With Uncertain Disturbance Generalized System Of Information Fusion Estimation

There are many discrete-time stochastic descriptor systems with uncertain dis-turbance in the practical applications, such as sensor networks, robots, economic systems and so on. Moreover, the problem of state estimation for above men-tioned systems has received intensive attention in the research ranging from control, communication, signal processing to fault detection and separation. With the rigid development of technologies, researching of the optimal fusion estimators has impor-tant significance and value in the practice, especially the computer technologies had advanced and the various and complicated sensors had applied. In this paper,we address the problem of optimal fusion reduced-order estimation for discrete-time stochastic descriptor systems with uncertain disturbance. The one of objectives is to derive optimal information fusion filters for the discrete-time stochastic descriptor systems with uncertain disturbance which affect system state by additional form. The other objective is to construct optimal information fusion filter, smoother and predictor for the descriptor discrete-time stochastic descriptor systems with multi-plicative uncertain observation by multiplicative form.The optimal fusion estimation is developed for multi-sensors time-invariant de-scriptor discrete-time stochastic linear systems with additional uncertain distur-bance and correlated noise, where there is no prior information on uncertain dis-turbance, by the following steps. Firstly, the descriptor systems is transferred to identical forms which are different reduced-order systems by various non-singular transformations. Secondly, the state filter which independent on the unknown in-puts is achieved for the reduced-order subsystems used on linear unbiased minimum variance formula. Thirdly, when there are multiple sensors, the formulistic method of cross-covariance matrices of filtering errors between arbitrary sensors and between two reduced-order subsystems are presented respectively. Further, the multi-sensors optimal information fusion state filters are derived based on the optimal fusion es-timation algorithm in the linear minimum variance sense for the original systems.In this section, the work considers the multi-sensors time-invariant descriptor discrete-time stochastic systems with multiplicative uncertain observation which is described by a series of Bernoulli distributed random variable. The the descriptor system is transformed into two identical reduced-order subsystems by non-singular transformation where the system noise and the observation noise are correlated. Furthermore, the local state filter, smoother and predictor of single sensor are con-structed based on Kalman filtering theory and projecting theory. Meanwhile, the cross-covariance matrices of estimation errors between arbitrary sensors and be-tween the reduced-order subsystems are determined when there are more than one sensors. Last the multi-sensors distributed optimal information fusion unbiased state filter,smoother and predictor are also derived based on the optimal fusion estimation algorithm in the linear minimum variance sense for descriptor system with uncertain disturbance affected sensors.