Multi-innovation-based online variable projection algorithm for a class of nonlinear models

Abstract

Separable nonlinear models (SNMs) are powerful tools for system identification, data analysis, and machine learning, thanks to their flexible structure and remarkable ability to capture nonlinear behaviors. However, compared with the offline one, the online identification of SNMs is more challenging, due to the dynamic nature of the nonlinear systems and the interdependence of the different parts of parameters in SNMs. Existing methods, such as the recursive Gauss-Newton (RGN) and recursive variable projection (RVP) methods, which cannot effectively handle the parameter interdependence, often suffer from slow convergence and poor performance in this scenario. In this paper, we propose a novel multi-innovation-based recursive variable projection (MIRVP) algorithm, which extends the RVP algorithm with a multi-innovation strategy. This strategy enables the algorithm to handle the interaction of the linear and nonlinear parameters more effectively, by using multiple past innovations instead of only the current one, thus improving the identification effect. We demonstrate the effectiveness of our MIRVP algorithm on both synthetic and real world datasets, showing its advantages in convergence speed and robustness over existing methods.