Distributed Kalman Filter with Embedded Consensus Filters

TLDR

Distributed Kalman filtering for sensor networks is a fundamental scalable estimation problem, and consensus filters—distributed algorithms enabling average‑consensus of time‑varying signals—provide the stability framework discussed in a companion CDC ’05 paper. The paper aims to solve distributed Kalman filtering by reformulating it as two dynamic consensus problems on weighted measurements and inverse‑covariance matrices. The authors solve the two consensus problems in a distributed manner using low‑pass and band‑pass consensus filters, and detail the computational and communication architecture of the algorithm. The decomposition into micro‑Kalman filters driven by two consensus filters yields state estimates identical to a central Kalman filter when nodes agree on two central sums, and simulations on 200 nodes and over 1000 links confirm that the consensus‑based approximation provides an effective distributed Kalman filtering algorithm.

Abstract

The problem of distributed Kalman filtering (DKF) for sensor networks is one of the most fundamental distributed estimation problems for scalable sensor fusion. This paper addresses the DKF problem by reducing it to two separate dynamic consensus problems in terms of weighted measurements and inverse-covariance matrices. These to data fusion problems are solved is a distributed way using low-pass and band-pass consensus filters. Consensus filters are distributed algorithms that allow calculation of average-consensus of time-varying signals. The stability properties of consensus filters is discussed in a companion CDC '05 paper [24]. We show that a central Kalman filter for sensor networks can be decomposed into n micro-Kalman filters with inputs that are provided by two types of consensus filters. This network of micro-Kalman filters collectively are capable to provide an estimate of the state of the process (under observation) that is identical to the estimate obtained by a central Kalman filter given that all nodes agree on two central sums. Later, we demonstrate that our consensus filters can approximate these sums and that gives an approximate distributed Kalman filtering algorithm. A detailed account of the computational and communication architecture of the algorithm is provided. Simulation results are presented for a sensor network with 200 nodes and more than 1000 links.