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

We derive and analyze distributed state estimators of dynamical stochastic processes, whereby 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.