JEGA: a joint estimation and gossip averaging algorithm for sensor network applications

Distributed consensus algorithms are widely used in the area of sensor networks. Usually, they are designed to be extremely lightweight at the price of computation time. They rely on simple local interaction rules between neighbor nodes and are often used to perform the computation of spatial statistical parameters (average, variance, regression). In this paper, we consider the case of a parameter estimation from input data streams at each node. An average consensus algorithm is used to perform a spatial regularization of the parameter estimations. A two step procedure could be used: each node first estimates its own parameter, and then the network applies a spatial regularization step. It is however much more powerful to design a joint estimation/regularization process. Previous work has been done for solving this problem but under very restrictive hypotheses in terms of communication synchronicity, estimator choice and sampling rates. In this paper, we study a modified gossip averaging algorithm which fulfills the sensor networks requirements: simplicity, low memory/CPU usage and asynchronicity. By the same way, we prove that the intuitive idea of mass conservation principle for gossip averaging is stable and asympotically verified under feedback corrections even in presence of heavily corrupted and correlated measures