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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_90</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_89.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_90</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_91.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 90</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">as the accelerometer model. Therefore the position and the velocity error dynamics are 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"></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="7bc180a0fa70538b3c23ee78e983e630.gif" border="0" alt="0090-01.GIF" width="341" height="40" /></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="10f050118a5b2826f8bd5ae7a8a7cf67.gif" border="0" alt="0090-02.GIF" width="342" height="40" /></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">Modeling the bias as a random-walk process</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="00ba177ea246c1d1e1d5b189f0d7e821.gif" border="0" alt="0090-03.GIF" width="297" height="41" /></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">yields the continuous-time error dynamic equation</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="4f59aa0faad6e3c8c3873c862ca68efc.gif" border="0" alt="0090-04.GIF" width="431" height="58" /></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">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"></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="502b695341002f716fd2dad3fd3af5ec.gif" border="0" alt="0090-05.GIF" width="439" height="56" /></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">where var(</font><font face="Symbol" size="3">u</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3">) = <i>R</i></font><i><font face="Symbol" size="1"><sub>u</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3"><i>d</i></font><font face="Times New Roman, Times, Serif" size="3">(</font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">), var(</font><font face="Symbol" size="3"><i>w</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>b</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">) = <i>Q</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>b</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3"><i>d</i></font><font face="Times New Roman, Times, Serif" size="3">(</font><font face="Symbol" size="3">t</font><font face="Times New Roman, Times, Serif" size="3">), var[</font><font face="Symbol" size="3">u</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i>), </font><font face="Symbol" size="3"><i>w</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>b</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">(</font><font face="Symbol" size="3">t</font><font face="Times New Roman, Times, Serif" size="3">)] = 0, and specific values for <i>R</i></font><i><font face="Symbol" size="1"><sub>u</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> and <i>Q</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>b</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> have been assumed.</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">For any time <i>t</i>, the state error covariance can be found in closed form as</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="2ef3a2b39913a2c0e3bcdc1a37bf3909.gif" border="0" alt="0090-06.GIF" width="395" height="38" /></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">In this example,</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="f05434f937ae0153deb868af1fd46e18.gif" border="0" alt="0090-07.GIF" width="326" height="58" /></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="e2a925e32d40f90c60dbe2124a2335c0.gif" border="0" alt="0090-08.GIF" width="387" height="92" /></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="10eb2158cfc75f5883c9e7818da6c389.gif" border="0" alt="0090-09.GIF" width="447" height="72" /></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">where it has been assumed that P(0) = diag(<i>P</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>p</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>P</i></font><i><font face="Symbol" size="1"><sub>u</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>P</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>b</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">). Therefore the error</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_89.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_90</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_91.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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