Editing Kalman filter (section)

== History ==
The filtering method is named for Hungarian [[émigré]] [[Rudolf E. Kálmán]], although [[Thorvald Nicolai Thiele]]<ref>{{cite journal |last1=Lauritzen |first1=S.&nbsp;L. |date=December 1981 |title=Time series analysis in 1880. A discussion of contributions made by T.N.&nbsp;Thiele |journal=International Statistical Review |volume=49 |number=3 |pages=319–331 |doi=10.2307/1402616 |jstor=1402616 |quote=He derives a recursive procedure for estimating the regression component and predicting the Brownian motion. The procedure is now known as Kalman filtering.}}</ref><ref>{{cite book |last=Lauritzen |first=S.&nbsp;L. |date=2002 |title=Thiele: Pioneer in Statistics |url=https://books.google.com/books?id=irugmNUwuG4C&q=kalman |location=New York |publisher=[[Oxford University Press]] |page=41 |isbn=978-0-19-850972-1 |author-link=Steffen Lauritzen |quote=He solves the problem of estimating the regression coefficients and predicting the values of the Brownian motion by the method of least squares and gives an elegant recursive procedure for carrying out the calculations. The procedure is nowadays known as ''Kalman filtering''.}}</ref> and [[Peter Swerling]] developed a similar algorithm earlier. Richard S. Bucy of the [[Johns Hopkins Applied Physics Laboratory]] contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering. Kalman was inspired to derive the Kalman filter by applying state variables to the [[Wiener filter|Wiener filtering problem]].<ref>{{Cite book |last1=Grewal |first1=Mohinder S. |title=Kalman filtering: theory and practice using MATLAB |last2=Andrews |first2=Angus P. |date=2015 |publisher=Wiley |isbn=978-1-118-98498-7 |edition=4th |location=Hoboken, New Jersey |pages=16–18 |chapter=1}}</ref>
[[Stanley F. Schmidt]] is generally credited with developing the first implementation of a Kalman filter. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements.<ref>{{Cite web |url=http://ieeecss.org/CSM/library/2010/june10/11-HistoricalPerspectives.pdf |title=Mohinder S. Grewal and Angus P. Andrews |access-date=2015-04-23 |archive-date=2016-03-07 |archive-url=https://web.archive.org/web/20160307142746/http://ieeecss.org/CSM/library/2010/june10/11-HistoricalPerspectives.pdf  }}</ref> It was during a visit by Kálmán to the [[NASA Ames Research Center]] that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the [[Project Apollo|Apollo program]] resulting in its incorporation in the [[Apollo Guidance Computer|Apollo navigation computer]].<ref>{{cite report
|title=A Linearized Error Analysis Of Onboard Primary Navigation Systems For The Apollo Lunar Module, NASA TN D-4027
|date=August 1967
|publisher= National Aeronautics and Space Administration
|type=NASA Technical Note 
|author=Jerrold H. Suddath
|author2=Robert H. Kidd
|author3=Arnold G. Reinhold
|url=https://ntrs.nasa.gov/api/citations/19670025568/downloads/19670025568.pdf}}</ref>{{rp|16}}

This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed by the [[Soviet]] [[mathematician]] [[Ruslan Stratonovich]].<ref>Stratonovich, R. L. (1959). ''Optimum nonlinear systems which bring about a separation of a signal with constant parameters from noise''. Radiofizika, 2:6, pp.&nbsp;892–901.</ref><ref>Stratonovich, R. L. (1959). ''On the theory of optimal non-linear filtering of random functions''. Theory of Probability and Its Applications, 4, pp.&nbsp;223–225.</ref><ref>Stratonovich, R. L. (1960) ''Application of the Markov processes theory to optimal filtering''. Radio Engineering and Electronic Physics, 5:11, pp.&nbsp;1–19.</ref><ref>Stratonovich, R. L. (1960). ''Conditional Markov Processes''. Theory of Probability and Its Applications, 5, pp.&nbsp;156–178.</ref> In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before the summer of 1961, when Kalman met with Stratonovich during a conference in Moscow.<ref name="stepanov_on_kalman">{{cite journal |last1=Stepanov |first1=O. A. |title=Kalman filtering: Past and present. An outlook from Russia. (On the occasion of the 80th birthday of Rudolf Emil Kalman) |journal=Gyroscopy and Navigation |date=15 May 2011 |volume=2 |issue=2 |page=105 |doi=10.1134/S2075108711020076 |bibcode=2011GyNav...2...99S |s2cid=53120402 }}</ref>

This Kalman filtering was first described and developed partially in technical papers by Swerling (1958), Kalman (1960) and Kalman and Bucy (1961).

{{blockquote|The Apollo computer used 2k of magnetic core RAM and 36k wire rope [...]. The CPU was built from ICs [...]. Clock speed was under 100 kHz [...]. The fact that the MIT engineers were able to pack such good software (one of the very first applications of the Kalman filter) into such a tiny computer is truly remarkable.|Interview with Jack Crenshaw, by Matthew Reed, TRS-80.org (2009) [http://www.trs-80.org/interview-jack-crenshaw/] }}

Kalman filters have been vital in the implementation of the navigation systems of [[U.S. Navy]] nuclear [[ballistic missile submarine]]s, and in the guidance and navigation systems of cruise missiles such as the U.S. Navy's [[Tomahawk (missile family)|Tomahawk missile]] and the [[U.S. Air Force]]'s [[AGM-86 ALCM|Air Launched Cruise Missile]]. They are also used in the guidance and navigation systems of [[reusable launch vehicle]]s and the [[Attitude dynamics and control|attitude control]] and navigation systems of spacecraft which dock at the [[International Space Station]].<ref>{{Cite book|doi=10.2514/6.2003-5445|chapter=GPS/INS Kalman Filter Design for Spacecraft Operating in the Proximity of International Space Station|title=AIAA Guidance, Navigation, and Control Conference and Exhibit|year=2003|last1=Gaylor|first1=David|last2=Lightsey|first2=E. Glenn|isbn=978-1-62410-090-1}}</ref>