Adaptive distributed Kalman filters for a class of continuous time finite dimensional linear systems

In this paper, we propose two different modifications to the distributed Kalman filtering algorithms for sensor networks. The distributed filters, whether are based on Luenberger observer or Kalman filter design, are coupled with terms that penalize the pairwise difference of their estimates. The weights of the penalty terms are adjusted adaptively using a Lyapunov-redesign approach. The two adaptive schemes are either node-dependent, in which case all pairwise differences of the state estimates are uniformly penalized by the same adaptive weight for every given node, or edge-dependent in which case the pairwise differences of the state estimates are penalized by different adaptive weights. The significant benefit of the proposed adaptive interconnected weights is described by the communication costs associated with information exchange amongst the nodes. Representative numerical results are included to demonstrate the proposed adaptive schemes.