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

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  • Case study for the IGS ultra-rapid orbit requirementsJan Doua

    Miami Beach, June 2-6, 2008

    Miami Beach, June 2-6, 2008

  • Outline

    quality of IGS ultra-rapid orbit prediction

    effect of ephemeris errors on ZTD (PPP case)

    effect in network solution

    simulation in network analysis

    summary

    Miami Beach, June 2-6, 2008

  • Monitoring the quality of IGU orbitsIGU w.r.t IGR orbitscomparison in terrestrial system after Helmert transformation3 Helmert rotations estimated epoch by epoch (15min) for relevant satellites onlyfitted portion compared in 0-24 hourspredicted portion compared on hourly basis (1,2,3,4,.., 23)monthly orbit prediction statistics evaluatedaccuracy code validated with IGU x IGR orbit differences

    the orbit quality and the accuracy codes validated separately

    Miami Beach, June 2-6, 2008

  • 2004-2008 time-series of IGU orbit predictions

    Miami Beach, June 2-6, 2008

  • Eclipsing periodstwo times per year every satellite undergoes eclipsingperiod(in yellow)plots generated from the IGS ACCs IGUxIGR comparison summary tables

    Miami Beach, June 2-6, 2008

  • Orbit quality dependance on the predictionorbit accuracy with respect to the prediction interval (monthly statistics)GPS Block IIR-MGPS Block IIAGPS Block IIA

    Miami Beach, June 2-6, 2008

  • Accuracy code validation (6h prediction)

    Miami Beach, June 2-6, 2008

  • Effect of ephemeris errors on PPP ZTDBasic GPS carrier phase observable (scaled to distance):Lrecsat = recsat + c.sat + c.rec + .nrecsat + ION + TRP + recsatrecsat .. receiver-satellite distance in vacuumTRP .. 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: Rrecsat / |Rrecsat| Xsat = e recsat Xsat = e recsat Rz (sat) Rz (sat) . XRACsat 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 recsat . Rz (sat) Rz (sat) . XRAC sat = cos() XRadsat + sin() XTansatwhere = arcsin(sin(z) . Rrec/Rsat) 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

    Miami Beach, June 2-6, 2008

  • Orbit errors in PPP ZTDAssumption: orbit errors only ZTD(usually also in ambiguities, clocks)Radial errorimpact=1.0 in zenithimpact=0.0 in horizonTangential errordepends on track orientationmax impact=0.13 (45deg)min impact=0.00 (0-90deg)Point positioning

    Miami Beach, June 2-6, 2008

  • Effect in network solutionIn network double-difference observables are used:Lklij = Lkli Lklj = ( Lki Lli ) ( Lkj L lj )

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

    Lkli = |R ki|-|R li| + (e ki e li ) X i + cos(zki) ZTD k - cos(zli) 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 ki e li ) Rz (i) Rz (i) . XRACi = ( cos(ki) XRadi + sin(ki) XTani ) ( cos( li) XRadi + sin( li) XTani )

    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 azimuthsequal zeniths zeniths to satellite are equal for both stationsWe calculate the impact in ZTD if the error is not absorbed by other parameters.

    Miami Beach, June 2-6, 2008

  • Radial orbit error in DD ZTDRadial errorimpact=0.0 cancelled in case of equal zenithsmax impact = 0.0023 (38deg) in case of equal azimuths min impact->0.0 above the baseline or close to horizonAssumption: (1000km)orbit errors only ZTD(usually also by ambiguities) Network solution

    Miami Beach, June 2-6, 2008

  • Tangential orbit error in DD ZTDTangential errordepends on satellite track orientation with respect to baselinemax impact = 0.027 is above the mid of baseline for both cases and orbit error paralalel to baselineimpact reduced always when error is perpendicular to baselineimpact reduced with decreasing elevation (slightly different for both cases)Network solution

    Miami Beach, June 2-6, 2008

  • Simulation in network analysisNetwork:- 16 sites approx. 1000km distances- star baselines strategy from central pointSolution:- 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

    Miami Beach, June 2-6, 2008

  • Effects of the synthetic orbit errors in ZTDSynthetic error in orbit position: 1m in along-track (G01, G03, G05)

    Miami Beach, June 2-6, 2008

  • Effect of the synthetic orbit errors in ZTD (2)Ambiguity fixedAmbiguity free

    Miami Beach, June 2-6, 2008

  • Orbit requirements particular exampleNote: 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 ZTDrequirements: 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/RTnominal situation: 1cm | 3-5cm | 2-3cm [R|A|O rms]during eclipsing period: 1-3cm | 4-20cm | 3-8cm [R|A|O rms]

    Miami Beach, June 2-6, 2008

  • Summary requirements for ZTDnetwork 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.

    Miami Beach, June 2-6, 2008

  • Summary quality of IGU predictionafter 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 ACs: 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).

    Miami Beach, June 2-6, 2008

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