Improving convergence of distributed LMS estimation by enabling propagation of good estimates through bad nodes

A noisy node that is the only passage between two parts of a network can obstruct propagation of a good estimate through the network. Assuming adapt-then-combine diffusion based least mean square algorithm that uses combiners minimizing the mean square weight deviations, we found a sufficient condition for mean square weight deviation convergence that also guarantees propagation of good estimates through the whole connected part of the network. A practical algorithmic implementation of this condition is developed and compared in performance with several known algorithms for a nontrivial network. The proposed algorithm demonstrates improved performance.