In this letter a robust incremental adaptation algorithm is presented to solve distributed estimation for a Hamiltonian network, where the measurements at each node may be corrupted by heavy-tailed impulsive noise. In the proposed algorithm, each node employs an error-nonlinearity into the update equation to mitigate the detrimental effects of impulsive noise. Moreover, the algorithm estimates both the optimal error non-linearity and the unknown parameter together, which in turn, obviates the requirement of prior knowledge about the statistical characteristics of measurement noise. In addition to algorithm development, its steady-state performance as well as convergence analysis have been provided. Simulation results validate the correctness of the analysis and reveal the superiority of the proposed algorithm over some existing algorithms.
