Distributed Estimation from Relative and Absolute Measurements

This note defines the problem of least-squares distributed estimation from relative and absolute measurements, by encoding the set of measurements in a weighted undirected graph. The role of its topology is studied by an electrical interpretation, which easily allows distinguishing between topologies that lead to “small” or “large” estimation errors. The least-squares problem is solved by a distributed gradient algorithm: the computed solution is approximately optimal after a number of steps that does not depend on the size of the problem or on the graphtheoretic properties of its encoding. This fact indicates that only a limited cooperation between the sensors is necessary.