  It has recently been shown by Egal et al. (2017) that some types of existing
meteor in-atmosphere trajectory estimation methods may be less accurate than
others, particularly when applied to high precision optical measurements. The
comparative performance of trajectory solution methods has previously only been
examined for a small number of cases. Besides the radiant, orbital accuracy
depends on the estimation of pre-atmosphere velocities, which have both random
and systematic biases. Thus it is critical to understand the uncertainty in
velocity measurement inherent to each trajectory estimation method.
  In this first of a series of two papers, we introduce a novel meteor
trajectory estimation method which uses the observed dynamics of meteors across
stations as a global optimization function and which does not require either a
theoretical or empirical flight model to solve for velocity. We also develop a
3D observational meteor trajectory simulator that uses a meteor ablation model
to replicate the dynamics of meteoroid flight, as a means to validate different
trajectory solvers.
  We both test this new method and compare it to other methods, using synthetic
meteors from three major showers spanning a wide range of velocities and
geometries (Draconids, Geminids, Perseids). We determine which meteor
trajectory solving algorithm performs better for: all-sky, moderate field of
view, and high-precision narrow-field optical meteor detection systems. The
results are presented in the second paper in this series. Finally, we give
detailed equations for estimating meteor trajectories and analytically
computing meteoroid orbits, and provide the Python code of the methodology as
open source software.
