Distributed Kalman filtering using consensus strategies

Abstract

Abstract-In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of message exchange per sampling time is small. Moreover, we prove that under certain conditions the optimal consensus matrix should be doubly stochastic. We also provide some numerical examples to clarify some of the analytical results. I. INTRODUCTIONThe recent technological advances in wireless communication and the decreasing in cost and size of electronic devices, are promoting the appearance of large inexpensive interconnected systems, each with computational and sensing capabilities. These complex systems of agents can be used for monitoring very large scale areas with fine resolution. However, collecting measurements from distributed wireless sensors nodes at a single location for on-line data processing may not be feasible due to several reasons among which long packet delay (e.g. due to multi-hop transmission) and/or limited bandwidth of the wireless network, due e.g. to energy consumption requirements.This problem is apparent in wireless ad-hoc sensor networks where information needs to be multi-hopped from one node to another using closer neighbors. Therefore there is a growing need for in-network data processing tools and algorithms that provide high performance in terms of on-line estimation while (i) reducing the communication load among all sensor nodes, (ii) being very robust to sensor node failures or replacements and packet losses, and (iii) being suitable for distributed control applications.In this work we will focus on distributed estimation of dynamical systems for which sensor nodes are not physically collocated and can communicate with each other according to some underlying communication network. For example, suppose that we want to estimate the temperature in a building that changes according to a random walk, i.e T (t + 1) = T (t) + w(t), where w(t) is a zero-mean random variable with covariance q, and we have N sensors that can measure temperature corrupted by some noise, i.e. y i (t) =

Model Based Information Fusion in Sensor Networks

“…Recent papers in this area include Olfati-Saber [2007], Spanos et al [2005] and Xiao et al [2005]. In Carli et al [2007] it was noted that if the assumption of agreement is not fulfilled the optimal Kalman gain for a centralized filter does not coincide with that of a distributed. This issue was also addressed in Schizas et al [2007].…”

A sensor placement and network design paradigm for future smart grids

“…The literature on this subject exists from earlier work in [1], [2] and references therein, where parallel Kalman filter architectures are considered, generally, for all-to-all connected networks, to more recent work in [3], [4], [5], [6], where Department of Electrical and Computer Engineering, Tufts University, {khan,mrd}@ece.tufts.edu.…”

Efficient distributed sensing using adaptive censoring based inference

“…Many distributed estimation algorithms use the notion of consensus to estimate the parameters/states of interest (e.g., [9][10][11][12][13][14][15][16]). In a typical consensus algorithm, an agent attempts to reach an agreement with its neighbors by performing a sequential update that brings its estimate closer to the states/parameters of (a subset of) all of its neighbors.…”