Consensus+Innovations Distributed Kalman Filter with Optimized Gains

In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a pre-specified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized meansquared error. Through numerical evaluations, we show that, the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.