Distributed Kalman Filter via Gaussian Belief Propagation

TL;DR

This paper demonstrates that the Gaussian belief propagation algorithm can be extended to perform Kalman filtering in a distributed manner, linking it to various optimization and information bottleneck methods, with practical applications in sensor networks.

Contribution

It reveals the equivalence of Gaussian BP with one iteration of Kalman filter and connects Kalman filtering to the information bottleneck and interior-point methods, enabling distributed implementation.

Findings

Gaussian BP with two operations equals one Kalman filter iteration

Kalman filter is a special case of the information bottleneck algorithm at β=1

Relation to affine-scaling interior-point method and its equivalence to Kalman filter

Abstract

Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $\beta = 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of resources in a communication network.