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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_166</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_165.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_166</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_167.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 166</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"><i>5.7.1<br />Doppler Carrier-Phase Processing</i></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">To avoid the need for a differential implementation, a time difference of the phase eliminates the integer ambiguity allowing direct estimation of velocity. If the linearization of Eq. (5.60) is differenced between two measurement times, an accurate measure of the change in satellite-to-receiver range results:</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="a19c0425fe641170324350cf108ce1a4.gif" border="0" alt="0166-01.GIF" width="479" height="45" /></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 the clock error is included in x(<i>t</i>). The change in phase over the time interval </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3"> is referred to as the Doppler measurement:</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="5019ccf83142bb4c24aa56c07f24ba53.gif" border="0" alt="0166-02.GIF" width="482" height="45" /></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 </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3"> is the differencing time and h</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>t</i>) = h</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>t</i>-</font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">) has been assumed. This assumption is accurate for small </font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">. If the relative acceleration of the base and rover is small during the differencing time, then a set of four Doppler measurements can be processed to yield an accurate estimate of relative velocity.</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 the Doppler measurement is more accurately modeled by either referring it to the center of the differencing interval Doppler(<i>t</i>-</font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">/2) or carrying both x(<i>t</i>) and x(<i>t</i>-</font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">) as filter states. Related techniques are discussed in Refs. 20, 50, and 51.</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 GPS literature, various related terms can be found: Doppler, delta range, carrier phase, and integrated Doppler. Doppler and delta range refer to the same GPS quantity. The latter is the more accurate name, as it describes the manner in which the measurement is actually made. Doppler is measured by the receiver as the change in phase (range) over a given time interval (i.e., delta range) divided by the interval length. Integrated Doppler refers to the integral of the delta ranges. Since each delta range measurement contains additive noise, the integrated Doppler signal will contain an integrated random-noise process that may slowly diverge from zero. Therefore integrated Doppler measurements may slowly diverge from the true value. The (continuous) carrier-phase measurement is distinct from the integrated Doppler signal. The carrier-phase measurement is the total phase change recorded by the receiver since locking on to a given satellite. Because of the manner in which the continuous phase is accumulated and measured [81], its additive-noise component is accurately modeled as white. The distinction described above between continuous carrier phase and integrated Doppler is not universal, and different authors or manufacturers may use this terminology differently.</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">Carrier phase (once the integer ambiguity is resolved) gives a very accurate measure of range, but requires continuous phase lock. Loss of lock requires that the integers be reestimated. Doppler or delta range measurements give a</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_165.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_166</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_167.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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