Study On Multi-sensor Information Fusion State Estimation Algorithms For Singular Systems With Multiplicative Noise

The signal estimation theory for stochastic systems with multiplicative noise is significant in the field of signal processing as well as in many applications such as oil seismic exploration, underwater remote targets detection and speech signal processing. Multi-sensor information fusion has been an interdisciplinary subject under consideration for more than three decades. There are rapidly growing applications of multi-sensor information fusion in various fields, such as guidance, defense, robotics, integrated navigation, target tracking and GPS positioning. The information fusion state estimation, as one of its branches, for the conventional systems has been widely studied in the previous works and applied in many fields.Recently, the state estimation problems for singular systems have received great attention due to extensive application background,including circuits, economies, and robotics etc.. However, the multi-sensor information fusion state estimation for singular systems, especially for the singular systems with multiplicative noise is an open problem. The main content of this dissertation focuses on multi-sensor information fusion state estimation algorithms for singular systems with multiplicative noise as follows:Firstly, multi-sensor information fusion technology is introduced simply. Moreover, the development and status quo of signal estimation for singular system with multiplicative noise is recalled in this dissertation.Secondly, multi-sensor information fusion state estimation problem for multi-channel stochastic singular systems with multiplicative noise is studied.The singular system under consideration is subject to the regular hypothesis and is transformed into two reduced-order subsystems by restricted equivalent transformation. Based on this transformation, then the information fusion state estimation problem for the original systems is converted into the state estimation problem of the two coupled normal subsystems.The methods for information fusion state estimation can generally be classified into two categories, depending on whether the measurement data are used directly or not. Both of these two methods are proposed in the dissertation. The first one is the centralized filter where global optimal state estimation is obtained via combining all measured sensor data directly. This method of information fusion is straightforward with minimal information loss, but it has the drawbacks of large computational overhead and high data rates for communication due to overloading of the filter with more data than it can handle. The second method is the distributed filter where the global optimal or suboptimal state estimation according to certain information fusion criterion is derived by using the information from local estimators. One advantage of this method is that it may overcome the problems that typically arise in the first method.The computational burden is reduced and the input data rates are increased considerably in distributed filter. Moreover, it makes fault detection and isolation easier. However, the distributed filter has a lower precision than the centralized filter in general when there is no data fault. It is worth while to point out that both of two methods are optimal in the sense of linear minimum-variance.Thirdly, there exist two approaches to distributed fusion filter, which are the information matrix approach and the weighted covariance approach. The third part of dissertation focuses on the latter which constitutes weighted fusion approach-based covariance with fusion rule weighted by matrices and scalars in the linear minimum variance sense. Using the singular value decomposition, the singular system is transformed into two reduced-order non-singular coupled subsystems, and its distributed fused estimation problem is converted into that for two non-singular subsystems. The formulas of computing the cross-variances between every pair of sensors are given in order to compute the optimal weights. Based on the fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion distributed filter is given for the singular systems with multiplicative noise.The algorithms presented in this dissertation are not only deduced theoretically but also tested through simulation software MATLAB.Satisfactory simulation results are given to validate the algorithms.