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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_313</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_312.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_313</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_315.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 313</font></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" border="2" width="383" cellpadding="4"><tr><td valign="top"></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE C.1 Summary of Various Horizontal Error Statistics and their Relationships to the One-Dimensional Error Standard Deviation </font><font face="Symbol" size="2">s</font><font face="Times New Roman, Times, Serif" size="2"> Assuming a Circular Error Distribution</font></td><td valign="top"></td></tr><tr><td colspan="3" valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="55174af1de1a4e6fd6ecc1be3f51b209.gif" border="0" alt="0313-01.GIF" width="343" height="60" /></font></td></tr></table></td></tr></table><br /><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 variances are not equal, the solution of Eq. (C.40) is more complex and not available in closed form. Two approximate formulas for the CEP are derived in Ref. 125. Let <img src="f45232d6a227091b27e528603c434e61.gif" border="0" alt="C0313-01.GIF" width="104" height="18" /> and </font><font face="Symbol" size="3"><u>s</u></font><font face="Times New Roman, Times, Serif" size="3"> = min(</font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>n</i></sub></font><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>e</i></sub></font><font face="Times New Roman, Times, Serif" size="3">). Define <img src="1c92dee03dc03a1b449ba110b81907e6.gif" border="0" alt="C0313-02.GIF" width="59" height="22" />. The first formula 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="2e17ef38cafde2ff11f4d2b6b797d2b9.gif" border="0" alt="0313-02.GIF" width="312" height="24" /></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 is accurate to 3% for </font><font face="Symbol" size="3">r</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> [0.2, 1.0]. The second formula 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="3519b0a604e0969b0e88c1e5b5ceeffb.gif" border="0" alt="0313-03.GIF" width="321" 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">which is much more accurate than the previous formula for </font><font face="Symbol" size="3">r</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> [0.3, 1.0]. For </font><font face="Symbol" size="3">r</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> [0.0, 0.1], <img src="33be55865b390c2a8f5fbc9a4a7b6c71.gif" border="0" alt="C0313-03.GIF" width="92" height="19" />.</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_312.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_313</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_315.html">next page ></a></td> </tr> </table> </body> </html>
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