Research On Networked State Estimation For Linear System

This thesis focused on the networked state estimation for linear systems,and we worked on two main fields:"The stability of networked state estimation with uncertain observations" and"The optimization of distributed state estimation for networked systems".In the field of "The stability of networked state estimation with uncertain observations",the main contribution from us is that we gave the necessary and sufficient stability condition for general linear systems with packet losses(so-called Critical Value Problem),which has been unsolved for nearly 12 years.Furthermore,we developed a general method for solving a class of stability condition problems and applied it to many other applications such as big data fusion and sensors scheduling.Moreover,we designed a linear temporal coding method to process the raw measurements before transmission.It would make the system easier to be stable under the packet losses without increasing the dimension of transmitted data.And we could also utilize the dimension compressing to make the transmitted data to be a scalar,which would minimize the channel burden and keep a near optimal stability condition.During the research of optimalization of networked distributed state estimation,we focused on the belief propagation algorithm,which is very popular in the field of signal processing.This algorithm can be applied to all kinds of connected topology and each node only requires very little information exchange with neighbors.It is suitable for the distributed state estimation in a large scale system.In recent years,it has been found in many works that the belief propagation algorithm often offers a near optimal state estimate while applied to many kinds of systems.While there is still no conclusion can be drawn that in which system belief propagation could work well and how good the performance is.In this thesis,we reconstructed the network topology,which is equivalent to the origin one,to make it easier analyzed.With the new network topology under consideration,we did a lot of math work to bound the gap between belief propagation estimate and the WLS optimal one.With the result on this bound,we could find in which situation belief propagation would offer a good estimate and how good it is.This result could partially solve the key theoretical problem on belief propagation.