📄 page_127.html
字号:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_127</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_126.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_127</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_128.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 127</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="75eda0709f1bd1eae9897f2e6df28094.gif" border="0" alt="0127-01.GIF" width="379" height="410" /></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4.11<br />Various聽forms聽of聽performance聽mismatch:聽top聽row,聽divergence;聽middle聽row,<br />optimistic聽performance聽prediction;聽bottom聽row,聽conservative聽design.</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 <i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>k</sub></font><font face="Times New Roman, Times, Serif" size="2"> = </font></i><font face="Times New Roman, Times, Serif" size="2">2.0<i>k</i> s for <i>k</i> = 1, 2, 3聽.聽.聽. and <i>R</i> = var(</font><font face="Symbol" size="2">n</font><font face="Times New Roman, Times, Serif" size="2">)</font><font face="Symbol" size="2">n</font><font face="Times New Roman, Times, Serif" size="2"> = 5.0. Therefore the Kalman filter is designed with <img src="3031abca662b582c9fe60b48ddc508ea.gif" border="0" alt="C0127-01.GIF" width="128" height="17" />, and <img src="2157577f26c6752842e32b6911f0af59.gif" border="0" alt="C0127-02.GIF" width="31" height="15" />. The value of </font><font face="Symbol" size="2">s</font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup> is not accurately known by the analyst at the design stage. For the purposes of the example, the actual value will be taken as <i>Q</i> = 0.5. Each row of plots in Fig. 4.11 portrays the actual and the predicted covariances and the Kalman gain for an assumed value of <img src="d2c46a8dd2b5ab313e1a357691435e19.gif" border="0" alt="C0127-03.GIF" width="12" height="17" />. In the first row, the analyst incorrectly models the state as a random constant (i.e., <img src="6d8031abf05fd7344a226553d219c933.gif" border="0" alt="C0127-04.GIF" width="35" height="17" />). Both the Kalman filter gain and predicted covariance are approaching zero. However, the actual error covariance is diverging and will grow without bound. This is due to the uncertainty in the actual state growing, while the (erroneously) computed variance of the estimated state approaches zero. The second row corresponds to an optimistic design. The design value of the driving-noise spectral density is too small (i.e., <img src="acd32a90f9024664450493ba2862af6f.gif" border="0" alt="C0127-05.GIF" width="43" height="17" />), resulting in the Kalman filter's predicting better performance than is actually achieved. The third row corresponds to a pessimistic design in which the analyst has selected too large a value for the driving-noise spectral density. The Kalman filter gain is larger than the optimal gain, and the filter achieves better performance than it predicts.</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">When the filter design is known to not perfectly match the plant, the pessimistic approach corresponds to the preferred situation. If the analyst designs a pessimistic</font><font face="Times New Roman, Times, Serif" size="2" 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_126.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_127</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_128.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -