【作者】 陈萌；

【导师】 褚东升；

【作者基本信息】 中国海洋大学 ， 信号与信息处理， 2004， 硕士

【摘要】 带乘性噪声系统的状态最优估计理论在石油地震勘探、水下目标探测、语音处理等诸多领域都有着重要的应用价值。近几年该领域取得了一系列新的理论和应用的研究成果，打破了乘性噪声为一维随机序列的限制，发展到多通道带乘性噪声意义下的最优估计算法，进而又发展到多传感器信息融合技术和二维带乘性噪声系统的最优估计等一系列研究成果。这些算法均在线性最小方差的意义下是最优的。但这些算法在进行实际应用时有可能会出现数值不稳定现象，在长时间的递推计算中出现数值不稳定会影响算法的计算精度，严重的会使算法发散完全失效。因此，对这些算法进行数值稳定性方法的研究是很有必要的。 本文针对更具普遍意义的多通道带乘性噪声系统的状态最优估计理论，在保证线性方差最小意义下最优性的同时，在数值稳定性方面主要做了如下工作： 第一，本文回顾了带乘性噪声系统最优估计理论的发展和现状，并介绍了在此领域数值稳定性研究的发展现状。 第二，在多通道带乘性噪声系统的观测模型中，乘性噪声不再是传统的一维随机序列，而是随机矩阵的形式，首先是随机对角矩阵，进而推广到一般随机矩阵。本文首先针对观测通道乘性噪声为随机对角矩阵的系统，利用奇异值分解(SVD)作为工具，给出了通道特性不相关时最优状态滤波的数值稳定性算法，然后将此方法应用到乘性噪声为一般随机矩阵的系统，同样给出了复杂多通道带乘性噪声系统的数值稳定性算法。这两种滤波算法均保持了线性方差最小意义下的最优性。 第三，针对多通道带乘性噪声系统，在最优状态滤波算法的基础上，首先推导了乘性噪声为随机对角阵情形下的最优固定域直接平滑算法，然后利用奇异值分解(SVD)方法对平滑算法中的误差协方差矩阵进行分解，给出了其数值稳定性算法，进而利用滤波和平滑的最优估计结果，给出了相应的固定域反褶积算法。然后又将以上各算法推广至乘性噪声为一般随机阵的情形，给出了复杂多通道情形下的直接固定域平滑算法、反褶积算法和数值稳定性算法。 第四，通过仿真实例，验证了上述各算法的有效性。更多还原

【Abstract】 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.更多还原