triple frequency precise point positioning with multi ... · multi-constellation biases •...
TRANSCRIPT
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Manoj Deo & A/Prof Ahmed El-Mowafy
Triple Frequency precise point positioning with multi-constellation GNSS
International Global Navigation Satellite Systems Conference
6-8 December 2016
Department of Spatial Sciences
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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
1
International Global Navigation Satellite Systems Conference, 6-8 December 2016
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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
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International Global Navigation Satellite Systems Conference, 6-8 December 2016
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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’
3 International Global Navigation Satellite Systems Conference, 6-8 December 2016
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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.
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International Global Navigation Satellite Systems Conference, 6-8 December 2016
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Triple Frequency PPP Model 1
5 International Global Navigation Satellite Systems Conference, 6-8 December 2016
Triple frequency phase-only and code-only linear combination
Ionosphere-free, Least noise propagation, Geometry preserving 𝑃 = 𝛼1𝑃1 + 𝛼2𝑃2 + 𝛼3𝑃3 = 𝜌 + 𝑇 + 𝜀𝑃 𝜙 = 𝛼1𝜙1 + 𝛼2𝜙2 + 𝛼3𝜙3 = 𝜌 + 𝑇 + 𝜆𝑁∗ +𝜀𝜙
Stochastic Model: • Apply weighting based on satellite elevation angle
• assuming uncorrelated measurements with code noise 𝜎𝑃1𝐺, 𝜎𝑃2𝐺 and 𝜎𝑃5𝐺, and carrier phase noise 𝜎𝜙1𝐺, 𝜎𝜙2𝐺 and 𝜎𝜙5𝐺
• 𝜎𝑃𝐺2 = 𝛼1,𝐺 ∙ 𝜎𝑃1𝐺
2+ 𝛼2,𝐺 ∙ 𝜎𝑃2𝐺
2+ 𝛼3,𝐺 ∙ 𝜎𝑃5𝐺
2
• 𝜎𝜙𝐺2 = 𝛼1,𝐺 ∙ 𝜎𝜙1𝐺
2+ 𝛼2,𝐺 ∙ 𝜎𝜙2𝐺
2+ 𝛼3,𝐺 ∙ 𝜎𝜙5𝐺
2
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Triple Frequency PPP Model 1…
6 International Global Navigation Satellite Systems Conference, 6-8 December 2016
Significant improvements in noise compared to dual-frequency reference signals.
GNSS Constellation
Signal Combination
𝛼1 𝛼2 𝛼3 Noise Amp. Factor (𝜖)
Percentage 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 K2 (CDMA)
L1-L2-L3 2.359 142 -0.404 596 -0.954 546 2.577 -13.6%
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.
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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 = 𝛼1,12𝜙1 + 𝛼2,12𝜙2 + 𝛽1,12𝑃1 + 𝛽2,12𝑃2 = 𝜌 + 𝑇 + 𝛼1,12𝜆1𝑁1∗ + 𝛼2,12𝜆2𝑁2∗ +𝜀Θ12 Θ15 = 𝛼1,15𝜙1 + 𝛼2,25𝜙5+ 𝛽1,25𝑃1 + 𝛽2,25𝑃5 = 𝜌 + 𝑇 + 𝛼1,15𝜆1𝑁1∗ + 𝛼2,25𝜆5𝑁5∗ +𝜀Θ15
𝜙𝑖𝑖,12 =𝑓12
𝑓12 − 𝑓22𝜙1 −
𝑓22
𝑓12 − 𝑓22𝜙2 = 𝜌 + 𝑇 +
𝑓12
𝑓12 − 𝑓22𝜆1𝑁1∗ −
𝑓22
𝑓12 − 𝑓22𝜆1𝑁2∗ + 𝜀𝜙
𝜙𝑖𝑖,15 =𝑓12
𝑓12 − 𝑓52𝜙1 −
𝑓52
𝑓12 − 𝑓52𝜙5 = 𝜌 + 𝑇 +
𝑓12
𝑓12 − 𝑓52𝜆1𝑁1∗ −
𝑓52
𝑓12 − 𝑓52𝜆1𝑁5∗ + 𝜀𝜙
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Triple Frequency PPP Model 2
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Stochastic model: consider correlations between measurements (reaches >0.7) Deo and El-Mowafy (2016).
Resulting coefficients measurement noise (m), using 𝜎𝑃 = 0.2𝑚 and 𝜎𝜙 = 0.002𝑚
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Triple Frequency PPP Model 2…
GNSS Constellation
Signal Combination
𝛼1 𝛼2 𝛽1 𝛽2 Noise (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
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PPP with individual uncombined signals • Use raw phase and code measurements without linear combinations • Each satellite introduces 6 measurements (3 code and 3 phase) • Use extra measurements to solve for the ionosphere error • Perform between satellite single differencing (BSSD) to eliminate
receiver biases
𝑃1 = 𝜌 + 𝐼 + 𝑇 + 𝜀𝑃1
𝑃2 = 𝜌 + 𝑖12
𝑖22𝐼 + 𝑇 + 𝜀𝑃2
𝑃5 = 𝜌 + 𝑖12
𝑖52𝐼 + 𝑇 + 𝜀𝑃5
𝜙1 = 𝜌 − 𝐼 + 𝜆1𝑁1∗ + 𝑇 + 𝜀𝜙1
𝜙2 = 𝜌 − 𝑖12
𝑖22𝐼 + 𝜆2𝑁2∗ + 𝑇 + 𝜀𝜙2
𝜙5 = 𝜌 − 𝑖12
𝑖52𝐼 + 𝜆5𝑁5∗ + 𝑇 + 𝜀𝜙5
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Triple Frequency PPP Model 3
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• Test data simulated for Hobart (HOB2), Alice Springs (ALIC), Yarragadee (YAR2) and Townsville (TOW2)
• Realistic biases (receiver clock, troposphere, ionosphere), measurement noise. Epoch Rate 30sec.
• Model 1 tested • Triple frequency phase-only and code-only linear combination • GPS (G), Beidou (C) and Galileo (E)
• Performance testing • Convergence: Time to attain and maintain 3-dimensional accuracy of 5cm • Precision: std. Accuracy: RMSE after convergence • Compare standard dual frequency model with triple frequency G, G+C,
G+C+E
• Analyse hourly blocks of 1-days data that converged
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Validation and Testing
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Dual Freq. G
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Results - ALIC
Triple Freq. G
Triple Freq. G+C
Triple Freq. G+C+E
Triple freq. G+C best performance with improvement of 5mm in RMSE East and 5.7 minutes in convergence time
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Dual Freq. G
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Results – HOB2
Triple Freq. G
Triple Freq. G+C
Triple Freq. G+C+E
Triple freq. G+C+E best performance with improvement of 4mm in RMSE up and 7.4 minutes in convergence time
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Dual Freq. G
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Results – TOW2
Triple Freq. G
Triple Freq. G+C
Triple Freq. G+C+E
Triple freq. G+C+E best performance with improvement of 4mm in RMSE up and 7.7 minutes in convergence time
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Dual Freq. G
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Results – YAR2
Triple Freq. G
Triple Freq. G+C
Triple Freq. G+C+E
Triple freq. G+C+E best performance with improvement of 11.5 minutes in convergence time. No noticeable improvement in accuracy
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Mean RMSE and convergence times with hourly blocks of data for the standard dual-frequency GPS only solution (L1-L2 G) and the triple frequency solutions for GPS only, GPS+Beidou (G+C) and GPS+Beidou+Galileo (G+C+E)
Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Summary of Results Site Solution Mean
RMSE East (m)
Mean RMSE
North (m)
Mean RMSE Up
(m)
Mean Convergence time
(min) ALIC L1-L2 G 0.017 0.006 0.015 26.9
Triple freq. G 0.018 0.006 0.014 24.9 Triple freq. G+C 0.012 0.007 0.016 21.2
Triple freq. G+C+E 0.012 0.007 0.018 22.1 HOB2 L1-L2 G 0.015 0.006 0.021 31.9
Triple freq. G 0.012 0.007 0.017 25.8 Triple freq. G+C 0.012 0.008 0.018 26.8
Triple freq. G+C+E 0.014 0.007 0.017 24.5 TOW2 L1-L2 G 0.014 0.004 0.019 30.9
Triple freq. G 0.012 0.005 0.015 26.3 Triple freq. G+C 0.012 0.006 0.017 24.4
Triple freq. G+C+E 0.014 0.007 0.015 23.2 YAR2 L1-L2 G 0.017 0.007 0.015 28.6
Triple freq. G 0.016 0.006 0.019 30.0 Triple freq. G+C 0.013 0.006 0.015 18.2
Triple freq. G+C+E 0.017 0.005 0.015 17.1
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Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16
Overall Results
Site Solution Mean RMSE
East (m)
Mean RMSE North
(m)
Mean RMSE Up (m)
Mean Converg
ence time (min)
Overall L1-L2 G 0.016 0.006 0.018 29.6 Triple freq. G 0.014 0.006 0.016 26.5
Triple freq. G+C 0.012 0.007 0.016 23.0 Triple freq.
G+C+E 0.014 0.007 0.016 22.0
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Presented a critique on biases in MFMC data
Three triple frequency PPP models with float ambiguity convergence for reducing convergence time
Validation with hourly solutions at four sites with a days data • Compared standard dual-frequency G only with triple frequency G, G+C, G+C+E
Improvements in positioning accuracy (by up to 5mm RMSE) and convergence times (by up to 11.5 minutes) noted at all four sites
Overall, G+C+E gave the best performance • Improvement of 7.6 minutes in convergence time • Improvements of 2mm in RMSE East and Up
Future work will consider PPP-AR with MFMC data
17 Curtin Spatial Sciences Colloquium – 22 Nov 2016
Conclusions and Future work