Agent Based Optimally Weighted Kalman Consensus Filter over a Lossy Network

We consider a distributed agent based state estimation problem where each agent has a local underdetermined observation space and is interested in a subset of states. At a particular time instant, each agent predicts its state and makes intermediate correction based on its local measurements. Information about the corrected state elements are then exchanged among neighboring (i.e., agents who share at least one state element) agents. Based on the final processing of the exchanged information, an agent based optimally weighted Kalman consensus Filter is formed in the light of well-established theory of distributed Kalman filtering. The optimal weighting of consensus is derived through Lyapunov function based stability analysis of corresponding estimation error. The effect of communication is also investigated by introducing random failures in the communication link among neighboring agents. The corresponding bounds on the degree of consensus and inter-agent link failure rate are also derived for stable implementation of the agent based dynamic estimation. The proposed filter is applied to a custom built 2- agent system to conform the desired optimal limit for the degree of consensus based information exchange both under perfect and lossy communication network.