Position and velocity estimation with a low Earth orbit regional navigation satellite constellation

Position and velocity estimation using Global Navigation Satellite Systems (GNSS) has been widely studied and implemented. In contrast to existing GNSS, the idea of using low Earth orbit (LEO) satellites for position and velocity determination is relatively new. On one hand, the launch to LEO is more affordable compared to GNSS orbits. On the other hand, LEO satellites provide reduced coverage and suffer from orbit determination uncertainties. In this article, we study position and velocity estimation for an aerial platform using signals from a LEO satellite constellation, designed to produce a relatively long coverage duration, while minimizing the geometric dilution of precision. We determine the receiver's position by using the trilateration method and the velocity by using Doppler estimation, and improve the accuracy thereof by utilizing an Extended Kalman Filter (EKF). We suggest a solution for the trilateration initialization problem, which arises for LEO navigation satellites, which relies on averaging the Earth projection of all the satellites within sight. We examine two scenarios, one wherein the EKF's dynamical model matches the reference dynamical model, and another with a model mismatch. When the dynamical model is approximated, the EKF reduces the position and velocity errors considerably. When the dynamical model is known, the position and velocity errors can be reduced by an order of magnitude.