On the Information Evolution and Sensor Deployment for Multi-Spacecraft Cooperative Visual 3D Sensing of Orbital Targets

Multi-spacecraft cooperative visual 3D sensing is an essential technique in space-based optical space situational awareness to acquire the 3D pose and structure of orbital targets, and how to optimize spacecraft deployment to improve sensing performance receives wide research concern. This paper establishes a statistical framework for multi-spacecraft cooperative visual 3D sensing of orbital targets under the natural fly-around mode from a perspective of information gains, and studies both the sensing information evolution during orbital motion and the optimal orbit deployment of multiple spaceborne camera sensors on spacecrafts. Specifically, a Fisher information matrix (FIM)-based metric is first proposed to evaluate the anisotropic sensing property of spaceborne camera sensors. Then the evolution of sensing information during orbital motion is characterized by closed-form expressions for the FIM contributed by visual observations captured by each spacecraft, with geometric interpretations given by information ellipsoid in the eigenspace. Based on the spatiotemporal complementarity of visual observations, we also determine the optimal orbit deployment of all the spaceborne camera sensors to improve cooperative sensing performance of the orbital target, and give a lower bound for sensing error through an extension without motion constraints. Numerical results validate the effectiveness of our theoretic results and the performance of our sensor deployment schemes, and also reveal the impacts of orbital motion on visual sensing. Our work provides guidelines for subtle cooperative orbit design for specific sensing tasks.