FCB estimation with three different PPP models: equivalence analysis and experiment tests

Precise and reliable fractional cycle bias (FCB) products are critical for ambiguity resolution of precise point positioning (PPP). Three PPP models are usually adopted to generate the FCB products, i.e., the traditional ionospheric-free combined PPP (IF-PPP) model, the uncombined and unconstrained PPP model (UU-PPP) as well as the ionospheric-constrained PPP (IC-PPP) model. Considering that different observation models and ionospheric delay constraints are used, the applicability and interoperability of the obtained FCB products are assessed. We presented the equivalent conversion formulas of different FCB products obtained with different PPP models, which are then converted and compared. The root mean square (RMS) of the wide-lane (WL) FCB differences for IF-UU, IF-IC and UU-IC is 0.021, 0.024 and 0.010 cycles, while the RMS of the narrow-lane FCB differences is 0.028, 0.018 and 0.021 cycles. The precision of the WL FCBs based on the uncombined PPP models is higher than that based on the IF-PPP model since the new WL ambiguities derived from the uncombined ambiguities are free of the pseudorange noise. The equivalence of the FCB products estimated from the three different PPP models is confirmed in theory and by experiment results. To further evaluate the performance of the three PPP models, the positioning accuracy, the convergence time and the ambiguity fixing success rate are calculated using IGS data. The maximum positioning difference is less than 0.9 mm among the three PPP models. Compared to the float solutions of the IF-PPP, UU-PPP, IC-PPP with GIM model or with re-injected ionospheric delay corrections, the convergence time is shortened by 38.5%, 46.2%, 50.0% and 87.8% and the positioning accuracy improved by 27.1%, 38.9%, 41.1% and 25.7%, respectively. The ambiguity fixing success rate of the uncombined PPP models is slightly higher than that of the combined model, and fast ambiguity-fixed solution can proceed with high-precise ionospheric delay corrections.

[1]  Tian Zeng,et al.  Estimating satellite phase fractional cycle biases based on Kalman filter , 2018, GPS Solutions.

[2]  Yang Gao,et al.  Real-Time Precise Point Positioning Using Single Frequency Data , 2005 .

[3]  Pan Li,et al.  Generating GPS satellite fractional cycle bias for ambiguity-fixed precise point positioning , 2016, GPS Solutions.

[4]  Jingnan Liu,et al.  Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning , 2012, Journal of Geodesy.

[5]  J. Zumberge,et al.  Precise point positioning for the efficient and robust analysis of GPS data from large networks , 1997 .

[6]  G. Gendt,et al.  Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations , 2008 .

[7]  Yang Gao,et al.  A Unified Model for Multi-Frequency PPP Ambiguity Resolution and Test Results with Galileo and BeiDou Triple-Frequency Observations , 2019, Remote. Sens..

[8]  Yang Gao,et al.  A comparison of three PPP integer ambiguity resolution methods , 2014, GPS Solutions.

[9]  Xingxing Li,et al.  Improving the Estimation of Uncalibrated Fractional Phase Offsets for PPP Ambiguity Resolution , 2012 .

[10]  R. Hatch.  The synergism of GPS code and carrier measurements , 1982 .

[11]  Jinling Wang,et al.  Statistical analysis and quality control for GPS fractional cycle bias and integer recovery clock estimation with raw and combined observation models , 2017 .

[12]  Qin Zhang,et al.  Switching and performance variations of on-orbit BDS satellite clocks , 2019, Advances in Space Research.

[13]  Stephen Malys,et al.  GEODETIC POINT POSITIONING WITH GPS CARRIER BEAT PHASE DATA FROM THE , 1990 .

[14]  Qin Zhang,et al.  Real-time estimation of BDS/GPS high-rate satellite clock offsets using sequential least squares , 2018 .

[15]  Maorong Ge,et al.  A method for improving uncalibrated phase delay estimation and ambiguity-fixing in real-time precise point positioning , 2013, Journal of Geodesy.

[16]  Harald Schuh,et al.  Multi-GNSS real-time clock estimation using sequential least square adjustment with online quality control , 2018, Journal of Geodesy.

[17]  F. Guo,et al.  Enhancing Precise Point Positioning with External Ionosphere Constraints , 2015 .

[18]  Sunil Bisnath,et al.  Current State of Precise Point Positioning and Future Prospects and Limitations , 2009 .

[19]  Yidong Lou,et al.  An improved approach to model ionospheric delays for single-frequency Precise Point Positioning , 2012 .

[20]  Yidong Lou,et al.  BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable , 2015, Journal of Geodesy.

[21]  Baocheng Zhang,et al.  On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of $$\mathcal {S}$$S-system theory , 2016 .

[22]  R. Nerem,et al.  GPS Carrier phase Ambiguity Resolution Using Satellite-Satellite Single Differences , 1999 .

[23]  Xingxing Li,et al.  Triple-frequency PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo , 2019, Journal of Geodesy.

[24]  Qin Zhang,et al.  An Improved Predicted Model for BDS Ultra-Rapid Satellite Clock Offsets , 2018, Remote. Sens..

[25]  M. Rothacher,et al.  Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations , 2008 .

[26]  John Aggrey,et al.  Performance Analysis of Atmospheric Constrained Uncombined Multi-GNSS PPP , 2017 .

[27]  Paul Collins,et al.  Precise Point Positioning with Ambiguity Resolution using the Decoupled Clock Model , 2008 .

[28]  Guanwen Huang,et al.  Estimation of antenna phase center offset for BDS IGSO and MEO satellites , 2018, GPS Solutions.

[29]  Guo Fei,et al.  Ambiguity resolved precise point positioning with GPS and BeiDou , 2016, Journal of Geodesy.

[30]  Flavien Mercier,et al.  Real Time Zero-difference Ambiguities Fixing and Absolute RTK , 2008 .

[31]  Markus Rothacher,et al.  The impact of the atmosphere and other systematic errors on permanent GPS networks , 2000 .

[32]  Peter Teunissen,et al.  Review and principles of PPP-RTK methods , 2015, Journal of Geodesy.

[33]  Yang Gao,et al.  Improving Ambiguity Convergence in Carrier Phase-Based Precise Point Positioning , 2001 .

[34]  Jinling Wang,et al.  Modeling and assessment of triple-frequency BDS precise point positioning , 2016, Journal of Geodesy.

[35]  F. N. Teferle,et al.  Integer ambiguity resolution in precise point positioning: method comparison , 2010 .

[36]  Harald Schuh,et al.  GAMP: An open-source software of multi-GNSS precise point positioning using undifferenced and uncombined observations , 2018, GPS Solutions.

[37]  Yang Gao,et al.  A NEW METHOD FOR CARRIER-PHASE–BASED PRECISE POINT POSITIONING , 2002 .

[38]  Pierre Héroux,et al.  Precise Point Positioning Using IGS Orbit and Clock Products , 2001, GPS Solutions.

[39]  P. Teunissen,et al.  On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlengt , 2015, Journal of Geodesy.