GNSS Satellite Orbit Modeling via a Behavioral Approach

摘要

In this paper, a behavioral framework is proposed to solvernthe GNSS satellite orbit prediction problems. The conceptrnof behavioral framework was first proposed by Jan C.rnWillems in a series of papers (J. C. Willems, "From timernseries to linear system - part Ⅰ， Ⅱ， and Ⅲ," AutomaticarnVol. 22, 1986.) as a generic tool for mathematical modelingrnof dynamical systems. In the proposed approach, thernmodel of GPS satellites is firstly described by a kernelrnrepresentation and then the problem can be solved by arnstructured total least-squares (STLS) algorithm. STLSrnalgorithm is a modified version of the traditional totalrnleast-squares (TLS) method. It can be shown that thernSTLS algorithm is able to provide better performancernthan the TLS algorithm for the problems that possess arnparticular structure. In the case of the present paper, it isrnshown that the orbital determination problem has arnHankel structure; therefore the problem can be solved byrnan STLS algorithm subject to a Hankel structure. GPSrnsatellite orbital prediction is particular useful for the indoorrnGPS application. By using the proposed method,rnusers need not to wait for the GPS receiver to downloadrnthe ephemeris data from the satellites which is usually arntime-consuming process. We simply store the behavioralrnmodel in the receiver’s software (or firmware). Then thernsatellite’s orbit can be computed without collecting thernbroadcast ephemeris data.