Estimation of General Nonlinear State-Space Systems

The field of linear dynamic system identification is by now quite mature. A comprehensive, unified and effective framework has been developed for understanding the various approaches which have proven effective. This involves noting the distinctions between model structure, estimation criterion, and employed algorithm. Central to this is the straightforward computability for linear systems of a mean square optimal one-step ahead predictor via a Kalman or Wiener filter. This paper presents a novel approach to the estimation of a general class of dynamic nonlinear system models. The main contribution is the use of a tool from mathematical statistics, known as Fishers' identity, to establish how so-called "Particle smoothing" methods may be employed to compute gradients of maximum-likelihood and associated prediction error cost criteria.