“卡尔曼滤波”掌门人近日退隐苍穹、控门绝技系由何毓琦先生命名

缅怀:一代宗师卡尔曼
中国指挥与控制学会 2016-07-11

　　导读：卡尔曼，一位划时代的大师！一位成就了无数人的智者，一座很难超越的里程碑。他提出了系统的能控性和能观性，为控制理论的出现奠定了坚实的基础。这位匈牙利裔美国数学家提出的卡尔曼滤波，颠覆了通信，导航，制导与控制等多个领域，这对现代科技的发展无疑是巨大的。2016年7月2日，这位巨人陨落了，今天就让我们回顾一下这位传奇人物的一生，再次走近他终其一生所追求的数学世界！

2016年7月2日凌晨，一代宗师卡尔曼与世长辞，享年86岁。

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      大师的一生
--------------------------------------------------------------------------------
        鲁道夫·卡尔曼（Rudolf Kalman），1930年5月19日出生于匈牙利首都布达佩斯，父亲是一位电气工程师，后来跟随父亲的脚步，移居美国并在麻省理工学院获得电气工程学士和硕士学位。之后，他又离开了麻省理工学院，前往哥伦比亚大学继续从事研究，并获得了哥伦比亚大学博士学位。（也曾是少年）
        卡尔曼早期在麻省理工学院和哥伦比亚大学对控制系统充满了兴趣。他早期的研究主要是从实际问题出发，对状态变量表示概念的研究，这种研究在数学上很先进。他曾表示，早期的研究方法非常个性化，却在他后续辉煌的职业生涯中发挥了很大作用。
        从1957到1958年，卡尔曼任职于纽约波基普西的IBM研究实验室。在纽约那段时间里，他对线性数据采样控制系统采用二次型性能标准的设计和控制系统分析与设计的Lyapunov理论的运用方面做出了重大贡献。当时，他已经预见到大规模数字计算机系统的重要性。
        1958年，卡尔曼加入由已故的Solomon Lefschetz创办的RIAS（the Research Institute for Advanced Study）研究所。刚开始，他是作为一个数学研究人员，后来晋升为副主任。正是在那段时间（1958-1964），他在现代控制理论方面做出了开拓性贡献。他的演讲和出版物反映了他的巨大创造力和控制理论方面研究工作。他在基本系统概念的研究，如可控性和可观性方面，为一些重要的工程系统奠定了坚实的理论基础。他统一了离散时间和连续时间情况下线性系统的理论和设计方面的二次标准。为引入Caratheodory到最优控制理论，他做出了很多贡献，并阐明了Caratheodory、庞特里亚金（Pontryagin）最大值原理和哈密尔顿-雅可比-Bellman方程之间的关系，以及一般的变分法。
        他的研究不仅强调数学的一般性，还将数字计算机作为设计过程的组成部分和控制系统实现的组成部分进行综合考虑。
        在RIAS期间，卡尔曼做出了他一生中最著名的贡献，也就是所谓的“卡尔曼滤波”。1958年底到1959年初期间，他在离散时间（采样数据）问题方面取得了一些成果，并将早期的基础工作应用在维纳滤波、Kolmogorov、伯德、香农、普加乔夫和其他现代状态空间方法上。他对离散问题的研究自然而然地将他引向连续时间问题，并于1960-1961年期间与R.S.布西共同提出了“连续时间Kalman滤波器”。
        ……（以下略）
附4：www.zhihu.com/question/23971601

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  如何通俗并尽可能详细解释卡尔曼滤波？
                                                                                 网友：小心假设
        个人觉得何毓琦老师（曾与Kalman合作，何老博客里有不少介绍）的这篇博文讲得算是非常好了，虽然仍有公式。blog.sciencenet.cn/blo...14253.html

附5：carpa.bokee.com/4725695.html

卡尔曼滤波器 Kalman Filter (zz)
作者：carpa 2006-03-24

        在学习卡尔曼滤波器之前，首先看看为什么叫“卡尔曼”。跟其他著名的理论（例如傅立叶变换，泰勒级数等等）一样，卡尔曼也是一个人的名字，而跟他们不同的是，他是个现代人！
        卡尔曼全名Rudolf Emil Kalman，匈牙利数学家，1930年出生于匈牙利首都布达佩斯。1953，1954年于麻省理工学院分别获得电机工程学士及硕士学位。1957年于哥伦比亚大学获得博士学位。我们现在要学习的卡尔曼滤波器，正是源于他的博士论文和1960年发表的论文《A New Approach to Linear Filtering and Prediction Problems》（线性滤波与预测问题的新方法）。如果对这编论文有兴趣[color=#000000]（陈昌春注：应是“这篇文献”），[/color]可以到这里的地址下载： http://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf
        简单来说，卡尔曼滤波器是一个“optimal recursive data processing algorithm（最优化自回归数据处理算法）”。对于解决很大部分的问题，他是最优，效率最高甚至是最有用的。他的广泛应用已经超过30年，包括机器人导航，控制，传感器数据融合甚至在军事方面的雷达系统以及导弹追踪等等。近年来更被应用于计算机图像处理，例如头脸识别，图像分割，图像边缘检测等等。
        卡尔曼滤波器的介绍（Introduction to the Kalman Filter）
        ……下略

附6：blog.sciencenet.cn/hom...g&id=14253

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Proximity to Fame (#2) The Draper Prize (Nobel for Engineering) for 2008
– the Kalman Filter : a technical explanation and personal account of its history

I must be prescient. In my June 21, 2007 blog article : On Prizes, Nobel and others, sciencenet.cn/blog/use...px?id=3574

I predicted that Dr. Rudolf E. Kalman should win the Draper Prize given by the National Academy of Engineering (NAE) of the US sometimes in the future. Little did I know that my prediction became true almost immediately as announced today by the US National Academy of Engineering. Kalman filter arguably is the crowning achievement of modern system and control theory. It is behind almost every aerospace guidance and control systems, the ubiquitous GPS unit in most automobiles and everywhere else, and countless industrial applications. Yet its principle goes way back to the least square method of Gauss, the famous mathematician of 18th century, and the ancient civil engineering method of triangulation for position determination. Except the Kalman filter takes this principle to such a sophisticated degree that even today most students who learn about the Kalman filter are unaware of this fundamental connection. ……（详见何先生博文）

附7：blog.sciencenet.cn/hom...&id=612378

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与国内师生谈科研输出4：作学术报告四建议
李晓榕

比如有一次我在一个国际专业大会上，指出卡尔曼滤波的种种局限，并报告我对它的重要拓展和推广，为了加深印象，我在结束时故意“危言耸听”地问：既然有我的结果，是否应该禁止使用卡尔曼滤波？会后有位学者很严肃地对我表示“抗议”，在场的另一位知名朋友解释说我这是夸张，他还不接受。还应对内容表现激情和自信，感染听众。与听众互动：注意听众的表情，向听众提问，邀请听众提问、猜想。

附8：blog.sciencenet.cn/hom...&id=799745

                                                                        我遭遇恶老师和自己当恶老师
                                                                                               应行仁
        当年卡尔曼发表他的滤波技术论文时，数学证明是错的，但卡尔曼滤波却成了随机控制最重要的结果。

附9：www.cs.unc.edu/~welch/kalman/（该网页有比较丰富的卡尔曼研究工作及卡尔曼滤波信息）

www.cs.unc.edu/~welch/...ontag.html

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Rudolph E. Kalman（卡尔曼正式简介）

The following was originally published in SIAM News in June of 1994, and then modified by Greg Welch in May of 2004 to correct and update some information.

Rudolf E. Kalman, a graduate research professor emeritus at the University of Florida and ad personam chair at the Swiss Federal Institute of Technology in Zurich, and Andrew J. Majda, a professor of mathematics and of applied and computational mathematics at Princeton University, were among the 60 new members and 15 foreign associates elected to the National Academy of Sciences in April.

The election of Kalman, a control theorist who is "without a doubt the most influential researcher in the field," provides "additional evidence, if more was needed, that the field of systems and control is now an established part of mathematics and science," says Eduardo Sontag of Rutgers University. Kalman is best known for the linear filtering technique that he developed in the years 1959-1961 (from 1960 on partly in collaboration with Richard Bucy) to strip unwanted noise out of a stream of data. The Kalman filter is widely used in navigational and guidance systems, radar tracking, sonar ranging, and satellite orbit determination (for the Ranger, Apollo, and Mariner missions, for instance), as well as in fields as diverse as seismic data processing, nuclear power plant instrumentation, and econometrics. (See "Engineers Look to Kalman Filtering for Guidance" in the August 1993 issue of SIAM News, page 8, for a discussion of the origin, function, and extraordinary usefulness of the Kalman filter.)

The Kalman filter, which is based on the use of state-space techniques and recursive algorithms, revolutionized the field of estimation. The filter was the first major contribution in Kalman's influential work in control theory, Sontag observes. Sontag and Yutaka Yamamoto of Kyoto University, both former students of Kalman's, provided SIAM News with the following summary of Kalman's work:

"During the 1960s, Kalman was the leader in the development of a rigorous theory of control systems. Among his many outstanding contributions were the formulation and study of most fundamental state-space notions (including controllability, observability, minimality, realizability from input/output data, matrix Riccati equations, linear-quadratic control, and the separation principle) that are today ubiquitous in control. While some of these concepts were also encountered in other contexts, such as optimal control theory, it was Kalman who recognized the central role that they play in systems analysis. The paradigms formulated by Kalman and the basic results he established have become an intrinsic part of the foundations of control and systems theory and are standard tools in research as well as in every exposition of the area, from undergraduate engineering textbooks to graduate-level mathematics research monographs. During the 1970s Kalman played a major role in the introduction of algebraic and geometric techniques in the study of linear and nonlinear control systems. His work since the 1980s has focused on a system-theoretic approach to the foundations of statistics, econometric modeling, and identification, as a natural complement to his earlier studies of minimality and realizability."

Born in Hungary, Kalman received his SB and SM degrees from the Massachusetts Institute of Technology (1953, 1954) and his DEngSci from Columbia University (1957). In the early years of his career he held research positions at IBM and at the Research Institute for Advanced Studies (RIAS) in Baltimore. From 1964 to 1971, he was at Stanford University. In 1971, he became a graduate research professor and director of the Center for Mathematical System Theory at the University of Florida, retiring with emeritus status in 1962; concurrently he held an "ad personam" chair in Mathematics at the Swiss Federal Institute of Technology (ETH) in Zurich from 1973 through statutory retirement in 1997. Kalman's contributions to control theory and to applied mathematics and engineering in general have been widely recognized. In 1985, he was one of the laureates of the Kyoto Prize, inaugurated in that year by the Inamori Foundation of Japan. The Kyoto prize is sometimes referred to as the "Japanese Nobel prize." It recognizes "outstanding intellectual or creative activities which have significantly enriched the human experience," but which are outside the five categories specifically designated in Alfred Nobel's will. Kalman received the first Kyoto Prize in the field of advanced technology. Among Kalman's other honors are the Institute of Electrical and Electronics Engineers' highest award, the Medal of Honor (1974), and the American Mathematical Society's Steele Prize (1986), which recognized the fundamental importance of the papers on linear filtering Kalman published in 1960 and 1961. Prior to his election to the National Academy of Sciences, Kalman has been elected member of the French, Hungarian, and Russian Academies of Sciences and of the National Academy of Engineering, as well as Fellow of the American Academy of Arts and Sciences.

Return to Welch and Bishop's Kalman filter page.
Return to Greg Welch's home page. May 1, 2004

附10：muchong.com/html/20160...59383.html

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光是卡尔曼滤波就影响了无数的工作，真正有贡献的学者，致敬。
另外查了下，卡尔曼滤波是何毓琦命名的。 blog.sciencenet.cn/hom...&id=988496

附11：bbs.kechuang.org/t/80393

Kalman filter 是一个非常典型的 Markov chain 模型，所以不难理解很多搞金融或者天气预报的人声称自己的工作中大量用到卡尔曼滤波。而且其求解思路跟 ML 里边的EM ( Expectation Maximization)是一个东西。

附12：www.zhihu.com/question/29477562

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光是卡尔曼滤波就影响了无数的工作，真正有贡献的学者，致敬。
另外查了下，卡尔曼滤波是何毓琦命名的。 blog.sciencenet.cn/hom...&id=988496

附11：bbs.kechuang.org/t/80393

Kalman filter 是一个非常典型的 Markov chain 模型，所以不难理解很多搞金融或者天气预报的人声称自己的工作中大量用到卡尔曼滤波。而且其求解思路跟 ML 里边的EM ( Expectation Maximization)是一个东西。

附12：www.zhihu.com/question/29477562

卡尔曼 Rudolf Kalman （卡尔曼滤波 Kalman Filter）有哪些奇闻轶事？

小心假设，当机器人遇到自动控制

39 人赞同

1 卡尔曼常对人抱怨说，觉得自己应该得诺贝尔经济学奖。

2 当年提出卡尔曼滤波时，主流其实是以维纳滤波为核心的频域滤波，卡尔曼滤波很长时间不被主流接纳。后来，扎德提出模糊逻辑与模糊控制之时，卡尔曼作为当时的主流，即状态空间模型的时域控制和滤波理论的代表人物，成了扎德的最大反对者之一。

3 一手把控制和滤波从频域带进时域状态空间方法的卡尔曼，过去的好多年其实一直在研究频域的一些东西。

4 卡尔曼的贡献包括状态空间系统分析，卡尔曼滤波，可控性，可观性，卡尔曼分解，最小实现等等。和香农一样，他不幸在于领域决定他基本不可能得诺贝尔奖，图灵奖等等，虽然，arguably，已经达到了这些奖的水平。但他其实也很幸运，因为至少卡尔曼滤波方法都是以他命名的。相比之下，知道动态规划是贝尔曼发明的又有几个？反而基于动态规划的维特比算法是以维特比命名。还有，多少人知道H无穷是Zames发明的？MPC呢？最后压轴，谁知道PID是谁发明的？

5 感谢 @pb博的信息。卡尔曼与扎德后来和好了。虽然卡尔曼公开说过 fuzzy is trash，但两人一笑泯恩仇（这是想象，哈哈哈）。从卡尔曼自己的新理论不被接受，到不接受扎德的新理论，再次说明了，别说是工程界与工程师了，就算是理论界与最顶尖的理论家，对完全跳出原来框架的新理论都如此难以接受。类似的例子还有贝尔曼的动态规划。

6 卡尔曼与扎德其实算是师兄弟，导师都是拉加奇尼（John R. Ragazzini）。拉加奇尼的学生还有Jury。拉加奇尼：Z变换，Jury：Jury判据。

7 岔开一条，讲贝尔曼的动态规划。扎德在 The Evolution of System Analysis and Control: A Personal Perspective IEEE Xplore Abstract 一文中的对于贝尔曼动态规划的回忆：
In the early '60s my doubts were not shared by many. The ascendancy of mathematical methods was unchallenged, and Lyapounov's stability theory and differential-equations-based theory of nonlinear systems moved to the center of the stage, as did the problems relating to optimal control and systems optimization. The highly original work of Rudy Kalman on controllability, observability, and filtering was at the center of attention. Another contribution of major importance, whose impact transcended disciplinary lines, was Bellman's development of dynamic programming. I became acquainted with Bellman's work in 1954 and perceived dynamic programming as a powerful tool of wide applicability. I suggested to Bellman to submit to the IRE Proceedings a paper describing his work. He did so, but to my embarrassment his paper was rejected by the referees, who felt that Bellman did not provide convincing examples of practical applicability. It is ironic that about 30 years later, Bellman was awarded IEEE's Medal of Honor for his development of dynamic programming.
怎么越看越像在哭诉自己的经历，哈哈哈。

8 在卡尔曼之前，其实不光维纳，扎德，乃至伯德，香农，都也研究过滤波问题。不过，应该说是到了卡尔曼才达到了一统江湖。

9 问题来了，下一个卡尔曼滤波式的结果会是什么？欢迎回答：
有哪些理论可能是下一个卡尔曼滤波似的结果？

10 可能会有争议的一条。有一种说法是，信息论第一代掌门是香农，第二代是Gallager，第三代是Tse。那如果说控制与滤波理论第一代掌门是维纳，第二代是卡尔曼的话，谁是第三代掌门？

11 卡尔曼当然不属于工程师，被工程师认为是做理论的。但数学家也并不承认卡尔曼是数学家，认为他是做工程的。在这一点上，他更像香农，而不是维纳。

未完待续。抛砖引玉，欢迎补充。

编辑于 2016-07-08

Rudolf Kalman 对现代控制工程贡献极大，尤其是导航领域，所以他非常自信，很少低头。但是他的一生还是低过一次头的。

2009年在白宫，奥巴骡把科学技术领域最高奖 2008 National Medals Of Science And Technology And Innovation颁给了Rudolf Kalman。

08年获得了工业界的诺贝尔奖之称的德雷伯奖,在获奖感言里，感谢何毓琦老师成功预测自己的获奖。附13：www.08kan.com/gwk/MzA4...d9bba.html 缅怀：一代宗师卡尔曼有一种说法是，信息论第一代掌门是香农，第二代是Gallager，第三代是Tse。那如果说控制与滤波理论第一代掌门是维纳，第二代是卡尔曼的话，谁是第三代掌门？R.E. Kalman先生虽然去世了，但是世界上有不计其数的、以他名字命名的Kalman Filter在日夜不停地运行，作为稳定世界的控制器默默工作着。他的精神化为代码，将永存在人类文明中。附14：news.sjtu.edu.cn/info/...990626.htm张钟俊：中国系统工程创始人
20世纪60年代初，张钟俊以极大的热情关注着卡尔曼和庞得里亚金在控制理论方面的新发展。1962年卡尔曼和布西提出新的滤波设计的时候，张钟俊认识到新的理论已经脱颖而出了。1964年，张钟俊将卡尔曼滤波技术应用到“远航仪”的接收信号处理中，在我国开创了应用现代控制理论的先例。1973年，张钟俊主持潜航惯性导航课题，为此他编写了《矩阵方法和现代控制理论》讲义，向课题组成员讲解现代控制理论，经过两年的努力，该课题完美地结题。设计中，他们再次应用卡尔曼滤波技术对惯性导航系统的反馈信号进行处理，大幅度提高了导航精度。总结该项研究成果的论文《陀螺角速度漂移数学模型的辨识》，获全国科学大会奖和上海市重大科技成果奖。

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