Module 14: Introduction to Signals and Systems

Lectures & Content

Folder description

Please click the folder link above to access the Module 14 instructional content. Module 14 contains twelve video lectures that present the following topics:

Introduction to Kalman Filter (14A)
Observability (14B)
Linear Systems Driven by Stochastic Noise (Example 1)
State Estimation (14C)
Statistical Steady States (Example 2)
Control using Estimated State (14D)
Kalman Filtering (14E)
Linear Gauss-Markov Models (Example 3)
Kalman Filters: First Use (Example 4)
General Controller Structure (14F)
Kalman Filters: Steady-State (Example 5)
Extended Kalman Filter for Artificial Pancreas (14G)

Technical

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Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

By the end of this module, you will be able to:

Explain the concept behind the Kalman filter and why it is used.
Apply the Kalman filter to the control of a simple dynamic system.
Define the observability problem for Kalman filters.
Describe how state estimation is important for Kalman filters.
Describe how to apply linear Kalman filters to a non-linear problem.
Describe how Kalman filters can be used for an artificial pancreas.
Apply a Kalman filter through Matlab.
Explain how Kalman filters are often seen in data fusion and machine learning problems.

How to Complete This Module:

View lectures 14A-14G and Examples 1-5.
Complete the assigned reading to supplement the material presented in the lectures.
Participate in the module discussion.
Complete and submit the module assignment.
Complete the required entry in your personal learning journal.

Technical

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Readings

Cell description

This week's reading assignment includes the following:

Text Books

Astrom, J. K. & Murray, R.M. (2008). Feedback systems: An introduction for scientists and engineers. Princeton, NJ: Princeton University Press.Available at: http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition
- Chapter 8
Chaparro, L. (2014). Signals and systems using MATLAB (2nd ed.). Academic Press.
- Review: Chapters 0-7, 9, 12 (basically this is a week to review any material from this book that you would like -- no homework from the book)

EReserves

The following supplemental readings are referenced in lecture 14G.

Wang, Q., Molenaar P., Harsh, S., Freeman, K., Xie, J., Gold, C., Rovine, M. & Ulbrecht J. (2014). Personalized state-space modeling of glucose dynamics for Type I diabetes using continuously monitored glucose, insulin doses and meal intake: An extended Kalman filter approach. Journal of Diabetes Science and Technology 8(2), pp. 331-345. DOI: 10.1177/1932296814524080. PDF

Technical

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K. &amp; Murray, R.M. (2008). <em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.<br>Available at:&nbsp;<span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>http</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">://</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>www</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>cds</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>caltech</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>edu</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>~murray</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>amwiki</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/index.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>php</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/Second_Edition</span> \n   <ul style=\"list-style-type: circle;\"> \n    <li>Chapter 8</li> \n   </ul> </li> \n  <li><span><span>Chaparro</span></span>, L. (2014). <em>Signals and systems using MATLAB </em>(2<span><span>nd</span></span> ed.). Academic Press. \n   <ul style=\"list-style-type: circle;\"> \n    <li>Review: Chapters 0-7, 9, 12 (basically this is a week to review any material from this book that you would like -- no homework from the book)</li> \n   </ul> </li> \n </ul> \n <p><strong style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px;\"><span style=\"color: #0067ac;\"><span><span>EReserves</span></span></span></strong></p> \n <p>The following supplemental readings are referenced in lecture 14G.</p> \n <ul> \n  <li>Wang, Q., <span><span>Molenaar</span></span> P., Harsh, S., Freeman, K., <span><span>Xie</span></span>, J., Gold, C., <span><span>Rovine</span></span>, M. &amp; <span><span>Ulbrecht</span></span> J. (2014). Personalized state-space modeling of glucose dynamics for Type I diabetes using continuously monitored glucose, insulin doses and meal intake: An extended <span><span>Kalman</span></span> filter approach. <em>Journal of Diabetes Science and Technology</em> 8(2), pp. 331-345. 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K. &amp; Murray, R.M. (2008). <em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.<br>Available at:&nbsp;<span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>http</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">://</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>www</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>cds</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>caltech</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>edu</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>~murray</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>amwiki</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/index.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>php</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/Second_Edition</span> \n   <ul style=\"list-style-type: circle;\"> \n    <li>Chapter 8</li> \n   </ul> </li> \n  <li><span><span>Chaparro</span></span>, L. (2014). <em>Signals and systems using MATLAB </em>(2<span><span>nd</span></span> ed.). Academic Press. \n   <ul style=\"list-style-type: circle;\"> \n    <li>Review: Chapters 0-7, 9, 12 (basically this is a week to review any material from this book that you would like -- no homework from the book)</li> \n   </ul> </li> \n </ul> \n <p><strong style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 13px;\"><span style=\"color: #0067ac;\"><span><span>EReserves</span></span></span></strong></p> \n <p>The following supplemental readings are referenced in lecture 14G.</p> \n <ul> \n  <li>Wang, Q., <span><span>Molenaar</span></span> P., Harsh, S., Freeman, K., <span><span>Xie</span></span>, J., Gold, C., <span><span>Rovine</span></span>, M. &amp; <span><span>Ulbrecht</span></span> J. (2014). Personalized state-space modeling of glucose dynamics for Type I diabetes using continuously monitored glucose, insulin doses and meal intake: An extended <span><span>Kalman</span></span> filter approach. <em>Journal of Diabetes Science and Technology</em> 8(2), pp. 331-345. DOI: 10.1177/1932296814524080. <span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_51355330_2\"></span></span>\n<a target=\"_blank\" href=\"https://blackboard.jhu.edu/bbcswebdav/pid-5740926-dt-content-rid-51355330_2/xid-51355330_2\">PDF</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.260.81.FA18/extended_Kalman_filter_type_I_diabetes_2014.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00vz&amp;course_id=_169707_1&amp;ctxMenuXythosId=51355330_2&amp;course_id=_169707_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_6299a17e958640cb8c646e1fac3231e4,open_with_browser_6299a17e958640cb8c646e1fac3231e4,open_with_bbdrive_6299a17e958640cb8c646e1fac3231e4,openWebId_6299a17e958640cb8c646e1fac3231e4,view360Id_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,ax-ally-placeholder_6299a17e958640cb8c646e1fac3231e4,ax-ally-markForAxAnalysis_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,content_settings_6299a17e958640cb8c646e1fac3231e4,content_editSettings_6299a17e958640cb8c646e1fac3231e4,content_edit_6299a17e958640cb8c646e1fac3231e4,properties_folder_6299a17e958640cb8c646e1fac3231e4,itemcarot_managerecord_6299a17e958640cb8c646e1fac3231e4,comments_tool_6299a17e958640cb8c646e1fac3231e4,subscriptions_list_6299a17e958640cb8c646e1fac3231e4,content_readfile_6299a17e958640cb8c646e1fac3231e4,content_overwrite_6299a17e958640cb8c646e1fac3231e4,passes_tool_6299a17e958640cb8c646e1fac3231e4,permissions_tool_6299a17e958640cb8c646e1fac3231e4,content_add_alignment_6299a17e958640cb8c646e1fac3231e4,content_tracking_6299a17e958640cb8c646e1fac3231e4,content_versions_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,bookmarkId_6299a17e958640cb8c646e1fac3231e4,itemsId_6299a17e958640cb8c646e1fac3231e4,packagesId_6299a17e958640cb8c646e1fac3231e4,emailId_6299a17e958640cb8c646e1fac3231e4,removeContentFolderId_6299a17e958640cb8c646e1fac3231e4,*separator*,copyContentId_6299a17e958640cb8c646e1fac3231e4,moveContentId_6299a17e958640cb8c646e1fac3231e4,*separator*,removeContentId_6299a17e958640cb8c646e1fac3231e4,*separator*,Metadata_General_6299a17e958640cb8c646e1fac3231e4,Metadata_Dublin_Core_6299a17e958640cb8c646e1fac3231e4,Metadata_IMS_6299a17e958640cb8c646e1fac3231e4,Metadata_Full_IMS_6299a17e958640cb8c646e1fac3231e4,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_6299a17e958640cb8c646e1fac3231e4\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_6299a17e958640cb8c646e1fac3231e4',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_6299a17e958640cb8c646e1fac3231e4',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_6299a17e958640cb8c646e1fac3231e4',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"51355330_2_fileReadWritePermAvl\" id=\"51355330_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('6299a17e958640cb8c646e1fac3231e4');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script></li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_5740926_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "body": "\n    <div> \n <p>This week's reading assignment includes the following:</p> \n <p><strong><span>Text Books</span> </strong></p> \n <ul> \n  <li><span><span>Astrom</span></span>, J. K. &amp; Murray, R.M. (2008). <em>Feedback systems: An introduction for scientists and engineers</em>. Princeton, NJ: Princeton University Press.Available at:&nbsp;<span><span><span>http</span></span></span><span>://</span><span><span><span>www</span></span></span><span>.</span><span><span><span>cds</span></span></span><span>.</span><span><span><span>caltech</span></span></span><span>.</span><span><span><span>edu</span></span></span><span>/</span><span><span><span>~murray</span></span></span><span>/</span><span><span><span>amwiki</span></span></span><span>/index.</span><span><span><span>php</span></span></span><span>/Second_Edition</span> \n   <ul> \n    <li>Chapter 8</li> \n   </ul> </li> \n  <li><span><span>Chaparro</span></span>, L. (2014). <em>Signals and systems using MATLAB </em>(2<span><span>nd</span></span> ed.). Academic Press. \n   <ul> \n    <li>Review: Chapters 0-7, 9, 12 (basically this is a week to review any material from this book that you would like -- no homework from the book)</li> \n   </ul> </li> \n </ul> \n <p><strong><span><span><span>EReserves</span></span></span></strong></p> \n <p>The following supplemental readings are referenced in lecture 14G.</p> \n <ul> \n  <li>Wang, Q., <span><span>Molenaar</span></span> P., Harsh, S., Freeman, K., <span><span>Xie</span></span>, J., Gold, C., <span><span>Rovine</span></span>, M. &amp; <span><span>Ulbrecht</span></span> J. (2014). Personalized state-space modeling of glucose dynamics for Type I diabetes using continuously monitored glucose, insulin doses and meal intake: An extended <span><span>Kalman</span></span> filter approach. <em>Journal of Diabetes Science and Technology</em> 8(2), pp. 331-345. DOI: 10.1177/1932296814524080. \n<a target=\"_blank\" href=\"https://blackboard.jhu.edu/bbcswebdav/pid-5740926-dt-content-rid-51355330_2/xid-51355330_2\">PDF</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.260.81.FA18/extended_Kalman_filter_type_I_diabetes_2014.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00vz&amp;course_id=_169707_1&amp;ctxMenuXythosId=51355330_2&amp;course_id=_169707_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_6299a17e958640cb8c646e1fac3231e4,open_with_browser_6299a17e958640cb8c646e1fac3231e4,open_with_bbdrive_6299a17e958640cb8c646e1fac3231e4,openWebId_6299a17e958640cb8c646e1fac3231e4,view360Id_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,ax-ally-placeholder_6299a17e958640cb8c646e1fac3231e4,ax-ally-markForAxAnalysis_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,content_settings_6299a17e958640cb8c646e1fac3231e4,content_editSettings_6299a17e958640cb8c646e1fac3231e4,content_edit_6299a17e958640cb8c646e1fac3231e4,properties_folder_6299a17e958640cb8c646e1fac3231e4,itemcarot_managerecord_6299a17e958640cb8c646e1fac3231e4,comments_tool_6299a17e958640cb8c646e1fac3231e4,subscriptions_list_6299a17e958640cb8c646e1fac3231e4,content_readfile_6299a17e958640cb8c646e1fac3231e4,content_overwrite_6299a17e958640cb8c646e1fac3231e4,passes_tool_6299a17e958640cb8c646e1fac3231e4,permissions_tool_6299a17e958640cb8c646e1fac3231e4,content_add_alignment_6299a17e958640cb8c646e1fac3231e4,content_tracking_6299a17e958640cb8c646e1fac3231e4,content_versions_6299a17e958640cb8c646e1fac3231e4,*separator*,*separator*,bookmarkId_6299a17e958640cb8c646e1fac3231e4,itemsId_6299a17e958640cb8c646e1fac3231e4,packagesId_6299a17e958640cb8c646e1fac3231e4,emailId_6299a17e958640cb8c646e1fac3231e4,removeContentFolderId_6299a17e958640cb8c646e1fac3231e4,*separator*,copyContentId_6299a17e958640cb8c646e1fac3231e4,moveContentId_6299a17e958640cb8c646e1fac3231e4,*separator*,removeContentId_6299a17e958640cb8c646e1fac3231e4,*separator*,Metadata_General_6299a17e958640cb8c646e1fac3231e4,Metadata_Dublin_Core_6299a17e958640cb8c646e1fac3231e4,Metadata_IMS_6299a17e958640cb8c646e1fac3231e4,Metadata_Full_IMS_6299a17e958640cb8c646e1fac3231e4,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_6299a17e958640cb8c646e1fac3231e4\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_6299a17e958640cb8c646e1fac3231e4',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_6299a17e958640cb8c646e1fac3231e4',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n  </span> \n \n \n \n \n \n</li> \n </ul> \n</div>\n  "
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Module 14 Discussion Participation GuidelinesQuestion:

Cell description

Discussion forum rubric: 625.260 Discussion Rubric

Participation Guidelines

Participation in class discussions are important in this course and to your final grade. Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.

Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.

There is one discussion thread in this module. Submit your posts by clicking on the "Module 14 Discussion" link above and creating a new thread. Please contribute to the class discussion with your discussion about:

Question:

Thread 14.1

Give an example problem where you’ve seen Kalman filtering used to address a problem that you are interested in pursuing and/or have knowledge about the primary system that it is being used for. How is this related to data fusion and machine learning?
Have you used a variant of Kalman filtering in any of your work or seen it used by anyone that you know?
Building on your knowledge from this last module, discuss a control problem that you find interesting where the linear Kalman filter clearly won’t work. Discuss how you might be able to solve the problem with a non-linear Kalman filter and/or why you think that it simply can’t be controlled via a Kalman filter.

For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.

Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.

You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.

Required Activity: 1 Original Post / 2 Responses Due by: Original Post 11:59PM Day 4, Responses 11:59PM Day 7

Technical

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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('fc9f7dae1e8e4b3399f2209239e8ee4c');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_14\">Participation Guidelines</h3> \n <p>Participation in class discussions are important in this course and to your final grade. Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p>Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p>There is one discussion thread in this module. Submit your posts by clicking on the \"Module 14 Discussion\" link above and creating a new thread. Please contribute to the class discussion with your discussion about:</p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_15\">Question:</h3> \n <p style=\"margin-left: 30px;\"><strong style=\"font-size: 13px;\">Thread 14.1</strong></p> \n <ul> \n  <li>Give an example problem where you’ve seen Kalman filtering used to address a problem that you are interested in pursuing and/or have knowledge about the primary system that it is being used for. How is this related to data fusion and machine learning?</li> \n  <li>Have you used a variant of Kalman filtering in any of your work or seen it used by anyone that you know?</li> \n  <li>Building on your knowledge from this last module, discuss a control problem that you find interesting where the linear Kalman filter clearly won’t work. Discuss how you might be able to solve the problem with a non-linear Kalman filter and/or why you think that it simply can’t be controlled via a Kalman filter.</li> \n </ul> \n <p>For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.</p> \n <p>Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.</p> \n <p>You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. 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#000000;\"><strong>Discussion forum rubric:</strong> <span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_51355346_2\"></span></span>\n<a target=\"_blank\" href=\"https://blackboard.jhu.edu/bbcswebdav/pid-5740927-dt-content-rid-51355346_2/xid-51355346_2\">625.260 Discussion Rubric</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.260.81.FA18/Module%201/Discussion_Rubric.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00w1&amp;course_id=_169707_1&amp;ctxMenuXythosId=51355346_2&amp;course_id=_169707_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('fc9f7dae1e8e4b3399f2209239e8ee4c');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script><p></p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_14\">Participation Guidelines</h3> \n <p>Participation in class discussions are important in this course and to your final grade. Be energetic in your participation, posting discussion responses assigned in each module, interacting with other students and your instructor, in your responses and postings.</p> \n <p>Check the rubric above to ensure you understand the expectations and how you will be assessed on these important assignments.&nbsp;</p> \n <p>There is one discussion thread in this module. Submit your posts by clicking on the \"Module 14 Discussion\" link above and creating a new thread. Please contribute to the class discussion with your discussion about:</p> \n <h3 style=\"color: #0067ac;\" id=\"anonymous_element_15\">Question:</h3> \n <p style=\"margin-left: 30px;\"><strong style=\"font-size: 13px;\">Thread 14.1</strong></p> \n <ul> \n  <li>Give an example problem where you’ve seen Kalman filtering used to address a problem that you are interested in pursuing and/or have knowledge about the primary system that it is being used for. How is this related to data fusion and machine learning?</li> \n  <li>Have you used a variant of Kalman filtering in any of your work or seen it used by anyone that you know?</li> \n  <li>Building on your knowledge from this last module, discuss a control problem that you find interesting where the linear Kalman filter clearly won’t work. Discuss how you might be able to solve the problem with a non-linear Kalman filter and/or why you think that it simply can’t be controlled via a Kalman filter.</li> \n </ul> \n <p>For responses to classmates' posts, please realize that just posting ‘I agree’ or ‘I disagree’ is not sufficient.</p> \n <p>Don’t be afraid to share your insights and discoveries. This is how we will build a community around the course.</p> \n <p>You are asked not only to create an original post, but also to thoughtfully respond to at least two of your peers for full credit. Your initial posts are due by midnight on Day 4 of this module. Responses to your peers are due by midnight on Day 7 of this module.</p> \n <p style=\"font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: small;\"><span style=\"text-decoration: underline;\">Required Activity</span>: 1 Original Post / 2 Responses<br> <span style=\"text-decoration: underline;\">Due by</span>: Original Post 11:59PM Day 4, Responses 11:59PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740927_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 14 Assignment

Cell description

In this module, you will complete the problem sets listed below as an assignment:

Astrom and Murray (http://www.cds.caltech.edu/~murray/amwiki/index.php/Second_Edition): problems 8.13 (yes, only the one problem, this last week, but it is going to be a challenge, hopefully a rewarding one for all of you -- remember that you can use other material on Kalman filters to help you understand and work through the problem)

Follow the general guidelines below to complete and submit the assignment.

Problems should be done neatly on paper and scanned or completed electronically using markup on a tablet device.
At the top of the page, include your name, module number, and page number (page 1 of 2, etc.)
Submit your answers in PDF (.pdf) format by uploading to Blackboard using the "Module 14 Assignment" link above.

Required Activity: Submit answers to the problem sets. Due by: 11:59 PM Day 7

Technical

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font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>http</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">://</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>www</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>cds</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>caltech</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>edu</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>~murray</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>amwiki</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/index.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>php</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">/Second_Edition)</span>: problems 8.13 (yes, only the one problem, this last week, but it is going to be a challenge, hopefully a rewarding one for all of you -- remember that you can use other material on <span><span>Kalman</span></span>&nbsp;filters to help you understand and work through the problem)</li> \n </ul> \n <p>Follow the general guidelines below to complete and submit the assignment.</p> \n <ul> \n  <li>Problems should be done neatly on paper and scanned or completed electronically using markup on a tablet device.</li> \n  <li>At the top of the page, include your name, module number, and page number (page 1 of 2, etc.)</li> \n  <li>Submit your answers in PDF (.<span><span>pdf</span></span>) format by uploading to Blackboard using the \"Module 14 Assignment\" link above.</li> \n </ul> \n <p><span style=\"text-decoration: underline;\">Required Activity</span>: Submit answers to the problem sets.<br> <span style=\"text-decoration: underline;\">Due by</span>: 11:59 PM Day 7</p> \n <br> \n</div>\n  </div>\n\n <div id=\"_5740928_1previewModule\" class=\"moduleSample\">\n </div>\n",
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font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>http</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">://</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>www</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; font-style: normal; background-color: #f4f4f4;\">.</span><span style=\"outline-width: 0px; font-style: normal; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 16.020000457763672px; color: #444444;\"><span><span>cds</span></span></span><span style=\"color: #444444; font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; 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Module 14 Personal Learning Journal

Cell description

In your learning journal entries for this week comment about:

Pick a longer term problem that you find fascinating that might benefit from data fusion/Kalman filters. How might you go about formulating what would be needed to address that problem – what sensors would be required? What types of data would be involved?
Take this last entry point in the journal as your time to reflect back on the 14-weeks of this course and what we’ve covered. What did you benefit from the most? What points did you find the least rewarding? Where did you find areas of growth that you enjoyed or felt were painful? If you have suggestions for next year’s variation of this course, what would you recommend?

Click on the “Module 14 Personal Learning Journal” above to access your journal and create your entry.

Required Activity: Create a reflective personal journal entry post in response to the prompts given. Due by: 11:59 PM Day 7

Technical

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