Orbit determination based on meteor observations using numerical integration of equations of motion

Recently, there has been a worldwide proliferation of instruments and networks dedicated to observing meteors, including airborne and future space-based monitoring systems . There has been a corresponding rapid rise in high quality data accumulating annually. In this paper, we present a method embodied in the open-source software program "Meteor Toolkit", which can effectively and accurately process these data in an automated mode and discover the pre-impact orbit and possibly the origin or parent body of a meteoroid or asteroid. The required input parameters are the topocentric pre-atmospheric velocity vector and the coordinates of the atmospheric entry point of the meteoroid, i.e. the beginning point of visual path of a meteor, in an Earth centered-Earth fixed coordinate system, the International Terrestrial Reference Frame (ITRF). Our method is based on strict coordinate transformation from the ITRF to an inertial reference frame and on numerical integration of the equations of motion for a perturbed two-body problem. Basic accelerations perturbing a meteoroid's orbit and their influence on the orbital elements are also studied and demonstrated. Our method is then compared with several published studies that utilized variations of a traditional analytical technique, the zenith attraction method, which corrects for the direction of the meteor׳s trajectory and its apparent velocity due to Earth's gravity. We then demonstrate the proposed technique on new observational data obtained from the Finnish Fireball Network (FFN) as well as on simulated data. In addition, we propose a method of analysis of error propagation, based on general rule of covariance transformation.