Study On Methods Of Optimal And Self-tuning Weighted Measurement Fusion Estimation For Multisensor Descriptor Linear Systems

Descriptor systems occur naturally in systems of robotics, economics, circuits, biomedical sciences, chemical technology and industrial control, which are a kind of description form for actual system and have more pervasiveness than conventional systems, attracting universal attention in recent years. This study is supported by three funds of National Natural Science Foundation of China under Grant 60874062,60504034 and 60874063, and a Key Project of Education Ministry under Grant 209038, which has both theoretical significance and practical significance.Recently, studies on fusion estimation problems about descriptor systems have appeared in some publications, but most of the fusers adopted are distributed state fusion algorithms, and these fusers are globally suboptimal, so the fusion estimation results of descriptor systems can not receive globally optimality. The algorithm of Weighted Measurement Fusion(WMF) not only has smaller computational burden, but also can reach globally optimal estimation result, but the present Weighted Measurement Fusion(WMF) methods have not been able to solve the fusion estimation problems of descriptor systems.In view of this case, the historical background and status quo of home and abroad in multisensor information fusion technology, state estimation technology, and descriptor system theories studies being comparatively analyzed, Linear Unbiased Minimum Variance(LUMV) estimation being taken as optimal information fusion criterion, and Least Square Recognition technology, Kalman filtering technology, and Modern Time Series Analysis technology being adopted, multisensor descriptor system weighted measurement fusion optimal and self-tuning estimation technology are studied. The main content and studying results are as following:l.By using two methods of singular value decomposition and front-back subsystem decompostion, descriptor linear system converted to normal system is accomplished, flexibilities of two methods is analyzed, observability of normal subsystem is proved, and then estimability of reduced order subsystem is stated, pointing out that three problems are needed to be solved using weighted measurement fusion method to realize optimal and self-tuning descriptor system fusion estimation.2. The first problem is solved, i.e., when all the multisensors have different measurement matrice, and correlated measurement noises, and input noise and all the multisensors' measurement noise are correlated, using matrix full rank decomposition, Lagrange multiplier method, Weighted Least Square theory, obeying the rule of LUMV, weighted measurement fusion Kalman estimation algorithm is presented, which is not influenced by measurement matrice and measurement noise correlatedness. The newly presented algorithm can universally deal with problems of fusion filtering, smoothing and predicating in state. It is proved that its estimation result is completely equivalent to centeralized fusion result, and then it also has global optimality. Expanding Gan's study that weighted measurement fusion algorithm can only deal with the case that each sensor has the same measurement matrice.3. The second problem is solved, i.e., for the multisensor system with different measurement matrice and correlated noise, when (?) column rank in the conditions of full rank, using projective theory, white noise estimation theory suitable for weighted measurement fusion(WMF) alogrithm is presented, and it is proved in theory that its function is equivalent to centralized fusion white noise estimation theory, which yields white noise predicator, filter and smoother with equal numeric value, so WMF algorithm also has global optimality in white noise estimation. The presented algorithm can also be used into fields of oil seismic exploration, signal processing and communication.4. The third problem is solved, i.e., when the statistical property of system noise is unknown, using Fadeeva formula and left co-prime factorization method to construct Autoregressive Moving Average(ARMA) innovation model with unknown parameters, identification ARMA innovation model is presented using two system parameter identification methods of sampling correlated function and least squares. Analyzing the applicability in different circumstances of these two methods, consistent estimation of unknown parameters is yielded through solving system of matrix equations, and then self-tuning weighted fusion Kalman estimator is presented. Therefore, multisensor descriptor system self-tuning weighted measurement fusion estimation problem is solved.