Triple Frequency precise point positioning with multi-constellation - - PowerPoint PPT Presentation

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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

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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’

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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

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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 𝑄 = 𝛽1𝑄1 + 𝛽2𝑄2 + 𝛽3𝑄3 = 𝜍 + 𝑈 + 𝜁𝑄 𝜚 = 𝛽1𝜚1 + 𝛽2𝜚2 + 𝛽3𝜚3 = 𝜍 + 𝑈 + 𝜇𝑂∗ +𝜁𝜚

• Stochastic Model:
• Apply weighting based on satellite elevation angle
• assuming uncorrelated measurements with code noise 𝜏𝑄1

𝐻, 𝜏𝑄2 𝐻 and 𝜏𝑄5 𝐻,

and carrier phase noise 𝜏𝜚1

𝐻, 𝜏𝜚2 𝐻 and 𝜏𝜚5 𝐻

• 𝜏𝑄𝐻

2 = 𝛽1,𝐻 ∙ 𝜏𝑄1

𝐻

2

+ 𝛽2,𝐻 ∙ 𝜏𝑄2

𝐻

2

+ 𝛽3,𝐻 ∙ 𝜏𝑄5

𝐻

2

• 𝜏𝜚𝐻

2

= 𝛽1,𝐻 ∙ 𝜏𝜚1

𝐻

2

+ 𝛽2,𝐻 ∙ 𝜏𝜚2

𝐻

2

+ 𝛽3,𝐻 ∙ 𝜏𝜚5

𝐻

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 𝛽1 𝛽2 𝛽3 Noise Amp. Factor (𝜗) 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
• nly combinations. E.g. GPS L1/L2 and L1/L5

Θ12 = 𝛽1,12𝜚1 + 𝛽2,12𝜚2 + 𝛾1,12𝑄1 + 𝛾2,12𝑄2 = 𝜍 + 𝑈 + 𝛽1,12𝜇1𝑂1∗ + 𝛽2,12𝜇2𝑂2∗ +𝜁Θ12 Θ15 = 𝛽1,15𝜚1 + 𝛽2,25𝜚5 + 𝛾1,25𝑄1 + 𝛾2,25𝑄5 = 𝜍 + 𝑈 + 𝛽1,15𝜇1𝑂1∗ + 𝛽2,25𝜇5𝑂5∗ +𝜁Θ15

𝜚𝑗𝑗,12 = 𝑔

1 2

𝑔

1 2 − 𝑔 2 2 𝜚1 −

𝑔

2 2

𝑔

1 2 − 𝑔 2 2 𝜚2 = 𝜍 + 𝑈 +

𝑔

1 2

𝑔

1 2 − 𝑔 2 2 𝜇1𝑂1∗ −

𝑔

2 2

𝑔

1 2 − 𝑔 2 2 𝜇1𝑂2∗ + 𝜁𝜚

𝜚𝑗𝑗,15 = 𝑔

1 2

𝑔

1 2 − 𝑔 5 2 𝜚1 −

𝑔

5 2

𝑔

1 2 − 𝑔 5 2 𝜚5 = 𝜍 + 𝑈 +

𝑔

1 2

𝑔

1 2 − 𝑔 5 2 𝜇1𝑂1∗ −

𝑔

5 2

𝑔

1 2 − 𝑔 5 2 𝜇1𝑂5∗ + 𝜁𝜚

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 𝜏𝑄 = 0.2𝑛 and

𝜏𝜚 = 0.002𝑛

Department of Spatial Sciences - Ph.D. seminar, Manoj Deo April 16

Triple Frequency PPP Model 2…

GNSS Constellation Signal Combination 𝛽1 𝛽2 𝛾1 𝛾2 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 𝑄1 = 𝜍 + 𝐽 + 𝑈 + 𝜁𝑄1

𝑄2 = 𝜍 + 𝑗

1 2

𝑗

2 2 𝐽 + 𝑈 + 𝜁𝑄2

𝑄5 = 𝜍 + 𝑗

1 2

𝑗

5 2 𝐽 + 𝑈 + 𝜁𝑄5

𝜚1 = 𝜍 − 𝐽 + 𝜇1𝑂1∗ + 𝑈 + 𝜁𝜚1 𝜚2 = 𝜍 − 𝑗

1 2

𝑗

2 2 𝐽 + 𝜇2𝑂2∗ + 𝑈 + 𝜁𝜚2

𝜚5 = 𝜍 − 𝑗

1 2

𝑗

5 2 𝐽 + 𝜇5𝑂5∗ + 𝑈 + 𝜁𝜚5

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

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Validation and Testing

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Dual Freq. G

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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

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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

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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

• nly 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 Converge nce 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

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Conclusions and Future work