Embedded Point Iteration Based Recursive Algorithm for Online Identification of Nonlinear Regression Models

TL;DR

This paper introduces a new online recursive algorithm for nonlinear regression models that efficiently exploits the structure of parameters, ensuring stability and demonstrating high performance on synthetic and real data.

Contribution

It develops an embedded point iteration-based recursive algorithm that leverages the parameter structure for improved online identification of nonlinear regression models.

Findings

Algorithm is mean-square bounded.

High efficiency demonstrated on synthetic data.

Robustness confirmed on real-world time series.

Abstract

This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the special structure of nonlinear regression models, in which the parameters can be partitioned into a linear part and a nonlinear part. In this paper, we develop an efficient recursive algorithm for nonlinear regression models based on analyzing the equivalent form of variable projection (VP) algorithm. By introducing the embedded point iteration (EPI) step, the proposed recursive algorithm can properly exploit the coupling relationship of linear parameters and nonlinear parameters. In addition, we theoretically prove that the proposed algorithm is mean-square bounded. Numerical experiments on synthetic data and real-world time series verify the high efficiency and robustness of the proposed algorithm.