A Kalman Filtering Mechanism Based on Generalized Interval Probability and its Application in Process Variation Estimation

The Kalman filter has been widely applied for state identification in controllable systems. As a special case of hidden Markov model, it is based on the assumption of linear dependency relationships and Gaussian noises. The classical Kalman filter does not differentiate systematic error from random error associated with observations. In this paper, we propose an extended Kalman filtering mechanism based on generalized interval probability, where systematic error is represented by intervals, state and observable variables are random intervals, and interval-valued Gaussian distributions model the noises. The prediction and update procedures in the new mechanism are derived. A case study of auto-body side frame assembly is used to illustrate the developed mechanism.