Comparative Performance Analysis of ARX, ARMAX and Output Error Models for Linear System Identification under Different Noise Conditions using MATLAB

Abstract 
System identification is an essential tool for obtaining mathematical models capable of representing the 
dynamic behavior of a plant from experimental or simulated data. However, the presence of noise in input 
and output signals can significantly affect the accuracy of the estimated models. This work analyzes the 
performance of different linear system identification structures using MATLAB, considering ARX 
(AutoRegressive with eXogenous input), ARMAX (AutoRegressive Moving Average with eXogenous 
input), and OE (Output Error) models under different noise conditions. 
The proposed methodology is based on the simulation of a plant and the generation of datasets with 
different noise levels. The performance of each identification method is evaluated using several metrics, 
including the FIT index, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Akaike 
Information Criterion (AIC), Bayesian Information Criterion (BIC), and computational execution time. 
The results demonstrate that increasing noise levels progressively degrade the identification accuracy of 
all evaluated models. The ARX model provides satisfactory performance under low-noise conditions with 
reduced computational cost, while ARMAX and OE models exhibit higher robustness against 
disturbances. In particular, the OE model achieves the best overall performance, providing higher FIT 
values and lower estimation errors in most evaluated scenarios. 
The obtained results allow establishing model selection criteria according to operating conditions, 
highlighting the importance of considering noise effects during the identification process of linear 
systems. 
Keywords: System identification, ARX, ARMAX, OE, noise conditions, MATLAB, dynamic modeling, 
model validation.