Studies Of State Partitioned Filtering Filtering Algorithm For Multi-Channel Systems With Multiplicative Noises

Signal estimation theory for discrete stochastic systems with multiplicative noises (SMN) is very important in many applications such as oil seismic exploration, underwater remote targets detection and speech signal processing. Its traditional optimal estimation algorithms, including filtering, smoothing and deconvolution, have been worked out by many papers. In recent years, there had been growing interests and many new algorithms in this field. The previous researches in the estimation theory are mainly based on the systems with multiplicative noises(SMN), recent years people paid more attention to the multi-channel systems(MSMN). However, most of these algorithms don't have high robustness and might be numerically unstable, and as technology has developed rapidly, parallel processor technology makes computation more faster than single processor, it becomes more and more important to apply numerical value stable and fast parallel algorithm to SMN.Unlike the traditional structure of Kalman filtering , partitioned filtering has unique recursive structure which makes it has numerical property. This dissertation proposed partitioned filtering with the multiplicative noises both of one-dimmension stochastic variable and of multi-dimmension stochastic variable.The main contents of this dissertation are as follows:1. In this dissertation, the development and status quo of signal estimation for SMN is recalled. Moreover, partitioned filtering algorithm is introduced simply.2. A partitioned optimal filtering algorithm for mono-channel systems with multiplicative noises among observation channel is proposed in a different way. It decomposes the traditional state vector into the sum of the nominal filtered estimate and the remainder estimate. The nominal filtered estimate can be computed individually, thus makes the parallel computation possible. This algorithm is optimal in the sense of linear minimum-variance.3. The partitioned optimal filtering algorithm for multi-channel systems with multiplicative noises among observation channels is proposed. This algorithm is optimal in the sense of linear minimum-variance.4. Using the simulation software MATLAB, some examples are given to illustrate the validity of the partitioned algorithm.