A Hybrid ECOM Model for Solar Radiation Pressure Effect on GPS Reference Orbit Derived by Orbit Fitting Technique

A hybrid ECOM (Empirical CODE Orbit Model) solar radiation pressure (SRP) model, which is termed ECOMC in this work, is proposed for global navigation satellite system (GNSS) orbit modeling. The ECOMC is mainly parameterized by both ECOM1 and ECOM2 models. The GNSS orbit mainly serves as a reference datum not only for its ranging measurement but also for the so-called precise point positioning (PPP) technique. Compared to a complex procedure of orbit determination with real tracking data, the so-called orbit fitting technique simply uses satellite positions from GNSS ephemeris as pseudo-observations to estimate the initial state vector and SRP parameters. The accuracy of the reference orbit is mainly dominated by the SRP, which is usually handled by either ECOM1 or ECOM2. However, the reference orbit derived by ECOM1 produces periodic variations on orbit differences with respect to International GNSS Service (IGS) final orbit for GPS IIR satellites. Such periodic variations are removed from a reference orbit formed using the ECOM2 model, which, however, yields large cross-track orbit errors for the IIR and IIF satellites. Such large errors are attributed to the fact that the ECOM2 intrinsically lacks 1 cycle per revolution (CPR) terms, which stabilize the estimations of the even-order CPR terms in the satellite-Sun direction when the orbit fitting is used. In comparison, a reference orbit constructed with the ECOMC model is free of both the periodic variations from the ECOM1 and the large cross-track orbit errors from the ECOM2. The above improvements from the ECOMC are associated with (1) the even CPR terms removing the periodic variations and (2) the 1 CPR terms compensating for the force mismodeling at = 90° and 270°, where the is the argument of the latitude of the satellite with respect to the Sun. The parameter correlation analysis also presents that the direct SRP estimation is sensitive to the 1 and 2 CPR terms in the ECOMC case. In addition, the root-mean-square (RMS) of orbit difference with respect to IGS orbit is improved by ~40%, ~10%, and ~50% in the radial, along-track, and cross-track directions, respectively, when the SRP model is changed from the ECOM2 to the ECOMC. The orbit accuracy is assessed through orbit overlaps at day boundaries. The accuracy improvements of the ECOMC-derived orbit over the ECOM2-derived orbit in the radial, along-track, and cross-track directions are 13.2%, 14.8%, and 42.6% for the IIF satellites and 7.4%, 7.7%, and 35.0% for the IIR satellites. The impact of the reference orbit using the three models on the PPP is assessed. The positioning accuracy derived from the ECOMC is better than that derived from the ECOM1 and ECOM2 by approximately 13% and 20%, respectively. This work may serve as a reference for forming the GNSS reference orbit using the orbit fitting technique with the ECOMC SRP model.

Precise Relative Orbit Determination for Chinese TH-2 Satellite Formation Using Onboard GPS and BDS2 Observations

TH-2 is China’s first short-range satellite formation system used to realize interferometric synthetic aperture radar (InSAR) technology. In order to achieve the mission goal of InSAR processing, the relative orbit must be determined with high accuracy. In this study, the precise relative orbit determination (PROD) for TH-2 based on global positioning system (GPS), second-generation BeiDou navagation satellite system (BDS2), and GPS + BDS2 observations was performed. First, the performance of onboard GPS and BDS2 measurements were assessed by analyzing the available data, code multipath errors and noise levels of carrier phase observations. The differences between the National University of Defense Technology (NDT) and the Xi’an Research Institute of Surveying and Mapping (CHS) baseline solutions exhibited an RMS of 1.48 mm outside maneuver periods. The GPS-based orbit was used as a reference orbit to evaluate the BDS2-based orbit and the GPS + BDS2-based orbit. It is the first time BDS2 has been applied to the PROD of low Earth orbit (LEO) satellite formation. The results showed that the root mean square (RMS) of difference between the PROD results using GPS and BDS2 measurements in 3D components was 2.89 mm in the Asia-Pacific region. We assigned different weights to geostationary Earth orbit (GEO) satellites to illustrate the impact of GEO satellites on PROD, and the accuracy of PROD was improved to 7.08 mm with the GEO weighting strategy. Finally, relative orbits were derived from the combined GPS and BDS2 data. When BDS2 was added on the basis of GPS, the average number of visible navigation satellites from TH-2A and TH-2B improved from 7.5 to 9.5. The RMS of the difference between the GPS + BDS2-based orbit and the GPS-based orbit was about 1.2 mm in 3D. The overlap comparison results showed that the combined orbit consistencies were below 1 mm in the radial (R), along-track (T), and cross-track (N) directions. Furthermore, when BDS2 co-worked with GPS, the average of the ambiguity dilution of precision (ADOP) reduced from 0.160 cycle to 0.153 cycle, which was about a 4.4% reduction. The experimental results indicate that millimeter-level PROD results for TH-2 satellite formation can be obtained by using onboard GPS and BDS2 observations, and multi-GNSS can further improve the accuracy and reliability of PROD.

A More Reliable Orbit Initialization Method for LEO Precise Orbit Determination Using GNSS

Precise orbit determination (POD) using GNSS has been rapidly developed and is the mainstream technology for the navigation of low Earth orbit (LEO) satellites. The initialization of orbit parameters is a key prerequisite for LEO POD processing. For a LEO satellite equipped with a GNSS receiver, sufficient discrete kinematic positions can be obtained easily by processing space-borne GNSS data, and its orbit parameters can thus be estimated directly in iterative manner. This method of direct iterative estimation is called as the direct approach, which is generally considered highly reliable, but in practical applications it has risk of failure. Stability analyses demonstrate that the direct approach is sensitive to oversized errors in the starting velocity vector at the reference time, which may lead to large errors in design matrix because the reference orbit may be significantly distorted, and eventually cause the divergence of the orbit parameter estimation. In view of this, a more reliable method, termed the progressive approach, is presented in this paper. Instead of estimating the orbit parameters directly, it first fits the discrete kinematic positions to a reference ephemeris in the form of the GNSS broadcast ephemeris, which construct a reference orbit that is smooth and close to the true orbit. Based on the reference orbit, the starting orbit parameters are computed in sufficient accuracy, and then the final orbit parameters are estimated with a high accuracy by using discrete kinematic positions as measurements. The stability analyses show that the design matrix errors are reduced in the progressive approach, which would assure more robust orbit parameter estimation than the direct estimation approach. Various orbit initialization experiments are performed on the KOMPSAT-5 and FY3C satellites. The results have fully verified the high reliability of the proposed progressive approach.

Asteroids orbit determination using INPOP19a adjusted on GAIA observations: strategy and validation.

<p>Since December 2013, the GAIA spacecraft (ESA) is observing the sky with an unprecedented accuracy. Gaia DR2, released in April 2018, contains the position and epoch of 14099 known solar system objects (SSOs) representing more than 2 million observations collected during the first 22 months of operation. In this presentation, w<span>e used the new released INPOP19a planetary ephemeride</span><span>s</span><span> to perform the</span><span>ir</span><span> orbital </span><span>ad</span><span>justment and compare them to radar and </span><span>optical </span><span>ground-based </span><span>observation</span><span>s.</span><span> In</span><span> order to reduce the time of computation and in </span><span>anticipation</span><span> of the huge amount of data</span><span>s</span><span> expected with future DR3, a specific solving strategy for the normal equations </span><span>of the Gauss-Newton algorithm</span><span> is presented, making the best use of the model design. </span><span>We obtain post-fit residuals that are closed to the expected performance of GAIA and overall consistent with the values announced by the DR2 reference orbit determination (see Gaia Collaboration et al 2018). </span><span>I</span><span>n orde</span><span>r t</span><span>o disccus the reliability of the obtained orbit</span><span>s</span><span>, a</span><span> combin</span><span>a</span><span>ti</span><span>on </span><span>with radar an</span><span>d</span><span> optical ground based observations </span><span>was performed</span><span> for 23 objects using two different </span><span>numerical </span><span>methods: </span><span>a </span><span>systematic exploration of the weighting scheme coupled with a residual post-fit analysis, and a Least Square Variance Component Estimation </span><span>adjustment </span><span>algorithm </span><span>(LSVCE). </span><span>Such methods </span><span>can be extended to </span><span>all </span><span>inverse problems </span><span>within the framework of </span><span>least-square formalism.</span></p>

A Hybrid-Precision Numerical Orbit Integration Technique for Next Generation Gravity Missions

<p>In Next Generation Gravity Missions (NGGM) the Laser Ranging Interferometer (LRI) is applied to measure inter-satellite range rate with nanometer-level precision. Thereby the precision of numerical orbit integration must be higher or at least same as that of LRI and the currently widely-used double-precision orbit integration technique cannot meet the numerical requirements of LRI measurements. Considering quadruple-precision orbit integration arithmetic is time consuming, we propose a hybrid-precision numerical orbit integration technique, in which the double- and quadruple-precision arithmetic is employed in the increment calculation part and orbit propagation part, respectively. Since the round-off errors are not sensitive to the time-demanding increment calculation but to the least time-consuming orbit propagation, the proposed hybrid-precision numerical orbit integration technique is as efficient as the double-precision orbit integration technique, and as precise as the quadruple-precision orbit integration. By using hybrid-precision orbit integration technique, the range rate precision is easily achieved at 10-12m/s in either nominal or Encke form, and furthermore the sub-nanometer-level range precision is obtainable in the Encke form with reference orbit selected as the best-fit one. Therefore, the hybrid-precision orbit integration technique is suggested to be used in the gravity field solutions for NGGM.</p>

Design of High Pointing Accuracy NPSAT-1 Satellite Attitude Systems of Armature Controlled DC Motor with utilization for PD Controller

An Attitude control system plays the important role to maintain the satellite to desired attitude orientations. The intended application of NANO satellite in low earth orbits (LEO) helps find transient responses with and without controllers. LEO satellites typically orbit at an altitude ranging between160-2000 km. LEO satellites are widely used for remote sensing, navigation, and military surveillance applications. The Nano NPSAT-1 satellite attitude control systems (ACS) are described in this research work. The high pointing accuracy attitude estimation and feedback control systems are presented. The design specifications have been taken to meet the accuracy requirements (desired value ≤ 0.2 seconds) of Nano satellite attitude control. The feedback signal from on-board sensors compared with reference orbit trajectory and implementation of the Proportional Derivative (PD) controller is constructed. An algorithm of Nano satellite (NPSAT-1) attitude control is implemented using MATLAB Tools. In addition, the closed loop poles help find the gain of the system using Root Locus (RL) methods. The satellite control system is used to improve the transient response like overshoot and settling time of the system. Thus, the design of attitude control to improve the rise time, the settling time, the maximum overshoot, and no steady state error was carried out.

Ballistic design of missions involving the delivery of Lunar soil to the Earth

The paper discusses the design of a mission for delivering lunar soil to the Earth. The analysis of its main stages is carried out. These stages include possible flight pattern selection, analysis of the flight from the Earth to the circular orbit of the Moon artificial satellite, determination of trajectories of removal from lunar surface into the reference orbit, the search for return paths that depart from the Moon and fall into a given area on the Earth’s surface. A variant of determining the initial approximation for the method of return paths constructing is proposed. It is based on solving a two-parameter boundary value problem in the central field of the Earth. Varying the duration of the flight from the Moon to the Earth and the time of the spacecraft approach to the Earth, pointing return trajectory into vicinity of the polygon P is achieved for a given perigee radius. The article presents the main characteristics of the mission obtained using this technique.