📄 page_80.html
字号:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd"> <html> <head> <title>page_80</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_79.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_80</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_81.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 80</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">with <i>P</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>x</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">(0) = 0 and var(</font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i>), </font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i> + </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">)) = <i>Q</i> </font><font face="Symbol" size="3"><i>d</i></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i> - </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">) (where <img src="e1d64e55604c3d471e3c3c2408527626.gif" border="0" alt="C0080-01.GIF" width="44" height="20" />) is called a Brownian motion or random-walk process. The mean and the variance of <i>x</i> can be calculated 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="ddbc4e094605c16df3118d9bf33a47ba.gif" border="0" alt="0080-01.GIF" width="321" height="19" /></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="931b235d36f80641f710eb83bf85c8d7.gif" border="0" alt="0080-02.GIF" width="287" height="39" /></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">and</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="31f325c7dc28db6e372ad0827530c03a.gif" border="0" alt="0080-03.GIF" width="431" height="125" /></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 if <i>x</i> is measured in meters, then var</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>x</i></sub></font><font face="Times New Roman, Times, Serif" size="3">(<i>t</i>, </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">) has units of m</font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup></font><font face="Times New Roman, Times, Serif" size="3">. Therefore the units of </font><font face="Symbol" size="3"><i>s</i></font><font face="Symbol" size="1"><sub>w</sub></font><font face="Times New Roman, Times, Serif" size="3"> are<img src="2d412c32ff9ed19ccbcf1d5b6d0de821.gif" border="0" alt="C0080-02.GIF" width="127" height="21" />.</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">One often-quoted measure of sensor accuracy is the random-walk parameter. For example, a fiber-optic gyro might list its random-walk parameter to be<img src="d00825aaf4170e810d710cb6e356fd55.gif" border="0" alt="C0080-03.GIF" width="58" height="21" />. By Eq. (3.115), the random-walk parameter for a sensor quantifies the rate of growth of the integrated (properly compensated) sensor output as a function of time. The <img src="b8aae3c4dda7d0ca6e231765712ab0d8.gif" border="0" alt="C0080-04.GIF" width="24" height="19" /> in the denominator of the specification reflects that the standard deviation and the variance of the random-walk variable grow with the square root of time and linearly with time, respectively.</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 navigation modeling, it is common to integrate the output of a sensor to determine particular navigation quantities. An example is integrating an accelerometer output to determine velocity. If it is accurate to consider the accelerometer error as white random noise, then the resulting error equations will result in a random-walk model for the velocity error.</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 An accelerometer output is known to be in error by an unknown slowly time-varying bias <i>b</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>a</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="2">. The turn-on bias is accurately known and accounted for in the accelerometer calibration. Therefore it is accurate to model the residual time-varying bias error as a random walk:</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="a42aedf2d9554232ba319f94fd192ab0.gif" border="0" alt="0080-04.GIF" width="262" height="36" /></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="64ec20bd4bf1e4745b129ee93388cd11.gif" border="0" alt="0080-05.GIF" width="259" 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"><img src="e5f7f9ad289ea9425c00a093cee4d032.gif" border="0" alt="0080-06.GIF" width="317" height="19" /></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 </font><font face="Symbol" size="2">w</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>b</i></sub></font><font face="Times New Roman, Times, Serif" size="2"> represents white noise and <i>Q</i></font><font face="Symbol" size="1"><sub>w</sub></font><font face="Times New Roman, Times, Serif" size="2"> is determined by the quality of the accelerometer.</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_79.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_80</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_81.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 + -