Multifrequency Algorithms for PPP: MAP3 · Multifrequency Algorithms for PPP: MAP3 MAP3 New and...

Multifrequency Algorithms Multifrequency Algorithms forfor PPP: MAP3 PPP: MAP3

B. Moreno Monge (1), G. Rodriguez Caderot (2) and M. C. de Lacy (3)

(1) GFZ German Research Center for Geosciences(2) University Complutense of Madrid (Spain)(3) University of Jaen (Spain)

Outline

(1)Global Navigation Satellite Systems (GNSS)

(2)Precise Point Positioning (PPP)

(3)Multifrequency Algorithms for PPP: MAP3

(4)Numerical Tests

(5)Conclusions

Geodaetische Woche 2012 Hannover 09.10 – 11.10.2012

Global Navigation Satellite Systems (GNSS)

Designed in the 70sMilitary → they have provided a wide variety of services

Signals in 2 frequencies

In development

Designed in the 70sMilitary → they have provided a wide variety of services

GPS and GLONASS in modernization process

→ They will include the triple frequency

System Current # sat Future # sat Frequencies Full Capability

GLONASS 23 24 G1 G2 G3 2011

Galileo 2 + 2 Giove 30 E1 E5 E6 2014

Mod. GPS 9 + 22 32 L1 L2 L5 2018

COMPASS 9 35 B1 B2 B3 2020

System Current # sat Future # sat Frequencies Full Capability

GLONASS 23 24 G1 G2 G3 2011

Galileo 2 + 2 Giove 30 E1 E5 E6 2014

Mod. GPS 9 + 22 32 L1 L2 L5 2018

COMPASS 9 35 B1 B2 B3 2020

Compatible and interoperable

→ allow the users to combine signals from different systems for their position determination

Precise Point Positioning (PPP)

● PPP is a positioning technique providing precise and accurate receiver position from undifferenced GNSS code and phase observations and precise satellite products.

● Great flexibility● Accurate results

● Great flexibility● Accurate results● In general, the accuracy in the

PPP is:At dm-level in kinematic mode

At cm-level in static mode (mm-level after 24 h observation)

● PPP software:

– CSRS-PPP (NRCan) www.geod.nrcan.gc.ca

– MagicGNSS (GMV) http://magicgnss.gmv.com/

– APPS (JPL) http://apps.gdgps.net/

– BSW v.5.0 http://www.bernese.unibe.ch/

● PPP software:

Only able to process GPS and GLONASS data in 1 or 2 frequenciesApply the ionofree linear combination → limits the positioning to the double frequency

It is necessary to design new algorithms adapted to the characteristics of the future GNSS scenario

Multifrequency Algorithms for PPP: MAP3

MAP3MAP3

New and original algorithmsNew and original algorithms

to perform to perform static PPPstatic PPP

from from multifrequency multifrequency observationsobservations

Allow to combine observations Allow to combine observations from different satellite systemsfrom different satellite systems

They can be used in the future GNSS scenario: Galileo, modernized GPS, GLONASS, They can be used in the future GNSS scenario: Galileo, modernized GPS, GLONASS, etcetc

MAP3 -1

MAP3 -2

Undifferenced multifrequency observations:Code Pi

Phase Lis

s = 1, 2, …, ni = 1, 2, 3, ...

MAP3 -1

Undifferenced multifrequency observations:Code Pi

Phase Lis

s = 1, 2, …, ni = 1, 2, 3, ...

MAP3 -1

Smoothed pseudodistan-ces ρs

Ionospheric delays J1Initial ambiguities βi

MAP3 -1

MAP3 -2

Smoothed pseudodis-tances ρs

Ionospheric delays J1Initial ambiguities βi

Station coordinates (δX, δY, δZ)Clock offset dtr

MAP3 -2

GPS observables (Euler and Goad, 1991)

Pi(t), Li (t): code and phase

ρ(t) : pseudodistances

J1(t) : ionosferic delay in f1

βi : initial ambiguities (constant, real)

Pi(t)=ρ(t)+k1i J 1(t)+νP i=1, 2Li(t)=ρ(t)−k1i J 1(t)+βi+νL

ρ(t)=D (t )+c (dtr−dt s)+Trop

MAP3 -1

Mathematical Model

P (t )=A1ξ (t)+νP

L(t)=A2ξ (t)+β+νL

P (t )=(P1(t )P2(t )P3(t )

) L(t )=(L1(t)L2(t)L3(t)

) A1=(1 11 k12

1 k13) A2=(

1 −11 −k 12

1 −k 13) ξ (t )=( ρ(t)

J 1(t)) β=(β1

MAP3 -1

For an observation period of nt epochs

MAP3 -1

Stochastic Model

νP : order of dm (20 cm)

νL : order of mm (2 mm)

QP=(νP1

0 νP20

0 0 νP3

) QL=(νL1

0 νL20

0 0 νL3

MAP3 -1

Stochastic Model

νP : order of dm (20 cm)

νL : order of mm (2 mm)

Not realistic → take into account sat. elevationNot realistic → take into account sat. elevation

QP=(νP1

0 νP20

0 0 νP3

) QL=(νL1

0 νL20

0 0 νL3

MAP3 -1

MAP3-1 expressions

MAP3 -1

MAP3-1 expressions

Initial Phase ambiguities

MAP3 -1

MAP3-1 expressions

Smoothed pseudoditancesIonospheric delays

MAP3 -1

MAP3-1 expressions

Covariance matrices

MAP3 -1

Position estimation

(Xs,Ys,Zs,dts) : Precise products must be used

Trops: is corrected with a model (Hopfield, Saastamoinen,etc)

→ a correction must be estimated every 2 hours ZWD

MAP3 -2

ρs(t)=Ds(t)+c (dt r(t)−dt s(t))+Trops(t)+ν

Ds=√(X s

−X r)2+(Y s

−Y r)2+(Z s

−Z r)2

Mathematical Model

(X0,Y0,Z0) : A priori station position

MAP3 -2

Mathematical Model

Int : identity matrixρ0 : a priori distance

MAP3 -2

Stochastic Model

MAP3 -2

Stochastic Model

MAP3 -2

Stochastic Model

MAP3 -2

MAP3-2 expressions

MAP3 -2

MAP3-2 expressions

Station coordinatesTropo delay

MAP3 -2

MAP3-2 expressions

Station clock offset

MAP3 -2

MAP3-2 expressions

Covariance matrices

MAP3 -2

Combination of different satellite systems

ISB estimation

MAP3 -2

Numerical Tests

Scenario 2. GPS and GIOVE

Scenario 1. GPS double frequency

Numerical Tests

Observations from USN3 (IGS)

Numerical Tests

2-hours

Numerical Tests

2-hours

21 different days

Positioning error with MAP3

Numerical Tests

2-hours

21 different days

Numerical Tests

2-hours

21 different days

Numerical Tests

2-hours

RMS of the error in positioning (cm)

Numerical Tests

24-hours

Numerical Tests

24-hours

Numerical Tests

24-hours

1.4 cm

Numerical Tests

24-hours

Numerical Tests

● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b

Numerical Tests

● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b● 2-hours● Precise products from Galileo

Processing Center (GPC)

Numerical Tests

GIOVE observations● ISB estimated● Electronic delays

corrected

Numerical Tests

GIOVE observations● ISB estimated● Electronic delays

corrected

Systematic variations have been found in the GESS code observations depending on satellite direction and signal (Crisci et al., 2007) and a low multipath rejection (Simsky et al., 2008)

Numerical Tests

GPS-only GPS+GIOVE

Conclusions

● MAP3 constitutes a new and original strategy to perform static PPP from multi-system and multifrequency observations

● Its flexibility is an advantage w.r.t the current PPP SW● MAP3 are able to process modernized GPS and

Galileo/GIOVE data along with IGS and GPC products

● In general, MAP3 provides an accuracy in positioning of 2.5 cm after 2 hours observation and of 7 mm in 1 day

● These results are at the same level as the online PPP programs and better results are obtained in short observation periods

Conclusions

● When processing GESS observations, the error in the estimated positions reached up to 15 cm, due to the systematic variations detected in the code observations and the high multipath, problems that will be solved after the installation of new antennas

● The combination of GPS and GIOVE data improved the accuracy in the positioning in almost 2 cm in every component with respect to the GPS-only solution

Continue analysing the improvements in the positioning due to the introduction of the new Galileo satellites

Analyse the improvement in positioning with the triple frequency

Study the influence and correction of electronic biases

Thank you for your attention!Thank you for your attention!

beatrizmorenomonge@gmail.comgrc@mat.ucm.esmclacy@ujaen.es

References

● M. Crisci, M. Hollreiser, M. Falcone, M. Colina, and J. Giraud. GIOVE mission sensor station performance characterization: overview of the results. In ION GNSS, 2007.

● A. Simsky, D. Mertens, J. M. Sleewaegen, M. Hollreiser, and M. Crisci. Experimental Results for theMultipath Performance of Galileo Signals Transmitted by GIOVE-A Satellite. International Journal of Navigation and Observation, Article ID 416380, 2008. doi: 10.1155/2008/41638.

● H. J. Euler and C. C. Goad. On optimal filtering of GPS dual frequency observations without using orbit information. Bulletin Geodesique, 65:130–143, 1991.

For an observation period of nt epochs

MAP3 -1

Observations must be free from cycle slipsObservations must be free from cycle slips

MAP3-1 expressions

MAP3 -1

L, P: mean of phase and code observationsN-1 = M-1 – M-1 A2

T QL-1 (I3 + A2 M-1A2

T QL-1)-1 A2 M

D-1 = I3 + A2 M-1A2T QL

-1 M = A1T QP

Multifrequency Algorithms for PPP: MAP3MAP3 -2

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