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Non-Gravitational Force Modeling and Single-Receiver Ambiguity Resolution

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Non-Gravitational Force Modeling and Single-Receiver Ambiguity Resolution Sentinel-3A/3B orbit determination using EGU2020-16611 non-gravitational force modeling and single-receiver ambiguity resolution European Geosciences Union Xinyuan Mao1∗, Daniel Arnold1, Valére Girardin2, Arturo Villiger1, General Assembly 2020 Adrian Jäggi1 04 May - 08 May 2020, Sharing Geoscience Online 1. Astronomical Institute, University of Bern, Bern, Switzerland 2. The Space Transportation directorate of the European Space Agency, Paris, France Introduction Sentinel-3 is a designated European Space Agency (ESA) Earth obser- Table 1: Four satellite orbit solutions generated in this research (Note that the PCA settings Table 3: Mean and standard-deviation statistics of SLR residuals in the line-of- AF* EMT REF SRP* NG:−8.4±29.7 NM:−46.5±22.1 vation satellite formation devoted to oceanography and land-vegetation align in the radial/along-track/cross-track directions). 50 50 sight direction and mean offsets for the two Sentinel-3 satellites using normal 2 0 0 Rad. points collected by 10 selected stations (elevation cut-off angle: 10 deg, outlier monitoring. Currently two identical satellites are flying at a circular sun- Solution Ambiguity Const. acc. PCA (σp, nm=s ) Ngrv −50 −50 synchronous orbit with an altitude of about 800 km. Their prime onboard screening: 200 mm) (Arnold et al. 2019). Unit: [mm]. FAKN Float No No No NG:−2.6±42.5 NM:−1.8±44.8 payload systems, e.g. radar altimeter, necessitate high-precision orbits, 50 50 Satellite Orbit Nr.obs [-] Mean STD Rad. Alo. Cro. IAKN Integer No No No 0 0 Alo. particularly in the radial direction. This can be fulfilled by using the col- IANM Integer Yes Yes (5.0/5.0/5.0) No −50 −50 S3A FAKN 12069 -8.22 17.42 -12.54 -1.36 2.13 lected measurements from the onboard dual-frequency high-precision 8- NG:−21.7±14.4 NM:−25.2±16.8 IANG Integer No Yes (0.5/0.5/0.5) Yes 50 50 IAKN 12069 -5.49 11.73 -8.20 -2.00 0.67 channel Global Positioning System (GPS) receivers. The equipped laser 0 0 IANM 12089 -5.57 10.41 -8.33 -1.93 0.38 Cro. retro-reflector allows for an independent validation to the orbits. Conventionally, the associated orbit solutions (KN, NM, NG) are computed −50 −50 IANG 12089 -0.57 9.97 -0.56 -2.32 2.53 using the zero-difference GPS observations and the ambiguities remain as 00:00 00:30 01:00 01:30 02:00 02:30 03:00 00:00 00:30 01:00 01:30 02:00 02:30 03:00 Time (HH/MM) Time (HH/MM) S3B FAKN 13194 -5.83 18.55 -8.49 3.80 6.31 float values (FA). Since the GPS week 2004 (3/Jun/2018), CODE has been IAKN 13194 -3.71 11.37 -5.55 3.23 2.58 routinely generating the GNSS OSB products, which allows for undiffer- Figure 3: Non-gravitational force modeling for the Sentinel-3A satellite during its first two IANM 13203 -3.62 9.96 -5.34 3.44 2.46 enced ambiguity resolution and enable BSW to generate an integer ambi- orbit revolutions on 7/Jun/2018. Left: Each modeled force in the NG orbit solution, SRP and AF are scaled. Right: Comparison between the sum of all modeled forces and the empirical IANG 13203 -1.08 9.46 -1.48 3.07 2.24 guity (IA) orbit solution (Schaer et al. 2020). acceleration estimates in the NM solution. Similar trend also happens to the Sentinel-3B satellite. Unit: [nm=s2]. S3A ° ° FAKN 270 (AZ) IAKN 270 (AZ) 240° 300° 240° 300° Internal Consistency Check 20 210° 330° 210° 330° The scale factor estimates for AF and SRP are depicted in Fig.4, which first 15 indicates an over-performed modeling of AF. This is caused by a high or- 180° 0° 180° 0° bit and often atmospheric density models are over-performing during the 90 60 30 0 90 60 30 0 10 low solar activity seasons. It is interesting to see that the scale factors for 150° 30° 150° 30° SRP slightly differ between the two satellites. Beside that, the IANG or- 5 Figure 2: The Sentinel-3A/3B satellite baseline length variation in 2018. bit solution significantly impacts on the scale factors by introducing more 120° 60° 120° 60° 90° 90° geometry constraints, particularly for the Sentinel-3A satellite. 0 ° ° A test period is selected from 7/Jun/2018 to 14/Oct/2018 (Day of Year: IANM 270 (AZ) IANG 270 (AZ) S3A S3B 240° 300° 240° 300° 158-287), when the two Sentinel-3 satellites operated in a tandem forma- 1 FA:0.96±0.01 IA:0.91±0.01 1 FA:0.94±0.01 IA:0.93±0.01 -5 tion maintained at a separation of about 30 s. This ensures nearly identical ° ° ° ° 0.9 0.9 210 330 210 330 in-flight environment for both satellites and thereby enables direct POD -10 SRP scl.[−] Figure 1: Artist’s image of a Sentinel-3 satellite and its prime payloads (credits:ESA). performance comparisons. FA:0.65±0.13 IA:0.39±0.20 FA:0.64±0.12 IA:0.56±0.10 0.9 0.9 180° 0° 180° 0° 90 60 30 0 90 60 30 0 0.6 0.6 -15 This research outlines the recent Low Earth Orbiter (LEO) Precise Orbit 0.3 0.3 AF scl.[−] Determination (POD) methodology developments at the Astronomical In- Non-gravitational Force Models 150° 30° 150° 30° stitute of the University of Bern (AIUB) and investigates the POD perfor- 25 25 -20 The non-gravitational forces profile used in Equation 1 can be given by, 120° 60° 120° 60° ° ° mances for the two Sentinel-3 satellites. LEO POD based on the Bernese Beta[deg] 20 20 90 90 GNSS Software (BSW) was advanced by two main developments: on the ~ ~ ~ ~ ~ Jul Aug Sep Oct Jul Aug Sep Oct fNgrv = SSRP fSRP + fREF + fEMT + SAF fAF (2) Date (MMM) Date (MMM) one hand, use is made of the GNSS Observation-Specific Bias (OSB) prod- Figure 6: The azimuth- and elevation-dependent SLR residual distributions on sky-plots for I ucts provided by the Center for Orbit Determination in Europe (CODE), where, Solar Radiation Pressure (SRP), Earth REFlectivity (REF) and EMis- Figure 4: The SRP (top) and AF (middle) scale factors for the Sentinel-3A (left) and -3B (right) the Sentinel-3A satellite. The mean of residuals of the ANG solution is the closest to zero. allowing for the resolution of GNSS carrier phase ambiguities for single- siviTy (EMT) radiation pressure, and Aerodynamic Force (AF) are sur- satellites. The satellite beta angle (elevation of the Sun above orbital plane) is depicted at Similar trend also happens to the Sentinel-3B satellite. Note the reference frame is originated from SLR stations. Unit: [mm]. receiver (Schaer et al. 2020). On the other hand, a refined satellite non- face forces acting on the satellite. This research uses a description of the bottom. gravitational force modeling strategy is constructed to reduce the amount Sentinel-3 satellites in terms of an 8-plate macro-model (Montenbruck et Fig.5 shows clear orbit shifts due to the non-gravitational force modeling of empirical parameters used to compensate force modeling deficiencies. al. 2018). SRP and AF, are scaled by factors SSRP and SAF that are co- strategy. In addition, the integer ambiguity resolution further constrains Conclusions The latter is the focus of this research. estimated in POD. orbits in particularly the cross-track direction, agreeing well with the con- • The single-receiver ambiguity resolution provides significantly more Table 2: Overview of the non-gravitational force models (Mao et al. 2020). clusions in (Montenbruck et al. 2018). geometry constraints to the orbit solutions. Orbit Solutions Aerodynamic Plate-wise lift and drag S3A S3B • The non-gravitational force modeling orbit solution generates the Force DTM-2013 atmospheric density model FA:9.22±1.14 IA:6.72±0.78 FA:5.30±1.16 IA:2.78±0.75 In BSW, a kinematic (KN) LEO orbit is described as an epoch-wise trajec- 10 10 superior orbit quality. In particular the orbit offset in the radial di- tory fully independent of force models, whereas a dynamic orbit heavily HWM-14 horizontal wind model rection is almost mitigated. Rad. 0 0 Goodman accommodation coefficients relies on them. A reduced-dynamic orbit draws a compromise and re- −10 −10 • These LEO POD implementations obtain significantly better orbits Scale factor FA:1.04±1.38 IA:−0.39±0.42 FA:0.28±1.78 IA:−0.12±0.43 duces the strengths of force models using constant and/or periodic em- 10 10 and are supposed to be released in the new Bernese GNSS Software. pirical accelerations, and the so-called pseudo-stochastic parameters, e.g., Solar Plate-wise direct pressure Alo. 0 0 −10 −10 Piecewise Constant Accelerations (PCA) (Jäggi et al. 2006). The equation Radiation Spontaneous thermal re-emission for non-solar panels FA:8.45±4.42 IA:2.38±0.40 FA:−1.24±4.67 IA:0.30±0.40 of motion for this nominal (NM) reduced-dynamic orbit is given by, Pressure Conical Earth and Moon shadow 10 10 References Coefficients for optical radiation Cro. 0 0 ~r −10 −10 Jäggi, A., Hugentobler, U., and Beutler, G. (2006). Pseudo-stochastic orbit modeling techniques ¨ ~ _ Jul Aug Sep Oct Jul Aug Sep Oct ~r = −GM + f(t; ~r; ~r; Q1; :::; Qd;P1; :::; Ps) (1) Scale factor for low-Earth orbiters.
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