A Robust Estimation Method for Nonlinear Model Coefficients Using Ridge Regression

Abstract

In this paper, we study the robustness of least squares (LS) estimation for the modeling of nonlinear systems, and propose an estimation method with enhanced robustness. We first show some motivations for improving the robustness when estimating coefficients of a nonlinear model. In particular, without a robust estimation, two recent linearization techniques would fail to linearize a practical nonlinear system. Then, we analyze the commonly-used LS estimation in the application of the nonlinear system modeling, and show its poor robustness is originated from the correlation effects. As a result, the estimated coefficients will deviate unpredictably from the true coefficients. Based on the above analysis, we present a ridge regression method to remove the correlation effects, and hence improve the robustness of the coefficients estimation. Some data is captured from a practical 1-watt power amplifier (PA) to estimate the coefficients of the PA model, and the superiority of our estimation method over the conventional LS-based method is demonstrated.