Scalar field estimation using adaptive networks

A new method for estimating scalar fields is proposed employing adaptive networks. The theoretical problem of function approximation is posed and the networked solution via distributed adaptive algorithms is introduced. Two approximate solutions employing adaptive networks are considered, and it is shown that both cases approach the theoretical solution in the limit case. In the first setup, nodes remain anchored during the network operation. The second version involves node relocation, either entirely at random over the region of interest or drifting according to a random walk model. Simulations illustrate the method for estimating a 2D scalar field.