Distributed Kalman filter via Gaussian Belief Propagation

Abstract

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 β = 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.

Gaussian belief propagation based multiuser detection

“…The first part discusses the theory of Gaussian belief propagation algorithm and covers the following papers: [7,14,15,16,17,18]. The second part discusses several applications that were covered in the following papers: [19,20,21,22,23,24,25].…”

In-Network Iterative Distributed Estimation for Power-Constrained Wireless Sensor Networks

“…10) and we perform the reduction from another well-known NP-Hard problem to this problem, which is a simplification of our problem (5). Notice that a communication cost can be expressed in terms of the set of flows f ij ∈ {0, 1} connecting sensors i and j, as it is usual in network flow problems.…”

“…In [4], authors propose a centralized solution based on performing a relaxation of an integer optimization problem using an efficient interior point method. A distributed version of this interior point method is introduced in [5]. In [6], a sampling framework based on linear minimum variance unbiased estimation is proposed to select a subset of sensors.…”

Distributed Kalman Filtering

“…Other DKF applications can be seen in [335], [336], [338], [339] . [38], [39], [40], [41], [42], [43], [44], [105], [106], [109], [114], [119], [156], [179], [191], [197], [213], [214], [215], [216], [221], [233], [237] , [238] and [242]. [204] • Only the estimates at each Kalman update over-head are exchanged [205] • Analyzes the number of messages to exchange between successive updates in DKF [206] • Global Optimality of DKF fusion exactly equal to the corresponding centralized optimal Kalman filtering fusion [276] • A parallel and distributed state estimation structure developed from an hierarchical estimation structure [297] • A computational procedure to transform an hierarchical Kalman filter into a partially decentralized estimation structure [298] • Optimal DKF based on a-priori determination of measurements [300] 2.3.…”