Density Estimation in the Regressor Space for Linear and Nonlinear System Identification

Abstract

In this paper, a new weighting approach for dynamic datasets is introduced. The overall goal of the new method is to improve data-driven model performance. This is achieved by increasing the weight of training data points in areas of the regressor space that are underrepresented in the loss function, while decreasing the weight for overrepresented data points. The method is based on estimating the parameters of a model using weighted error norms, where the weighting is carried out with the inverse values of the kernel density estimated in the regressor space. The performance of the new method is investigated using ARX models as examples in three different cases: when using datasets with different data distributions, datasets with different noise levels, and incorrectly assumed model orders. Additionally, a first attempt of weighted nonlinear system identification is performed. Overall, models weighted by the new method show a significantly improved performance compared to unweighted models while requiring an insignificant amount of additional computational effort.