In Memoriam: Rudolf Kalman 1930–2016

Engineer and mathematician Rudolf Kalman passed away July 2, 2016, at the age of 86. The Hungarian-born scientist was best known for the eponymous "Kalman filter," an algorithm widely used for signal processing, control systems, and guidance and navigation, work for which U.S. President Barack Obama awarded him the National Medal of Science in 2009.

Kalman was born in Budapest in 1930 and emigrated to the U.S. in 1943, where he studied electrical engineering at the Massachusetts Institute of Technology. He received his doctoral degree at the Columbia University in New York City in 1957. 

Kalman worked as a researcher in Baltimore and Zurich, and also as a professor at Stanford University (1964-1971) and at the University of Florida (1971-1992).

The Kalman filter (or Kalman-Bucy Filter, also named for Richard S. Bucy of the University of Southern California, who contributed to the theory) is a mathematical technique used to extract a signal from a long sequence of noisy and/or incomplete technical measurements. Also known as linear quadratic estimation, the Kalman filter is an algorithm that uses a series of measurements observed over time containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more precise than those based on a single measurement alone, by using Bayesian inference and estimating a joint probability distribution over the variables for each timeframe.

Kalman's ideas on filtering initially were met with skepticism. However, after he presented his ideas while visiting Stanley F. Schmidt at the U.S. National Aeronautics and Space Administration (NASA) Ames Research Center in 1960, Kalman filters were used during the Apollo space program, in the NASA Space Shuttle, in U.S. Navy submarines, and in unmanned aerospace vehicles and weapons.

Observed Richard G. Baraniuk, Victor E. Cameron Professor of Electrical and Computer Engineering, as well as founder and director of OpenStax at Rice University, "The impact of the Kalman filter has been vast.

"Kalman filters are ubiquitous in control and navigation; basically the first tool you reach for when you have any kind of tracking problem. Kalman filters have been used in space flight, all the way back to the Apollo mission that put men on the moon, and are standard tools for tracking aircraft by radar (improving significantly on the Wiener filter). Kalman filtering is also the cornerstone of GPS, which has been described as 'one enormous Kalman filter'."

Baraniuk added, "On the theory side, the Kalman filter is one of the bridges that connects signal processing and control theory. The Kalman filter is also applied in machine learning, to forecasting problems like the stock market, for example."

Kalman published several seminal papers during the 1960s establishing what is now known as the state-space representation of dynamical systems. He introduced the formal definition of a system and the notions of controllability and observability, eventually leading to the Kálmán decomposition (which provides a way to use math to convert a representation of a linear time-invariant control system to a form in which the system can be decomposed into a standard form which makes clear the observable and controllable components of the system). He also contributed to the theory of optimal control and provided, in his work with J. E. Bertram of the IBM Research Laboratory in Ossining, NY, a comprehensive exposure of stability theory for dynamical systems. He also worked with Yu-Chi Ho on the minimal realization problem, resulting in what came to be known as the Ho-Kálmán algorithm.

A member of the U.S. National Academy of Sciences, Kalman also belonged to the American National Academy of Engineering, and the American Academy of Arts and Sciences. He was a foreign member of the Hungarian, French, and Russian Academies of Sciences, and was awarded an Honorary Doctorate by Heriot-Watt University in 1990.

Kalman was awarded the IEEE Medal of Honor in 1974, the IEEE Centennial Medal in 1984, the Inamori Foundation's Kyoto Prize in Advanced Technology in 1985, the Leroy P. Steele Prize of the American Mathematical Society in 1987, the Richard E. Bellman Control Heritage Award in 1997, and the National Academy of Engineering's Charles Stark Draper Prize for Engineering in 2008.