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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_88</title> <link rel="stylesheet" href="reset.css" type="text/css" media="all"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> </head> <body> <table summary="top nav" border="0" width="100%"> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_87.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_88</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_89.html">next page ></a></td> </tr> <tr> <td id="ebook_page" align="left" colspan="3" style="background: #ffffff; padding: 20px;"> <table border="0" width="100%" cellpadding="0"><tr><td align="center"> <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td> <td align="right"></td> </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 88</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="54eacb3b00dd867e31f023fd506ec2be.gif" border="0" alt="0088-01.GIF" width="417" height="91" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="6745a5501c83ba10f2ee4ff205f67ca0.gif" border="0" alt="0088-02.GIF" width="471" height="22" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">Note that Eqs. (3.156) and (3.158) are valid for any zero-mean noise process. No other assumptions were used in the derivations. If w(<i>k</i>) and v(<i>k</i>) happen to be zero-mean Normal processes, then x(k) is also a Normal process with mean and variance given by Eqs. (3.156) and (3.158).</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">By analyzing Eq. (3.158) in the limit as the sampling period approaches zero (see Chap. 4 in Ref. 53), the covariance propagation for the continuous-time system</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="492f1f1f00b8f549724e08fc1c9e7da8.gif" border="0" alt="0088-03.GIF" width="86" height="17" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">can be shown to be described by</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="ed24317e7a2d65051c8daf5485f916c6.gif" border="0" alt="0088-04.GIF" width="154" height="20" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">Example Consider the scalar Gauss-Markov process with</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="f0b3b151111cd2d7257fd661a4511b2b.gif" border="0" alt="0088-05.GIF" width="111" height="18" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">where var(</font><font face="Symbol" size="2"><i>w</i></font><font face="Times New Roman, Times, Serif" size="2">) = <i>Q</i>. By letting var(<i>x</i>) = <i>P</i>,</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="0a679f35631ba897bb5648bee5ebf245.gif" border="0" alt="0088-06.GIF" width="309" height="20" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="3d2903530d01b29e714ff025a793a72c.gif" border="0" alt="0088-07.GIF" width="295" height="17" />1</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3"><img src="81e83e8609b844d3957ddf18aff1b543.gif" border="0" alt="0088-08.GIF" width="320" height="35" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td> <td colspan="3" height="12"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">In steady state, <i>P</i>(</font><font face="Symbol" size="2">楼</font><font face="Times New Roman, Times, Serif" size="2">) = [<i>Q</i>/(2</font><font face="Symbol" size="2"><i>b</i></font><font face="Times New Roman, Times, Serif" size="2">)].</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td> <td colspan="3" height="12"></td> <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="3">State estimation was introduced in Sec. 3.3.5 for deterministic systems. The equivalent linear stochastic state-estimation problem is defined in Table 3.1,</font><font face="Times New Roman, Times, Serif" size="3" color="#FFFF00"></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="491" cellpadding="4"><tr><td colspan="3" valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE 3.1 Stochastic State-Estimation Process Equations</font></td></tr><tr><td valign="top"></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Actual process</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">Estimation process</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Measurement</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>y</i>(<i>k</i>) = H(<i>k</i>)x(<i>k</i>) + </font><font face="Symbol" size="2"><i>n</i></font><font face="Times New Roman, Times, Serif" size="2">(<i>k</i>)</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="6b3b487dd488470c1d2ef0ff2da73e0c.gif" border="0" alt="0088-09.GIF" width="86" height="17" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Residual calculation</font></td><td valign="top"></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="d4d09d44c4a11a729db88b3dad84b0fd.gif" border="0" alt="0088-10.GIF" width="92" height="17" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Estimate correction</font></td><td valign="top"></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="bf201f558a4990e8c78e2921b093f00d.gif" border="0" alt="0088-11.GIF" width="127" height="17" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">State prediction</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">x(<i>k</i> + 1) = </font><font face="Symbol" size="2">F</font><font face="Times New Roman, Times, Serif" size="2">x(<i>k</i>) + </font><font face="Symbol" size="2">G<i>w</i></font><font face="Times New Roman, Times, Serif" size="2">(<i>k</i>)</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="680f181e0a5197304481a06d6df45fa1.gif" border="0" alt="0088-12.GIF" width="101" height="16" /></font></td></tr></table></td></tr></table><br /></td></tr></table><p><font size="0"></font></p>聽 </td> </tr> <tr> <td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_87.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_88</strong></td> <td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_89.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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