Difference between revisions of "NCS: Kalman Filtering"

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== Reading ==
 
== Reading ==
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop</p>
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* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p>
  
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter]</p>
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* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p>
  
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D,  1960. </p>
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* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D,  1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p>
  
 
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. -->
 
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. -->
  
 
== Additional Resources ==
 
== Additional Resources ==
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter],  G. Welch and G. Bishop.</p>
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* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter],  G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p>
  
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005.</p>
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* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from  1979. It contains a detailed mathematical presentation of the filtering problems. A very good book.</p>
  
 
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<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. -->

Revision as of 00:18, 16 April 2006

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In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.

Lecture Materials

Reading


Additional Resources

  • The Kalman Filter, G. Welch and G. Bishop. A webpage with many links on Kalman filter.

  • Optimal Filtering, B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of the filtering problems. A very good book.