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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_148</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_147.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_148</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_149.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 148</font></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="514" cellpadding="4"><tr><td colspan="5" valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE 5.3 Receiver Position in ECEF Coordinates (meters) as a Function of Iteration Number</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><i>k</i></font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"><i>x</i></font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"><i>y</i></font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"><i>z</i></font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2"><i>c</i></font><font face="Symbol" size="2">D</font><font face="Times New Roman, Times, Serif" size="2"><i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>r</sub></font></i></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">0</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">0000000.000</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">0000000.000</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">0000000.000</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">000000.000</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">1</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-2977571.476</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-5635278.159</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">4304234.505</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">162523.980</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">2</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-2451728.534</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-4730878.461</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3573997.520</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">314070.732</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">3</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-2430772.219</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-4702375.802</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3546603.872</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">264749.706</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">4</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-2430745.096</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-4702345.114</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3546568.706</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">264691.129</font></td></tr></table></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">5</font></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-2430745.096</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td rowspan="5"></td> <td colspan="3" height="1"></td> <td rowspan="5"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="1" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td align="right"><font face="Times New Roman, Times, Serif" size="2">-4702345.114</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">3546568.706</font></td></tr></table></td><td valign="top"><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="center"><font face="Times New Roman, Times, Serif" size="2">264691.129</font></td></tr></table></td></tr></table></td></tr></table><br /><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">Assuming no prior position information, the iterative linearization process will be initialized at the ECEF origin. The position-estimation convergence as a function of iteration number is shown in Table 5.3. Note that the estimated position converges to a fixed estimate (to millimeter precision) in five iterations. This does not necessarily mean that the estimated position is accurate to millimeters. In this example, the presurveyed receiver ECEF position in meters is known to be</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="0bc1d4df6c6b0e5efcb193e4d8d4ec56.gif" border="0" alt="0148-01.GIF" width="349" height="15" /></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">At each iteration, the error between the estimated position and the correct position is shown in Table 5.4. This table shows that while the error due to linearization (i.e., <i>hot</i>'s) has been essentially eliminated, the bias due to the measurement errors remains.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td>
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