广义随机2-D系统的状态估计

State Estimation of Singular Stochastic 2-D System

考虑广义随机 2 -D系统的卡尔曼估计问题。目的是利用最小方差准则 ,在系统同时受到动态噪声和测量噪声干扰下 ,得到一类 2 -D系统的卡尔曼滤波。通过运用斜割支线和几何方法 ,给出状态向量的卡尔曼滤波与最优预测。同时 ,给出滤波和预测误差的方差与协方差阵的显示公式。

The problem of Kalman filtering is considered for stochastic signular secondary 2-D Fornasini-Marchesini Models (2-D SFMMII) subjected to white noises in both the state and measurement equations. The aim is to design a kind of 2-D Kalman filter to ensure the minimum variances of the filtering error system for all admissible noises. A sufficient condition for the solvability of the problem is obtained. The desired filter can be constructed by using the cross-cut and geometry method. The optimum prediction of the state vector is also given. The explicit formulae are provided for the variance matrices and covariance matrices of the filtering and prediction problems.