Input-output modeling of nonlinear systems with time-varying linear models

Time-varying ARMA (AutoRegressive Moving Average) and ARMAX (AutoRegressive Moving Average with Exogenous Inputs) models are proposed fur input-output modeling of nonlinear deterministic and stochastic systems. The coefficients of these models are estimated by a Random Walk Kalman Filter (RWKF). This method requires no prior assumption on the nature of the model coefficients, and is suitable for real-time implementation since no off-line training is needed. A simulation example illustrates the method. Goodness of performance is judged by the quality of the residuals, histograms, autocorrelation functions and the Kolmogorov-Smirnoff test.