Distributed order estimation for continuous-time stochastic systems

Abstract

In this paper, we investigate the distributed estimation problem of continuous-time stochastic dynamic systems over sensor networks when both the system order and parameters are unknown. We propose a local information criterion (LIC) based on the L0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_0$$\\end{document} penalty term. By minimizing LIC at the diffusion time instant and utilizing the continuous-time diffusion least squares algorithm, we obtain a distributed estimation algorithm to simultaneously estimate the unknown order and the parameters of the system. By dealing with the effect of the system noises and the coupling relationship between estimation of system orders and parameters, we establish the almost sure convergence results of the proposed distributed estimation algorithm. Furthermore, we give a simulation example to verify the effectiveness of the distributed algorithm in estimating the system order and parameters.