# IMC Colloquium Series: "A Particle Filter Approach to Identification of Discrete Stochastic Nonlinear Processes Under Missing Observations"

*Dr. Bhushan Gopaluni*

### Abstract

A novel maximum likelihood solution to the problem of identifying parameters of a nonlinear model under missing observations will be presented. If the observations are missing, then it is difficult to build a partial likelihood function consisting of only the available observations. Hence, a variant of 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. In order to reduce the variance on the smoothed states, a point-wise (as opposed to path- based) state estimation procedure is used. The maximization step (M-step) in the EM algorithm is performed using standard optimization routines. The proposed nonlinear identification approach is illustrated through numerical and industrial examples.