NCS: Packet-based Estimation - Revision history

Sinopoli: /* Reading */

2006-04-25T20:09:01Z

Reading

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	* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p>		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p>

	* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p>		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter 3 of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p>

Sinopoli at 20:03, 25 April 2006

2006-04-25T20:03:07Z

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	== Reading ==		== Reading ==
	* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p>

	* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p>		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p>

Sinopoli at 20:01, 25 April 2006

2006-04-25T20:01:57Z

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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~~. ~~A brief introduction to~~ the ~~Kalman filter in discrete time~~. ~~No proofs are given~~, but it is ~~a good first read~~.~~</p>~~		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.

	* <p>[http://en.~~wikipedia~~.~~org~~/~~wiki~~/~~Kalman_filter Wikipedia: Kalman Filter~~] ~~A webpage that gives a proof and some applications~~.</p>		* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</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. 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. -->

Sinopoli at 19:46, 25 April 2006

2006-04-25T19:46:48Z

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	<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful -->		<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful -->
	<!-- 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]] -->
	* [[Media:L4-~~1_Kalman~~.pdf\|Lecture: ~~Kalman Filtering~~]]		* [[Media:L5-1_packet_based_estimation.pdf \|Lecture: Packet-based Estimation]]

	== Reading ==		== Reading ==

Sinopoli at 19:38, 25 April 2006

2006-04-25T19:38:13Z

New page

{{cds270-2 header}} 


In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.

== Lecture Materials ==


* [[Media:L4-1_Kalman.pdf|Lecture: Kalman Filtering]]

== Reading ==
* [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.

* [http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.

* [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. 



== Additional Resources ==
* [http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.

* [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 filtering problems and the Kalman filter. A very good book.