Dynamic Multi-scale Projection Operator And Non-linear Filter Design,

In the last two decades, multiscale system theory has been developed quickly with the broad application of multiscale techniques in signal processing. Multiscale systems can be divided into two categories: SMS (Statistical Multiscale System) and DMS (Dynamic Multiscale System). SMS theory is to discuss the multiscale processing techniques of stochastic signals. DMS theory is to get the real time estimation of the states of the dynamic systems. Now its research efforts can not be compared with that of SMS. The detailed implement method and its system frame are rather incomplete. This thesis is focused on these problems to do some extended research of dynamic multiscale system theory. The main contributions are as follows:1. It is introduced that what the main application background of multiscale system theory is and how it has developed recently. Next, the two frames ofmultiscale system--Static Multiscale System and dynamic multiscale system arepresented detailedly and compared.2. A new approach is present to estimate the multiscale projection operator by using the Linear least square estimation (LLSE). For application, A recursive edition of this algorithm is also present. Computer simulation results are presented to show the effectiveness of the algorithm. According to the estimation procedure and the simulation result, we get an additional key restriction that is not included in the original theory. This nuclear restriction is that as long as the observation matrixes of all scales (expect the finest scale) are full column rank, the operator's estimation algorithm will always be efficient.3. We extend the multiscale research to a nonlinear field. Firstly, a nonlinear multiscale model is established. Secondly, we discussed two types of the nonlinear multiscale system, and a set of nonlinear multiscale fusion algorithms based on Unscented Kalman Filter (UKF) and sequential estimation method is presented. Simulation results show that this new algorithm is superior to single scale tracking algorithm.