Inversion of nonlinear stochastic models for parameter estimation

Prediction error and maximum likelihood estimation of nonlinear stochastic models requires inversion of the model, a step which may require substantial efforts, either in terms of manual calculations or through the use of software capable of symbolic computations. We show that model inversion can be easily implemented in numerical software such as, e.g., Simulink and Matrix_X, by means of a feedback connection based on the model. We derive sufficient conditions for the existence of a stable causal inverse as well as sufficient conditions for the initial transient to decay. These conditions are given in terms of properties for a linear time-varying system associated with the nonlinear model. The method is illustrated on a numerical example