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 graph-theoretic properties of its encoding. This fact indicates that only a limited cooperation between the sensors is necessary.