Methods And Application Of Distributed Estimation Based On Networked Systems

Networked multi-intelligent systems can be applied to solve various complex problems through inter-intelligent collaboration,and thus there are many advantages of flexibility,reliability,and parallelism,and they are more suitable for uncertain environments.Therefore,in recent years,research on networked multiintelligence collaborative control has a wide range of potential applications in scientific and engineering fields,such as unmanned aircraft formation,intelligent transportation,and distributed estimation of sensor networks.Distributed estimation is essential for improving the efficiency,reliability,economy,and sustainability of large-scale networked systems.Unlike traditional centralized estimation method,the distributed estimation method utilizes both the local measurements of each node and the information exchange between neighboring nodes,but without a centralized coordinator.This means that each node has lower computational complexity,smaller storage space,and lower communication load.In this dissertation,we study the problem of distributed weighted least-squares(WLS)estimation based on networked systems,using a fast distributed WLS estimation method proposed by Marelli in[24].Compared with existing results,our contribution is mainly to give a theoretical justification for the ability of this method to converge to a globally optimal estimate in a cyclic graph,thus extending the application of this distributed estimation to general graph models.For the convergence analysis,we divide the study object into two cases:networked systems with scalar node variables and vector node variables.The conditions for the convergence of this WLS estimation method are given by using the belief propagation(BP)estimation method and the walk-summability method,respectively.Meanwhile,the distributed WLS estimation is combined with the Kalman filter to give the distributed Kalman filter and applied to measurement systems with multiplicative noise.The main advantage of this distributed WLS estimation is that it is much faster than other existing distributed estimation methods to obtain the global optimal solution in the applicable network that meets its convergence condition,and thus it is of great theoretical importance and wide application value.The main works of this dissertation consist of the following three aspects:(Ⅰ)Distributed weighted least-squares estimation for networked systems with scalar node variablesThe problem of distributed WLS estimation in linear measurement networks with scalar node variables is studied.We divide the measurements in the network into two types:self measurement(which is related to the node’s state only)and edge measurement(where the measurement is related to the states of the nodes at both endpoints connecting this edge).The distributed WLS estimation method we study is linked to the well-known belief propagation(BP)estimation method,and proof of equivalence is given for the case where the node states are scalar variables based on these two estimation methods.A key conclusion is also given,that under a mild assumption,the information matrix is always generalized diagonally dominant.Using these two results and some existing conclusions of BP estimation,the convergence conditions of this distributed WLS estimation in general graph models(with or without loops)are given.In acyclic graphs,the distributed WLS estimation can converge to the global optimal solution after finite iterations,the number of iterations of which is at most the diameter of the graph.In the cyclic graph,it can asymptotically converge to the global optimal solution.Also,the rate of convergence for obtaining this estimate is given,which is inscribed by the spectral radius of the graph.Finally,based on a practical example:the IEEE 118-bus network,it is shown that our method can obtain the global optimal estimate faster compared to the estimation obtained by the existing distributed consensus algorithm based on orthogonal projection.(Ⅱ)Distributed weighted least-squares estimation for networked systems with vector node variablesThe problem of distributed WLS estimation in general large-sacle networks where each node is represented by a vector parameter(variable)is studied and its convergence analysis is further given.First,the concept of diagonal dominance is extended to the block matrix.After that,an important tool required for the convergence analysis of the Gaussian BP algorithm is introduced:the concept of walk-summability,which is vectorially generalized.The definition of block walksummability is given,and the relationship between block diagonal dominance and block walk-summability is given.Thus,the distributed WLS estimation method is further applied to a networked system with vector node variables in a general network graph,and the conditions for its asymptotic convergence to the optimal estimation are given.Also,compared with the existing distributed algorithm:Richardson’s method,it can be seen that this distributed WLS estimation method converges much faster than the existing methods.The significance of this work is that it provides theoretical guarantees for a new class of distributed WLS estimation problems for large-scale network systems with vector parameters.(Ⅲ)Distributed Kalman filter for networked systems with multiplicative noiseThe application of distributed WLS estimation is extended to give distributed Kalman filtering estimation by combining it with conventional Kalman filter.In particular,we generalize networks with additive noise to networks with multiplicative noise and interference from both state systems and measurement systems with multiplicative noise,compared to existing results.We first give centralized Kalman filter for networked systems with multiplicative noise,and then further distributed Kalman filter estimation by using the idea of distributed WLS estimation in the form of Kalman filter.Due to the multiplicative noise,when dealing with the distributed estimation,we divide the original form into several parts that can be used by the distributed estimation method and then use the idea of an message-passing algorithm to derive the distributed Kalman filter estimation.In the convergence analysis,we first give a conclusion for acyclic graphs,and then convert cyclic graphs into acyclic graphs by removing the cyclic edges by a distributed depth-first search algorithm,thus demonstrating the convergence of the estimation.Finally,by using two practical examples:underground mine personnel location problem and radar location problem,which can be regarded as single target tracking problem and multi-target tracking problem respectively,it shows that this distributed Kalman filter can converge to central Kalman filter.This dissertation presents an in-depth study of a fast distributed WLS estimation method based on networked systems,which provides a new method for convergence analysis and expands the application of distributed estimation to networked systems.This study provides a theoretical guarantee for the study of distributed estimation of large-scale networked systems,which is of great significance and influence.