Studies Of The Multi-scale State Smoothing And The Filtering Algorithms Based On Measurement Preprocessing For System With Multiplicative Noises

The system with multiplicative noises (SMN) is very important in many applications such as oil seismic exploration, underwater remote targets detection and tracking etc, the research of it's optimal estimation algorithms is developed greatly. In this dissertation, optimal state fixed-interval smoothing problem under multi-scale observation for systems with multiplicative noise and filtering problem based on preprocessing using wavelet de-noising are considered.Although the research of the state estimation for classical linear stochastic systems has run to the complicated conditions for multi-scale (sample rate) and multi-sensor observation, the research on the system with multiplicative noises is not developed deeply. Using the wavelet transform and multi-scale analysis, an optimal state fixed-interval smoothing algorithm in the sense of linear minimum-variance is further developed based on multi-scale optimal filtering fusion for system with multiplicative noises. The optimal filtering for the system with multiplicative noises as same as the traditional filtering needs to use measured information as much as possible. However, in the application, measured information will be disturbed badly by the noises when the measure is observed on certain distinguish level. The problem of restraining the noises from measured information is the key for improving the filtering precision and reliability. In this dissertation, a new optimal filtering algorithm for systems with multiplicative noise based on measurement preprocessing is proposed, by combining the thresholding of wavelet de-noising and the optimal filter for system with multiplicative noise.The main researching contents of this dissertation are as follows:1. Based on multi-scale optimal filtering fusion, research of the optimal state fixed-interval smoothing algorithm in the sense of linear minimum-variance is further developed. This paper proposes a simplified optimal fixed-interval smoothing algorithm that doesn't need to use local parameters after filtering fusing and only uses one-step prediction and filtering value.2., De-noising is carried on using the thresholding of wavelet for the measured information for the filtering of systems with multiplicative noise. The influence from the measurement noise of sensors signal on the filtering is reduced and the filtering precision is improved.3. The algorithms are tested by computer simulations, which show the validity of these algorithms.