Case study for the IGS ultra-rapid orbit requirements Jan Douša Miami Beach, June 2-6, 2008

Case study for the IGS ultra-rapid Case study for the IGS ultra-rapid

orbit requirementsorbit requirements

Jan DoušaJan Douša

MiamiMiami Beach Beach, June 2-6, 2008, June 2-6, 2008

Miami Beach, June 2-6, 2008 2

OutlineOutline

• quality of IGS ultra-rapid orbit predictionquality of IGS ultra-rapid orbit prediction

• effect of ephemeris errors on ZTD (PPP case)effect of ephemeris errors on ZTD (PPP case)

• effect in network solutioneffect in network solution

• simulation in network analysissimulation in network analysis

• summarysummary


Monitoring Monitoring the the quality of IGU quality of IGU orbitsorbits

- IGU w.r.t IGR orbitsIGU w.r.t IGR orbits- comparison in terrestrial system comparison in terrestrial system afterafter Helmert Helmert

transftransformationormation- 3 3 Helmert Helmert rotations estimated epoch by epoch (15min) rotations estimated epoch by epoch (15min)

forfor relevant relevant satellites satellites only only- fitted portion compared fitted portion compared inin 0-0-2424 hhoursours- predicted portion compared on hourly basis (1,2,3,4,.., predicted portion compared on hourly basis (1,2,3,4,..,

23)23)- monthly orbit prediction statistics evaluatedmonthly orbit prediction statistics evaluated- accuracy code validated with IGU x IGR orbit differencesaccuracy code validated with IGU x IGR orbit differences

the the orbit qualityorbit quality and and the the accuracy codesaccuracy codes validated validated separatelyseparately


2004-2008 time-series2004-2008 time-series of IGU of IGU orbit orbit predictiopredictionnss


two times per year

every satellite undergoe

s eclipsingperiod

(in (in yellow)yellow)

Eclipsing periodsEclipsing periods

satellite G15 upgraded

plots generated from the IGS ACC’s IGUxIGR comparison summary tables


Orbit quality dependance on the Orbit quality dependance on the predictiopredictionn

orbit accuracy with respect to the

prediction interval (monthly statistics)(monthly statistics)

GPS Block IIR-MGPS Block IIR-M

GPS Block IIAGPS Block IIA

GPS Block IIAGPS Block IIA

eclipsing period

normal situation


Accuracy code validation (6h Accuracy code validation (6h prediction)prediction)

satellite G04:

eclipsing

satellite G30:

maintenance


Effect of ephemeris errors on PPP Effect of ephemeris errors on PPP ZTDZTD

Basic GPS carrier phase observable (scaled to distance):Basic GPS carrier phase observable (scaled to distance):

LLrereccsatsat = = recrec

satsat + c. + c.satsat + c. + c.recrec + + .n.nrecrecsatsat + + IONION + + TRPTRP + + rerecc

satsat

recrecsatsat .. .. receiver-satellite distance in vacuumreceiver-satellite distance in vacuum

TRPTRP .. .. troposphere path delay we approximate astroposphere path delay we approximate as 1/cos(z) * ZTD 1/cos(z) * ZTD

The ephemeris error is projected into the observables via a unit vector The ephemeris error is projected into the observables via a unit vector directing from receiver to satellite:directing from receiver to satellite:

RRrecrecsatsat / |/ |RRrecrec

satsat| | XXsatsat = = ee recrecsatsat XXsatsat

= = ee recrecsatsat RRzz ( (satsat) R) Rzz ( (satsat) . ) . XXRACRAC

satsat

We are interested in Radial/Along-track/Cross-track component errors, but we We are interested in Radial/Along-track/Cross-track component errors, but we distinct only Radial and Tangential (Along-track + Cross-track) distinct only Radial and Tangential (Along-track + Cross-track) components and we do not need to consider the satellite track direction. components and we do not need to consider the satellite track direction.

Generalizing the situation to be independent of the receiver/satellite positions, Generalizing the situation to be independent of the receiver/satellite positions, we express the errors as zenith dependent only:we express the errors as zenith dependent only:

ee recrecsatsat . . RRzz ( (satsat) R) Rzz ( (satsat) . ) . XXRACRAC

satsat = cos(= cos() ) XXRadRadsat sat + sin(+ sin() ) XXTanTan

satsat

where where = arcsin(sin(z) . R= arcsin(sin(z) . Rrecrec/R/Rsatsat))

is a paralax for the satellite between the geocenter and the station.is a paralax for the satellite between the geocenter and the station.

Putting equal the projected orbit errors with troposphere model we get an Putting equal the projected orbit errors with troposphere model we get an impactimpact


Orbit Orbit errors errors in PPP in PPP ZTDZTD

Assumption:

orbit errors only ZTD

(usually also in ambiguities, clocks)

Radial errorRadial error• impact=1.0 impact=1.0 in zenithin zenith• impact=0.0 impact=0.0 in horizonin horizon

Tangential errorTangential error• depends on track depends on track

orientationorientation• max impact=0.13 max impact=0.13

(45deg)(45deg)• min impact=0.00 min impact=0.00 (0- (0-

90deg)90deg)

Point positioning


Effect in network solutionEffect in network solution

In network double-difference observables are used:In network double-difference observables are used:

LLklklijij = L = Lklkl

i i – L– Lklklj j = ( L= ( Lkk

i i – L– Llli i ) – ( L) – ( Lkk

j j – L – L llj j ))

but for single satellite error we can consider only single difference for baseline, but for single satellite error we can consider only single difference for baseline, relevant portion of the observation equation is:relevant portion of the observation equation is:

LLklkli i = = ||RR kk

ii||--||RR ll

ii|| + ( + (ee kk

i i – – ee ll

i i ) ) XX

ii + cos(z+ cos(zkkii) ZTD ) ZTD k k - cos(z- cos(zll

ii) ZTD ) ZTD l l + ...+ ...

Again, we distinguish the Radial and Tangential error only and we project them Again, we distinguish the Radial and Tangential error only and we project them into the receiver-satellite distance as zenith (or paralax, into the receiver-satellite distance as zenith (or paralax, ) dependant ) dependant function: function:

((ee kki i – – ee ll

i i )) R Rzz ( (ii) R) Rzz ( (ii) . ) . XXRACRAC

i i = ( cos( = ( cos(kkii) ) XXRadRad

i i + sin(+ sin(kkii) ) XXTanTan

i i ) )

– – ( cos(( cos( llii) ) XXRadRad

i i + sin(+ sin( llii) ) XXTanTan

i i ) )

but we need the coordinates for estimating the zenith angle at the second but we need the coordinates for estimating the zenith angle at the second station.station.

Studying the two marginal cases we can keep a general description limited only Studying the two marginal cases we can keep a general description limited only by defining the baseline lenght 1000 km: by defining the baseline lenght 1000 km:

equal azimuthsequal azimuths –satellite and second station are in –satellite and second station are in equal equal azimuthazimuthss equal zenithsequal zeniths – zenith – zenithss toto satellite satellite are equal for both stationsare equal for both stations

We calculate the impact in ZTD if the error is not absorbed by other parameters. We calculate the impact in ZTD if the error is not absorbed by other parameters.


Assumption: (1000km)

orbit errors only ZTD

(usually also by ambiguities)

Radial orbit Radial orbit error in DD error in DD

ZTDZTD

Radial errorRadial error• impact=0.0 impact=0.0 cancelled in case cancelled in case

of equal zenithsof equal zeniths

• max impact = max impact = 0.0023 0.0023 (38deg) in case of equal (38deg) in case of equal azimuths azimuths

min impact->0.0min impact->0.0 above the above the baseline or close to horizonbaseline or close to horizon

Network solution


Tangential Tangential orbit error orbit error in DD ZTDin DD ZTD

Tangential errorTangential error

• depends on satellite track orientation with respect to baselinedepends on satellite track orientation with respect to baseline

• max impact = max impact = 0.027 0.027 is above the mid of baseline for both cases and orbit is above the mid of baseline for both cases and orbit error ‘paralalel’ to baselineerror ‘paralalel’ to baseline

• impact reduced impact reduced always when error is ‘perpendicular’ to baselinealways when error is ‘perpendicular’ to baseline

• impact reduced impact reduced with decreasing elevation (slightly different for both cases)with decreasing elevation (slightly different for both cases)

Network solution


Simulation in Simulation in network analysisnetwork analysis

Network:Network:

- 16 sites approx. 1000km distances- 16 sites approx. 1000km distances

- ‘star’ baselines strategy from central point- ‘star’ baselines strategy from central point

Solution:Solution:

- synthetic (constant) errors (1,5,10,25,100cm) introduced in the - synthetic (constant) errors (1,5,10,25,100cm) introduced in the orbits consequently in radial, along-track and cross-track orbits consequently in radial, along-track and cross-track component for selected satellitecomponent for selected satellite

- pre-processing of 24h data with the original IGS final orbits- pre-processing of 24h data with the original IGS final orbits

- ZTD estimated with original IGS final orbits (reference ZTD)- ZTD estimated with original IGS final orbits (reference ZTD)

- ZTD estimated with biased orbits (tested ZTD)- ZTD estimated with biased orbits (tested ZTD)

- ZTD estimated with ambiguities free (estimated simultaneously)- ZTD estimated with ambiguities free (estimated simultaneously)

- ZTD estimated with ambiguities fixed (using original IGS orbits)- ZTD estimated with ambiguities fixed (using original IGS orbits) comparison of resulted ZTDscomparison of resulted ZTDs


Synthetic error in orbit position:Synthetic error in orbit position: 1m in along-track (G01, (G01, G03, G05) G03, G05)

Effects of the synthetic orbit errors in Effects of the synthetic orbit errors in ZTDZTD

errors in ZTD


Effect of the synthetic orbit errors in ZTD Effect of the synthetic orbit errors in ZTD (2)(2)

Ambiguity Ambiguity fixedfixed

Ambiguity freeAmbiguity free


Orbit requirements – particular Orbit requirements – particular exampleexample

Note: solving for the ambiguities significantly helps to overcome the limits in quality of the predicted orbits (and predicted accuracy codes)

network solutionnetwork solution

baselines 1000 km (ZTD bias reduces to half if 500km)baselines 1000 km (ZTD bias reduces to half if 500km)

max 1cm error in max 1cm error in ZTDZTD requirements:requirements: 217cm in radial and 19cm in tangential 217cm in radial and 19cm in tangential directiondirection

PPP solutionPPP solution

max 1cm error in ZTD max 1cm error in ZTD requirements:requirements: 1cm in radial and 7cm in tangential 1cm in radial and 7cm in tangential directiondirection

currently IGU prediction quality observed:currently IGU prediction quality observed:

prediction length:prediction length: 1-9h for NRT/RT 1-9h for NRT/RT

nominal situation: nominal situation: 1cm | 3-5cm | 2-3cm [R|A|O rms] 1cm | 3-5cm | 2-3cm [R|A|O rms]

during eclipsing period: during eclipsing period: 1-3cm | 4-20cm | 3-8cm [R|A|O rms]1-3cm | 4-20cm | 3-8cm [R|A|O rms]


Summary – requirements for ZTDSummary – requirements for ZTD network solution (ZTD)network solution (ZTD) is negligibly sensitive to the radial error, but is negligibly sensitive to the radial error, but

along (cross)-track errors can occasionally affects the ZTDs. The along (cross)-track errors can occasionally affects the ZTDs. The baseline configuration plays a crucial role during such period - only baseline configuration plays a crucial role during such period - only specific baselines are sensitive in specific situation and unfortunatelly specific baselines are sensitive in specific situation and unfortunatelly the averaging with respect to other satellite observables is limited.the averaging with respect to other satellite observables is limited.

PPP solution (ZTD)PPP solution (ZTD) depends on the accuracy of radial component depends on the accuracy of radial component (100% in zenith) in nominal situation, but on the along(cross)-track (100% in zenith) in nominal situation, but on the along(cross)-track component for eclipsing Block-IIA satellites. Fortunatelly, error component for eclipsing Block-IIA satellites. Fortunatelly, error averaging performs over all the satellites. Satellite clocks (especially in averaging performs over all the satellites. Satellite clocks (especially in regional solution) can absorb significant portion of the radial error.regional solution) can absorb significant portion of the radial error.

the ambiguitiesthe ambiguities are in both cases able to absorb a significant portion are in both cases able to absorb a significant portion of the orbit errors and currently help to reduce the effect. of the orbit errors and currently help to reduce the effect.

only a few weakly predicted satellites occur inonly a few weakly predicted satellites occur in a a single product, thus single product, thus usually a usually a robust satellite checking (and excluding) strategyrobust satellite checking (and excluding) strategy applied by the user should be satisfactory in many cases for the applied by the user should be satisfactory in many cases for the network solution, although as much as satellites is generally requested. network solution, although as much as satellites is generally requested.


Summary – quality of IGU Summary – quality of IGU predictionprediction

after decommission of satellite G29 (October, 2008) there is no more after decommission of satellite G29 (October, 2008) there is no more significant difference in the standard orbit prediction performance.significant difference in the standard orbit prediction performance.

different pattern of the prediction can be seen during the eclipsing different pattern of the prediction can be seen during the eclipsing periods. We have to distinguish between satellites of old periods. We have to distinguish between satellites of old Block-IIA Block-IIA (fastly degrading)(fastly degrading) and new and new Block-IIR Block-IIR (modestly degrading)(modestly degrading) types. types.

there are still 14 [15] ofthere are still 14 [15] of old-type old-type satellites satellites active (45%):active (45%): G01, G03, G01, G03, G04, G05, G06, G08, G09, G10, G24, G25, G26, G27, G30, [G32].G04, G05, G06, G08, G09, G10, G24, G25, G26, G27, G30, [G32].

accuracy codes are in most cases relevant for the prediction, but accuracy codes are in most cases relevant for the prediction, but usually usually underestimated for Block-IIA during eclipsingunderestimated for Block-IIA during eclipsing periods periods and at and at the start of the maintenance periodsthe start of the maintenance periods..

currently 1-9h prediction are at least necessary for NRT/RT usage currently 1-9h prediction are at least necessary for NRT/RT usage shorter prediction will be appreciated especially due to old Block-IIA shorter prediction will be appreciated especially due to old Block-IIA

satellites, but mainly for the NRT/RT (global) PPP applications.satellites, but mainly for the NRT/RT (global) PPP applications. Relevant question to AC’s:Relevant question to AC’s: how simply they can provide the orbits how simply they can provide the orbits

upgraded every 3h (+2h delay ?) with the same quality as of today ? upgraded every 3h (+2h delay ?) with the same quality as of today ? (Even higher update rate could be requested for the PPP solutions).(Even higher update rate could be requested for the PPP solutions).

Documents

Case study for the IGS ultra-rapid orbit requirements Jan Douša Miami Beach, June 2-6, 2008