Summary
Satellite tracking data typically consist of range, range rates, azimuth or elevation angles. The measurement times are usually clustered, not all states are measured and outliers may occur due to measurement errors. Moreover, range measurements are subject to ambiguities.
Due to the fact that the actual injection orbit of a satellite may significantly deviate from the planned one, e.g. if the launcher exhibits under-performance or malfunction, a fast and reliable the determination of initial orbits using the available data is particularly important.
Based on practical problems provided by European Space Agency (ESA) the paper first gives a mathematical formulation of orbit determination problems. An l1 objective function is chosen in order to reduce the influence of outliers.
For the numerical treatment of orbit determination problems shooting strategies for estimation problems in nonlinear differential equations are described. Emphasis is put on the efficient treatment of the resulting large-scale nonlinear constrained weighted l1 optimization problem.
The performance of the resulting codes is demonstrated using tracking data from ESA's Artemis mission.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
G. Oppenhaeuser, A.G. Bird and L. van Holtz. Artemis — “A Lost Mission” on Course for a Full Recovery, ESA Bulletin No. 110, 9–16 (2002)
H. G. Bock. Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics. In: Ebert et al (eds.) Modelling of Chemical Reaction Systems, Springer Series in Chemical Physics 18, Berlin Heidelberg (1981)
H. G. Bock. Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, Bonner Mathematische Schriften 183, Bonn (1987)
H. G. Bock, E. Kostina, and J. P. Schlöder. On the Role of Natural Level Functions to Achieve Global Convergence for Damped Newton Methods. System Modelling and Optimization. Methods, Theory and Applications, M. Powell et al (Eds.), Kluwer, 51–74 (2000)
R. Gabasov, F. M. Kirillova, E. A. Kostina. An adaptive method of solving l1 extremal problems, Computational Mathematics and Mathematical Physics, vol. 38, 9, 1400–1411 (1998)
P. J. Huber. Robust Statistics, John Wiley and Sons (1981)
E. A. Kostina. The long step rule in the bounded-variable dual simplex method: numerical experiments, Mathematical Methods of Operations Research, 55, 3 (2002)
O. Montenbruck, E. Gill. Satellite Orbits, Springer, Berlin Heidelberg New York (2000)
NAG Fortran Library Manual, Mark 20, The Numerical Algorithms Group Ltd.
Spaceflight now, Febr. 21 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bock, H.G., Kostina, E., Schlöder, J.P., Gienger, G., Pallaschke, S., Ziegler, G. (2005). Robust Parameter Estimation for Identifying Satellite Injection Orbits. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-27170-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23027-4
Online ISBN: 978-3-540-27170-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)