Rudolf Emil Kálmán (May 19, 1930 – July 2, 2016) was a

Hungarian-American Hungarian Americans ( Hungarian: ''amerikai magyarok'') are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people wit ...

electrical engineer Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...

, and inventor. He is most noted for his co-invention and development of the

Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimat ...

, a mathematical algorithm that is widely used in

signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, d ...

, control systems, and

guidance, navigation and control Guidance, navigation and control (abbreviated GNC, GN&C, or G&C and within the context of NASA operations, often pronounced 'Gintsee' or (IPA) ʤɪnsiː) is a branch of engineering dealing with the design of systems to control the movement o ...

. For this work, U.S. President

Barack Obama Barack Hussein Obama II ( ; born August 4, 1961) is an American politician who served as the 44th president of the United States from 2009 to 2017. A member of the Democratic Party, Obama was the first African-American president of the U ...

awarded Kálmán the

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

on October 7, 2009.

Life and career

Rudolf Kálmán was born in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population o ...

, Hungary, in 1930 to Otto and Ursula Kálmán (née Grundmann). After emigrating to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territo ...

in 1943, he earned his bachelor's degree in 1953 and his master's degree in 1954, both from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

, in

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

. Kálmán completed his doctorate in 1957 at Columbia University in

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

. Kálmán worked as a Research Mathematician at the Research Institute for Advanced Studies in

Baltimore, Maryland Baltimore ( , locally: or ) is the most populous city in the U.S. state of Maryland, fourth most populous city in the Mid-Atlantic, and the 30th most populous city in the United States with a population of 585,708 in 2020. Baltimore was ...

, from 1958 until 1964. He was a professor at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...

from 1964 until 1971, and then a Graduate Research Professor and the Director of the Center for Mathematical System Theory, at the

University of Florida The University of Florida (Florida or UF) is a public land-grant research university in Gainesville, Florida. It is a senior member of the State University System of Florida, traces its origins to 1853, and has operated continuously on its Ga ...

from 1971 until 1992. He periodically returned to

Fontainebleau Fontainebleau (; ) is a commune in the metropolitan area of Paris, France. It is located south-southeast of the centre of Paris. Fontainebleau is a sub-prefecture of the Seine-et-Marne department, and it is the seat of the ''arrondissement'' ...

from 1969 to 1972 at

MINES ParisTech Mines Paris - PSL, officially École nationale supérieure des mines de Paris (until May 2022 Mines ParisTech, also known as École des mines de Paris, ENSMP, Mines de Paris, les Mines, or Paris School of Mines), is a French grande école and a c ...

where he served as scientific advisor for Centre de recherches en automatique. Starting in 1973, he also held the chair of Mathematical System Theory at the

Swiss Federal Institute of Technology The Swiss Federal Institutes of Technology are two institutes of higher education in Switzerland (part of the ETH Domain): * Swiss Federal Institute of Technology in Lausanne Swiss may refer to: * the adjectival form of Switzerland *Swiss people ...

in Zürich, Switzerland. Kálmán died on the morning of July 2, 2016, at his home in

Gainesville, Florida Gainesville is the county seat of Alachua County, Florida, and the largest city in North Central Florida, with a population of 141,085 in 2020. It is the principal city of the Gainesville metropolitan area, which had a population of 339,247 in ...

Work

Kálmán was an

by his undergraduate and graduate education at M.I.T. and Columbia University, and he was noted for his co-invention of the

(or Kalman-Bucy Filter), which is a mathematical technique widely used in the

digital computers A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These progr ...

of control systems,

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

systems,

avionics Avionics (a blend of ''aviation'' and ''electronics'') are the electronic systems used on aircraft. Avionic systems include communications, navigation, the display and management of multiple systems, and the hundreds of systems that are fi ...

, and outer-space vehicles to extract a

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...

from a long

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...

of noisy or incomplete measurements, usually those done by electronic and

gyroscopic A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotat ...

systems. Kálmán's ideas on filtering were initially met with vast skepticism, so much so that he was forced to do the first publication of his results in

mechanical engineering Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, an ...

, rather than in electrical engineering or systems engineering. Kálmán had more success in presenting his ideas, however, while visiting

Stanley F. Schmidt Stanley F. Schmidt (January 21, 1926 – August 13, 2015) was an American aerospace engineer who pioneered the Schmidt-Kalman filter used in air and space navigation, most notably in Apollo program, Apollo spacecraft. Early life and education S ...

at the

NASA Ames Research Center The Ames Research Center (ARC), also known as NASA Ames, is a major NASA research center at Moffett Federal Airfield in California's Silicon Valley. It was founded in 1939 as the second National Advisory Committee for Aeronautics (NACA) labora ...

in 1960. This led to the use of Kálmán filters during the Apollo program, and furthermore, in the NASA

Space Shuttle The Space Shuttle is a retired, partially reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. Its official program nam ...

, in Navy

submarine A submarine (or sub) is a watercraft capable of independent operation underwater. It differs from a submersible, which has more limited underwater capability. The term is also sometimes used historically or colloquially to refer to remotely op ...

s, and in unmanned

aerospace Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and astr ...

vehicles and weapons, such as

cruise missile A cruise missile is a guided missile used against terrestrial or naval targets that remains in the atmosphere and flies the major portion of its flight path at approximately constant speed. Cruise missiles are designed to deliver a large warhea ...

s. Kálmán published several seminal papers during the sixties, which rigorously established what is now known as the

state-space representation In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables wh ...

of dynamical systems. He introduced the formal definition of a system, the notions of

controllability Controllability is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observabil ...

and

observability Observability is a measure of how well internal states of a system can be inferred from knowledge of its external outputs. In control theory, the observability and controllability of a linear system are mathematical duals. The concept of observa ...

, eventually leading to the Kalman decomposition. Kálmán also gave groundbreaking contributions to the theory of

optimal control Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering an ...

and provided, in his joint work with J. E. Bertram, a comprehensive and insightful exposure of stability theory for dynamical systems. He also worked with B. L. Ho on the minimal realization problem, providing the well known Ho-Kalman algorithm.

Awards and honors

Kálmán was a foreign member of the French, Hungarian and Russian Academies of Sciences, as well as a member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Natio ...

, the

National Academy of Engineering The National Academy of Engineering (NAE) is an American nonprofit, non-governmental organization. The National Academy of Engineering is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of ...

, and the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

. He has been awarded many honorary doctorates from other universities. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Kálmán received the

IEEE Medal of Honor The IEEE Medal of Honor is the highest recognition of the Institute of Electrical and Electronics Engineers (IEEE). It has been awarded since 1917, when its first recipient was Major Edwin H. Armstrong. It is given for an exceptional contributio ...

in 1974, the

IEEE Centennial Medal The IEEE Centennial Medal was a medal minted and awarded in 1984 ''to persons deserving of special recognition for extraordinary achievement'' to celebrate the Centennial of the founding of the Institute of Electrical and Electronics Engineers (I ...

in 1984, the Inamori foundation's

Kyoto Prize in Advanced Technology The Kyoto Prize in Advanced Technology is awarded once a year by the Inamori Foundation. The Prize is one of three Kyoto Prize categories; the others are the Kyoto Prize in Basic Sciences and the Kyoto Prize in Arts and Philosophy. The first Kyot ...

in 1985, the

Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have ...

of the

in 1987, the Richard E. Bellman Control Heritage Award in 1997, and the National Academy of Engineering's

Charles Stark Draper Prize The U.S. National Academy of Engineering annually awards the Draper Prize, which is given for the advancement of engineering and the education of the public about engineering. It is one of three prizes that constitute the "Nobel Prizes of Enginee ...

in 2008. Kálmán also received an Honorary Doctorate from

Heriot-Watt University Heriot-Watt University ( gd, Oilthigh Heriot-Watt) is a public research university based in Edinburgh, Scotland. It was established in 1821 as the School of Arts of Edinburgh, the world's first mechanics' institute, and subsequently granted univ ...

in 1990. and an Honorary doctorate from the Politecnico di Milano in 2012. Kalman died a few weeks before the conferment of the latter doctorate, so that his wife Dina attended the ceremony on his behalf, held in the Conference room of the Departement of Electronics, Information and Bioengineering of the Politecnico di Milano on 12 September 2016.

Selected publications

* * * * * * *

References

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operati ...

{{DEFAULTSORT:Kalman, Rudolf Emil 1930 births 2016 deaths 20th-century American mathematicians 21st-century American mathematicians American electrical engineers American inventors American people of Hungarian-Jewish descent Columbia School of Engineering and Applied Science alumni Control theorists Electrical engineering academics Academic staff of ETH Zurich Fellows of the American Mathematical Society Foreign Members of the Russian Academy of Sciences Hungarian emigrants to the United States IEEE Centennial Medal laureates IEEE Medal of Honor recipients Draper Prize winners Kyoto laureates in Advanced Technology MIT School of Engineering alumni Members of the French Academy of Sciences Members of the Hungarian Academy of Sciences Members of the United States National Academy of Engineering Members of the United States National Academy of Sciences Richard E. Bellman Control Heritage Award recipients Stanford University faculty Systems engineers University of Florida faculty