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

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

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, mathematical structure, structure, space, Mathematica ...

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

Kalman filter In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...

, 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 audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomograph ...

control system A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial ...

s, and guidance, navigation and control. For this work, U.S. President

Barack Obama Barack Hussein Obama II (born August 4, 1961) is an American politician who was the 44th president of the United States from 2009 to 2017. A member of the Democratic Party, he was the first African American president in American history. O ...

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 science, behavior ...

on October 7, 2009.

Life and career

Rudolf Kálmán was born in

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

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

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

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 university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

, in

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

. Kálmán completed his doctorate in 1957 at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

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

Baltimore, Maryland Baltimore is the List of municipalities in Maryland, most populous city in the U.S. state of Maryland. With a population of 585,708 at the 2020 United States census, 2020 census and estimated at 568,271 in 2024, it is the List of United States ...

, from 1958 until 1964. He was a professor at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

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 university, public land-grant university, land-grant research university in Gainesville, Florida, United States. It is a senior member of the State University System of Florida and a preem ...

from 1971 until 1992. He periodically returned to

Fontainebleau Fontainebleau ( , , ) is a Communes of France, commune in the Functional area (France), metropolitan area of Paris, France. It is located south-southeast of the Kilometre zero#France, centre of Paris. Fontainebleau is a Subprefectures in Franc ...

from 1969 to 1972 at MINES ParisTech 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 in

Zurich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. 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, United States, and the most populous city in North Central Florida, with a population of 145,212 in 2022. It is the principal city of the Gainesville metropolitan area, Florida, Gainesv ...

Work

Kálmán was an

by his undergraduate and graduate education at

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

and

, 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 of

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

systems,

avionics Avionics (a portmanteau of ''aviation'' and ''electronics'') are the Electronics, electronic systems used on aircraft. Avionic systems include communications, Air navigation, navigation, the display and management of multiple systems, and the ...

, and outer-space vehicles to extract a

signal A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

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 cal ...

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 rot ...

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 and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principl ...

, rather than in electrical engineering or systems engineering. Kálmán had more success in presenting his ideas, however, while visiting Stanley F. Schmidt 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) laborat ...

in 1960. This led to the use of Kálmán filters during the

Apollo program The Apollo program, also known as Project Apollo, was the United States human spaceflight program led by NASA, which Moon landing, landed the first humans on the Moon in 1969. Apollo followed Project Mercury that put the first Americans in sp ...

, and furthermore, in the NASA

Space Shuttle The Space Shuttle is a retired, partially reusable launch system, 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. ...

, in Navy

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

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 astron ...

vehicles and weapons, such as

cruise missile A cruise missile is an unmanned self-propelled guided missile that sustains flight through aerodynamic lift for most of its flight path. Cruise missiles are designed to deliver a large payload over long distances with high precision. Modern cru ...

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

state-space representation In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations o ...

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 plays a crucial role in many regulation problems, such as the stabilization of unstable systems using feedback, tracking problems, obtaining optimal control strategies, or, simply p ...

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 control theory 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 and operations ...

and provided, in his joint work with J. E. Bertram, a comprehensive and insightful exposure of

stability theory In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differ ...

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, NGO, 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 ...

, the

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

,Prof. Dr. Rudolf Kalman was elected in 1991 as a member of National Academy of Engineering in Electronics, Communication & Information Systems Engineering.
/ref> and the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) 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 other ...

. 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 American Institute of Electrical and Electronics Engineers (IEEE). It has been awarded since 1917, and is presented to an individual or team of up to three who have made exceptional contri ...

in 1974, the IEEE Centennial Medal in 1984, the Inamori foundation's Kyoto Prize in Advanced Technology in 1985, the Steele Prize 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 () 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 was subsequently granted university status by roya ...

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 an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

{{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 American systems engineers University of Florida faculty Stanford University Department of Electrical Engineering faculty