Research On Convergence Of A Class Of Stochastic Distributed Parameter Estimation Algorithms

In recent years,with the development of the Internet of Things(IoT),wireless sensor networks have been widely used in various fields,such as border surveillance,target detection,environmental monitoring,etc.To a great extent,these applications would lead to the issue of distributed parameter estimation.In a networked system,each node serves as an agent,which simultaneously possesses the capability of sensing,computing,storage,and communication.Therefore,these agents can jointly estimate an unknown parameter through information exchange.However,in most cases,there exist interferences from uncertain factors in an actual network environment,such as measurement noises and communication noises,which will affect the estimation of unknown parameters.For this reason,research on distributed parameter estimation in an noisy environment are of great significance for achieving e cient information processing.In this paper,by martingale convergence,algebraic graph and stochastic time-varying system theories,we analyze the convergence of distributed parameter estimation algorithms with communication noises.The main results include the following two aspects.1.We develop the consensus+innovations distributed parameter estimation algorithm with both additive measurement and communication noises.At each time step,each node iteratively updates its estimate through interaction with its neighbors and its own measurement.Furthermore,the linear observation of the unknown parameter by each node,the underlying noisy communication network therein are respectively characterized by a sequence of randomly time-varying observation matrices and random digraphs.Moreover,the random time-varying observation matrix,random digraph and communication noise sequences can all be dependent both in time and space,and the former two can also be dependent on each other and do not need to meet special statistical properties.Under the assumption that the noises are simultaneously independent of the sequences of observation matrices and random digraphs,we propose su cient conditions for the distributed parameter estimation algorithm to achieve mean square convergence.We prove that if the graph sequence is conditionally balanced,and the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition,then the algorithm gains can be designed properly such that all nodes' estimates respectively converge to the real parameter in mean square.2.Based on mean square convergence,we further study the almost sure convergence of the distributed parameter estimation algorithm.Under the assumption that the sample paths of the sequences of observation matrices and random digraphs are bounded almost surely,we prove that if the graph sequence is conditionally balanced,and the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition,then the algorithm gains can be designed properly such that all nodes' estimates respectively converge to the real parameter with probability 1.Especially,we also apply the above results to the Markovian switching communication graphs and observation matrices.We show that the stochastic spatio-temporal persistence of excitation condition holds if the stationary graph is balanced with a spanning tree and the measurement model is spatially-temporally jointly observable,i.e.mean square convergence and almost sure convergence both can be achieved,implying that neither local observability of each node nor instantaneous global observability of the entire measurement model is necessary.