Dynamic Triangulation for Cislunar Initial Orbit Determination

Abstract Conventional angles-only initial orbit determination algorithms assume Keplerian dynamics and are not always well-adapted to finding the orbits of objects on cislunar trajectories. We propose a solution to this problem based on the concept of dynamic triangulation, which is a type of triangulation algorithm that produces a full state estimate from non-simultaneous, line-of-sight measurements and an approximate dynamical model. In this approach, an object’s motion is approximated as rectilinear over a short segment of its orbit, which permits dynamic triangulation to generate an initial guess. This guess is then refined using the full dynamical model and a nonlinear least squares solver. The performance of this technique was tested on several types of scenarios where the observer is in low lunar orbit and the target follows a periodic cislunar orbit or an Earth-Moon transfer orbit. In these scenarios it was found that the rectilinear initial guess is typically accurate enough to converge to the true trajectory after refinement with the full dynamical model. An analytic expression for the state covariance was derived and validated.