Chengliang Huang¹, Xiao-Ping Zhang¹ and Fang Wang², ¹Ryerson University, Canada and ²Wilfrid Laurier University, Canada

EM algorithm is popular in maximum likelihood estimation of parameters for state-space models. However, extant approaches for the realization of EM algorithm are still not able to fulfill the task of identification systems, which have external inputs and constrained parameters. In this paper, we propose new approaches for both initial guessing and MLE of the parameters of a constrained state-space model with an external input. Using weighted least square for the initial guess and the partial differentiation of the joint log-likelihood function for the EM algorithm, we estimate the parameters and compare the estimated values with the “actual” values, which are set to generate simulation data. Moreover, asymptotic variances of the estimated parameters are calculated when the sample size is large, while statistics of the estimated parameters are obtained through bootstrapping when the sample size issmall. The results demonstrate that the estimated values are close to the “actual” values.Consequently, our approaches are promising and can applied in future research.

State-Space Model, Maximum Likelihood Estimation, Expectation Maximization Algorithm, Kalman filtering and smoothing, Asymptotic variances, Bootstrapping