Dach, Rolf

McNair, Stephanie Lauren

Prange, Lars

Sidorov, Dmitry

Bern Open Repository and Information System (BORIS)

Astronomical Institute, University of BernInternational Symposium on Geodesy & GNSS 2018Xuzhou China, November 3-4 2018Astronomical Institute University of BernMulti-GNSS: more satellites –more challenges for orbit determinationRolf Dach, Lars Prange, Dmitry Sidorov, S. Lauren McNair and the CODE AC teamSlide 2 Astronomical Institute University of BernNumber of Satellites in the CODE solutionsSlide 3 Astronomical Institute University of BernNavigation Satellite Systems todayGlobal Navigation Satellite SystemsGPS GLONASS Galileo BeiDouRegional and Augmentation SystemsQZSS NAVIC SBASSlide 4 Astronomical Institute University of BernTheoretical backgroundSlide 5 Astronomical Institute University of BernEquation of Motion applies for all satellitesThe shape of a satellite orbit is influenced by Keplerian motion Gravitational forces Attraction by the Earth and other bodies Mass distribution in/on the Earth Non-gravitational forcesSlide 6 Astronomical Institute University of BernGravitational Forces Resolution of the Earth gravity field relevant for modelling the orbits of GNSS satellites in MEO orbits.Slide 7 Astronomical Institute University of BernGravitational Forces Resolution of the Earth gravity field relevant for modelling the orbits of GNSS satellites in GEO/IGSO orbits.Slide 8 Astronomical Institute University of BernGravitational ForcesRelevant gravitational effects for GNSS orbit modelling: Oblateness of the EarthGPS: ≈40 km Galileo: ≈27 km QZSS: ≈15 km Lunar gravitational attractionGPS: ≈1.5 km Galileo: ≈3 km QZSS: ≈5 km Solar gravitational attractionGPS: ≈1 km Galileo: ≈2 km QZSS: ≈6 km Earth gravity field (remaining parts)GPS: ≈500 m Galileo: ≈300 m QZSS: ≈200 m Gravitational effect due to ocean tidesGPS: <1 cm Galileo: <5 mm QZSS: ≈1 mmSlide 9 Astronomical Institute University of BernEquation of Motion applies for all satellitesThe shape of a satellite orbit is influenced by Keplerian motion Gravitational forces Attraction by the Earth and other bodies Mass distribution in/on the Earth Non-gravitational forces Any interaction of radiation with a surface causes an exchange of momentum and therefore a force. Thermal emission also generates a force.Slide 10 Astronomical Institute University of BernDirect Solar Radiation PressureOne of the biggest effect on GNSS satellites is theforce produced by the photons directly coming fromthe Sun.Effect on the satellite orbit after one day: GPS satellites: ≈250 m Galileo satellites: ≈350 msatellites have comparable dimensions but only half of the mass QZSS satellites: ≈700 msatellite dimensions are much bigger than for the other GNSS satellitesSlide 11 Astronomical Institute University of BernRadiation Effect in the Orbit DeterminationWe need to know which amount of photons arrives at the satellite. According to the surface properties the resulting force can be derived.ps-specular Reflectionpd-diffuse Reflectionpa-absorbtionps + pd + pa = 1Slide 12 Astronomical Institute University of BernRadiation Effect in the Orbit DeterminationWe need to know which amount of photons arrives at the satellite. According to the surface properties the resulting force can be derived.Slide 13 Astronomical Institute University of BernAnalytical ModellingFor an analytical modelling of the radiation and re-radiation effects one needs a detailed decomposition of the satellite into the geometrical elements, the optical properties of all surfaces (including the consequences of aging effects), a reasonable knowledge about the radiation arriving at the satellite, and sufficient information about the thermal conditions of the satellite surfaces.With a ray tracing the resulting acceleration can be computed but this needs a big computational effort.Slide 14 Astronomical Institute University of BernSemi-analytical modellingTo reduce the computational effort, the satellite is typically re-presented by a box-wing model.+empirical orbitparameters thatneed to beestimatedSlide 15 Astronomical Institute University of BernEmpirical modellingSlide 16 Astronomical Institute University of BernEmpirical modellingSlide 17 Astronomical Institute University of BernEmpirical modellingSlide 18 Astronomical Institute University of BernEmpirical modellingSlide 19 Astronomical Institute University of BernEmpirical modellingSlide 20 Astronomical Institute University of BernEmpirical modellingSlide 21 Astronomical Institute University of BernEmpirical modellingSlide 22 Astronomical Institute University of BernEmpirical modellingSlide 23 Astronomical Institute University of BernEmpirical modellingSlide 24 Astronomical Institute University of BernEmpirical modellingSlide 25 Astronomical Institute University of BernEmpirical modellingSlide 26 Astronomical Institute University of BernEmpirical modellingSlide 27 Astronomical Institute University of BernEmpirical modellingSlide 28 Astronomical Institute University of BernEmpirical modellingSlide 29 Astronomical Institute University of BernEmpirical modellingSlide 30 Astronomical Institute University of BernEmpirical modellingSlide 31 Astronomical Institute University of BernThe Empirical CODE orbit modelThe ECOM is well established for GNSS satellites in yaw-steering modeSlide 32 Astronomical Institute University of BernScaling factors for box-wing modelsL. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 33 Astronomical Institute University of BernOrbit Misclosures: ECOM-onlyGalileo FOVIOCGLONASSGPS IIFIIR-MIIR-BIIR-AIIAFeb 2017 Mar 2017 Apr 2017 May 2017 Jun 2017 Jul 2017 Aug 2017 Sep 2017 Oct 2017 Nov 2017 Dec 2017 Jan 2018 Feb 2018180Orbit misclosures [cm]L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.One-day solutions: Galileo has less than two revolutions within one daySlide 34 Astronomical Institute University of BernOrbit Misclosures: ECOM-plus-boxwingGalileo FOCIOVGLONASSGPS IIFIIR-MIIR-BIIR-AIIAFeb 2017 Mar 2017 Apr 2017 May 2017 Jun 2017 Jul 2017 Aug 2017 Sep 2017 Oct 2017 Nov 2017 Dec 2017 Jan 2018 Feb 2018180Orbit misclosures [cm]L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.One-day solutions: Galileo has less than two revolutions within one daySlide 35 Astronomical Institute University of BernMonoscaleSmartscale-2Smartscale-4Smartscale-3Validate boxwing modelMacromodel defines: Plates of the satellite with its areas andsurface propertiesUsed to compute forces acting on thesatellite because of solar radiation pressure.Whether these models are correct can beassessed by estimating scale factors for theresulting force:Plate Mod Area (𝐴𝐴) [m2] Normal (𝑒𝑒𝑛𝑛) Specularity (𝜌𝜌) Diffusivity (𝛿𝛿) Rotation Sys. Description1 1 5.720 [+1, 0, 0] 0.112 0.448 +X2 1 5.720 [-1, 0, 0] 0.112 0.448 -X3 1 7.010 [0, +1, 0] 0.112 0.448 +Y4 1 7.010 [0, -1, 0] 0.112 0.448 -Y5 1 5.400 [0, 0, +1] 0.112 0.448 +Z6 1 5.400 [0, 0, -1] 0.000 0.000 -Z7 0 22.250 [+1, 0, 0] 0.195 0.035 +SUN: [0,+1, 0] Solar panels front8 0 22.250 [-1, 0, 0] 0.196 0.034 -SUN: [0,+1, 0] Solar panels back[Montenbruck et al, 2015. Adv. In Space Research]MultiscaleL. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 36 Astronomical Institute University of BernCalculating the SRP-ForceRadiation Pressure force calculation per plate:1. Without immediate thermal re-radiation:(needed if energy is absorbed, e.g., the solar panel is taking energy)?⃗?𝐹 = −Φ𝑐𝑐⋅ 𝐴𝐴 cos𝜃𝜃 ⋅ 𝛼𝛼 + 𝛿𝛿 𝑒𝑒⨀ + 23 𝛿𝛿𝑒𝑒𝑛𝑛 + 2𝜌𝜌 cos𝜃𝜃 ⋅ 𝑒𝑒𝑛𝑛2. With immediate thermal re-radiation (e.g., for Multi-layer insulation): ?⃗?𝐹 = −Φ𝑐𝑐⋅ 𝐴𝐴 cos𝜃𝜃 ⋅ 𝛼𝛼 + 𝛿𝛿 𝑒𝑒⨀ + 23 𝑒𝑒𝑛𝑛 + 2𝜌𝜌 cos𝜃𝜃 ⋅ 𝑒𝑒𝑛𝑛Explanation for the variables:L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 37 Astronomical Institute University of BernExample for Galileo Satellite geometry and optical properties as provided by GSA Front side of solar panel has two different “materials” Using eqn. (1) or (2) resulted in different scaling factors of about 10%-> eqn. (2) is correct-> parts of the panel are not used?Plate Mod Area (𝐴𝐴) [m2] Normal (𝑒𝑒𝑛𝑛) Specularity (𝜌𝜌) Diffusivity (𝛿𝛿) Rotation Sys. Description1 1 1.320 [+1, 0, 0] 0.000 0.070 -X Material A2 1 0.440 [-1, 0, 0] 0.000 0.070 +X Material A3 1 0.880 [-1, 0, 0] 0.730 0.190 +X Material C4 1 1.244 [0, +1, 0] 0.000 0.070 -Y Material A5 1 1.539 [0, +1, 0] 0.730 0.190 -Y Material C6 1 1.129 [0, -1, 0] 0.000 0.070 +Y Material A7 1 1.654 [0, -1, 0] 0.730 0.190 +Y Material C8 1 1.053 [0, 0, +1] 0.000 0.070 +Z Material A9 1 1.969 [0, 0, +1] 0.220 0.210 +Z Material B10 1 2.077 [0, 0, -1] 0.000 0.070 -Z Material A11 1 0.959 [0, 0, -1] 0.730 0.190 -Z Material C12 0 7.760 [+1, 0, 0] 0.080 0.000 +SUN: [0,+1, 0] Solar Panels Material E13 ? 3.060 [+1, 0, 0] 0.100 0.000 +SUN: [0,+1, 0] Solar Panels Material D14 0 10.820 [-1, 0, 0] 0.196 0.034 -SUN: [0,+1, 0] Solar Panels back[https://www.esa.int/spaceinimages/Images/2014/07/Galileo_satellite]L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 38 Astronomical Institute University of BernYearly Scale Factors: MonoscaleGalileo FOCIOVGLONASSBlock IIFIIR-MIIR-BBlock IIR-A1.80.41.41.00.81.61.20.20.6Monoscale:(one factor per satellite)The scale factors show clearly the different types of satellites.L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 39 Astronomical Institute University of BernYearly Scale Factors: Smartscale-2Galileo FOCIOVGLONASSBlock IIFIIR-MIIR-BBlock IIR-A1.80.41.41.00.81.61.20.20.6L. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Smartscale-2:(two factor per satellite:solar panel and body)GLONASS & Galileo: stable scale factors for all satellites in same block-> close to 1GPS: more variation between satellites in same block-> farther away from 1.Slide 40 Astronomical Institute University of BernMonoscale vs. Smartscale/MultiscaleL. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.∥+ = ∥+ =Correlation between scale factors due to: Similar optical properties Parallel plates Attitude geometry Parallel resultant forceSlide 41 Astronomical Institute University of BernMonoscale vs. Smartscale/MultiscaleL. McNair, A.Villiger, R. Dach, A. Jäggi: Validation of boxwing models for GNSS satellites. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.∥+ = ∥+ =Correlation between scale factors due to: Similar optical properties Parallel plates Attitude geometry Parallel resultant forceConclusion:How many scaling factors can be estimateddepend on the satellite type.Slide 42 Astronomical Institute University of BernOrbit modelling during eclipseD. Sidorov, R. Dach, L. Prange, A. Jäggi: Improved orbit modelling of Galileo satellites during eclipse seasons. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 43 Astronomical Institute University of BernSLR residuals for SVN 101 ERP, antenna thrustComparison of MGEX solutions from http://mgex.igs.org/analysisCODEGFZGRGSECOM2 SRP modelarc length 72 hoursarc length 24 hoursarc length 30 hoursSlide 44 Astronomical Institute University of BernOrbit misclosures at midnightGPS: SVNs: 34-73Galileo IOV: SVNs: 101-103Galileo FOC: SVNs: 201-213D. Sidorov, R. Dach, L. Prange, A. Jäggi: Improved orbit modelling of Galileo satellites during eclipse seasons. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 45 Astronomical Institute University of BernDesign of Galileo satellitesGalileo satellites (Galileo Satellite Metadata, URL: https://www.gsceuropa.eu).Radiators are installed on  IOV satellites: +X, +Y, -Y FOC satellites: +X, +Y, -Y and -ZD. Sidorov, R. Dach, L. Prange, A. Jäggi: Improved orbit modelling of Galileo satellites during eclipse seasons. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.IOV FOCSlide 47 Astronomical Institute University of BernExpected effect of the +X radiatorD. Sidorov, R. Dach, L. Prange, A. Jäggi: Improved orbit modelling of Galileo satellites during eclipse seasons. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 48 Astronomical Institute University of BernExtending the ECOM2 orbit modelTo be accounted by ECOM2: for low β<12deg angles requires a once-per-rev sine term in D for high β angles a constant term in D is sufficient. This additional empirical parameter shall also be active during eclipse season. Also the Y-bias parameter is kept active during eclipse to compensate for imbalanced thermal radiation between +Y and –Y radiators.Slide 49 Astronomical Institute University of BernOrbit misclosures at midnightD. Sidorov, R. Dach, L. Prange, A. Jäggi: Improved orbit modelling of Galileo satellites during eclipse seasons. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 52 Astronomical Institute University of BernAdvancing ECOM for satellite in orbit normal modeL. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 53 Astronomical Institute University of BernOrientation of the spacescraftL. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 54 Astronomical Institute University of BernOrientation of the spacescraftL. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 55 Astronomical Institute University of BernOrientation of the coordinate systemL. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 56 Astronomical Institute University of BernOrientation of the coordinate systemL. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 57 Astronomical Institute University of BernECOM updated for orbit normal modeIn the terminator-based coordinate system variousconstant and periodic terms are estimated instead: QZSS-1: switches at abs(β)<20°a 9 parameter model is most efficient BDS-2: MEO/IGSO switch at abs(β)<4°MEO: a 9 parameter model is most efficientIGSO: a 2 parameter model is sufficient(possibly limited because of the coverage with tracking stations)L. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 58 Astronomical Institute University of BernFormal error for radial orbit componentThe formal error justify the weak coverage with observations forBDS-IGSO satellites (reason for reduced set of orbit parameters).Slide 59 Astronomical Institute University of BernECOM updated for orbit normal modeComparison between CODE-MGEX and JAXA solution forQZSS-satellite(s)(from http://mgex.igs.org/analysis) ECOM2 orbit model(classical parameters designed foryaw-steering mode) ECOM-TB orbit model(parameters in the terminator-based coordinate system designedfor orbit normal mode)L. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.Slide 60 Astronomical Institute University of BernECOM updated for orbit normal modeBDS2-MEO BDS2-IGSO QZSS-1Old model 20.5 cm 21.0 cm 62.0 cmNew model 12.2 cm 12.2 cm 15.2 cmImprovement 40.5 % 41.9% 75.5%L. Prange, R. Dach, D. Arnold, G. Beutler, S. Schaer, A. Villiger, A. Jäggi: An Empirical SRP Model for the Orbit Normal Mode. Presented at IGS workshop, Wuhan, China, 29 Oct. - 02 Nov. 2018.BDS2-MEO BDS2-IGSO QZSS-1Old model 1.72 ns 1.61 ns 1.43 nsNew model 0.72 ns 0.69 ns 0.35 nsImprovement 58.1% 57.1% 75.5%RMS from SLR residulals (IQR):Median of a linear fit of the satellite clock corrections:Slide 61 Astronomical Institute University of BernMulti-GNSS: more satellites –more challenges for orbit determinationSummaryThese three examples shall demonstrate challenge accepted by CODE and other groupsdeveloping GNSS satellite orbit models, step by step a progress is made to get the modelsfor the new satellites on the level of GPS orbits, a support by the system providers by disclosinginformation on the satellites is very helpful.Slide 62 Astronomical Institute University of Bern

Multi-GNSS: more satellites - more challenges for orbit determination

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Multi-GNSS: more satellites - more challenges for orbit determination

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