Stereovision for surveillance of Earth orbiting objects: Two methods and their validation with synthetic data

Due to the new trend of space economy and to the resulting increase of space objects, Space Surveillance and Space Traffic Management are becoming essential to reduce the risk of in-orbit collisions and of potential on Earth damages from uncontrolled re-entries. Ground based optical observations, where cameras are coupled with telescopes, represent an invaluable resource for space debris monitoring and tracking. Observations from one single site may provide angular celestial coordinates of a space object, but they must be supplemented with filters and astrodynamic models to provide an estimate of the object trajectory. An alternative approach is the use of multi-site optical observations, where images of the same portion of sky collected with different cameras are matched to retrieve the instantaneous position of space objects without the need of a priori knowledge of the object orbit parameters. Therefore, multi-site observations are extremely convenient to track uncontrolled Earth re-entry and close approach, where the orbit parameters are generally not stable. Here we focus on two-cameras systems and we discuss the use of two triangulation methods: one based on analytic geometry, the other one based on projective geometry. As a proof-of-concept, we compare the performance of the two methods in terms of accuracy in the reconstruction on synthetic images that reproduce the night sky - including orbiting objects and stars - from different locations. To simulate realistic data sets, we produced images taking into account the effect of refraction and annual aberration on the stars, and we added gaussian noise to the position of the stars and of the space objects on the images. The comparison between the two methods shows that they are both valuable, with the projective method being more robust against noise.