Design of Adaptive Kalman Consensus Filters (a-KCF)

This paper addresses the problem of designing an adaptive Kalman consensus filter (a-KCF) which embedded in multiple mobile agents that are distributed in a 2D domain. The role of such filters is to provide adaptive estimation of the states of a dynamic linear system through communication over a wireless sensor network. It is assumed that each sensing device (embedded in each agent) provides partial state measurements and transmits the information to its instant neighbors in the communication topology. An adaptive consensus algorithm is then adopted to enforce the agreement on the state estimates among all connected agents. The basis of a-KCF design is derived from the classic Kalman filtering theorem; the adaptation of the consensus gain for each local filter in the disagreement terms improves the convergence of the associated difference between the estimation and the actual states of the dynamic linear system, reducing it to zero with appropriate norms. Simulation results testing the performance of a-KCF confirm the validation of our design.