Global convergence of the EM algorithm for ARX models with uncertain communication channels - Chen, Jing; Huang, Biao; Zhu, Quanmin; Liu, Yanjun; Li, Lun (Systems & control letters, 2020)
An expectation maximization (EM) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the ARX model are assumed to be unknown, a modified Kalman filter is derived to estimate the output, and then the parameters are estimated by the EM algorithm using the estimated outputs. The Kullback–Leibler divergence and the submartingale are used to prove that the parameter estimates can converge to the true values with the EM algorithm. Furthermore, a simulation example is presented to verify the theoretical results.