Triple Frequency precise point positioning with multi ... · Multi-constellation Biases •...

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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



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



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

2




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



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.

4




Triple Frequency PPP Model 1


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



Triple Frequency PPP Model 1…


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.


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



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


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


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




• 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


Validation and Testing


Dual Freq. G


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


Dual Freq. G


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


Dual Freq. G


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


Dual Freq. G


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


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)


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+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+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+C+E 0.017 0.005 0.015 17.1



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



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

Triple Frequency precise point positioning with multi ... · Multi-constellation Biases •...

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