# Kalman, Rudolf Emil

# Rudolf Emil Kalman

Hungarian-born U.S. scientist and professor Rudolf Emil Kalman (born 1930) is widely regarded as the creator of modern control theory and system theory. His research reshaped the field of control engineering and placed the groundwork for future research and innovation. His most widely known accomplishment is his development of the Kalman filter, a mathematical method now widely used in navigation, particularly in aviation.

Kalman was born in Budapest, Hungary, on May 19, 1930, the son of an electrical engineer. Early in his life he decided to follow in his father's footsteps, and pursue a career in a field that involved mathematics. Along with his family, he immigrated to the United States in 1943, as World War II raged in Europe, and after high school he studied electrical engineering at the Massachusetts Institute of Technology (MIT) in Cambridge. Kalman received his bachelor's degree in 1953 and his master's degree the next year. From MIT, he continued his studies at Columbia University in New York City, where he received his doctorate of science in 1957. At Columbia Kalman had the good fortune to study under Professor John R. Ragazzini, head of the school's electronics lab and a man noted for his research on ultra-high frequency—or UHF—techniques, analog computers, and control systems.

## Focused Research on Control Systems

During his years at MIT and Columbia, Kalman explored his interests in control theory, the study of how to engineer via mathematical applications a controlling device to alter the output of a given data stream or other input to achieve a desired outcome. (The governor installed on some automobile engines, designed to limit the vehicle's top speed, is one example of a mathematically engineered control.) In addition to directing his research toward state variable representations, Kalman also began demonstrating an individualistic approach to research that would characterize much of his later career.

From 1955 to 1957 Kalman was an instructor in control theory at Columbia University, and in 1958, he became an adjunct assistant professor. At the same time, he was employed as a staff engineer at the IBM Research Laboratory in Poughkeepsie, New York. During these years, through his research Kalman developed significant contributions to the design of linear sampled-data control systems and the use of Lyapunov theory for the analysis and design of control systems. Already, he understood how the digital computer would one day become important to his area of research.

In 1958 Kalman moved to Maryland, where he was employed as a research mathematician at the Research Institute for Advanced Studies in Baltimore (RIAS). The Institute was founded by Solomon Lefschetz (1884-1972), an influential mathematician noted for his groundbreaking work in algebraic geometry, algebraic topology, and differential equations. Kalman worked at RIAS until 1964, first as a research mathematician and then as associate director of research. While at the Institute, he focused his work on the search for a unified theory of control. Through lectures and published papers, he helped advance knowledge about modern control theory, which involves programming robotics and machines to respond to constantly changing conditions and still maintain self-control. One application of such control theory is the automatic pilot system installed in airplanes that prevents an unmanned craft from crashing to the ground. In mathematics, control is a time-dependent function that influences a dynamic engineered system, such as an automatic pilot.

## Conducted Innovative Research

Kalman's innovative work, which stressed mathematical generality, had an enormous impact within his field. He was involved in research about fundamental systems concepts such as controllability and observability, and he helped develop solid theories on the structural aspects of engineering systems. In addition, he unified the theory and design of linear systems with respect to quadratic criteria; introduced the analytical work of Constantin Caratheodory (1873-1950) in optimal control theory; and added to the understanding of the interrelations between Russian mathematician Lev Pontryagin's maximum principle and the Hamilton-Jacobi-Bellman equation, as well as variational calculus in general. At the time, he was one of the first to employ the digital computer as an important—and inevitable—part of the design process as well as of the control system's implementations.

However, the most important part of Kalman's work at RIAS was the development of the "Kalman filter," which would become his greatest contribution to his field. During his initial research, conducted in late 1958 and early 1959, he acquired solutions to the discrete-time filtering problems associated with discrete time. (Discrete time systems are linear; that is, they are measurements taken in sequence.) Kalman used as the basis of his research the work on filtering already done by Norbert Wiener (Wiener Filtration), Andrey Nikolaevich Kolmogorov (Wiener-Kolmogorov filter), Henrik W. Bode (electric filters and equalizers), Claude Shannon, Vladimir Pugachev and others, applying the modern stage space approach to this existing body of research. Based on utilization of state-space techniques and recursive algorithms, the Kalman filter revolutionized the field of estimation.

## Developed the Kalman Filter

The Kalman filter is a set of mathematical equations that provides an efficient computational—or recursive—solution to discrete time data filtering problems, in essence removing extraneous "noise" from a given stream of data. His mathematical filter involves two sets of algebraic equations that solve real-time problems. Kalman's solution to the discrete-time problem led him to tackle the continuous-time problem. He then fully developed the continuous-time version of the Kalman filter with Richard Bucy between 1960 and 1961 and published an important paper discussing the two men's work. Essentially, the paper describes a way to recursively find solutions to the discrete-data linear filtering problem.

One of the driving forces behind the development of the Kalman filter were the needs of the U.S. Air Force, which helped fund Kalman's work. By the late 1950s and early 1960s, aircrafts had advanced to the point where they required advanced flight-control mechanisms, and the Air Force Office of Scientific Research (AFOSR) funded research on control theory as it related to these advanced aircrafts, as well as to space vehicles. The AFOSR sponsored several efforts in this area, including the research done at RIAS by Kalman and Bucy, which the Air Force believed had the potential to alter control applications. As the AFOSR hoped, Kalman and Bucy's work revolutionized the field of estimation and had an enormous impact on the design and development of precise navigation systems. The Kalman filter was a major breakthrough in guidance technology.

Kalman's algorithm also found practical application in the National Aeronautics and Space Administration (NASA) space program. NASA first used the Kalman filter to solve the problems associated with determining satellite orbits. In the 1960s the Kalman filter was used preparing for in the Ranger, Mariner, and Apollo missions, and when the Apollo 11 lunar module landed on the Moon in July of 1969, it was guided by the Kalman filter. The filter would also be used in NASA space shuttles.

The Kalman filter, and its subsequent extensions to solve nonlinear problems, is the most widely applied byproduct of modern control theory, and is used in just about every modern military and commercial control system. It is used in navigational and guidance systems, radar tracking algorithms for anti-ballistic missile applications, sonar ranging, and satellite orbit determination. It also has been used in other fields, such as seismic data processing, nuclear power-plant instrumentation, and even socioeconomic systems.

Thanks to the advances in digital computing, the Kalman filter continues to be a focus of a great deal of research and application, particularly in the area of autonomous or assisted navigation; for example, the Global Positioning System or GPS makes use of the Kalman filter.

## Reputation and Horizons Widened

Kalman's achievement was a landmark, and the significance of his findings was immediately grasped. His reputation spread to an international scale, and it led to many honors. In 1962 Kalman received the Outstanding Young Scientist of the Year award from the Maryland Academy of Sciences. In 1964 he became a fellow of the Institute of Electrical and Electronics Engineers (IEEE).

In 1964 Kalman moved to California to assume a professorship at Stanford University, where he worked in the departments of electrical engineering, mechanics, and operations research. By this time, he had shifted the focus of his research to issues relating to the realization theory and algebraic system theory. As with his previous research efforts, his contributions helped create a new field of research in modern system theory, as he developed new directions of study. His contributions involved the formulation and study of many fundamental state-space notions, including controllability, observability, minimality, realizability from input/output data, matrix Riccati equations, linear-quadratic control, and the separation principle. His concepts had a far-ranging impact, because he was the first in his field to understand the crucial part such notions play in systems analysis. Kalman's mathematical advances have become part of educational textbooks and monographs relating to engineering and mathematics.

In 1971 Kalman became a graduate research professor and director of the Center for Mathematical System Theory at the University of Florida in Gainesville. In this position he taught and conducted research in the areas of mathematics, electrical engineering, system engineering, and mathematical system theory. During this period, he was instrumental in the introduction of algebraic and geometric techniques into the study of linear and nonlinear control systems. Starting in 1973, he also held the position of chair for Mathematical System Theory at the Swiss Federal Institute of Technology in Zurich, and also served as a scientific consultant to research centers in the École des Mines in Paris, France. Kalman remained at the University of Florida posts until he retired in 1992.

In the 1980s, Kalman focused his research efforts on a system-theoretic approach to the foundations of statistics, econometric modeling, and identification. This direction was a natural outgrowth of his earlier work in the areas of minimality and realizability. In the meantime, his career achievements—specifically his contributions to control theory and to applied mathematics and engineering in general—continued receiving official recognition.

## Received IEEE Medals, Kyoto Prize

In 1974 Kalman received the IEEE Medal of Honor, that association's highest award. The IEEE recognized him "for pioneering modern methods in system theory, including concepts of controllability, observability, filtering, and algebraic structures." Other honors he has received include the 1976 Rufus Oldenburger Medal from the American Society of Mechanical Engineers. In 1984 he received the IEEE Centennial Medal.

In 1985 Kalman was among the first four recipients to receive the Kyoto Prize, established that year to recognize "outstanding intellectual or creative activities which have significantly enriched the human experience." Created to honor pioneering research in the fields of basic science, frontier science, and philosophy, the prize is administered through the Inamori Foundation, established to serve as the Japanese counterpart of the Nobel Foundation. Kalman was honored for his development of a control theory to explain the workings of a dynamic system. The next year Kalman was awarded the American Mathematical Society's Steele Prize for his papers on linear filtering published in 1960 and 1961.

In April of 1994 Kalman was one of 60 new members elected to the National Academy of Sciences. In 1997 the American Automatic Control Council presented him with its Richard E. Bellman Prize, given for distinguished career contributions to the theory or application of automatic control. The award is the highest recognition of professional achievement for U.S. control systems engineers and scientists. He has also been the recipient of several honorary degrees.

## Active in Promoting Information

By the end of his illustrious career, Kalman was widely recognized as the individual who, first, all but created the field of modern control theory and, second, was instrumental in advancing its widespread application. He greatly influenced numerous researchers through his significant accomplishments, openness and accessibility, and his appearance at numerous lectures. In addition, he published more than 50 technical articles. His major papers included "Nonlinear Aspects of Sampled-Data Control Systems" (1956), "On The General Theory of Control Systems" (1960), "New Results on Linear Filtering and Prediction Theory" (1961), "Mathematical Description of Linear Dynamical Systems" (1963), and "Algebraic Structure of Linear Dynamical Systems" (1965). In 1969 Kalman coauthored the book *Topic in Mathematical System Theory.* In addition, he served on the editorial boards of numerous technical journals.

Kalman, who is married and has two children, also held memberships in a number of professional societies. Along with his memberships in the IEEE and the National Academy of Sciences, he also belongs to the U.S. National Academy of Engineering and is a fellow of the American Academy of Arts and Sciences. In addition, he is a foreign member of the Hungarian, French, and Russian academies of science.

## Online

*Air Force Research Laboratory Technology Horizons,*http://www.afrlhorizons.com/ (December 16, 2003).

"Creating a Moving Picture of the Earth's Climate," *Insights*, http://sdcd.gsfc.nasa.gov/ESS/insights/vol6/climate.htm (December 16, 2003).

*IEEE History Center,*http://www.ieee.org/organizations/history_center/legacies/ (December 16, 2003).

*Inamori Foundation Web site,*http://www.inamori-f.or.jp/KyotoPrizes/contents_e/laureates/ (December 16, 2003).

*Kalman Filter,*http://www.cae.wisc.edu/~ece539/project/presentation/gissel/Kalman.html (December 16, 2003).

*Nobel Prize Winners and Famous Hungarians,*http://www.hungary.org/~hipcat/sciencemathandtech2.htm (December 16, 2003).

"Rudolf Emil Kalman," http://icel.me.pusan.ac.kr/ResearchArea/kalman/sub/kalmanbiblio.htm (December 16, 2003).

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