System identification subject to missing data

In this paper we study parameter estimation when the measurement information may be incomplete. As a basic system representation we use an ARX-model. The presentation covers both missing output and input. First reconstruction of the missing values is discussed. The reconstruction is based on a state-space formulation of the system, and is performed using the Kalman filtering or fixed-interval smoothing formulas. Several approaches to the identification problem are then presented, including a new method based on the so called EM algorithm. The different approaches are tested and compared using Monte-Carlo simulations. The choice of method is always a trade off between estimation accuracy and computational complexity. According to the simulations the gain in accuracy using the EM method can be considerable if much data are missing.