Precise orbit determination for LEO satellites: single-receiver ambiguity resolution using GREAT products

Figures & data

Figure 1. Processing scheme for IAR POD of LEO satellites on GREAT software.

Table 1. Overview of satellites employed

Mission	Satellite	Altitude(km)	Inclination(°)	Receiver
GRACE-FO	GRACE-C	492	89.1	TriG
	GRACE-D	492	89.1
Swarm	Swarm-A	480	87.4	RUAG
	Swarm-B	530	87.8
	Swarm-C	480	87.4
Jason	Jason-3	1336	66.04	BlackJack
Sentinel-3	Sentinel-3A	814.5	98.65	RUAG
	Sentinel-3B	814.5	98.65

Table 2. Reduced-dynamic POD strategy of LEO satellites

Items	Description
Dynamic models
N-body	JPL DE405 (Standish 1998)
Earth gravity field	EIGEN-6S4 (Förste et al. 2016)
Ocean tide	FES2004 (Lyard et al. 2004)
Solid tide	IERS2010 (Petit and Luzum 2010)
Relativity	IERS2010 (Petit and Luzum 2010)
Atmosphere drag	Macro-model, NRLMSISE00 thermosphere model (Picone et al. 2002)
Solar radiation pressure	Macro-model with surface optical properties
Empirical acceleration	A set of accelerations in along-track and cross-track per cycle
Observation models
GPS observations	Undifferenced ionosphere-free code and phase observations
Arc length	30 h
Sampling	10 s
Elevation cutoff	1°
Observation weight	Elevation dependent weight
GPS antenna correction	Correct PCO and PCV with igs14.atx (Rebischung and Schmid 2016)
LEO antenna correction	Correct PCO and PCV
Phase windup	Modeled (Wu et al. 1992)
Relativistic correction	Applied
Estimation
Filter	Batch least squares
Parameters	Position and velocity at initial epoch of LEO satellites, SRP scale factor, drag scale factor, empirical accelerations, phase ambiguities, and LEO satellites’ clock offsets of epochs

Figure 2. NL ambiguity fixing rates of POD IAR solutions for GRACE-FO, Swarm, Jason-3 and Sentinel-3 missions, in DOY 001–180, 2020. The red, green and blue colors indicate the fixed solutions computed with OSB, IRC and UPD products respectively. The average values are displayed in the top right corners in different colors. The data gap of GRACE-C covering DOY 038–042, GRACE-D covering DOY 018–022 and Jason-3 covering DOY 031–044, 168–171 in 2020 is due to the lack of observations.

Figure 3. Distributions of the estimated WL (left) and NL (right) ambiguity residuals of GRACE-C IAR solutions in DOY 005, 2020. The mean and STD values of residuals are displayed in the top right corners.

Table 3. The average 3D RMS values of differences between PSO products and our orbits derived from different solutions (Unit: mm)

LEO	OSB		IRC		UPD
	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed
GRACE-C	16.8	11.9	17.7	12.8	16.9	12.4
GRACE-D	16.2	11.9	17.2	12.9	16.4	12.5
Swarm-A	15.2	14.7	17.4	15.2	15.7	14.8
Swarm-B	13.3	13.2	15.2	13.9	14.1	13.5
Swarm-C	15.2	14.4	17.1	14.9	15.7	14.5
Jason-3	20.2	15.4	21.4	17.3	20.8	16.4
Sentinel-3A	22.3	17.7	22.6	18.5	22.3	17.3
Sentinel-3B	22.7	19.1	23.4	19.8	22.8	18.9

Figure 4. Average RMS values of orbit differences of GRACE-FO, Swarm, Jason-3 and Sentinel-3 in along-track, cross-track, and radial directions (from top to bottom) in DOY 001–180, 2020. The red, green and blue colors indicate the OSB solutions, the IRC solutions and the UPD solutions respectively. The color bars without edges represent the ambiguity-float solutions, while the bars with black edges represent the ambiguity-fixed solutions.

Table 4. The average RMS values of phase residuals of our orbits for different solutions (Unit: mm)

LEO	OSB		IRC		UPD
	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed
GRACE-C	6.4	7.4	7.1	8.0	6.5	7.6
GRACE-D	6.4	7.3	7.0	8.0	6.4	7.6
Swarm-A	6.2	7.1	6.6	7.6	6.3	7.4
Swarm-B	6.2	7.0	6.5	7.5	6.3	7.2
Swarm-C	6.2	7.2	6.6	7.7	6.3	7.5
Jason-3	10.3	11.4	10.8	12.0	10.3	11.3
Sentinel-3A	7.4	8.3	8.0	9.0	7.2	8.1
Sentinel-3B	8.2	9.2	8.5	9.5	8.2	9.3

Table 5. The mean and STD values of SLR residuals of our orbits for different solutions (Unit: mm)

LEO	OSB		IRC		UPD
	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed	AMB. Float	AMB. Fixed
GRACE-C	−0.2 ± 14.3	−2.0 ± 10.4	0.1 ± 16.8	−2.1 ± 13.5	0.2 ± 15.0	−1.6 ± 10.9
GRACE-D	−6.1 ± 14.7	−5.1 ± 10.3	−6.0 ± 18.4	−5.3 ± 12.9	−6.2 ± 14.8	−4.9 ± 10.6
Swarm-A	−5.4 ± 14.2	−5.1 ± 13.0	−5.1 ± 15.9	−5.2 ± 13.4	−5.4 ± 14.4	−5.0 ± 13.3
Swarm-B	−8.1 ± 16.2	−8.9 ± 14.8	−8.1 ± 17.3	−8.8 ± 15.4	−8.3 ± 16.1	−8.8 ± 15.1
Swarm-C	−6.6 ± 15.9	−8.1 ± 15.3	−5.8 ± 18.0	−7.8 ± 15.8	−6.5 ± 16.2	−8.0 ± 15.7
Jason-3	1.4 ± 24.9	1.0 ± 21.8	1.2 ± 25.4	0.8 ± 22.4	1.3 ± 24.8	0.7 ± 21.2
Sentinel-3A	1.3 ± 15.9	0.6 ± 12.6	1.4 ± 19.3	0.6 ± 14.3	1.5 ± 16.6	0.8 ± 12.4
Sentinel-3B	0.8 ± 17.4	0.2 ± 14.3	1.2 ± 18.6	0.3 ± 15.1	1.1 ± 17.7	0.4 ± 13.5

Figure 5. SLR residuals of ambiguity-fixed orbits for GRACE-FO, Swarm, Jason-3 and Sentinel-3 satellites, in DOY 001–180, 2020. The red, green and blue dots indicate the ambiguity-fixed solutions computed with OSB, IRC, and UPD products respectively. The mean and STD values are displayed in the top right corners in different colors.

Figure 6. Daily KBR residuals STD of our GRACE-FO orbits for different solutions in DOY 001–180, 2020, with ambiguity fixed computed with OSB, IRC, and UPD products (from top to bottom) respectively. The blue and red colors indicate the ambiguity-float and ambiguity-fixed solutions respectively. The average values are displayed in the top right corners in different colors.

Standish, E.M. 1998. “JPL Planetary and Lunar Ephemerides.”

 Google Scholar

Förste, C., S. Bruinsma, O. Abrikosov, S. Rudenko, and R. Biancale. 2016. “EIGEN-6S4 A Time-variable Satellite-only Gravity Field Model to D/o 300 Based on LAGEOS, GRACE and GOCE Data from the Collaboration of GFZ Potsdam and GRGS Toulouse.” doi: https://doi.org/10.5880/icgem.2016.008.

 Google Scholar

Lyard, F., T. Lefevre, F. Letellier, and O. Francis. 2004. “Modelling the Global Ocean Tides: Modern Insights from FES2004.” Journal of Geophysical Research Atmospheres 56 (5): 394–415. doi:https://doi.org/10.1007/s10236-006-0086-x.

 Google Scholar

Petit, G., and B. Luzum 2010. “IERS Conventions.” IERS Technical Note.

 Google Scholar

Picone, J.M., A.E. Hedin, D.P. Drob, and A.C. Aikin. 2002. “NRLMSISE-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues.” Journal of Geophysical Research: Space Physics 107 (A12): SIA 15-1-SIA 15–16. doi:https://doi.org/10.1029/2002ja009430.

 Google Scholar

Rebischung, P., and R. Schmid. 2016. “IGS14/igs14.atx: A New Framework for the IGS Products.” AGU Fall Meeting, 12-16 December, 2016, San Francisco, USA.

 Google Scholar

Wu, J.T., S.C. Wu, G.A. Hajj, W.I. Bertiger, and S.M. Lichten. 1992. “Effects of Antenna Orientation on GPS Carrier Phase.” Astrodynamics 1991.

 Google Scholar

Data availability statement

We are grateful to International GNSS Service (IGS) for providing the precise orbit and clock products of GPS as well as OSB and IRC correction products at ftp://cddis.gsfc.nasa.gov for free. The UPD products generated by GREAT software can be accessed at http://igmas.users.sgg.whu.edu.cn/. The data onboard GRACE-FO, Swarm, Jason-3 and Sentinel-3 are publicly available from ftp://isdcftp.gfz-potsdam.de, ftp://swarm-diss.eo.esa.int, ftp://ftp-access.aviso.altimetry.fr and https://scihub.copernicus.eu respectively.