多通道带乘性噪声2-D广义系统状态最优估计算法

Optimal State Estimation Algorithm for 2-D Generalized System with Multi-Channel Multiplicative Noise

2-D系统及其广义系统在图像处理,电力网络等领域有着广泛的应用,本文基于多通道带乘性噪声的2-D广义Roesser模型提出一套状态最优估计算法。在以往基于2-D广义系统的研究中乘性噪声因子多假设是一维随机序列,本文的乘性噪声因子是对角矩阵,矩阵对角线上每个元素都是一维随机序列,这意味着系统不仅具有多个观测通道而且每个观测通道都受到不同乘性噪声的影响,更加符合实际情况,能够解决系统在更加复杂环境中的状态估计问题。仿真结果验证了该算法的有效性。

The two-dimensional（2-D）system and it＇s generalized model are widely used in many fields such as image processing,power grid.The system state of the two-dimensional（2-D）state space model is the function of two independent variables.With the expansion of the scope of study objects for modern control theory,the research achievement based on 2-D state space model is becoming more and more abundant.The multiplicative noise is widely existed in the problems studied in 2-D model,for instance,the salt-and-pepper noise in the territory of image processing.In this paper,a set of optimal state estimation algorithm is proposed for 2-D generalized Roesser model with multi-channel multiplicative noise.In previous research on the 2-D generalized system,the multiplicative noise factor is usually assumed as a scalar stochastic sequence.In this paper,the multiplicative noise factor is a diagonal matrix,whose elements in the diagonal matrix are scalar stochastic sequences,which means the system is not only multi-channel but also each channel is interfered by different multiplicative noises.The system model and the corresponding optimal estimation algorithm can be flexibly applied for the state estimation problem in more complicated environment.The algorithm has recursive structure and can overcome the problem of＂dimensional disaster＂in previous method by adopting line by line state filtering sequence.The algorithm is convenient for realization on computer due to low computational complexity.The simulation results verified the effectiveness of the proposed algorithm.