Improved Laplace Earth Satellite Orbit Determination Using Line-of-Sight Projective Coordinates

Abstract

This study aimed to improve the accuracy, efficiency, range of applicability, and numerical stability of the classical Laplace method for preliminary orbit determination when the observing sensor and the observed object are both in idealized Keplerian geocentric elliptical orbits. The improvements that were made flow largely from representing the line of sight by stabilized projective rather than angular coordinates, such as declination and right ascension or local azimuth and elevation. The Laplace classical method determines the orbital position and velocity of an object in space from three line-of-sight unit vectors pointing from the observing sensor to the observed object and the corresponding sensor inertial positions and velocities at the three observation times. The performance improvement of the modernized algorithm on a set of two orbit test cases is shown, in which the observing electro-optical sensor is carried aboard a geostationary satellite. Moreover, this paper shows how to solve the problem of choosing the right orbit from the two feasible candidates that correspond to the two roots of the classical deflated seventh degree polynomial with a single additional line-of-sight observation.