Semimajor Axis Errors Research Articles

Improved Initial Orbit Determination Based on the Gooding Method of Low Earth Orbit Space Debris Using Space-Based Observations

Initial orbit determination (IOD), as a basis for initial orbit association and accurate orbit determination (OD), has a crucial role in the process of obtaining space debris orbit information. Among the traditional methods, the Gooding method has better convergence and stability. In this study, the Gooding method is enhanced to solve the issues discovered. A novel initial orbit determination (IOD) method is developed using the proposed improvement measures of the single-parameter initial value determination (SIVD) method, the fitted-curve noise suppression method, the restricted corrective value solution method, the removal of trivial solutions, etc. The experimental results verify the effectiveness of the improved method. The success rate of the initial orbit determination reached 99%, and the accuracy of the solved orbit parameters was significantly improved, especially the semi-major axis (SMA) error of less than 50 km, accounting for 88% of the total. It can be seen that the method meets the demand of space-based space debris cataloging for initial orbit association and can serve in the field of space situational awareness, which has important practical significance and application potential.

Test of pulsar navigation with POLAR on TG-2 space station

Pulsar navigation, which utilizes pulsar observations to determine the position or orbit of a spacecraft, has raised interests of many countries. Several projects, such as NICER, have been proposed. POLAR on-board the TG-2 space station of China has worked for about half year and its main task is to measure the polarization of the gamma-ray bursts. POLAR can also detect the photons from pulsars due to its large effective area (about 200 cm2) and wide field of view (more than 2π Sr). In this work we report our first results testing pulsar navigation with POLAR observations. A new navigation algorithm has been used that combines the orbit dynamics and pulsar profile analysis. With 31-day-long observations of the Crab pulsar, the TG-2 orbit was determined successfully. The parameter values of the orbital elements are solved and the errors are estimated by bootstrap method. The errors with 99.7% confidence are: semi-major axis error of 7.0 m, eccentricity error of 0.00026, inclination error of 0.023° Right Ascension of the Ascending Node (RAAN) error of 0.17°, error for argument of perigee of 0.042° and mean anomaly error of 0.042°.

Long-term orbit prediction for Tiangong-1 spacecraft using the mean atmosphere model

China is planning to complete its first space station by 2020. For the long-term management and maintenance, the orbit of the space station needs to be predicted for a long period of time. Since the space station is expected to work in a low-Earth orbit, the error in the a priori atmosphere model contributes significantly to the rapid increase of the predicted orbit error. When the orbit is predicted for 20days, the error in the a priori atmosphere model, if not properly corrected, could induce a semi-major axis error of up to a few kilometers and an overall position error of several thousand kilometers respectively. In this work, we use a mean atmosphere model averaged from NRLMSISE00. The a priori reference mean density can be corrected during the orbit determination. For the long-term orbit prediction, we use sufficiently long period of observations and obtain a series of the diurnal mean densities. This series contains the recent variation of the atmosphere density and can be analyzed for various periodic components. After being properly fitted, the mean density can be predicted and then applied in the orbit prediction. Here we carry out the test with China’s Tiangong-1 spacecraft at the altitude of about 340km and we show that this method is simple and flexible. The densities predicted with this approach can serve in the long-term orbit prediction. In several 20-day prediction tests, most predicted orbits show semi-major axis errors better than 700m and overall position errors better than 400km.

Satellite formation design in orbits of high eccentricity with performance constraints specified over a region of interest: MMS phase II

The formation design problem for Phase II of the Magnetospheric Multiscale (MMS) mission is addressed using differential mean orbital elements as design variables and the Gim–Alfriend state transition matrix for relative motion propagation. The MMS mission requires a formation of four satellites in a nearly regular tetrahedron throughout a Region of Interest (RoI), defined near apogee of a highly eccentric orbit. Previous papers have addressed the problem of formation design with performance constraints specified over a RoI, and these methods are now applied to the present problem. In addition, the use of a modified along-track drift condition as a constraint to ensure long-term formation stability is investigated. The performance of the designed formations in the presence of differential semimajor axis errors is also examined. Finally, the results are verified using the NASA General Mission Analysis Tool.

Optimal Formation Design for Magnetospheric Multiscale Mission Using Differential Orbital Elements

The Magnetospheric Multiscale Mission requires a formation of four satellites in a nearly regular tetrahedron throughout a region of interest defined near the apogee of a highly eccentric reference orbit. Previous papers have addressed the design of formations in orbits of high eccentricity to maximize a quality factor in a region of interest, including the use of differential mean orbital elements as design variables. In this paper, a robust optimization method is presented to improve formation performance in the presence of formation initialization errors. Several design methods are analyzed by applying differential semimajor axis errors, which have a strong effect on the long-term stability of spacecraft formations. It is shown that large formations can satisfy mission requirements for a longer time than smaller formations, when the same magnitude of errors are considered, and generally exhibit less variation in quality factors due to these errors. The robust optimization method is applied to these smaller formations and produces results that are much more stable when semimajor axis errors are included, at a cost of some performance in the nominal error-free case. The results are verified using the NASA General Mission Analysis Tool and are shown to be reasonably accurate, except in predicting very long-term behavior. A physical analysis of the geometry of several magnetospheric multiscale formation designs is provided, and eight distinct optimal tetrahedron orientations are identified (two configurations, in which the chief satellite can be placed at any of the four vertices).

Relative Semimajor Axis Uncertainty in High Earth Orbits

S EVERAL proposed missions have identified satellite formation flying in high Earth orbit (HEO) as an enabling technology for increasing the science return while decreasing total mission risk [1,2]. Precision formationflying inHEO requires accurate estimation of the semimajor axis difference between the vehicles for state prediction, formation control, and formation maneuver planning [3– 5]. This Note derives the complete linearized mapping relating relative position and velocity error to semimajor axis uncertainty for HEO formations. The majority of relative navigation filters estimate the state of the secondary vehicle with respect to the primary in Cartesian position and velocity coordinates [6–13]. The uncertainty in the semimajor axis is found by rotating the estimated position and velocity covariance into orbital element space. Carpenter and Schiesser [3] presented the complete linearized relationship between absolute position and velocity uncertainty and semimajor axis error; however, the form of their result is not particularly intuitive. Carpenter and Alfriend [4] used a similar method to develop a simplified expression for the semimajor axis uncertainty that assumes the radial position and velocity and intrack velocity are the primary contributions. However, this assumption is not justified for eccentric orbits. The generalized relationship between relative position and velocity uncertainty and semimajor axis uncertainty is derived here explicitly. The resulting equation shows that the semimajor axis error is dependent on all of the coplanar position and velocity uncertainties in highly eccentric orbits. The coordinate frames that form the foundation of this research are described in Sec. II. The generalized relationship between position and velocity error and semimajor axis uncertainty is derived in Sec. III, and the conclusions are summarized in Sec. IV.

Differential Semimajor Axis Estimation Performance Using Carrier-Phase Differential Global Positioning System Measurements

This paper investigates the impact of navigation errors on the navigation and control aspects of formation flying spacecraft. The use of carrier-phase differential Global Positioning System measurements in relative navigation filters is analyzed, with a particular focus on the semimajor axis error. Semimajor axis error is shown to be the sum of two positive quantities that are related to the satisfaction of the balance and correlation requirements. Previous publications have suggested that a good navigation filter would yield estimates of the along-track velocity and radial position that are strongly correlated. However, practical experience with filters based on the carrier-phase differential Global Positioning System measurements has shown that this seldom occurs, even when the estimation accuracies are very good. Analytical methods and numerical simulations are used to show that the optimal semimajor axis estimate from a Kalman filter does not satisfy these requirements for any combination of measurement and process noise. Numerical examples with a fully nonlinear extended Kalman filter appear to bear out these conclusions. The combination of these simulations and analysis provides new insights on the crucial role of the process noise in determining semimajor axis knowledge.

Cyclic Spacecraft Formations: Relative Motion Control Using Line-of-Sight Measurements Only

In this paper, we develop a new nonlinear relative spacecraft motion control law based on line-of-sight measurements only. Each spacecraft tracks its neighboring spacecraft to produce a line-af-sight vector measurement, and the last spacecraft tracks again the first spacecraft to create a cyclic formation. We show that cyclic leaderless formations controlled by line-of-sight measurements only are stable in the sense of energy matching. The initial semimajor axis errors relative to a reference semimajor axis all tend to the same value, which is the centroid of the initial semimajor axis errors. The stable behavior is achieved by using both full line-of-sight feedback (range and bearing) and partial line-of-sight feedback (bearing only). We also investigate the case of leader formations, where a designated leader does not track any other spacecraft. In this case, the semimajor axes of all follower spacecraft will converge to the initial semimajor axis of the leader. We also discuss an intermediate case, in which only part of the spacecraft forms a cycle. In this case, the cyclic formation members will determine the semimajor axes of all the other, noncyclic, spacecraft. We use elementary graph theory to describe the resulting formation topologies and conclude the development with an illustrating example.