Distributed Estimation for Spacecraft Formations Over Time-Varying Sensing Topologies

Abstract

In this paper we present the analysis and design of distributed estimators for formation flying spacecraft with time-varying sensing topologies. We first develop a discrete-time, switched linear model of the formation translational dynamics in which the the measurement vector is characterized in terms of the edge matrix of a graph associated with the sensing topology. Then a switched, linear estimator is developed, called a λ-estimator, for a general class of discrete-time, switched linear systems. This estimator is replicated on each spacecraft to estimate the entire relative translational state of a formation, and estimator gain switching occurs as a function of the instantaneous sensing topology. These estimators guarantee that the mean of the estimation error decays to the origin with a prescribed decay rate and that the error covariance decays to an ultimate bound, also with a prescribed decay rate. In addition, linear matrix inequality-based design procedures are developed for λ-estimators. It is proven that a stable formation λ-estimator exists if all of the possible sensing topologies describe connected graphs. This observation leads to the design of opportunistic l-estimators for formations switching among connected sensing topologies in which more sensing links are available than considered in estimator design.