Aguirre Luis Antonio, Teixeira Bruno Otávio S, Tôrres Leonardo Antônio B
Programa de Pós-Graduação em Engenharia Elétrica, Laboratory of Modeling, Analysis and Control of Nonlinear Systems--MACSIN, Universidade Federal de Minas Gerais, Avenida Antônio Carlos 6627, 31270-901 Belo Horizonte, Minas Gerais, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026226. doi: 10.1103/PhysRevE.72.026226. Epub 2005 Aug 31.
This paper addresses the problem of state estimation for nonlinear systems by means of the unscented Kalman filter (UKF). Compared to the traditional extended Kalman filter, the UKF does not require the local linearization of the system equations used in the propagation stage. Important results using the UKF have been reported recently but in every case the system equations used by the filter were considered known. Not only that, such models are usually considered to be differential equations, which requires that numerical integration be performed during the propagation phase of the filter. In this paper the dynamical equations of the system are taken to be difference equations--thus avoiding numerical integration--and are built from data without prior knowledge. The identified models are subsequently implemented in the filter in order to accomplish state estimation. The paper discusses the impact of not knowing the exact equations and using data-driven models in the context of state and joint state-and-parameter estimation. The procedure is illustrated by means of examples that use simulated and measured data.
本文通过无迹卡尔曼滤波器（UKF）解决非线性系统的状态估计问题。与传统的扩展卡尔曼滤波器相比，UKF在传播阶段不需要对系统方程进行局部线性化。最近已有使用UKF得到的重要结果报道，但在每种情况下，滤波器所使用的系统方程都被认为是已知的。不仅如此，此类模型通常被认为是微分方程，这就要求在滤波器的传播阶段进行数值积分。在本文中，系统的动力学方程采用差分方程——从而避免了数值积分——并且是根据无先验知识的数据构建的。随后将识别出的模型应用于滤波器以完成状态估计。本文讨论了在状态估计以及联合状态和参数估计的背景下，未知精确方程和使用数据驱动模型的影响。通过使用模拟数据和实测数据的示例来说明该过程。
