Multifrequency Algorithms for PPP: MAP3 · Multifrequency Algorithms for PPP: MAP3 MAP3 New and...
Transcript of 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
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Global Navigation Satellite Systems (GNSS)
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Designed in the 70sMilitary → they have provided a wide variety of services
Signals in 2 frequencies
Global Navigation Satellite Systems (GNSS)
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In development
Signals in 3 frequencies
Global Navigation Satellite Systems (GNSS)
Geodaetische Woche 2012 Hannover 09.10 – 11.10.2012
Designed in the 70sMilitary → they have provided a wide variety of services
Signals in 2 frequencies
GPS and GLONASS in modernization process
→ They will include the triple frequency
Global Navigation Satellite Systems (GNSS)
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
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Global Navigation Satellite Systems (GNSS)
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
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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.
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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
Geodaetische Woche 2012 Hannover 09.10 – 11.10.2012
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● 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)
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Precise Point Positioning (PPP)
● 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/
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Precise Point Positioning (PPP)
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● 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/
Precise Point Positioning (PPP)
Geodaetische Woche 2012 Hannover 09.10 – 11.10.2012
● 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/
Precise Point Positioning (PPP)
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● 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/
Precise Point Positioning (PPP)
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● 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/
Precise Point Positioning (PPP)
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● 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/
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
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Multifrequency Algorithms for PPP: MAP3
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MAP3 -1
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Undifferenced multifrequency observations:Code Pi
s
Phase Lis
s = 1, 2, …, ni = 1, 2, 3, ...
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MAP3 -1
Multifrequency Algorithms for PPP: MAP3
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Undifferenced multifrequency observations:Code Pi
s
Phase Lis
s = 1, 2, …, ni = 1, 2, 3, ...
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
Smoothed pseudodistan-ces ρs
Ionospheric delays J1Initial ambiguities βi
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MAP3 -1
Multifrequency Algorithms for PPP: MAP3
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MAP3 -2
Smoothed pseudodis-tances ρs
Ionospheric delays J1Initial ambiguities βi
Multifrequency Algorithms for PPP: MAP3
Station coordinates (δX, δY, δZ)Clock offset dtr
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MAP3 -2
Multifrequency Algorithms for PPP: MAP3
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)
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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
Multifrequency Algorithms for PPP: MAP3
Mathematical Model
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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
β2
β3)
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
For an observation period of nt epochs
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MAP3 -1
Multifrequency Algorithms for PPP: MAP3
Stochastic Model
νP : order of dm (20 cm)
νL : order of mm (2 mm)
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QP=(νP1
0 0
0 νP20
0 0 νP3
) QL=(νL1
0 0
0 νL20
0 0 νL3
)
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
Stochastic Model
νP : order of dm (20 cm)
νL : order of mm (2 mm)
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Not realistic → take into account sat. elevationNot realistic → take into account sat. elevation
QP=(νP1
0 0
0 νP20
0 0 νP3
) QL=(νL1
0 0
0 νL20
0 0 νL3
)
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
MAP3-1 expressions
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MAP3 -1
Multifrequency Algorithms for PPP: MAP3
MAP3-1 expressions
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Initial Phase ambiguities
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
MAP3-1 expressions
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Smoothed pseudoditancesIonospheric delays
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
MAP3-1 expressions
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Covariance matrices
MAP3 -1
Multifrequency Algorithms for PPP: MAP3
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
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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
Multifrequency Algorithms for PPP: MAP3
Mathematical Model
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(X0,Y0,Z0) : A priori station position
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Mathematical Model
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Int : identity matrixρ0 : a priori distance
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Stochastic Model
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MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Stochastic Model
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MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Stochastic Model
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MAP3 -2
Multifrequency Algorithms for PPP: MAP3
MAP3-2 expressions
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MAP3 -2
Multifrequency Algorithms for PPP: MAP3
MAP3-2 expressions
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Station coordinatesTropo delay
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
MAP3-2 expressions
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Station clock offset
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
MAP3-2 expressions
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Covariance matrices
MAP3 -2
Multifrequency Algorithms for PPP: MAP3
Combination of different satellite systems
ISB estimation
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MAP3 -2
Numerical Tests
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Scenario 2. GPS and GIOVE
Scenario 1. GPS double frequency
Numerical Tests
Observations from USN3 (IGS)
Scenario 1. GPS double frequency
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Numerical Tests
Observations from USN3 (IGS)
2-hours
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Scenario 1. GPS double frequency
Numerical Tests
Observations from USN3 (IGS)
2-hours
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21 different days
Positioning error with MAP3
Scenario 1. GPS double frequency
Numerical Tests
Observations from USN3 (IGS)
2-hours
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21 different days
Positioning error with MAP3
2 cm
Scenario 1. GPS double frequency
Numerical Tests
Observations from USN3 (IGS)
2-hours
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21 different days
Positioning error with MAP3
2 cm
4 cm
Scenario 1. GPS double frequency
Numerical Tests
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Scenario 1. GPS double frequency
Numerical Tests
2-hours
RMS of the error in positioning (cm)
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Scenario 1. GPS double frequency
Numerical Tests
24-hours
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Scenario 1. GPS double frequency
Numerical Tests
24-hours
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7 mm
Scenario 1. GPS double frequency
Numerical Tests
24-hours
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1.4 cm
7 mm
Scenario 1. GPS double frequency
Numerical Tests
24-hours
RMS of the error in positioning (cm)
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Scenario 1. GPS double frequency
Numerical Tests
● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b
Scenario 2. GPS and GIOVE
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Numerical Tests
● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b● 2-hours● Precise products from Galileo
Processing Center (GPC)
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Scenario 2. GPS and GIOVE
Numerical Tests
● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b● 2-hours● Precise products from Galileo
Processing Center (GPC)
GIOVE observations● ISB estimated● Electronic delays
corrected
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Scenario 2. GPS and GIOVE
Numerical Tests
● GESS stations● GPS P1, P2 + GIOVE E1, E5b, E5a+b● 2-hours● Precise products from Galileo
Processing Center (GPC)
GIOVE observations● ISB estimated● Electronic delays
corrected
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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)
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)
Scenario 2. GPS and GIOVE
Numerical Tests
GPS-only GPS+GIOVE
RMS of the error in positioning (cm)
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Scenario 2. GPS and 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
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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
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Thank you for your attention!Thank you for your attention!
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.
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Multifrequency Algorithms for PPP: MAP3
For an observation period of nt epochs
MAP3 -1
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Observations must be free from cycle slipsObservations must be free from cycle slips
Multifrequency Algorithms for PPP: MAP3
MAP3-1 expressions
MAP3 -1
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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
-1
D-1 = I3 + A2 M-1A2T QL
-1 M = A1T QP
-1 A1
Multifrequency Algorithms for PPP: MAP3MAP3 -2
Auxiliar expressions
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