Cooperative Estimation for Under-determined Linear Systems

Let us consider a parameter estimation for linear model where the ensemble of N sensors acquire enough measurements to estimate the set of p-parameters theta = [theta(1), ... , theta(p)](T), but the set of T measurements acquired by each sensor is not enough and the estimation problem is under-determined (T < p < NT). Rather than collecting all the N T measurements into a common fusion center as for a centralized estimate, in this paper we investigate the use of consensus methods to let each sensor to reach the same estimate without the need to exchange the measurements. More specifically, based on the local regressor model, each node solves locally an under-determined least-norm and the set of estimated parameters are exchanged with the neighbours jointly with the subspace corresponding righ eigenvectors. The weighted consensus iterations tailored for these settings refine these estimates up to the consensus. For a network of connected nodes, the method attains the Cramer Rao bounds as for a centralized estimate within a small set of iterations. Practical implications range from interference/spectrum analysis in cognitive radio systems or 3D shape reconstructions from multiple views.