Learning Nonlinear Dynamical Systems Using an EM Algorithm

Abstract

The Expectation-Maximization (EM) algorithm is an iterative pro(cid:173) cedure for maximum likelihood parameter estimation from data sets with missing or hidden variables [2]. It has been applied to system identification in linear stochastic state-space models, where the state variables are hidden from the observer and both the state and the parameters of the model have to be estimated simulta(cid:173) neously [9]. We present a generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems. The "expec(cid:173) tation" step makes use of Extended Kalman Smoothing to estimate the state, while the "maximization" step re-estimates the parame(cid:173) ters using these uncertain state estimates. In general, the nonlinear maximization step is difficult because it requires integrating out the uncertainty in the states. However, if Gaussian radial basis func(cid:173) tion (RBF) approximators are used to model the nonlinearities, the integrals become tractable and the maximization step can be solved via systems of linear equations.