Arnold, D.

Jäggi, A.

Kalarus, M.

Kobel, C.

Villiger, A.

English

Bern Open Repository and Information System (BORIS)

source: https://doi.org/10.48350/182269 | downloaded: 15.5.2023AIUBEGU23-12153European Geosciences UnionGeneral Assembly 202323 April - 28 April 2023, Vienna, AustriaC. Kobel, D. Arnold, M. Kalarus, A. Villiger, A. JäggiAstronomical Institute,University of Bern,Bern, SwitzerlandPoster compiled by C. Kobel, April 2023Astronomical Institute, University of Bern, Berncyril.kobel@aiub.unibe.chImpact of incorporating SPIRE CubeSat GPSobservations in a global GPS network solutionIntroductionTypically, precise orbit determination (POD) of low earth orbiters (LEOs)and computation of network solutions for the Global Positioning System(GPS) are separate processes. The orbits and clocks of GPS satellites, whichwere previously determined as part of a network solution, are usuallyfixed in a LEO POD. Various studies have shown that GPS observationsof LEOs can contribute to a global solution, particularly in terms of de-termining geodetic parameters, such as the Earth’s center-of-mass coor-dinates (Haines et al. 2015, Männel and Rothacher 2017). Since recently,scientifically designed experiments can be carried out using GPS data thatwas collected by cubesats operated by Spire Global, which are equippedwith dual-frequency GPS receivers. The aim of the present study is todetermine how incorporating GPS observation data from specific SPIREsatellites affects the computation of a global network solution. A com-bined GPS-LEO solution is obtained by processing the code and phase ob-servations received by GPS receivers aboard selected SPIRE cubeSats withthose from IGS ground stations together. Using this approach, SPIRE satel-lite orbits are determined jointly with GPS orbit parameters and geodeticparameters, such as station coordinates, Earth rotation parameters, andthe Earth’s center-of-mass. The procedure is carried out exemplary for thetime period 1st May 2020 - 13th July 2020.Ground station selectionToday, the IGS networkconsists of more than 500stations. Due to geograph-ical conditions, however,there are regions that arepoorly covered, e.g., overthe oceans. In this study,a subset from all avail-able ground stations is se-lected. Only GPS obser-vations from stations thatcontributed to the CODEFigure 1: Selected ground stations(Center for Orbit Determination in Europe) repro3 product series (Selmkeet al. 2020) are made use of. A reduced ground station network drasticallyreduces the computation time and in turn, also increases the effect of in-cluding LEO data in the processing. In the present study, a subset with240 ground stations is used, as indicated in Fig. 1. In the analyzed timespan, on average 231 stations provided data to a one day (24h) solution.Low Earth OrbitersApart from the GPS data received aboard specific SPIRE satellites (FM)also GPS observations from scientific LEO missions are included. Orbitcharacteristics of these satellites are provided in Table 1.Name Launch Altitude InclinationFM 099 JohanLoran 01/04/2019 505 km 97.36◦FM 101 Elham 01/04/2019 505 km 97.36◦FM 102 Victor-Andrew 01/04/2019 505 km 97.35◦FM 103 Wanli 05/07/2019 530 km 97.64◦FM 104 LillyJo 05/07/2019 530 km 97.64◦FM 106 Ejatta 05/07/2019 530 km 97.63◦FM 107 Morag 05/07/2019 530 km 97.64◦FM 108 GregRobinson 05/07/2019 530 km 97.63◦FM 115 JpgSquared 11/12/2019 550 km 36.92◦Sentinel-3A 16/02/2016 800 km 98.60◦Sentinel-3B 25/04/2018 800 km 98.60◦Grace Follow-On 1 22/05/2018 500 km 89.00◦Grace Follow-On 2 22/05/2018 500 km 89.00◦SWARM-A 22/11/2013 446 km 87.30◦SWARM-B 22/11/2013 511 km 87.80◦SWARM-C 22/11/2013 446 km 87.30◦Jason-3 17/01/2016 1343 km 66.04◦Table 1: Processed Low Earth OrbitersIntegrated processing parametrizationThe integrated processing method utilized in this study necessitates theestimation of a large number of parameters, including geodetic and orbitparameters for both GPS and LEO satellites, as well as necessary clock cor-rections and ground station coordinates. Table 2 provides comprehensivedetails on the parametrization of the determined solutions in terms of thetotal number of parameters and corresponding constraints.Parameter Number ConstraintStation coordinates 3/station (X/Y/Z) No-Net-Translation(Datum definition) No-Net-RotationStation clocks 288/station zero-meanZenith path delay 12/station relative: 1mHorizontal gradient 1 set (N/E)/station -Earth rotation 2 sets/day (X&Y-pole,dT ) dT1:10−4msEarth’s center-of-mass 3 -GPS orbital elements 13/satellite -GPS stoch.param.(Pulses) 3/satellite R:10−6,A:10−5,C:10−8m/sGPS satellite clocks 288/satellite -LEO orbital elements 9/satellite -LEO stoch. param. (PCA) 3·240/satellite (R/A/C):5 · 10−9m/sLEO satellite clocks 288/satellite -Ambiguities ∼9000 -Table 2: Parametrization of computed solutions of a one day (24h) arcIt is evident in Table 2 that for many of the estimated parameters no con-straints are applied. For each GPS satellite a set of velocity pulses (inRadial/Along-track/Cross-track) is set up at orbit midnight. For detailsabout the parametrization for the GPS orbit solutions see Selmke et al.2020. To compensate for modelling errors in the LEO POD, in particularneglecting non-gravitational force modelling like solar radiation pressureand air drag, piece-wise constant accelerations (PCA) are estimated to-gether with six Keplerian elements plus constant accelerations over onearc in radial (R), along-track (A) and cross-track (C) directions. A datasampling of 5 min has been utilized, whereby all observations from sta-tions and LEOs have equal weights.Low Earth Orbiter Precise Orbit DeterminationIn order to ascertain the potential utility of GPS observations obtainedfrom GPS receivers onboard of LEOs in determining a global GPS net-work solution, it is first necessary to evaluate the quality the observations.To achieve this, a classical LEO-only POD is conducted and the resultingdaily phase RMS is analyzed. The data quality of GPS observations fromSPIRE satellites is evaluated by comparing the phase RMS to the resultsobtained from the POD of scientific LEOs (from Table 1).Figure 2: Phase RMS of processed LEOsAs Fig. 2 illustrates, the phase RMS indicate that the POD of LEOs withscientific mission objectives is of superior performance compared to thatof the SPIRE satellites. For the SPIRE satellites FM099, FM103 and FM115 aphase center variation map was used in the processing explaining the bet-ter performance of the three satellites. Given the varied quality of PODs,it is worth to investigate how different scientific and SPIRE LEOs impactthe resulting solution. In all the present plots, the solution including allSPIRE satellites from Table 1 is indicated with "SPIR". "SLEO" describesthe solution including all LEOs from Table 1 with scientific mission goals,and "ALEO" includes all LEOs.Earth’s center-of-mass coordinatesThe estimated Earth’s center-of-mass coordinates are compared to reference values computed by the Jet Propulsion Laboratory JPL (Sun et al. 2016). Itis of interest to determine whether the proposed solution via LEO integrated processing allows for an improvement. Based on the mean and standarddeviation of the differences shown in Fig. 3, it is apparent that the estimated Z-coordinate of the Earth’s center-of-mass coordinates is notably morerobust, in terms of standard deviation of differences to the reference solution, when GPS-LEO observations are incorporated.Figure 3: Earth’s center-of-mass estimates (differences to JPL solution)Figure 4: Formal errors Earth’s center-of-mass estimatesThe "ref" label describes the solution, where no GPS observations from LEOs are integrated. The extent of improvement is dependent on the LEOincluded, with the influence of GPS observations from scientific LEOs being especially high. The formal errors, shown in Fig. 4, clearly reflect theseresults. Of particular note is the determination of the Z-coordinate, which exhibits a noticeable improvement. The results do not vary much whenexchanging the integrated SPIRE satellite, but show an even better improvement when observations from multiple LEOs are included.GPS orbit misclosuresIn addition to geodetic parameters, it is important to examine the qualityof the resulting GPS orbits. For this purpose orbit differences are com-puted for the overlapping epoch of two consecutive arcs. Figure 5 showsdaily mean values over all 32 GPS satellites for radial, along-track andcross-track direction each. The results indicate that incorporating GPS ob-servations from multiple LEOs is advantageous. For the solutions whereall SPIRE satellites are included, the mean values for the radial and along-track direction get smaller compared to the reference solution. The resultsfor the cross-track direction show a significantly smaller standard devia-tion of daily means than the reference solution, whereby the improvementis about 20%.Figure 5: GNSS orbit misclosuresEarth orientation parametersThe resulting Earth rotation parameters (ERPs) were compared to the com-bined reference solution C04, which is consistent with the InternationalTerrestrial Reference Frame 2014 (ITRF14). The differences between thevarious solutions are not significant, e.g. for the X-pole estimate an over-all maximum difference of 2% in terms of standard deviation results. Itappears that including GPS observations from LEOs does not provide anyadvantage. The formal errors indicate that integrating additional GPS-LEO observations does not improve the determination of Earth RotationParameters (ERPs), whereby no significant difference for the integratedLEOs exist.Ground stations coordinatesFigure 6: Repeatability of ground station coordinatesThe repeatability (given in N/E/U) of the ground stations are shown inFig. 6. When multiple LEOs are used, it is evident that integrating GPS-LEO observations in a global GPS network solution can be disadvanta-geous with respect to the repeatability of the station coordinates, whichdemands for further investigations.ConclusionsThe results of the estimation of Earth’s center-of-mass coordinates, as wellas their formal errors and the orbit misclosures of the derived GPS or-bit trajectories, confirm that including GPS-LEO observations is beneficialwhen determining a global GPS network solution. The repeatability of thestation coordinates shows that the procedure has room for improvement.Especially by explicitly modeling non-gravitational forces in the LEO pro-cessing, the results may be improved. When different SPIRE LEOs areincluded, no significant changes in the resulting solution can be observed.Moreover, it is clearly evident that GPS-LEO observations from scientificLEOs have a more advantageous impact on the solution than those fromSPIRE-included solutions. It is evident that including multiple LEOs, asopposed to only one, leads to an improvement in all estimated parametersexcept station coordinates.ReferencesHaines, Bruce J et al. (2015). “Realizing a terrestrial reference frame using the Global Positioning System”.Journal of Geophysical Research: Solid Earth 120.8, pp. 5911–5939.Männel, Benjamin and Markus Rothacher (2017). “Geocenter variations derived from a combined process-ing of LEO-and ground-based GPS observations”. Journal of Geodesy 91.8, pp. 933–944.Selmke, Inga et al. (2020). “CODE repro3 product series for the IGS”. DOI: 10.7892/boris.135946.Sun, Yu, Riccardo Riva, and Pavel Ditmar (2016). “Optimizing estimates of annual variations and trendsin geocenter motion and J2 from a combination of GRACE data and geophysical models”. Journal ofGeophysical Research: Solid Earth 121.11, pp. 8352–8370.

Impact of incorporating SPIRE CubeSat GPS observations in a global GPS network solution

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Impact of incorporating SPIRE CubeSat GPS observations in a global GPS network solution

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