Studies Of Numerically Stable Estimation For Multi-Channel Systems With Multiplicative Noises

Optimal estimation theory for multi-channel systems with multiplicative noises is very important in many applications such as oil seismic exploration, under water remote targets detection and speech signal processing. In recent years there had been growing research interests and giving many new algorithms in this field. The previous researches in the estimation theory are based on the systems with multiplicative noises(SMN), recent years people paid more attention to the multi-channel systems(MSMN). Many optimal estimation algorithms are given, but these recursive algorithms are numerically unstable, it means that they will become invalid some times when use it to solve problems. So, new methods which have excellent numerical stability are necessary. All the proposed algorithms in this dissertation are optimal in the sense of linear minimum-variance.Numerically stable methods for MSMN are proposed in this paper. The main contents of this dissertation are as follows:1. The development and status quo of signal estimation for MSMN is recalled. Moreover, numerical stability theory is introduced simply.2. Give an SVD-based optimal filtering for MSMN, it has an excellent numerical stability. It is optimal still in the sense of linear minimum-variance.3. Optimal smoothing algorithms for MSMN are proposed, then numerically stable algorithms based on singular value decomposition(SVD) methods are given for smoothing. Deconvolution algorithms are proposed subsequently based on the results of filtering and smoothing algorithms. They are still optimal in the sense of linear minimum-variance.4. Simulation examples are given to demonstrate the performance of all algorithms.