LYAPUNOV STABILITY ANALYSIS OF AN ORBIT DETERMINATION PROBLEM

Statistical orbit determination is an important part of tracking satel lites and predicting their future location. This is accomplished by pr ocessing the raw observation data from ground stations tracking satell ites in orbit and estimating the location of these satellites. Kalman filter theory is a popular statistical process but it is not commonly used for satellite orbit determination because it exhibits poor stabil ity characteristics in this application. In particular, an Extended Ka lman Filter (EKF) is needed for this application because the orbit det ermination problem is a nonlinear one. The EKF does not lend itself we ll to the traditional eigenvalue stability analysis, which is applicab le for linear, time-invariant systems. If the stability characteristic s of the EKF used for the orbit determination problem were better unde rstood, it could become useful for these applications. A stability ana lysis concept which has received much attention is Lyapunov's stabilit y theory. The focus of this paper is to apply the second method of Lya punov (or the direct method) to evaluate the stability characteristics of an EKF estimating a satellite's orbit using simulated radar data f rom ground tracking stations at Mahe Island and Thule. Specifically, a Lyapunov function is used to analyze the stability characteristics of that EKF while selecting the weighting matrices of the filter for the satellite orbit determination problem.