Nonlinear filters: Beyond the Kalman filter
Nonlinear filters: Beyond the Kalman filter
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DOI：
10.1109/maes.2005.1499276
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发表时间：
2005-08-01
影响因子：
3.6
通讯作者：
Daum, F
中科院分区：
文献类型：
--
作者：
Daum, F
对于一些重要的实际应用，非线性滤波器可以提供远远优于扩展卡尔曼滤波器的估计精度。我们比较了几种类型的非线性滤波器，包括：粒子滤波器 (PF)、无迹卡尔曼滤波器、扩展卡尔曼滤波器、批处理滤波器和精确递归滤波器。非线性滤波的关键实际问题是计算复杂性，这通常被称为“维数灾难”。有人断言 PF 可以避免维数灾难，但这通常是不正确的。设计良好的 PF 具有良好的提案密度，有时可以避免维数灾难，但除此之外并非如此。非线性滤波的未来研究将利用准蒙特卡罗算法的最新进展（而不是无聊的旧蒙特卡罗方法），以及从物理学借用的思想（例如维度插值）和用于求解偏微分方程的新无网格伴随方法。本教程是为普通工程师编写的，他们早餐没有非线性滤波器。
Nonlinear filters can provide estimation accuracy that is vastly superior to extended Kalman filters for some important practical applications. We compare several types of nonlinear filters, including: particle filters (PFs), unscented Kalman filters, extended Kalman filters, batch filters and exact recursive filters. The key practical issue in nonlinear filtering is computational complexity, which is often called "the curse of dimensionality." It has been asserted that PFs avoid the curse of dimensionality, but this is generally incorrect. Well-designed PFs with good proposal densities sometimes avoid the curse of dimensionality, but not otherwise. Future research in nonlinear filtering will exploit recent progress in quasi-Monte Carlo algorithms (rather than boring old Monte Carlo methods), as well as ideas borrowed from physics (e.g., dimensional interpolation) and new mesh-free adjoint methods for solving PDEs. This tutorial was written for normal engineers, who do not have nonlinear filters for breakfast.