State Estimation And Information Fusion For Linear Systems With Multiplicative Uncertainty

This paper is concerned with state estimate and fusion problem of a class of un-certain systems. With the increasing complexity of engineering, control theory is be-coming more and more complex. Especially with the development of network control system, dynamic systems also include a growing number of interference and uncer-tainties which can not be ignored. All these results in new problems for control theory. Therefore, the basis theoretical issues, such as state estimation, feedback control and optimal control, for all kinds of uncertain systems need to be kept research in-depth.State estimation has been one of the fundamental problems of control theory and application, which plays an important role in many fields such as aerospace, military, transportation, economics and management science. It is well known that one of the most widely used of state estimation algorithm is the Kalman filtering, which is in the sense of mean square error and is restricted to a dynamic system with random Gaussian noises. Due to its wide applications in many aspects, a number of Kalman filtering algorithms such as robust Kalman filter, nonlinear Kalman filter, particle filter as well as many corresponding fusion filtering and adaptive filter were derived. With more and more complex dynamic applications, the relevant state estimation theory has also been in development. Although there are many excellent results, many problems should be further studied and some results should be improved.State estimation and fusion for linear systems with multiplicative uncertainty is studied by using a basic geometric method-projection theory, combined with some classic theories and methods, such as Riccati equation, least square. Some new prob-lems are studied and some existing results are improved. Specifically, the main contents include:I. The optimal state estimation (Kalman filtering) problem is studied for the mul-tiplicative white noise uncertain systems with output delay and an iterative estimation algorithm is presented. The idea is that the noise of the state and the measurement are compensated by virtual noise compensation at first. And then, optimal filter and smoother are obtained by solving a Riccati equation with the same dimension of the original system based on projection theorem in the Hilbert space and innovation reor-ganized analysis. Note that this method does not require the state augmentation, and hence it has great computational advantages.Ⅱ. For the optimal state estimation problem of linear system with a multiplicative white noise and time-delay in state, a one-step prediction algorithm is presented. Two coupled Riccati difference equations are obtained based on the Hilbert space projection theorem after virtual noises are introduced. Then an iterative algorithm is presented by using the two coupled Riccati equations. Filtering and fixed-lag smoothing algorithm are given based on this prediction algorithm.Ⅲ. A linear optimal weighted fusion algorithm is presented for the multiplicative white noise uncertain systems with output delay. The optimal distributed weighted multi-sensor fusion algorithm is presented after giving the estimation error cross-covariance matrix between any two sensor subsystems based on the linear optimal weighted fusion estimation algorithm in the linear minimum variance sense. The algo-rithm does not require state augmentations. Then it has great computational advantages compared with the centralized fusion estimation algorithm.Ⅳ. Steady-state robust multi-sensor optimal fusion problems is studied for uncer-tain systems with white and colored noises. The robust filtering algorithm for uncertain systems with colored noises is presented based on the the robust least square (RLS) method. Compared with existing algorithms, mainly due to the fact that uncertainty is considered in the weight matrix calculation, optimization of parameters and filters, the accuracy and robustness of estimation has been improved significantly. Based on the linear minimum variance criterion, a steady-state weighted multi-sensor fusion algo-rithm for the uncertain systems is proposed.Innovations of the dissertation mainly include the following three aspects:For the multiplicative white noise uncertain system with output delay, state delay and noise delay, the optimal estimate iterative algorithms which dimensions are same as the ones of original systems are presented based on innovation reorga- nized analysis method. The algorithms have a smaller computational burden;For the uncertain time-delay stochastic system with multiplicative white noise, the optimal distributed iterative fusion algorithms is presented based on the linear optimal weighted fusion estimation algorithm in the linear minimum variance sense. Then it has great computational advantages compared with the centralized fusion estimation algorithm;Distributed steady-state robust fusion algorithms are studied for uncertain sys-tems with white and colored noises based on robust least-squares algorithm. The accuracy and robustness of estimation has been improved significantly.