Distributed and Recursive Parameter Estimation in Parametrized Linear State-Space Models

Abstract

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is perturbed by random noise and parametrized by an unknown parameter.To estimate the unknown parameter from the measurements that the sensors sequentially collect, we propose a distributed and recursive estimation algorithm, which we refer to as the incremental recursive prediction error algorithm. This algorithm has the distributed property of incremental gradient algorithms and the on-line property of recursive prediction error algorithms. We study the convergence behavior of the algorithm and provide sufficient conditions for its convergence. Our convergence result is rather general and contains as special cases the known convergence results for the incremental versions of the least-mean square algorithm. Finally, we use the algorithm developed in this paper to identify the source of a gas-leak (diffusing source) in a closed warehouse and also report some numerical results.

Distributed Adaptive Convex Optimization on Directed Graphs via Continuous-Time Algorithms

“…In view of Lemma 1, (L ⊗ I n )x = 0 iff x = 1 N ⊗ τ , for some τ ∈ R n . Then, it can be concluded that the problem (1) is equivalent to the problem (2). By reformulating the problem (1), the problem is transformed into a distributed minimization problem under a consensus condition.…”

“…In this section, we propose a fully distributed algorithm to solve the problem (2). Consider the following algorithm with dynamic coupling gainṡ…”

“…is a global minimizer of (2). Note that if (x,ṽ) is a solution of (2), so is (x,ṽ + 1 N ⊗ κ), κ ∈ R n .…”

Distributed inference in wireless sensor networks

“…In addition to these extreme configurations, one can envision configurations that are combinations of these basic topologies, e.g. tree or hierarchical topologies [11,12], or even completely distributed topologies where the sensors communicate with each other over a wireless ad hoc network [13][14][15], as shown in figure 1b. Figure 1.…”

“…Consensus-based approaches for distributed estimation have been discussed [14,[89][90][91][92]. In addition, specific approaches to distributed estimation of diffusive sources have been studied [15,93,94].…”