SOI-KF: Distributed Kalman filtering with low-cost communications using the sign of innovations

When dealing with decentralized estimation, it is important to reduce the cost of communicating the distributed observations-a problem receiving revived interest in the context of wireless sensor networks. In this paper, we derive and analyze distributed state estimators of dynamical stochastic processes, whereby the low communication cost is effected by requiring the transmission of a single bit per observation. Following a Kalman filtering (KF) approach, we develop recursive algorithms for distributed state estimation based on the sign of innovations (SOI). Even though SOI-KF can afford minimal communication overhead, we prove that in terms of performance and complexity it comes very close to the clairvoyant KF which is based on the analog-amplitude observations. Reinforcing our conclusions, we show that the SOI-KF applied to distributed target tracking based on distance-only observations yields accurate estimates at low communication cost.