Studies Of Reversed-time Filtering And One-pass Deconvolution Algorithms For Complicated Multi-channel Systems With Multiplicative Noises

Systems with Multiplicative Noises (SMN) universally exist in many application fields, such as oil seismic exploration, underwater remote targets detection, engineering of telecommunication and speech signal processing, etc. Concerning the optimal estimation of this system, it is very important for the problems of state estimation of the dynamic system, the signal deconvolution estimation and the parameter recognition estimation, etc. Among them, the deconvolution estimation theory has the important significance in the realms, such as oil seismic exploration and signal processing, etc. The deconvolution estimation based on the reversed time filtering has the advantage of off - line processing and the small storage quantity advantage and is more practical. This dissertation mainly makes the further studies about reversed-time filtering and one-pass deconvolution algorithms for complicated multi-channel SMN.The researches in complicated multi-channel SMN currently are not enough perfect. In observation model, we often suppose the multiplicative noise as one dimension stochastic serial, or the observation is multi dimensioni( multichannel), the multiplicative noise of each channel is completely same. This kind of assumption usually is not in accordance with the actual circumstance. Reversed-time filtering and one-pass deconvolution algorithms for complicated multi-channel SMN that this dissertation discussed describes the situation that the multiplicative noise is expanded to a general stochastic matrix. It has a kind of more complicated channel characteristic and matchs the actual circumstance more. In addition, along with the rapid development of the computer technology, the highly complicated data processing has become possible. Stability problem and multi-sensor information fusion for the optimal estimation algorithm of the Systems with Multiplicative Noises become the people's extensive concern in numerous realms. Therefore, this dissertation still studies reversed-time filtering and one-pass deconvolution algorithms respectively based on singular value decomposition(SVD) for complicated multi-channel SMN and reversed-time filtering and one-pass deconvolution algorithms for multi-sensor complicated multi-channel SMN.The mainly research works of this dissertation are as follows: 1. According to the practical requirement of complicated multi-channel SMN, this paper expanded the filter algorithms of Rajasekaran. A filtering algorithm for SMN is developed under the condition that the multiplicative noise is in the form of ageneral stochastic matrix and each component of the multiplicative noise matrix is correlated at the same time. This algorithm is optimal in the sense of linear minimum-variance.2. This dissertation used the singular value decomposition theory to the covariance matrix, forming a kind of rOeversed time filtering and one pass deconvolution algorithm based on SVD, which kept optimal in the sense of linear minimum-variance and raised the numerical robustness at the same time.3. This dissertation aiming at complicated multi-channel SMN under multi-sensor observation gave reversed time filtering and one pass deconvolution fusion algorithm.4. This papers proved the validity of above-mentioned algorithms using a great deal of simulated example.