International Journal of Engineering and Technology, Vol. 3, No. 2, 2006, pp. 263-271 ISSN 1823-1039 2006 FEIIC 263 SATELLITE ORBIT ESTIMATION USING EARTH MAGNETIC FIELD MEASUREMENTS Mohammad Nizam Filipski, Renuganth Varatharajoo Department of Aerospace Engineering, Universiti Putra Malaysia, 43400 Serdang, Selangor D.E., Malaysia Email: nizam@eng.upm.edu.my ABSTRACT This paper presents the design of an estimation algorithm for the determination of a low-Earth satellite orbit based only on the measurements of the Earth magnetic field. The algorithm is based on the extended Kalman filter (EKF) and the measure of the magnitude of the magnetic field, which provides an estimation method independent of the satellite attitude. The satellite orbit is described with a state vector formed by the classical Keplerian orbital elements. The simulation test resulted in an accurate estimation of the state vector components and yielded only a few kilometres error on the satellite position. The effect of the variation of the orbit inclination and eccentricity on the filter performances was also investigated. Keywords: Orbit Estimation, Extended Kalman Filter, Magnetic Field Measurements INTRODUCTION The issue of determining the satellite position on its orbit with the greatest possible accuracy has been investigated since the 1960s. Today’s systems of orbit determination provide position errors at the meter level and even at the centimetre level for some very specific missions like TOPEX/Poseidon [1] or GFO [2] satellites. However that degree of accuracy is not attainable without the support of some system external to the satellite: mainly Earth based stations using Satellite Laser Ranging or a combination of radar and optical sensors, and Global Positioning System (GPS). Autonomous orbit estimation methods, that do not rely on equipments other than those available onboard the satellite, have the advantages of being more reliable, less costly to operate and less vulnerable in hostile environment (jamming, loss of Earth station). One way to achieve this autonomy is to use magnetometers to measure the Earth magnetic field, which is a function of time and position. This function is well known and can easily be modelled onboard to compute the magnetic field at the satellite assumed position [3,4]. The difference between the computed and the measured magnetic field is a function of the error made in the satellite position. It is possible to determine both the orbital position and the attitude of a satellite from only the Earth magnetic field, with rate data available [5,6] or without [7-9]. The magnitude of the Earth magnetic field is sufficient to determine the satellite position. Greater accuracy can be achieved if we also know the vector direction but this requires the knowledge of the satellite attitude and is computationally more expensive [6]. In this paper we present an algorithm based on the EKF using only the magnitude of the Earth magnetic field to estimate both the satellite position and its rate of rotation. The influence of the orbit inclination and eccentricity on the efficiency of the filter is assessed through simulations. ORBIT DYNAMICS The satellite position is described by the classical Keplerian orbital elements (a, e, i, Ω, ω, ν). The semi-major axis a and the eccentricity e define the shape of the orbit. The inclination i, the right ascension of the ascending node Ω and the argument of perigee ω define the orientation of the orbit with respect to an inertial reference frame. The last element is the true anomaly; it defines the satellite position on the orbit with respect to the periapsis. The simplest and also least realistic way to model the satellite movement on its orbit is to assume that the only force acting on the satellite is the gravitational attraction from the Earth, which is represented as a perfect sphere of uniform density. The most influential forces neglected in this model, for a low-Earth orbit (LEO) satellite, are caused by the Earth’s atmosphere and the Earth’s gravitational field. The variation of the true anomaly s is given [10] (in Ref. 10, Chap. 1) by