NCS: Packet-based Estimation: Difference between revisions
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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: | * [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]] | ||
== Reading == | == Reading == | ||
* <p>[http:// | * <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:// | * <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> | ||
<!-- 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. --> | ||
Latest revision as of 20:09, 25 April 2006
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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
Reading
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.
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.
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 filtering problems and the Kalman filter. A very good book.
