📄 page_234.html
字号:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_234</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_233.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_234</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_235.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 234</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">When the velocity is near zero (i.e., a nominally stationary platform), the error dynamics redue to</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="5afe5b1a1810d2845ec69062515d6d42.gif" border="0" alt="0234-01.GIF" width="754" height="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">In the level stationary case, the observability matrix is</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="32d54f3f2ea9d6bd0ed2a8ca5e3192f3.gif" border="0" alt="0234-02.GIF" width="406" height="113" /></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">which has rank equal to 5. The five nominal states are observable from the north and the east velocity measurements, denoted by y(<i>t</i>). Therefore alignment is possible from velocity, even in stationary conditions, if the INS instrument biases are known.</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">When the instrument biases are not known and calibration is required, then the estimation analysis problem becomes more interesting. When the five instrument biases are augmented by the error state, the system dynamics are defined 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="5c0756c93c4cf06895a1ff3cb476c62f.gif" border="0" alt="0234-03.GIF" width="330" 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">where F is the dynamic matrix described for the basic five error states in Eq. (6.170). When the calibration phase is short and distinct from the operation phase, it is common to let the PSD of </font><font face="Symbol" size="3">z</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>b</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> be equal to zero. This is equivalent to assuming that the bias is constant for the short time period of calibration. The assumption is not critical to the analysis, and we chose to include the bias driving noise for generality. In this analysis, b = b</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>n</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> = [<i>b</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>N</sub></font><font face="Times New Roman, Times, Serif" size="3">, b</font><font face="Times New Roman, Times, Serif" size="1"><sub>E</sub></font><font face="Times New Roman, Times, Serif" size="3">, d</font><font face="Times New Roman, Times, Serif" size="1"><sub>N</sub></font><font face="Times New Roman, Times, Serif" size="3">, d</font><font face="Times New Roman, Times, Serif" size="1"><sub>E</sub></font><font face="Times New Roman, Times, Serif" size="3">, d</font><font face="Times New Roman, Times, Serif" size="1"><sub>D</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">]. For a strap-down system, b</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>n</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> = R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>n</i></sub></font><font face="Times New Roman, Times, Serif" size="3">b</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>p</i></sup></font><font face="Times New Roman, Times, Serif" size="3">. The model above assumes that R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>n</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = I, which is equivalent to assuming that the vehicle is level and north pointing. Deviations from this assumption, as long as R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>n</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> is not time varying, will change the onobservable subspace, but similar conclusions would apply. Applications in which R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>p</i>2<i>n</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> can be changed have better observability properties.</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">Under low dynamic conditions (i.e., <i>f</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>N</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>f</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>E</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">禄</font><font face="Times New Roman, Times, Serif" size="3"> 0 and v </font><font face="Symbol" size="3">禄</font><font face="Times New Roman, Times, Serif" size="3"> 0), this ten-state system is not completely observable, as can be shown by analysis of the observability matrix [8, 39, 75]. In fact, the observability matrix has a rank of only 7.</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_233.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_234</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_235.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 + -