Auto-regressive with exogenous inputs

Forward Dynamic Neural MIMO NARX model used in this paper is a combination between the Multi-Layer Perception Neural Networks (MLPNN) stiucturc aird the Auto-Regressive with exogenous input (ARX) model. Due to this corrrbirratiorr. Forward MIMO NARX model possesses both of powerful universal approximating feature from MLPNN stmcturc aird strong predictive feature from nonlinear ARX model. 

In this section, the Kalman filter is implemented on a time-varying auto-regressive model with exogenous inputs, which is abbreviated as the TVAREX model [105] ... 

In order to be able to establish confidence intervals, it also assumed that Ck is Gaussian distributed. The ARX model (1) is characterized by 3 numbers Ua, the auto-regressive order ny, the exogeneous order and rik, the pure time delay between input and output. A regression model is an ARXOlO model (with [ua, ny, n-k] = [0,1,0]). 

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