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

2. 2 Outline 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

3. Miami Beach, June 2-6, 20083 Monitoring the quality of IGU orbits -IGU w.r.t IGR orbits -comparison in terrestrial system after Helmert transformation -3 Helmert rotations estimated epoch by epoch (15min) for relevant satellites only -fitted portion compared in 0-24 hours -predicted portion compared on hourly basis (1,2,3,4,.., 23) -monthly orbit prediction statistics evaluated -accuracy code validated with IGU x IGR orbit differences the orbit quality and the accuracy codes validated separately

4. Miami Beach, June 2-6, 20084 2004-2008 time-series of IGU orbit predictions

5. Miami Beach, June 2-6, 20085 two times per year every satellite undergoes eclipsing period (in yellow) Eclipsing periods satellite G15 upgraded plots generated from the IGS ACC’s IGUxIGR comparison summary tables

6. Miami Beach, June 2-6, 20086 Orbit quality dependance on the prediction orbit accuracy with respect to the prediction interval (monthly statistics) GPS Block IIR-M GPS Block IIA eclipsing period normal situation

7. Miami Beach, June 2-6, 20087 Accuracy code validation (6h prediction) satellite G04: eclipsing satellite G30: maintenance

8. Miami Beach, June 2-6, 20088 Effect of ephemeris errors on PPP ZTD Basic GPS carrier phase observable (scaled to distance): L rec sat =  rec sat + c.  sat + c.  rec +.n rec sat +  ION +  TRP +  rec sat  rec sat.. receiver-satellite distance in vacuum  TRP.. troposphere path delay we approximate as 1/cos(z) * ZTD The ephemeris error is projected into the observables via a unit vector directing from receiver to satellite: R rec sat / |R rec sat |  X sat = e rec sat  X sat R rec sat / |R rec sat |  X sat = e rec sat  X sat = e rec sat R z ( sat ) R z (  sat ).  X RAC sat = e rec sat R z ( sat ) R z (  sat ).  X RAC sat We are interested in Radial/Along-track/Cross-track component errors, but we distinct only Radial and Tangential (Along-track + Cross-track) components and we do not need to consider the satellite track direction. Generalizing the situation to be independent of the receiver/satellite positions, we express the errors as zenith dependent only: e rec sat. R z ( sat ) R z (  sat ).  X RAC sat = cos(  )  X Rad sat + sin(  )  X Tan sat e rec sat. R z ( sat ) R z (  sat ).  X RAC sat = cos(  )  X Rad sat + sin(  )  X Tan sat where  = arcsin(sin(z). R rec /R sat ) is a paralax for the satellite between the geocenter and the station. Putting equal the projected orbit errors with troposphere model we get an impact

9. Miami Beach, June 2-6, 20089 Orbit errors in PPP ZTD Assumption: orbit errors only ZTD (usually also in ambiguities, clocks) Radial error impact=1.0 in zenithimpact=1.0 in zenith impact=0.0 in horizonimpact=0.0 in horizon Tangential error depends on track orientationdepends on track orientation max impact=0.13 (45deg)max impact=0.13 (45deg) min impact=0.00 (0-90deg)min impact=0.00 (0-90deg) Point positioning

10. Miami Beach, June 2-6, 200810 Effect in network solution In network double-difference observables are used: L kl ij = L kl i – L kl j = ( L k i – L l i ) – ( L k j – L l j ) but for single satellite error we can consider only single difference for baseline, relevant portion of the observation equation is: L kl i = |R k i |-|R l i | + (e k i – e l i )  X i + cos(z k i ) ZTD k - cos(z l i ) ZTD l +... Again, we distinguish the Radial and Tangential error only and we project them into the receiver-satellite distance as zenith (or paralax,  ) dependant function: (e k i – e l i ) R z ( i ) R z (  i ).  X RAC i = ( cos(  k i )  X Rad i + sin(  k i )  X Tan i ) (e k i – e l i ) R z ( i ) R z (  i ).  X RAC i = ( cos(  k i )  X Rad i + sin(  k i )  X Tan i ) – ( cos(  l i )  X Rad i + sin(  l i )  X Tan i ) – ( cos(  l i )  X Rad i + sin(  l i )  X Tan i ) but we need the coordinates for estimating the zenith angle at the second station. Studying the two marginal cases we can keep a general description limited only by defining the baseline lenght 1000 km:  equal azimuths –satellite and second station are in equal azimuths  equal zeniths – zeniths to satellite are equal for both stations We calculate the impact in ZTD if the error is not absorbed by other parameters.

11. Miami Beach, June 2-6, 200811 Assumption: (1000km) orbit errors only ZTD (usually also by ambiguities) Radial orbit error in DD ZTD Radial error impact=0.0 cancelled in case of equal zenithsimpact=0.0 cancelled in case of equal zeniths max impact =  0.0023 (38deg) in case of equal azimuthsmax impact =  0.0023 (38deg) in case of equal azimuths min impact->0.0 above the baseline or close to horizon min impact->0.0 above the baseline or close to horizon Network solution

12. Miami Beach, June 2-6, 200812 Tangential orbit error in DD ZTD Tangential error depends on satellite track orientation with respect to baselinedepends on satellite track orientation with respect to baseline max impact =  0.027 is above the mid of baseline for both cases and orbit error ‘paralalel’ to baselinemax impact =  0.027 is above the mid of baseline for both cases and orbit error ‘paralalel’ to baseline impact reduced always when error is ‘perpendicular’ to baselineimpact reduced always when error is ‘perpendicular’ to baseline impact reduced with decreasing elevation (slightly different for both cases)impact reduced with decreasing elevation (slightly different for both cases) Network solution

13. Miami Beach, June 2-6, 200813 Simulation in network analysis Network: - 16 sites approx. 1000km distances - ‘star’ baselines strategy from central point Solution: - synthetic (constant) errors (1,5,10,25,100cm) introduced in the orbits consequently in radial, along-track and cross-track component for selected satellite - pre-processing of 24h data with the original IGS final orbits - ZTD estimated with original IGS final orbits (reference ZTD) - ZTD estimated with biased orbits (tested ZTD) - ZTD estimated with ambiguities free (estimated simultaneously) - ZTD estimated with ambiguities fixed (using original IGS orbits)  comparison of resulted ZTDs

14. Miami Beach, June 2-6, 200814 Synthetic error in orbit position:(G01, G03, G05) Synthetic error in orbit position: 1m in along-track (G01, G03, G05) Effects of the synthetic orbit errors in ZTD errors in ZTD

15. Miami Beach, June 2-6, 200815 Effect of the synthetic orbit errors in ZTD (2) Ambiguity fixed Ambiguity free

16. Miami Beach, June 2-6, 200816 Orbit requirements – particular example Note: solving for the ambiguities significantly helps to overcome the limits in quality of the predicted orbits (and predicted accuracy codes) network solution baselines 1000 km (ZTD bias reduces to half if 500km) max 1cm error in  ZTD  requirements: 217cm in radial and 19cm in tangential direction PPP solution max 1cm error in ZTD  requirements: 1cm in radial and 7cm in tangential direction currently IGU prediction quality observed: prediction length: 1-9h for NRT/RT nominal situation: 1cm | 3-5cm | 2-3cm [R|A|O rms] during eclipsing period: 1-3cm | 4-20cm | 3-8cm [R|A|O rms]

17. Miami Beach, June 2-6, 200817 Summary – requirements for ZTD  network solution (ZTD) is negligibly sensitive to the radial error, but along (cross)-track errors can occasionally affects the ZTDs. The baseline configuration plays a crucial role during such period - only specific baselines are sensitive in specific situation and unfortunatelly the averaging with respect to other satellite observables is limited.  PPP solution (ZTD) depends on the accuracy of radial component (100% in zenith) in nominal situation, but on the along(cross)-track component for eclipsing Block-IIA satellites. Fortunatelly, error averaging performs over all the satellites. Satellite clocks (especially in regional solution) can absorb significant portion of the radial error.  the ambiguities are in both cases able to absorb a significant portion of the orbit errors and currently help to reduce the effect.  only a few weakly predicted satellites occur in a single product, thus usually a robust satellite checking (and excluding) strategy applied by the user should be satisfactory in many cases for the network solution, although as much as satellites is generally requested.

18. Miami Beach, June 2-6, 200818 Summary – quality of IGU prediction  after decommission of satellite G29 (October, 2008) there is no more significant difference in the standard orbit prediction performance.  different pattern of the prediction can be seen during the eclipsing periods. We have to distinguish between satellites of old Block-IIA (fastly degrading) and new Block-IIR (modestly degrading) types.  there are still 14 [15] of old-type satellites active (45%): G01, G03, G04, G05, G06, G08, G09, G10, G24, G25, G26, G27, G30, [G32].  accuracy codes are in most cases relevant for the prediction, but usually underestimated for Block-IIA during eclipsing periods and at the start of the maintenance periods.  currently 1-9h prediction are at least necessary for NRT/RT usage  shorter prediction will be appreciated especially due to old Block-IIA satellites, but mainly for the NRT/RT (global) PPP applications.  Relevant question to AC’s: how simply they can provide the orbits upgraded every 3h (+2h delay ?) with the same quality as of today ?  (Even higher update rate could be requested for the PPP solutions).