For PDF file viewing.

Quick Links

Rudolph E. Kalman

• Biographical information
  • A little biographical information.
  • More information, thanks to Eduardo Sontag, a former student of R.E. Kalman's.
  • Yet more information in Wikipedia.
  • There is a nice article on Kalman in the IEEE History Center.
  • On November 16, 2005, Kalman was awarded Columbia Engineering School Alumni Association’s Egleston Medal for Distinguished Engineering Achievement. See online article or local copy.
• His seminal (1960) paper.

Printed Reference Material

• For beginners, we highly recommend reading Chapter 1 of this book by Peter S. Maybeck on the subjects of stochastic models, estimation, and control. Although the remaining chapters may appear daunting, the book is thorough and complete.
• For a somewhat more advanced presentation, we have written "An Introduction to the Kalman Filter" (also available in Chinese) and a more substantial course pack (booklet) for our tutorial on the Kalman filter presented at ACM SIGGRAPH 2001. (Please read the ACM Copyright Notice for the latter.)
• In addition, here are several other Kalman filter books, and several of the sites below provide reading lists.
• Kalman's seminal paper (1960).
• Sorenson's "Gauss to Kalman" article (1970).

Courses

• June 11-15, 2007, Fullerton, California, USA
  • "Application of Kalman Filtering to GPS, INS, & Navigation"
    Dr. M. S. Grewal, California State University, Fullerton
• At ACM SIGGRAPH 2001 we presented a tutorial on the Kalman filter. (Please read the ACM Copyright Notice.)

Other Sites and Electronic Reference

Local Material

• "An Introduction to the Kalman Filter" by Greg Welch and Gary Bishop. The article has also been translated into Chinese by Xuchen Yao, a student at Institute of Acoustics, the Chinese Academy of Sciences (January, 2007. See also the local archived copy.).
• Course notes from our tutorial on the Kalman filter presented at ACM SIGGRAPH 2001. (Please read the ACM Copyright Notice.)
• Slides from an older introductory talk by Greg Welch and Gary Bishop.
• Our very own Java-based Kalman Filter Learning Tool.

External Material

• Wikipedia has an excellent article on the Kalman filter.
• In a 1997 Innovation column of GPS World, Larry J. Levy wrote a very nice introduction to the Kalman filter titled "The Kalman Filter: Navigation's Integration Workhorse." (Also available as PDF file.) Levy provides some historical perspective, a non-mathematical explanation, and of course a mathematical explanation with examples.
• Kevin Murphy, a postdoc in the MIT AI Lab, has a nice Kalman filter web page. There he provides several MatLab toolboxes, including a Kalman filter toolbox. (MatLab is a product of The MathWorks.)
• Eric Wan, Rudolph van der Merwe, and their Neural Speech Enhancement group (Center for Spoke Language and Understanding at OGI) maintain a very nice web site on signal processing research including work on Unscented Kalman Filters. (The idea for the UKF was originally introduced by Simon Julier and Jeff Uhlmann.) Their site contains papers and some MatLab toolkit of functions and scripts for the Kalman filter, particle filters (in general), and the Unscented Kalman Filter. (MatLab is a product of The MathWorks.) Here are the slides from a June 2002 talk Rudolph gave at a CSLU weekly seminar.
• "Engineers Look to Kalman Filtering for Guidance," an article by Barry Cipra, SIAM News, Vol. 26, No. 5, August 1993.
• Innovatia Software's Kalman Filtering Page, provided by Dr. Dan Simon.
• Peter D. Joseph's Home Page containing material on Kalman filters.
• Intel's OpenCV Reference Manual includes some introductory Kalman filter prose and library functions.
• R. W. R. Darling has a very nice online survey of nonlinear filtering.
• Harmonic Software sells a Kalman Filter Interface Pack (KBF) for their O-Matrix product. KBF is a GUI-based environment for graphically designing, building, and analyzing Kalman filters using the Kalman filter functions available in O-Matrix.
• Jean-Philippe Drecourt, a PhD student working on the DHI Data Assimilation in Hydrological and Hydrodynamic Models site project, wrote a literature review on Kalman filtering with references to hydrological modelling. He reviews the Kalman filter itself, and some of the most important suboptimal schemes.
• Andre Adrian, a Senior Engineer at DFS in Germany, used the Kalman filter (and variations) to create a central tracker for the german air traffic control. He has provided a few articles here. There is an additional "README" here.

Software

• A zip file of some MatLab source code for a prototype of our Java-based Kalman Filter Learning Tool.
• OpenCV includes some Kalman Filter functions, and the Reference Manual includes some introductory prose. (The prose is quite similar to our introductory paper.) The entire library can be downloaded after agreeing to their license. The Reference Manual is in the opencv-doc package.
• Michael Stevens (a Senior Research Engineer at the Australian Centre for Field Robotics) has developed a nice library of C++ Bayesian Filtering Classes. The classes represent and implement a wide variety of numerical estimation algorithms for Bayesian/Kalman Filtering. The classes provide tested and consistent numerical methods and the class hierarchy explicitly represents the variety of filtering algorithms and model types.
• Kevin Murphy (see above) provides several MatLab toolboxes, including a Kalman filter toolbox. (MatLab is a product of The MathWorks.)
• Magnus Norgaard provides a MATLAB toolbox for design of Kalman filters for nonlinear systems. There you will find implementations of a new (and clever!) filter that performs very well and is easy to use compared to, e.g., the extended Kalman filter. (MatLab is a product of The MathWorks.)
• The DHI Data Assimilation in Hydrological and Hydrodynamic Models site includes their DAIHM Matlab toolbox. The toolbox is designed for data assimilation and ensemble modelling. Even though the toolbox has been developped for hydrological models, they believe it is very general and can be used in other domains/applications.
• Got an HP 48G graphing calculator? Martin Murillo of Idaho State University has written some Kalman filter code for you.
• Navtech sells some Kalman filtering software tools developed by Lupash Consulting.
• Eric Wan and Rudolph van der Merwe (see above) maintain a MatLab toolkit of functions and scripts for the Kalman filter, particle filters (in general), and the Unscented Kalman Filter. (MatLab is a product of The MathWorks.)
• Klaas Gadeyne, a Ph.D. student in the Mechanical Engineering Robotics Research Group at K.U.Leuven, has developed a C++ Bayesian Filtering Library that includes software for Sequential Monte Carlo methods, Kalman filters, particle filters, etc.
• Conor Dolan has made available an executable, limited source, and documentation for a program to carry out state-space modeling based on Harvey's text. It includes facilities to model multi-subject data and multi-group data. You can get a zip file from his web site (see mkfm6 program). Note that Conor says "The source is limited to parts I wrote (in fortran). Optimization of the normal theory ML function is carried out by the NPSOL routine, which I am not at liberty to disseminate."
• Ruben R. Raygosa has contributed a Spanish tutorial for the Kalman filter.

Research & Applications

• Here at UNC we are using an Kalman filters and related estimators to track users' heads and limbs in virtual environments. See for example our 1997 ACM SIGGRAPH paper and our 2001 Presence journal article.
• Simon Julier and Jeff Uhlmann have done some great work on nonlinear filtering. In particular check out “A New Extension of the Kalman Filter to Nonlinear Systems,” SPIE AeroSense Symposium, April 21–24, 1997. Orlando, FL, SPIE. In addition here are some other papers on non-linear filtering work by Simon and Jeff.
• The kalman filter has been used extensively for data fusion in navigation, but Joost van Lawick shows an example of scene modeling with an extended Kalman filter.
• Hugh Durrant-Whyte and researchers at the Australian Centre for Field Robotics do all sorts of interesting and impressive research in data fusion, sensors, and navigation. Browse their publications for related articles.
• From Zhengyou Zhang's Image and Vision Computing Journal paper (1996) "Parameter Estimation Techniques: A Tutorial with Application to Conic Fitting," some information about the Kalman filter as applied to image processing.
• The Danish organization DHI, maintains a relevant site on their Data Assimilation in Hydrological and Hydrodynamic Models project. There you will find results of their work, publications, and their DAIHM Matlab toolbox. (See above in "Software" for more information.)
• Dr. Stephen Pollock (Department of Economics, Queen Mary, University of London) is investigating the use of signal processing and stochastic estimation in economics. For example, he is investigating the use of filters (including the Kalman filter) on short non-stationary econometric data sequences to extract such components as the trends and seasonal fluctuations.
• For another example of the Kalman filter used in Economics, check out the Johnson and Sakoulis article "Maximizing Equity Market Sector Predictability in a Bayesian Time Varying Parameter Model." (See http://ssrn.com/abstract=396642.)
• Bjarne Hansen and colleagues at the Meteorological Service of Canada (Français) are working on an "Ensemble Kalman Filter" (Français) for assimilation of observations in atmospheric models.
• Jan Kybic's 1998 research report “Kalman Filtering and Speech Enhancement” details his work aimed at suppression of noise in a running car environment for hands-free mobile telephony. (Thanks to Richard Kilgour at Navman for suggesting this.)
• NASA is hosting a technical report of historical interest: McGee and Schmidt, Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry, November 1985, NASA-TM-86847. This says it is an expanded version of Schmidt's 1981 invited paper in the AIAA Journal of Guidance: The Kalman filter---Its recognition and development for aerospace applications, SCHMIDT, S. F. (Analytical Mechanics Associates, Inc., Mountain View, Calif.) Journal of Guidance, Control, and Dynamics, Vol. 4, No. 1, pp. 4-7, 1981. Thanks to Ed Mirmak for pointing this out.