Analysis of a general recursive prediction error identification algorithm

• Authors: Lennart Ljung
• Venue: Automatica (Journal of IFAC)
• Year: 1981

A general class of algorithms for recursive identification of (stochastic) dynamical systems is studied. In this class, the discrepancy between the measured output and the output, predicted from previous data according to a candidate model ('the prediction error') is minimized over the model set using a stochastic approximation approach. It is proved that this class of methods has the same convergence properties as its off-line counterparts under mild and general assumptions. These assumptions do not, for example, include stationary conditions or conditions that the true system can be exactly represented within the model set. The considered class of methods contains as special cases several well-known algorithms. Other common recursive identification methods, like the extended least squares method and the extended Kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations. Therefore, the approach taken here, may also serve as a basis for unified description of many recursive identification methods.