Distributed decentralized EKF for very large-scale networks with application to satellite mega-constellations navigation

The design of a decentralized and distributed filtering solution for large-scale networks of interconnected systems is addressed considering (i) generic nonlinear dynamics and (ii) generic coupled nonlinear outputs in a generic, possibly time-varying, topology. The local filters, which follow the structure of the extended Kalman filter, are implemented in each system, which estimates its own state exclusively. To be suitable for the heavily restricted implementation to very large-scale systems, a novel algorithm is proposed, which: (i) does not rely on instantaneous data transmission; (ii) allows local communication exclusively; and (iii) requires computational, memory, and data transmission resources for each system that do not scale with the dimension of the network. The scalability of the proposed algorithm allows for its application to the cooperative localization problem of very large-scale systems. In particular, it is applied herein to the on-board position estimation problem of LEO mega-constellations using GNSS featuring numerical simulations for the Starlink constellation.