A new least squares adjustment approach for the determination of linear meteor trajectories

Context. Precise astrometric measurements performed on meteor images are required to derive the dynamical parameters of a mete-oroid. As a consequence, the measurements carried out in this initial step will have a strong impact on the dynamical solution of an orbiting meteoroid. These measurements relate to the position of the meteor defined by the positions of pixels along its path, as well as by their uncertainties. Therefore, the use of all available information is of great importance for the subsequent processing steps. Aims. This paper examines a new geometrical approach for computing the trajectory of a meteor from multi-station observations. The model considers a more general weighting scheme based on existing stochastic information from the measurements, including the geometry between each station and the observed meteor. Methods. We present a novel mathematical model for least squares adjustment of the linear meteor trajectories within the Gauss-Helmert model, which allows the use of stochastic information from the measured direction vectors from multiple stations. Additionally, an extended stochastic model is presented that takes into account the geometric relationship between each station and the observed meteor as a weight component for each group of observations. Results. The solution of the new approach is demonstrated on a synthetic meteor example, with observations generated from multiple stations with differing precision. The geometric configuration of the stations has been chosen in such a way that it creates the necessity to include stochastic information for the observed direction vectors for a realistic solution. The results of the newly developed approach are compared with those from established methods in the literature. Future investigations and optimisations for developing an even more improved meteor trajectory model are being addressed.