Robust Optimal Filtering Over Lossy Networks

Filtering technology has been one of most popular problems in the field of digital processing.It has a wide range of applications in aerospace,industrial production,military technology and other aspects.In recent years,the filtering method for the networked control system has received great attention due to the fast development of the network technology.Thanks to the improvement and development of filtering theory and technology,network-based filtering methods has been witnessed,wihc effectively solve a large number of practical problems and increase productivity in industrial production.In this thesis,we use the non-zero Nash game to describe the multi-objective filtering problem.Considering the robust optimal filtering with packet loss,we estabilish the robust optimal filter gain and the worst-case disturbance signal on the finite time horizon and infinite time horizon,respectively.Robust optimal filter design is fulfilled for the modelsubject to both random noise and uncertain disturbance,togethe with packet loss occuring uding data transmission.Specifically,the content can be divided into:The first part: we definie the robust optimal filtering problem for systerms with both uncertainties and stochastic noises.The physical system and the network model involved in signal transmission is given.The robust optimal filters on finite time and infinite time are designed,respectively,together with the cost functionals based on the error signal.A set of Nash equilibrium inequalities is also proposed on finte time and infinite time to evaluate the estiasmtion performance.The second part: this part is about the design of a finite time robust optimal filter with packet loss.With a set of cross-coupled Riccati difference equations,the corresponding filter is given and the optimal filter gain is constructed analytically.The design method presents the worst case signal with which the robust performance becomes the worst,and then gives the form of the robust optimal filter under the worst case.The third part: this part is dedicated to the design of an infinite time robust optimal filter with packet loss.With a set of cross-coupled modified algebraic Riccati equations,the corresponding filter is given and the optimal filter gain is constructed analytically.Specifically,a full and rogurous analysis of the mean square stability for the error system is given.Based on the mean square stability,the worst case signal is presented,and then the form of the robust optimal filter is given under the worst case.The fourth part: car speed simulation and experiment are used to show the effectiveness of the proposed algorithms.It presents the model of the car,and uses an iterative algorithm to solve the cross-coupled modified algebraic Riccati equations.The worst case singal and robust optimal filter gain are obtained.Compared with some existing methods,the effectiveness of the present algorithm is verified by estimation.Then the experiment is also given to further verify the accuracy of the algorithm by the ultrasonic ranging of the car with ZigBee platform.The error between the estimated speed curve and the actual speed curve are also anslyzed.Finally,the results of this thesis are summarized,and prospectives of future research directions are also mentioned.