Dynamic consensus estimation of weighted average on directed graphs

Recent applications call for distributed weighted average estimation over sensor networks, where sensor measurement accuracy or environmental conditions need to be taken into consideration in the final consensused group decision. In this paper, we propose new dynamic consensus filter design to distributed estimate weighted average of sensors’ inputs on directed graphs. Based on recent advances in the filed, we modify the existing proportional-integral consensus filter protocol to remove the requirement of bi-directional gain exchange between neighbouring sensors, so that the algorithm works for directed graphs where bi-directional communications are not possible. To compensate for the asymmetric structure of the system introduced by such a removal, sufficient gain conditions are obtained for the filter protocols to guarantee the convergence. It is rigorously proved that the proposed filter protocol converges to the weighted average of constant inputs asymptotically, and to the weighted average of time-varying inputs with a bounded error. Simulations verify the effectiveness of the proposed protocols.