Stochastic Modeling and Estimated with Application to Orbit Prediction

Abstract

<p>The objective of satellite orbit determination is to accurately estimate a set of orbital elements which describes the orbit of the satellite, using observations of the satellite. The extended Kalman filter has been extensively used for the estimation of the orbital states. The purpose of this work is to find alternative approaches that would reduce the amount of on-line computation required. A nonlinear estimator combining the invariant imbedding concept with stochastic approximation is proposed for this application. A switching criterion utilizing the properties of tile innovations sequence is applied to the combined estimator. Pugacev's estimation theory is also highlighted and the Kalman filter equations are derived as a special case of the general theory. Alternative approaches for forecasting the observables of the satellite via stochastic modeling techniques are proposed. One-step ahead forecasts are obtained using both univariate and multivariate time-series methods. Also, a recursive algorithm for estimating the degree of differencing most suitable for a given time-series is proposed. The results of simulation indicate the efficiency and reliability of the proposed schemes.</p>