Department of Spatial Sciences Triple Frequency precise point positioning with multi-constellation GNSS Manoj Deo & A/Prof Ahmed El-Mowafy International Global Navigation Satellite Systems Conference 6-8 December 2016 Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
Outline Introduction to Multi-Frequency Multi-constellation (MFMC) PPP Modelling of Biases • Single constellation biases • Multi-constellation biases Triple Frequency PPP Models • Functional and Stochastic Validation and Testing • Test data, analysis results • GPS+Beidou+Galileo Conclusions and future work Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 1 CRICOS Provider Code 00301J
Introduction to PPP PPP originally presented by Zumberge et al. 1997 • Dual frequency, single constellation model • Widely used for real-time applications e.g. mining, agriculture, construction surveying • Drawback : requires float Ambiguity Convergence of typically 30min • Various enhancements introduced over the years, e.g. PPP-AR. Convergence time remains an issue This Contribution : Use MFMC (>2 freq.) data to develop enhanced PPP models with reduced convergence time Focus on float ambiguity convergence • PPP-AR considered in future research Novel triple frequency linear combinations Compare and evaluate performance Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 2 CRICOS Provider Code 00301J
Modelling of Biases Models for cm-mm level errors: solid earth tide, ocean tide, atmospheric loading, phase wind-up, satellite antenna phase centre offset, relativity. Troposphere: model hydrostatic and estimate wet component Ionosphere: form iono-free combinations or estimate with multi-frequency data Single Constellation Biases • Satellite and receiver hardware biases: affects phase and code. Digital delays in the signal generator, signal distortion, etc. Removed at receiver end by BSSD. Satellite end stable over typical PPP session • Differential Code Biases (DCB) : differences in hardware bias due to frequency difference. Not required if using iono-free combination of ‘reference signals’ Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 3 CRICOS Provider Code 00301J
Modelling of Biases Single Constellation Biases… • Initial Fractional Phase Bias (IFPB): exist in satellite and receiver and <1cycle. Constant for each session; reset when receiver is switched off and on. Removed at receiver end by BSSD • Differential Phase Biases (DPB): due to phase hardware bias differing for each frequency. Inseparable from IFPB, combined as one term. • Lumped with non-integer carrier phase ambiguity term. PPP-AR requires accurate calibration. Multi-constellation Biases • Inter-System Time Bias (ISTB): due to each constellation having own timescales. Accounted for by: 1. estimating a separate bias for each system, or 2. estimating the bias for one system and then estimating the differences for other systems with reference to this system • Inter System Biases (ISB): Due to signals from different constellations having different hardware biases (even though having same frequency). • Estimate as a parameter or BSSD within same constellation. Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 4 CRICOS Provider Code 00301J
Triple Frequency PPP Model 1 Triple frequency phase-only and code-only linear combination Ionosphere-free, Least noise propagation, Geometry preserving 𝑄 = 𝛽 1 𝑄 1 + 𝛽 2 𝑄 2 + 𝛽 3 𝑄 3 = 𝜍 + 𝑈 + 𝜁 𝑄 𝜚 = 𝛽 1 𝜚 1 + 𝛽 2 𝜚 2 + 𝛽 3 𝜚 3 = 𝜍 + 𝑈 + 𝜇𝑂 ∗ + 𝜁 𝜚 Stochastic Model: • Apply weighting based on satellite elevation angle assuming uncorrelated measurements with code noise 𝜏 𝑄 1 𝐻 , 𝜏 𝑄 2 𝐻 and 𝜏 𝑄 5 • 𝐻 , and carrier phase noise 𝜏 𝜚 1 𝐻 , 𝜏 𝜚 2 𝐻 and 𝜏 𝜚 5 𝐻 2 2 2 2 = 𝛽 1 , 𝐻 ∙ 𝜏 𝑄 1 𝜏 𝑄 𝐻 + 𝛽 2 , 𝐻 ∙ 𝜏 𝑄 2 + 𝛽 3 , 𝐻 ∙ 𝜏 𝑄 5 • 𝐻 𝐻 𝐻 2 2 2 2 𝜏 𝜚 𝐻 = 𝛽 1 , 𝐻 ∙ 𝜏 𝜚 1 + 𝛽 2 , 𝐻 ∙ 𝜏 𝜚 2 + 𝛽 3 , 𝐻 ∙ 𝜏 𝜚 5 • 𝐻 𝐻 𝐻 Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 5 CRICOS Provider Code 00301J
Triple Frequency PPP Model 1… Significant improvements in noise compared to dual- frequency reference signals. 𝛽 1 𝛽 2 𝛽 3 GNSS Signal Noise Amp. Percentage Factor ( 𝜗 ) Constellation Combination change GPS L1-L2-L5 2.326 944 -0.359 646 -0.967 299 2.546 -14.5% QZSS L1-LEX-L5 2.269 122 -0.024 529 -1.244 592 2.588 -13.1% Galileo E1-E5a-E5b 2.314 925 -0.836 269 -0.478 656 2.507 -3.1% BeiDou B1-B3-B2 2.566 439 -0.337 510 -1.228 930 2.865 -1.1% GLONASS L1-L2-L3 2.359 142 -0.404 596 -0.954 546 2.577 -13.6% K2 (CDMA) Coefficients for triple-frequency linear combinations for different GNSS constellations and signals. Percentage change in noise compared to dual-frequency ‘reference signals’. For GLONASS K2, the L1/L2 CDMA assumed as the reference signals. Curtin University is a trademark of Curtin University of Technology International Global Navigation Satellite Systems Conference, 6-8 December 2016 CRICOS Provider Code 00301J Curtin University is a trademark of Curtin University of Technology 6 CRICOS Provider Code 00301J
Triple Frequency PPP Model 2 Refined Dual Frequency Mixed code-carrier linear combination • Same properties as model 1 (iono-free, low noise, geometry preserving) • Use two proposed combinations, with dual frequency iono-free phase only combinations. E.g. GPS L1/L2 and L1/L5 Θ12 = 𝛽 1 , 12 𝜚 1 + 𝛽 2 , 12 𝜚 2 + 𝛾 1 , 12 𝑄 1 + 𝛾 2 , 12 𝑄 2 = 𝜍 + 𝑈 + 𝛽 1 , 12 𝜇 1 𝑂1 ∗ + 𝛽 2 , 12 𝜇 2 𝑂2 ∗ + 𝜁 Θ12 Θ15 = 𝛽 1 , 15 𝜚 1 + 𝛽 2 , 25 𝜚5 + 𝛾 1 , 25 𝑄 1 + 𝛾 2 , 25 𝑄5 = 𝜍 + 𝑈 + 𝛽 1 , 15 𝜇 1 𝑂1 ∗ + 𝛽 2 , 25 𝜇 5 𝑂5 ∗ + 𝜁 Θ15 2 2 2 2 𝑔 𝑔 𝑔 𝑔 2 𝜇 1 𝑂1 ∗ − 2 𝜇 1 𝑂2 ∗ + 𝜁 𝜚 1 2 1 2 𝜚 𝑗𝑗 , 12 = 2 𝜚 1 − 2 𝜚 2 = 𝜍 + 𝑈 + 2 − 𝑔 2 − 𝑔 2 − 𝑔 2 − 𝑔 𝑔 𝑔 𝑔 𝑔 1 2 1 2 1 2 1 2 2 2 2 2 𝑔 𝑔 𝑔 𝑔 2 𝜇 1 𝑂1 ∗ − 2 𝜇 1 𝑂5 ∗ + 𝜁 𝜚 1 1 5 5 𝜚 𝑗𝑗 , 15 = 2 𝜚 1 − 2 𝜚5 = 𝜍 + 𝑈 + 2 − 𝑔 2 − 𝑔 2 − 𝑔 2 − 𝑔 𝑔 𝑔 𝑔 𝑔 1 1 1 1 5 5 5 5 Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16 Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
Triple Frequency PPP Model 2… Stochastic model: consider correlations between measurements (reaches >0.7) Deo and El-Mowafy (2016). Resulting coefficients measurement noise (m), using 𝜏 𝑄 = 0. 2𝑛 and 𝜏 𝜚 = 0. 002𝑛 𝛽 1 𝛽 2 𝛾 1 𝛾 2 GNSS Signal Noise Constellation Combination (m) GPS L1-L2 2.529802 -1.533226 0.001509 0.001915 0.006 GPS L1-L5 2.250109 -1.252675 0.001108 0.001458 0.005 GPS L2-L5 10.078988 -9.169588 0.044338 0.046263 0.030 QZSS L1-LEX 2.905273 -1.910056 0.002150 0.002632 0.007 QZSS LEX-L2 10.329707 -9.426643 0.047481 0.049456 0.031 QZSS LEX-L5 6.166649 -5.194059 0.013137 0.014273 0.017 BeiDou B1-B2 2.472483 -1.475721 0.001422 0.001816 0.006 BeiDou B1-B3 2.917418 -1.922248 0.002173 0.002657 0.007 BeiDou B2-B3 -8.209041 9.138934 0.035920 0.034186 0.026 Galileo E1-E5a 2.250109 -1.252675 0.001108 0.001458 0.005 Galileo E1-E5b 2.408595 -1.411632 0.001327 0.001709 0.006 Galileo E5a-E5b -11.70299 12.514784 0.095313 0.092891 0.043 GLONASS K2 L1-L2 2.533086 -1.536521 0.001514 0.001921 0.006 GLONASS K2 L1-L3 2.280974 -1.283628 0.001149 0.001506 0.005 GLONASS K2 L2-L3 10.812700 -9.923189 0.054208 0.056281 0.033 Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16 Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
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