Optimizing Radiation Pressure Modeling for Improved Thermospheric Density and Wind Estimation from GRACE Accelerometer Data

The real-time precise orbit is an essential prerequisite for a real-time precise point positioning service. Focusing on the impact of ambiguity resolution on real-time orbital precision, we propose an efficient approach for real-time ambiguity resolution, which consists of two modules. The first module resolves the double-differenced ambiguities according to their proximity to the nearest integer. The second module sequentially adds the resolved integer ambiguity constraints to the square-root information filter process, after confirming that the same constraints have not been imposed before the current epoch. To validate our method, GPS data collected from 100 globally distributed stations are used to simulate a real-time precise orbit determination. The convergence performance is analyzed, and the accuracy of the orbit is evaluated. The results show that: (1) Almost 90% of the double-differenced ambiguities are fixed correctly in real time for baselines shorter than 1000 km. (2) After application of the proposed approach, the root-mean-square errors of all the satellite orbits are reduced from (5.9, 3.4, 2.3) cm to (4.7, 2.6, 2.2) cm for the along-track, cross-track and radial directions, respectively, with improvements of about 22% for the along-track and cross-track directions, and 6% for the radial direction. (3) Simulated real-time orbits determined with this method can obtain almost the same accuracy as some ultra-rapid products and, particularly, better accuracy can be achieved for eclipsing satellites.

No abstract available.

Impact of orbit modeling on DORIS station position and Earth rotation estimates

For precise orbit determination (POD) and precise applications with POD products, one of the critical issues is the modeling of non-conservative forces acting on satellites. Since the official publication of Galileo satellite metadata in 2017, analytical models including the box-wing model and thermal thrust models have been established to absorb a substantial amount of solar radiation pressure (SRP) and thermal thrust. These models serve as the foundation for the best overall modeling approach, combining the analytical box-wing model and thermal thrust model with parameterization of the remaining non-conservative perturbing forces using various optimized Empirical CODE Orbit Models (ECOMs) of the Center for Orbit Determination in Europe (CODE). Firstly, we have demonstrated the significance of the second-order signals in the D direction and the first-order signals in the B direction through spectral analyses of the pure box-wing model, which are consistent with the currently recommended 7-parameter Empirical CODE Orbit Model 2 (ECOM2). In spite of this, we still found that degradation in orbit accuracy frequently occurs during deep eclipse seasons when using the ECOM2 model. We confirm a high-frequency signal existing in the fluctuating orbit overlap differences through the spectral analysis. Considering this, the ECOM2 force model should be extended to higher order and adapted to absorb the remaining effects of potential perturbing forces. After extending the ECOM2 force model to the sixth order in the Sun direction, we demonstrated the significance of fourth- and sixth-order sine terms for deep eclipses. Due to the higher-order periodic terms, the averaged RMS values of orbit overlap difference over deep eclipses can be reduced from 5.3, 10.8, and 23.8 cm to 3.2, 3.9, and 9.9 cm for in-orbit validation (IOV) satellites, from 5.0, 8.6, and 17.7 cm to 3.0, 3.0, and 7.1 cm for the first generation of full operational capability (FOC-1) satellites, and from 5.4, 8.6, and 19.0 cm to 3.6, 3.6, and 7.4 cm for the second generation of FOC (FOC-2) satellites, in the radial, cross-track, and along-track directions, respectively. Fluctuations with a peak amplitude of approximately 0.4 nm/s2 in the bias in the solar panel axis (Y) direction (Y-bias) are effectively mitigated by the higher-order terms. Due to the higher-order terms, the vertical positioning errors during kinematic precise point positioning (PPP) convergence can be improved from 42.3 to 37.1 cm at the 95.5% confidence level. Meanwhile, a low correlation level of up to 0.02 is found between the newly introduced higher-order parameters and earth rotation parameters (ERPs).

Due to an increasing requirement for high accuracy orbital information for low Earth orbit (LEO) satellites, precise orbit determination (POD) of LEO satellites is a topic of growing interest. To assure the safety and reliability of the applications requiring high accuracy LEO orbits in near-real-time, integrity monitoring (IM) is an essential operation of the POD process. In this contribution, the IM strategy for LEO POD in both the kinematic and reduced-dynamic modes is investigated. The overbounding parameters of the signal-in-space range error are investigated for the GPS products provided by the International GNSS Service’s Real-Time Service and the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis service. Benefiting from the dynamic models used and the improved model strength, the test results based on the data of the LEO satellite GRACE FO-1 show that the average-case mean protection levels (PLs) can be reduced from about 3–4 m in the kinematic mode to about 1 m in the reduced-dynamic mode in the radial, along-track and cross-track directions. The overbounding mean values of the SISRE play the dominant role in the final PLs. In the reduced-dynamic mode and average-case projection, the IM availabilities reach above 99% in the radial, along-track and cross-track directions with the alert limit (AL) set to 2 m. The values are still above 98% with the AL set to 4 m, when the duty cycle of tracking is reduced to 40%, e.g., in the case of power limits for miniature satellites such as CubeSats.

Orbit determination and gravity field recovery from Doppler tracking data to the Lunar Reconnaissance Orbiter

Attitude determination & control system design for gravity recovery missions like GRACE

The electrostatic accelerometer, assembled on gravity satellite, serves to measure all non-gravitational accelerations caused by atmosphere drag or solar radiation pressure, etc. The proof-mass center of the accelerometer needs to be precisely positioned at the center of gravity satellite, otherwise, the offset between them will bring measurement disturbance due to angular acceleration of satellite and gradient. Because of installation and measurement errors on the ground, fuel consumption during the in-flight phase and other adverse factors, the offset between the proof-mass center and the satellite center of mass is usually large enough to affect the measurement accuracy of the accelerometer, even beyond its range. Therefore, the offset needs to be measured or estimated, and then be controlled within the measurement requirement of the accelerometer by the center of mass (COM) adjustment mechanism during the life of the satellite. The estimation algorithm based on EKF, which uses the measurement of accelerometer, gyro and magnetometer, is put forward to estimate the offset, and the COM adjustment mechanism then adjusts the satellite center of mass in order to make the offset meet the requirement. With the special configuration layout, the COM adjustment mechanism driven by the stepper motors can separately regulate X, Y and Z axes. The associated simulation shows that the offset can be controlled better than 0.03 mm for all the axes with the method mentioned above.

In gravimetry satellite missions GRACE (Gravity Recovery and Climate Experiment) and GRACE-FO (GRACE Follow-On), accelerometer measurements from both satellites are necessary for the gravity field recovery. The accelerometer provides accurate measurements of the non-gravitational forces acting on the spacecraft, such as atmospheric drag, solar radiation pressure and albedo. These measurements are required to separate any non-gravitational effect from the sought-after gravitational perturbations on the spacecraft motion. Therefore, the quality of accelerometer data, denoted as ACC products, significantly affects the quality of gravity field models.Near the end of the GRACE mission, due to the reduced battery capacity, the on-board accelerometer of the GRACE-B was turned off and its measurements were replaced by synthetic accelerometer data, called transplant data. The transplant data are generated by a series of adjustments to the GRACE-A ACC data. A similar approach was also employed for the GRACE-FO mission, when the GRACE-D ACC data degraded and were required to be replaced with synthetic data as well. Using the transplant data in both missions is one of the main challenges of providing high-quality gravity field models.We investigate the feasibility of Machine Learning (ML) algorithms for the recovery of GRACE-B ACC based on GRACE-A measurements and orbital data such as shadow factor and β angle. Taking advantage of ~14 years of GRACE-B measurements, this work aims to develop a model which can predict the missing accelerometer data under different orbital conditions. Two different architectures are implemented to forecast GRACE-B accelerometer data: Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). The performance is evaluated using the Root Mean Square Error (RMSE) and by comparing the predicted data with the calibrated real data in the evaluated period. Furthermore, the ML-based ACC products will be compared to the transplant products and their impact on the gravity field will be discussed.

Thanks to the high performance of the spaceborne GPS receiver and the availability of precise IGS orbit and clock products, Zero-difference kinematic precise orbit determination (POD) has turned out to be a new method in orbit determination for the LEO satellites. Zero-difference Kinematic POD, which is based on the GPS measurements only from the spaceborne GPS receiver, is independent of force models and orbit design. From that point of view, kinematic POD is well suited for the Earth Observation satellites at very low altitudes, such as CHAMP, GRACE and GOCE et al. This paper reviews the basic zero-difference GPS model, and the corrections in the model are discussed. A block-wise least squares algorithm, which firstly separates the parameters in to groups and then solves the parameter by elimination and back-substitution, is discussed and proposed for the kinematic orbit determination. The orbit solutions for one week of GRACE observations are calculated Comparisons with the published Rapid Science Orbit (RSO) indicate that the accuracy in radial, along-track and cross-track direction can achieve 5.5cm, 5.5cm and 6.6cm respectively, and the RMS in distance is better than 8.6cm.

Compared to the traditional ionospheric-free (IF) precise point positioning (PPP) model, the undifferenced and uncombined (UU) PPP has the advantages of lower observation noise and the ability to obtain ionospheric information. Thanks to the IGS (International GNSS Service), real-time service (RTS) can provide RT vertical total electron content (VTEC) products, and an enhanced RT UU-PPP based on the RT-VTEC constraints can be achieved. The global performance of the BeiDou Navigation Satellite System-2 (BDS-2) and BDS-3 joint RT UU-PPP using different RTS products was investigated. There is not much difference in the RTS orbit accuracy of medium earth orbit (MEO) satellites among all analysis centers (ACs), and the optimal orbit accuracy is better than 5, 9, and 7 cm in the radial, along-track, and cross-track directions, respectively. The orbit accuracy of inclined geosynchronous orbit (IGSO) satellites is worse than that of MEO satellites. Except for CAS of 0.46 ns, the RTS clock accuracy of MEO satellites for other ACs achieves 0.2–0.27 ns, and the corresponding accuracy is about 0.4 ns for IGSO satellites. In static positioning, due to the limited accuracy of RT-VTEC, the convergence time of the enhanced RT UU-PPP is longer than that of RT IF-PPP for most ACs and can be better than 25 and 20 min in the horizontal and vertical components, respectively. After convergence, the 3D positioning accuracy of the static RT UU-PPP is improved by no more than 8.7%, and the optimal horizontal and vertical positioning accuracy reaches 3.5 and 7.0 cm, respectively. As for the kinematic mode with poor convergence performance, with the introduction of RT-VTEC constraints, the convergence time of RT UU-PPP can be slightly shorter and reaches about 55 and 60 min in the horizontal and vertical components, respectively. Both the horizontal and vertical positioning accuracies of the kinematic RT UU-PPP can be improved and achieve around 7.5 and 10 cm, respectively.

Modeling approaches for precise relativistic orbits: Analytical, Lie-series, and pN approximation

In many applications of satellite geodesy one is interested in derivatives of the gravitational potential, expressed in a satellite fixed triad, which is oriented in the along-track, cross-track and radial direction. For instance Hill equations or Gauss-type of equations employ such triads. Perturbation analyses, using these equations, require potential derivatives along the coordinate axes. Also space-borne gradiometry makes use of the concept of a local cartesian triad along the orbit, in which the gradient of the gravity vector is expressed.KeywordsSpherical HarmonicGravitational PotentialGravity GradientGravity VectorRepresentation CoefficientThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Russian Global Navigation Satellite System (GLONASS) satellites have a stretched body shape and take a specific attitude mode inside the eclipse. Based on previous studies, the new Empirical CODE orbit model (ECOM2) performs better than the classical ECOM model if a satellite has elongated shape or does not maintain yaw-steering mode, and the use of an a priori box-wing (BW) model improves the orbits significantly when employing the ECOM model. However, we find that the ECOM model performs better than the ECOM2 model for GLONASS satellites outside eclipse seasons, while it performs two times worse in eclipse seasons. The use of the conventional box-wing model results in very little improvement. By assessing the ECOM Y _{0} estimates, we conclude that there are potential radiators on the -x surface of GLONASS satellites causing orbit perturbations also inside the eclipse. The higher-order Fourier terms of the ECOM2 model can compensate for such effects better than the ECOM model. Based on this finding, we first confirm that GLONASS-K satellites take a similar attitude mode as GLONASS-M satellites inside the eclipse. Then, we adjust optical parameters of GLONASS satellites as part of precise orbit determination (POD) considering the potential radiator and thermal radiation effects. Finally, the adjusted parameters are introduced into a new box-wing model and jointly used with the ECOM and ECOM2 model, respectively. Results show that the amplitude and the dependency of the empirical parameters on the beta angle are greatly reduced for both ECOM and ECOM2 models. Rather than the conventional box-wing model, the new box-wing model reduces the orbit misclosure between two consecutive arcs for both GLONASS-M and GLONASS-K satellites. In particular, the improvement in GLONASS-M satellites is more than 30% for the ECOM model during eclipse seasons. Further evaluation from 24-h predicted orbits demonstrates that the improvement during eclipse seasons is mainly in along- and cross-track directions. Finally, we validate GLONASS satellite orbits using Satellite Laser Ranging (SLR) observations. The use of the new box-wing model reduces the spurious pattern of the SLR residuals as a function of beta and Delta u significantly, and the linear dependency of the SLR residuals on the elongation drops from as large as -0.760 mm/deg to almost zero for both ECOM and ECOM2 models. In general, GLONASS-M satellites benefit more from the new a priori box-wing model and the BW+ECOM model results in the best SLR residuals, with an improvement of about 50% and 20%, respectively, for the mean and standard deviation (STD) values with respect to the orbit products without a priori model.

In order to study the outflows from accretion disks, we solve the set of hydrodynamic equations for accretion disks in the spherical coordinates ($r\theta\phi$) to obtain the explicit structure along the $\theta$ direction. Using self-similar assumptions in the radial direction, we change the equations to a set of ordinary differential equations (ODEs) about the $\theta$-coordinate, which are then solved with symmetrical boundary conditions in the equatorial plane, and the velocity field is obtained. The $\alpha$ viscosity prescription is applied and an advective factor $f$ is used to simplify the energy equation.The results display thinner, quasi-Keplerian disks for Shakura-Sunyaev Disks (SSDs) and thicker, sub-Keplerian disks for Advection Dominated Accretion Flows (ADAFs) and slim disks, which are consistent with previous popular analytical models. However, an inflow region and an outflow region always exist, except when the viscosity parameter $\alpha$ is too large, which supports the results of some recent numerical simulation works. Our results indicate that the outflows should be common in various accretion disks and may be stronger in slim disks, where both advection and radiation pressure are dominant. We also present the structure dependence on the input parameters and discuss their physical meanings. The caveats of this work and possible improvements in the future are discussed.