一类广义系统Kalman滤波新方法

A new approach to Kalman filtering for descriptor systems

基于矩阵理论[8]和时域上的Kalman滤波理论[5],对广义离散随机线性系统进行研究.运用矩阵约当分解,将一类广义系统化为正常系统,并利用已有的正常系统结果,给出一类广义最优Kalman滤波器,其算法简单,为递推算法,且避免了计算ARMA新息模型和白噪声估值器,便于实时应用.仿真例子说明了算法的有效性.

Based on matrix theory and Kalman filtering theory in the time domain, linear discrete -time descriptor stochastic systems were studied. Using Jordan decomposition for matrixes, descriptor systems can be changed into normal systems. An optimal descriptor Kalman filter is given by using normal systems＇ result. It is a simple and recursive algorithm. It avoids the calculation of ARMA innovation model and white noise estimators. It is suitable for real time applications. A simulation example shows its effectiveness.