ABSTRACT
The time series output of a variety of processes and systems across different disciplines may be fit with regression models. The parameters of these regression models may be approximated in several conventional ways in the presence of complete datasets collected from the processes in question. However, missing observations may arise in these datasets for a number of reasons, and many of these conventional parameter estimation tools may produce biased or incorrect parameter estimates in the presence of these missing observations. In this paper, the missing data-estimation of the parameters of a particular regression model class, the autoregressive-exogenous (ARX) model is considered. The state-space model, Kalman filter, and expectation maximization (EM) algorithm are all employed to not only determine the maximum likelihood parameter estimates, but also fill in missing observations in the datasets. Structural vibration data collected from a two-bay steel frame is used to test the proposed methodology.
