Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables

作     者：Servadio, Simone Zanetti, Renato Jones, Brandon A. 

作者机构：Univ Texas Austin Austin TX 78712 USA 

出 版 物：《IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS》 (IEEE航空航天与电子系统汇刊)

年 卷 期：2021年第57卷第1期

页      面：647-658页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 08[工学] 0825[工学-航空宇航科学与技术] 

基　　金：Air Force Office of Scientific Research [FA9550-18-1-0351] 

主　　题：Taylor series Kalman filters Algebra Nonlinear dynamical systems Gaussian approximation Approximation algorithms Estimation Differential algebra (DA) nonlinear filtering polynomial update 

摘      要：Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. Nonlinear filters that relax the Gaussian assumption, on the other hand, typically approximate the distribution of the state with a finite sum of point masses or Gaussian distributions. In this work, the distribution of the state is approximated by a polynomial transformation of a Gaussian distribution, allowing for all moments, central and raw, to be rapidly computed in a closed form. Knowledge of the higher order moments is then employed to perform a polynomial measurement update, i.e., the value of the measurement enters the update function as a polynomial of arbitrary order. A filter employing a Gaussian approximation with linear update is, therefore, a special case of the proposed algorithm when both the order of the series and the order of the update are set to one: it reduces to the extended Kalman filter. At the cost of more computations, the new methodology guarantees performance better than the linear/Gaussian approach for nonlinear systems. This work employs monomial basis functions and Taylor series, developed in the differential algebra framework, but it is readily extendable to an orthogonal polynomial basis.