Parameter Estimation of a Linear ARX Model With Skewed Heavy-Tailed Noise

An online variational Bayesian algorithm based on a skewed Student'st-distribution, referred to as OVB-skewt, is proposed for robust parameter estimation in linear AutoRegressive with eXogenous inputs (ARX) models. In practical applications, measurement data are often contaminated by non-Gaussian, heavy-tailed, and asymmetric noise, which poses significant challenges to conventional identification methods that typically assume Gaussian noise. To address this issue, the proposed method incorporates the generalized hyperbolic skewed Student'st-distribution into a variational Bayesian inference framework, allowing the noise characteristics to be adaptively learned during online estimation. By explicitly modeling both heavy-tailed behavior and skewness, the proposed algorithm improves robustness against outliers and asymmetric disturbances. The online formulation enables efficient processing of streaming data, making the method suitable for time-varying industrial environments. Numerical simulations and a continuous fermentation reactor (CFR) benchmark demonstrate that the proposed OVB-skewt approach achieves improved estimation accuracy compared with symmetric noise-based methods under skewed and contaminated noise conditions, while maintaining stable performance in online settings.