Fundmentals of Kalman Filtering 翻译

本书探讨了在现代计算机上实现原始卡尔曼滤波器及最小二乘技术的方法,并介绍了SDRE技术、UKF和IMM方法等新技术,通过实例对比它们与扩展卡尔曼滤波技术在性能、鲁棒性和计算效率等方面的差异。

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前言---编者的话     

《Fundmentals of Kalman Filtering : A practical Approach》 之前发布的版本主要讨论了如何将原始的卡尔曼滤波器和各种各样的最小二乘技术在当今的64位个人电脑中实现。最近几年,学术文献中出现了一些新的理论,提出了改进卡尔曼滤波器的方法。

      不幸的是,这些新技术的描述高度数学化,并且实现方法从工程实现的角度来看不够清晰。写这个最新版书的出发点是让感兴趣的读者能容易的实现新技术,同时看看新技术相比现有技术对读者感兴趣的应用领域有没有提升。
      在这个版本中有三个新的章节,分别介绍 the State Dependent Riccati Equation (SDRE)技术,the Unscented Kalman Filter (UKF)和 the Interactive Multiple Model (IMM)方法。这些新的章节首次以 "cookbook style" 的形式出现,使读者不用理解技术的推导就能进行编程。接下来,利用一些在之前章节给出的例子,从性能、鲁棒性、计算效率几个方面对比新技术与扩展卡尔曼滤波技术。强烈建议想将运用新技术的读者进行类似的比较。最后,增加了第四个新章节关于  Cramer-Rao Lower bound  的应用。尽管关于寻找最佳滤波器的技术经常在学术论文中出现,但将公式转化成代码的实现通常缺失或者不够清晰。本文给出了将公式转成代码的过程,同时比较了利用黎卡提微分得到的理论结果和卡尔曼滤波器得到的实际结果。

      应读者的特殊要求,《Fundmentals of Kalman Filtering : A practical Approach》前三个版本中出现的Fortran代码全部转化成MATLAB代码。在书本后面的支持材料中仔细说明了,感兴趣的读者如何在AIAA 网站上获得所有的MATLAB代码和等价的Fortran代码 。

    《Fundmentals of Kalman Filtering : A practical Approach》之前版本的读者可能注意到了,尽管第四版增加了四个新的章节,但几乎与第三版的厚度一样。能取得这样的奇迹是由于精简了第1,5,14 章内容,删除了第 10,13 章,删除了附录 A 。尽管材料从第四版删除了,感兴趣的读者可以在 AIAA 的网站上找到删减材料。

      就我个人而言,当得知许多从事或者需要学习卡尔曼滤波的人认为《Fundmentals of Kalman Filtering : A practical Approach》不仅nonintimidating而且有用时,非常欣慰。过去几年,一些读者联系我询问了一些书中说明不清楚的地方,为了让所有的读者能从我与读者的交流中获益,现在的章节中已经对这些地方做了解释。在此我希望,本书的第四版不仅对第一次接触本书有用,同时对已经读过之前版本的读者有益。

                                                                                                                                                 Paul Zarchan

                                                                                                                                                 August 2015

This is a practical guide to building Kalman filters that shows how the filtering equations can be applied to real-life problems. Numerous examples are presented in detail, showing the many ways in which Kalman filters can be designed. Computer code written in FORTRAN, MATLAB®, and True BASIC accompanies all of the examples so that the interested reader can verify concepts and explore issues beyond the scope of the text. In certain instances, the authors intentionally introduce mistakes to the initial filter designs to show the reader what happens when the filter is not working properly. The text carefully sets up a problem before the Kalman filter is actually formulated, to give the reader an intuitive feel for the problem being addressed. Because real problems are seldom presented as differential equations, and usually do not have unique solutions, the authors illustrate several different filtering approaches. Readers will gain experience in software and performance tradeoffs for determining the best filtering approach. The material that has been added to this edition is in response to questions and feedback from readers. The third edition has three new chapters on unusual topics related to Kalman filtering and other filtering techniques based on the method of least squares.Chapter 17 presents a type of filter known as the fixed or finite memory filter, which only remembers a finite number of measurements from the past. Chapter 18 shows how the chain rule from calculus can be used for filter initialization or to avoid filtering altogether. A realistic three-dimensional GPS example is used to illustrate the chain-rule method for filter initialization. Finally, Chapter 19 shows how a bank of linear sine-wave Kalman filters, each one tuned to a different sine-wave frequency, can be used to estimate the actual frequency of noisy sinusoidal measurements and obtain estimates of the states of the sine wave when the measurement noise is low.
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