GNSS Satellite Orbit Modeling via a Behavioral Approach

H-S. Wang, F.R. Chang

Abstract:	In this paper, a behavioral framework is proposed to solve the GNSS satellite orbit prediction problems. The concept of behavioral framework was first proposed by Jan C. Willems in a series of papers (J. C. Willems, ""From time series to linear system - part I, II, and III,"" Automatica Vol. 22, 1986.) as a generic tool for mathematical modeling of dynamical systems. In the proposed approach, the model of GPS satellites is firstly described by a kernel representation and then the problem can be solved by a structured total least-squares (STLS) algorithm. STLS algorithm is a modified version of the traditional total least-squares (TLS) method. It can be shown that the STLS algorithm is able to provide better performance than the TLS algorithm for the problems that possess a particular structure. In the case of the present paper, it is shown that the orbital determination problem has a Hankel structure; therefore the problem can be solved by an STLS algorithm subject to a Hankel structure. GPS satellite orbital prediction is particular useful for the indoor GPS application. By using the proposed method, users need not to wait for the GPS receiver to download the ephemeris data from the satellites which is usually a time-consuming process. We simply store the behavioral model in the receiver's software (or firmware). Then the satellite's orbit can be computed without collecting the broadcast ephemeris data.
Published in:	Proceedings of the 2011 International Technical Meeting of The Institute of Navigation January 24 - 26, 2011 Catamaran Resort Hotel San Diego, CA
Pages:	583 - 590
Cite this article:	Wang, H-S., Chang, F.R., "GNSS Satellite Orbit Modeling via a Behavioral Approach," Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 583-590.
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