Nonlinear estimation by Hermite polynomial-based uncorrelated conversion within LMMSE framework

Abstract

In this paper, within the linear minimum mean square error (LMMSE) framework and with the Gaussian assumption, we propose a novel nonlinear estimation algorithm using a Hermite polynomial based uncorrelated conversion (UC), which is a nonlinear function of the original measurement while being uncorrelated with the original measurement. The UC can be regarded as a “new” measurement and additional information can be exploited to update the state estimate in a nonlinear way. Due to the orthogonality property of Hermite polynomials, each UC is not only uncorrelated with the original measurement, but also uncorrelated with already generated UCs automatically. It provides a systematic method to generate multiple UCs. The simulation results reveal the superiority of the new nonlinear estimation over the conventional quadrature based nonlinear Gaussian estimation in the sense of root mean square error (RMSE) and consistency.