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 for 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.