Latent Autoregressive Gaussian Processes Models for Robust System Identification

Abstract

We introduce GP-RLARX, a novel Gaussian Process (GP) model for robust system identification. Our approach draws inspiration from nonlinear autoregressive modeling with exogenous inputs (NARX) and it encapsulates a novel and powerful structure referred to as latent autoregression. This structure accounts for the feedback of uncertain values during training and provides a natural framework for free simulation prediction. By using a Student-t likelihood, GP-RLARX can be used in scenarios where the estimation data contain non-Gaussian noise in the form of outliers. Further, a variational approximation scheme is developed to jointly optimize all the hyperparameters of the model from available estimation data. We perform experiments with five widely used artificial benchmarking datasets with different levels of outlier contamination and compare GP-RLARX with the standard GP-NARX model and its robust variant, GP-tVB. GP-RLARX is found to outperform the competing models by a relatively wide margin, indicating that our latent autoregressive structure is more suitable for robust system identification.