Identification of Nonlinear Processes with Known Model Structure under Missing Observations

A novel maximum likelihood solution to the problem of identifying parameters of a nonlinear model under missing observations is presented. An expectation maximization (EM) algorithm, which uses the expected value of the complete log-likelihood function including the missing observations, is developed. The expected value of the complete log-likelihood (E-step) in the EM algorithm is approximated using particle filters and smoothers. New expressions for particle filters and smoothers under missing observations are derived. The maximization step (M-step) in the EM algorithm is performed using standard optimization routines. The above nonlinear identification approach is illustrated through numerical examples.