丢失数据下的条件极大似然辨识

Conditional maximum likelihood identification under missing data

针对仿射结构形式在丢失数据下的条件极大似然辨识问题,首先引入交换矩阵将原随机矢量分解成观测和丢失部分;然后确定出观测数据在丢失数据下的条件均值和条件方差,以此建立条件似然函数;进而从理论上给出了条件极大似然函数关于未知参数矢量、未知白噪声方差值和丢失数据的求导公式,并从工程上给出一种可分离的优化算法;最后通过仿真算例验证了该辨识方法的有效性.

To the conditional maximum likelihood identification problem of an affine structure under missing data, a permutation matrix is used to divide a random vector into observed and missing parts. Then conditional mean and covariance under missing data are set up to obtain a conditional likelihood function. In the theory, expressions of the derivatives about the conditional maximum likelihood function on the unknown parameter vector, unknown white noise variance and missing data are derived. A separable optimum algorithm is given to be applied in engineering. Finally, simulation results show the effectiveness of the identification method.