Contribution of Galileo Observations to PPP Accuracy Enhancement - - PowerPoint PPT Presentation

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Contribution of Galileo Observations to PPP Accuracy Enhancement

Mahmoud Abd Rabbou and Ahmed El-Rabbany

Department of Civil Engineering, Ryerson University Toronto, Canada Arab Institute of Navigation (AIN) Conference MELAHA 2014

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OUTLINES

Introduction Research objectives Mathematical models. Results and analysis Conclusion

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INTRODUCTION

 Accurate GNSS positioning solution can be obtained through carrier-phase

• bservables in differential mode, involving two or more receivers. However, the

requirement of a base station is usually problematic for some applications due to the limitation of the operational range of the system.

 Fortunately, comparable positioning accuracy, without requiring extra infrastructure,

can be achieved through a technique known as precise point positioning (PPP).

 PPP uses either un-differenced or between-satellite single-differenced carrier phase

and pseudorange observations from a single receiver. This, however, requires the availability of precise orbit and clock data.

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INTRODUCTION

 However, in dense urban areas, the number of visible satellites is usually reduced,

which might affect the accuracy of the PPP solution. To overcome this limitation, PPP solution can be enhanced by combining the observations of multiple GNSS systems.

 Currently, GPS system is the most widespread GNSS system and the only fully

• perational system.

 Galileo satellite navigation system is being built by the European Union (EU) and

European Space Agency (ESA).



The first two (out of four) operational satellites were launched to validate the system on October 21, 2011.

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INTRODUCTION

 The remaining two operational satellites were launched on October 12, 2012, which

made it possible to examine Galileo as a separate satellite navigation system.

 Additional satellites are expected to be launched in the future to make it a

constellation of 30 satellites.

 Combining the observations from GPS and Galileo makes it possible to enhance the

positioning solution under poor satellite visibility or weak constellation geometry in urban areas.

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RESEARCH OBJECTIVES

 This research aims to;  Develop a mathematical model for the combined GPS/Galileo PPP

for precise positioning

 Investigate the accuracy of the first stand alone Galileo PPP using

the four operational Galileo satellites launched

 Investigate the accuracy of the combined GPS/ Galileo PPP in static

mode.

 Investigate the accuracy of the combined GP/Galileo PPP in

Kinematic mode

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MATHEMATICAL MODELS

• The mathematical model of ionosphere-free PPP can be written as (Hofmann-

Wellenhof et. al, 2008):

2 2 1 2 1 1 2 2 3 2 2 2 1 2 s s s r r1 r

f P f P P = =ρ +cdt -cdt +T+c(Ad -Bd ) c(Ad -Bd )+e f f   

2 2 1 2 1 1 2 2 3 2 2 2 1 2 s s s r r1 r

f f = =ρ +cdt -cdt +T+c(A

• B

) c(A

• B

)+( N )+ f f            

• The ionosphere-free linear combinations of GPS and Galileo observations can be

written as:

1 2 3 2 s s s G G r G G g r1 g r G g g G G

P =ρ +cdt -cdt +T +c[A d

• B d

] -c[A d

• B d

] +e

1 2 3 2 s s s E E r E E e r1 e r E e e E sys E

P =ρ +cdt -cdt +T +c[A d -B d ] -c[A d -B d ] +GE e 

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MATHEMATICAL MODELS

1 2 3

G

s s s G G r G G g r1 g r2 G g g G G

=ρ +cdt -cdt +T +c[A

• B

] -c[A

• B

] +( N ) +       

1 2 3 2 s s s E E r E E e r1 e r E e e E sys E E

=ρ +cdt -cdt +T +c[A

• B

] -c[A

• B

] +GE ( N ) +        

Which may be written again in a more compact and simplified form as:

3 r s s G G r G G G G p1

P =ρ +c[dt +IFCD ]-c[dt

• IFCD

]+T +e

3 r s s E E r G E E E E E

P =ρ +c[dt +IFCD ]-c[dt

• IFCD

]+T +c[ISCB ]+e

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G

r s s r s G G r G G G G G

=ρ +c[dt +IFCD ]-c[dt

• IFCD

]+T +( N+IFBD -IFBD ) +   

3 r s s r s E E r G E E E E E E

=ρ +c[dt +IFCD ]-c[dt

• IFCD

]+T +c[ISCB ]+( N+IFBD -IFBD ) +   

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1 1 1 1 1 1 1 k,k k,k k T k,k k,k k k,k

x x P P  

      

      

1 1 1 1 1 1 T T k k,k k k k,k k k k k,k k k k k,k k k k ) k,k

K P H ( H P H R ) x x K ( Z H x ) P ( I K H P    

     

         

Extended Kalman filter (EKF) Apply linearization to the nonlinear models using first order Tylor expansion and neglecting higher order terms.  Restrict the probability distribution of measurement models to Gaussian distribution. Prediction step Update step

MATHEMATICAL MODELS

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RESULTS AND ANALYSIS

• Data from three GNSS stations, namely BRST, BRUX and DLF1, were selected

to assess the positioning accuracy of Galileo-only static PPP considering the four

• perational Galileo satellites.

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RESULTS AND ANALYSIS

• The un-differenced ionosphere-free GPS/Galileo PPP accuracy for station DLF1.

The contribution of Galileo observations can be considered marginal because of the limited number of available Galileo satellites at present, in comparison the number of visible GPS satellites.

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RESULTS AND ANALYSIS

• The GPS/Galileo internal system bias (ISB) for the four stations.

Although the same receiver type was utilized at the four stations (Trimble R9), the GPS/Galileo ISB shows different values, which indicate that the ISB is receiver firmware-dependent.

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RESULTS AND ANALYSIS

• A vehicular test was conducted to evaluate the performance of the developed

combined GPS/Galileo PPP model.

• The test was carried out in the downtown core of Kingston, Ontario, on

December 12, 2012 (DOY 347), under challenging scenarios for satellite navigation availability.

• The positioning accuracy is assessed referenced to carrier phase-based

differential GNSS (DGNSS) solution.

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RESULTS AND ANALYSIS

GPS/Galileo positioning accuracy using un-differenced ionosphere-free model

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CONCLUSION

 The contribution of Galileo observations to PPP accuracy enhancement has been

investigated in this research.



The accuracy of Galileo-only un-differenced ionosphere-free PPP model has been investigated using data from MGEX IGS stations.



It has been shown that Galileo-only PPP can achieve decimeter-level accuracy. However, due to the limited number of available satellites and the presence of code biases, the solution convergence time exceeds the one-hour level.



The mathematical model for combined GPS/Galileo PPP has also been developed for both static and kinematic applications.



It has been shown that the contribution of Galileo observations to the PPP accuracy and convergence time is insignificant due to the limited number of Galileo satellites in comparison with those of GPS..

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Thanks Questions