Consensus+Innovations Distributed Kalman Filter with Optimized Gains

TL;DR

This paper introduces a novel distributed Kalman filter called Consensus+Innovations Kalman Filter for estimating dynamic fields over networks, optimizing gains for faster convergence and improved accuracy.

Contribution

It develops a new distributed estimator with optimized gains, analyzing its convergence and demonstrating superior performance over existing methods.

Findings

Estimator converges faster with optimal gains.

Achieves approximately 3dB better mean-squared error.

Convergence depends on the field's dynamics and network structure.

Abstract

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 mean-squared 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.