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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_145</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_144.html">&lt;&nbsp;previous page</a></td>				<td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_145</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_146.html">next page&nbsp;&gt;</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 145</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">that can be determined based on the following system of equations, representing measurements from four different satellites:</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="e62d280ef2345a15b922567946f624f4.gif" border="0" alt="0145-01.GIF" width="420" height="48" /></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="ad9baf40eb10cbeef20134c35b7fc11d.gif" border="0" alt="0145-02.GIF" width="422" height="48" /></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="4f612111b165f97cf817786fc8f35ebc.gif" border="0" alt="0145-03.GIF" width="422" height="48" /></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="466919ff9add7f62cdca671a5ec1b561.gif" border="0" alt="0145-04.GIF" width="423" height="49" /></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 <img src="c3f70d2d74794a68c68a5bd1f756654e.gif" border="0" alt="C0145-01.GIF" width="79" height="18" />, and <img src="ea89102c8085a756cdb85495bafccdeb.gif" border="0" alt="C0145-02.GIF" width="24" height="17" /> are the measured pseudoranges, (<i>X</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3">, <i>Y</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3">, <i>Z</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3">) are the ECEF position coordinates of satellite <i>i</i>, (<i>x, y, z</i>) are the ECEF position coordinates of the receiver antenna, </font><font face="Symbol" size="3">D</font><font face="Times New Roman, Times, Serif" size="3"><i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>r</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> is receiver clock bias, <img src="06eab9a5c6abaa756e30c695dcff700e.gif" border="0" alt="C0145-04.GIF" width="28" height="18" /> is the clock bias of the SV, <img src="a8de05f73a509f7656e937f674ef23f1.gif" border="0" alt="C0145-03.GIF" width="28" height="18" /> is the atmospheric delay, SA</font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3"> represents the deliberate corruption of the satellite signals under the policy of selective availability, <i>E</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3"> represents error in the broadcast ephemeris data, MP</font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3"> represents multipath error, </font><font face="Symbol" size="3"><i>h</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3"> represents receiver tracking error noise, and <i>c</i> is the speed of light. The ()</font><font face="Times New Roman, Times, Serif" size="2"><sup>(<i>i</i>)</sup></font><font face="Times New Roman, Times, Serif" size="3"> notation refers to the quantity in parenthesis referenced to the <i>i</i>th satellite.</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">Each of the above error sources is discussed separately in Sec. 5.4. In solving Eqs. (5.1)(5.4), the effective SV positions are required. The position of the space-vehicle antenna phase center in ECEF coordinates can be computed with data derived from the GPS navigation messages, as described in App. E.</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="17"></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">5.3<br />Solution of the Pseudorange Equations</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 equations (5.1)(5.4), the pseudorange measurements are dependent on the receiver coordinates in a nonlinear fashion. Although closed-form solutions are available (see, e.g., Refs. 5, 38, and 97), in this section the typical method of solution, based on linearization of the measurement equations, is presented. This approach is straightforward, converges quickly, and allows linear analysis techniques to be applied. The linearization approaches of this chapter leads into the EKF technique used in later examples. If improved accuracy is desired, the linearization and solution procedure can be repeated iteratively with the result from one iteration serving as the linearization point for the next iteration; however, the more typical approach (for a stationary antenna) is to perform a single iteration for each measurement epoch with the result of one epoch serving as the linearization point for the next epoch. Nonstationary antenna situations are discussed in Chap. 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>  </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_144.html">&lt;&nbsp;previous page</a></td>				<td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_145</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_146.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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