# Difference between revisions of "NCS: Kalman Filtering"

From Murray Wiki

Jump to navigationJump to searchLine 8: | Line 8: | ||

<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --> | <!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --> | ||

− | == Reading | + | == Reading == |

+ | * <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html An Introduction to the Kalman Filter], G. Welch and G. Bishop</p> | ||

+ | |||

+ | * <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter]</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> | ||

+ | |||

<!-- 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 == | ||

<!-- 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. --> | <!-- 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 00:05, 16 April 2006

Prev: Alice Planner | Course Home | Next: MHE |

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

An Introduction to the Kalman Filter, G. Welch and G. Bishop

A New Approach to Linear Filtering and Prediction Problem, R.E. Kalman.

*Transactions of the ASME*, Series D, 1960.