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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_70</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_69.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_70</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_71.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 70</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="ef470829f2ddc719153b22f471476a09.gif" border="0" alt="0070-01.GIF" width="258" height="150" /></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" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="2">Figure聽3.7<br />State-estimator聽implementation.</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">The above analysis is meant to motivate the idea of state estimation (also called state observation). Several questions remain unanswered. In the above analysis it has been tacitly assumed that it is possible to choose the matrix L so that the eigenvalues of (</font><font face="Symbol" size="3">F</font><font face="Times New Roman, Times, Serif" size="3"> - LH) have a magnitude of less than 1. This may not always be possible. This issue is related to the question of when the system state can be estimated from a given set of measurements and is discussed in Sec. 3.3.6. Once it is determined that state estimation is possible for a given system, it is natural to consider whether it is possible to derive an optimal state estimator relative to given optimality criteria. Optimal stochastic state estimation is discussed in Chap. 4.</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">The above analysis also discusses only time-invariant systems. The time-varying case is more complex and is discussed herein only in the context of optimal estimation in Chap. 4.</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 the resulting state-estimation algorithm is recursive in nature. If at the beginning of the <i>k</i>th time step, <img src="f090754f50daa0e52ebe28b2762c1c4a.gif" border="0" alt="XCIRC.GIF" width="15" height="16" /></font><font face="Times New Roman, Times, Serif" size="2"><sup>-</sup></font><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>), <i>y</i>(<i>k</i>), and <img src="f090754f50daa0e52ebe28b2762c1c4a.gif" border="0" alt="XCIRC.GIF" width="15" height="16" /></font><font face="Times New Roman, Times, Serif" size="2"><sup>-</sup></font><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>) are available, the computation for the <i>k</i>th time step proceeds as follows:</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="ca9492155925cbc92b99f23df31defef.gif" border="0" alt="0070-02.GIF" width="304" 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"><img src="e3eb2b4c0051f8573e9c534cbc5fe189.gif" border="0" alt="0070-03.GIF" width="309" 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"><img src="8e1f59e6e1e17a863471dbef6a3a23e1.gif" border="0" alt="0070-04.GIF" width="327" 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"></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="e7a0bad28f3d299e3b4001239cda10a3.gif" border="0" alt="0070-05.GIF" width="330" 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">The calculation can be broken up into two components, Eqs. (3.72) and (3.73) and Eqs. (3.74) and (3.75). Equations (3.72) and (3.73) are computed first to provide the best estimate of x(<i>k</i>) at time <i>k</i>, as a blending of the previous best-predicted estimate <img src="f395fc6e02d297be561c4c8efd2b502b.gif" border="0" alt="XCIRC_K.GIF" width="36" height="15" /> and the new measurement <i>y</i>(<i>k</i>). This estimate <img src="0205b8a11526f3c417502a01bdad9a9f.gif" border="0" alt="C0070-01.GIF" width="36" height="17" /> can be used for control [e.g., calculation of <i>u</i>(<i>k</i>)], navigation, and planning purposes. After these computations are complete, Eqs. (3.74) and (3.75) prepare the data necessary for the (<i>k</i> + 1)th iteration.</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">Equation (3.73) can be thought of as a blending of all past measurement information propagated to the present time [as represented by <img src="0205b8a11526f3c417502a01bdad9a9f.gif" border="0" alt="C0070-01.GIF" width="36" height="17" />] with the new information available from the current measurement [as represented by </font><font face="Symbol" size="3"><i>d</i></font><i><font face="Times New Roman, Times, Serif" size="3">y</font></i><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>)].</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></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_69.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_70</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_71.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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