Fitting Multistage Models to Input/Output Data

摘要

The paper treats the problem of fitting a linear multistage model to a set of scalar input/output data. A Kalman filter is used to represent the system and the unknown parameters are estimated from the filter's measurement residuals by the maximum likelihood method. Many of the numerical problems associated with identifying the Kalman filter parameters are alleviated by rescaling the likelihood function to eliminate a singularity in its gradient. A recursive equation for the gradient of the likelihood function is derived. A numerical example is presented. Some extensions of these results to more general problems are discussed. (Author)