Optimization of multi-satellite constellations for GNSS spectrum monitoring applications via AOA-TDOA receivers in LEO

Satellite-based platforms in Low Earth orbit (LEO) constellations equipped with advanced sensors can be a solution to detect and locate non-cooperative emitters, such as ground-based interferences. This article deals with the fundamental question on the distribution of the satellites within a constellation in order to improve the precision of the location estimation and addresses the problem of the spatial optimization of a cluster of satellites in LEO which are able to perform both Angle of Arrival (AOA) and Time Difference of Arrival (TDOA) measurements. The study provides a step-by-step theoretical methodology to build the optimization problem on the Position Dilution of Precision (PDOP) taking into account the orbital kinematics of the satellites, the measurement errors on AOA-TDOA receivers, the constraints due to the Line of Sight (LOS), and minimum Signal-to-Noise Ratio (SNR) values in order to guarantee certain probabilities of detection and false alarms. An exemplary application of the optimization approach is presented for GNSS (Global Navigation Satellite System) spectrum monitoring in L1/E1 band through a system composed of two satellites in LEO considering a conservative constrained scenario not too far from the Nadir direction. The results obtained reveal emerging patterns of symmetry and anti-symmetry in the angles related to the optimal deployment of the satellite constellation, such as the right ascension of the ascending node, the true anomaly, and the spacing angle between the satellites with respect to the emitter position.