https://murray.cds.caltech.edu/index.php?title=Does_lim_(t_to_infty)_E(x-x_hat)_%3D_0_imply_that_there_will_be_less_disturbance_over_time%3F&feed=atom&action=history Does lim (t to infty) E(x-x hat) = 0 imply that there will be less disturbance over time? - Revision history 2021-10-17T14:53:34Z Revision history for this page on the wiki MediaWiki 1.35.3 https://murray.cds.caltech.edu/index.php?title=Does_lim_(t_to_infty)_E(x-x_hat)_%3D_0_imply_that_there_will_be_less_disturbance_over_time%3F&diff=8335&oldid=prev Han at 02:39, 28 October 2008 2008-10-28T02:39:11Z <p></p> <p><b>New page</b></p><div>&lt;math&gt;E(x)\,&lt;/math&gt; here denotes the expected value of &lt;math&gt;x\,&lt;/math&gt;, where &lt;math&gt;x\,&lt;/math&gt; is a random variable. &lt;math&gt;\lim_{t\to\infty} E(x-\hat x)=0\,&lt;/math&gt; only implies that the mean estimation error will converge to zero over time. Disturbance, however, will affect the variance of the error, which is given by &lt;math&gt; E(x-\hat x)^2\,&lt;/math&gt;. In CDS 110b, we will learn how to design observers that minimize this estimation variance if the disturbance can be modeled as Gaussian noise.<br /> <br /> --Shuo<br /> <br /> [[Category: CDS 101/110 FAQ - Lecture 5-1]]<br /> [[Category: CDS 101/110 FAQ - Lecture 5-1, Fall 2008]]</div> Han