in Table 1 have been greatly improved. A 44.3% improvement (from 0.0379 to 0.0211 m) has been obtained by integer ambiguity resolution applied to PPP when using the COSMIC RO as the reference, while a 33.3% improvement (from 0.0457 to 0.0305 m) when using the IGS reference as the reference.
Table 1. Zenith path delay comparison between PPP-inferred solutions
with float and fixed ambiguities, COSMIC RO and IGS troposphere products (unit: m)
(Click to enlarge.)
Summary of Findings
- For the case of using IGS products as the external reference, the bias in the PPP-inferred troposphere estimates is reduced from -0.0037 to 0.0010 m by applying PPP ambiguity resolution. The RMS accuracy improvement is 33.3% (from 0.0457 to 0.0305 m).
- For the case of using COSMIC radio occultations as the external reference, the bias in the PPP-inferred troposphere estimates is reduced from -0.0038 to 0.0009 m by applying PPP ambiguity resolution. The RMS accuracy improvement is 44.3% (from 0.0379 to 0.0211 m).
- All above improvements are obtained based on IGS hourly data sets, which indicates the potential to greatly reduce the convergence time of precise PPP troposphere estimates and thus to support near real-time meteorological applications.
References
Collins P., S. Bisnath, L. Francois, and P. Heroux (2010) “Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing”, Journal of Navigation, 57 (2): 123-135.
Shi J. and Y. Gao (2010) “Analysis of the integer property of ambiguity and characteristics of code and phase clocks in PPP using a decoupled clock model”, Proceedings of ION/GNSS 2010, 21-24 September 2010, Portland, OR.
Shi J. and Y. Gao (2011) “Integer Ambiguity Resolution to Improve Accuracy and Convergence of PPP-Inferred PWV Estimates”, Proceedings of ION/GNSS 2011, 19 -23 September 2011, Portland, OR.
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