论文标题

Ultimatekalman:使用正交转换的灵活的卡尔曼过滤和平滑

UltimateKalman: Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

论文作者

Toledo, Sivan

论文摘要

Ultimatekalman是一种灵活的线性Kalman滤波器,并以三种流行的编程语言实现了更平滑:Matlab,C和Java。 Ultimatekalman是对优雅的卡尔曼过滤器的轻微简化和略微的概括,这是Paige和Saunders在1977年提出的。它们的算法在数字上比其他Kalman过滤器和Smoothers更优越,更灵活,但奇怪的是从未实施或使用过。 Ultimatekalman是灵活的:它可以轻松处理时间依赖的问题,状态向量的问题,其尺寸因步骤而异,在不同步骤中具有不同观察值的问题(或根本没有观察到某些步骤)以及对初始状态的期望的问题尚不清楚。 Ultimatekalman的编程界面被分解为简单的构建块,可用于构建过滤器,单步预测变量,多步或全轨smoothorts以及组合。本文描述了该算法及其实现以及测试套件的示例和测试套件。

UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying number of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-track smoothers, and combinations. The paper describes the algorithm and its implementation as well as with a test suite of examples and tests.

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