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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_245</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_244.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_245</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_246.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 245</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">This model allows different acceleration correlation times </font><font face="Symbol" size="3"><i>t</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>h</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> and </font><font face="Symbol" size="3"><i>t</i></font><font face="Symbol" size="1"><sub>u</sub></font><font face="Times New Roman, Times, Serif" size="3">, respectively, for the horizontal and the vertical dynamics. The </font><font face="Symbol" size="3"><i>w</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>a</sub></font><font face="Times New Roman, Times, Serif" size="3"> process driving-noise terms would be selected to model the random variations in the acceleration. Driving noise for the receiver clock bias states would also be required.</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"><i>7.1.5<br />General Comments</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">The three models specified above are referred to as the <i>position model</i> (P), the <i>position-velocity model</i> (PV), and the <i>position-velocity-acceleration</i> (PVA) model [23]. A few specific comments are relevant to the approaches specified above:</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">1. The various DOP factors defined in Sec. 5.5 describe the amplification of the range error in the pointwise least-squares position solution. The DOP factors can be used to calculate the error variance of the pointwise position estimate at a given instant of time based on the expected range error variance. The covariance matrices involved in the Kalman filter implementation also measure the state-estimate error covariance, if F, H, P(0), Q, and R accurately describe the application. The Kalman filter error covariance is usually less than the pointwise error covariance, since the Kalman filter averages the measurements through time.</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">2. When a GPS receiver uses a Kalman filter with one of the above models in its position calculation, the user may be allowed to specify a dynamic level (e.g., stationary, medium, high), which effectively specifies the filter F and Q matrices. Before using the position (or velocity) outputs of a receiver, it is important to understand the position (or velocity) calculation method. For instance, if the PV model is implemented in a GPS receiver, then an abrupt vehicle velocity change will appear in the estimated position and velocity only after a time lag. The amount of lag will be a function of the modeled process noise covariance. The lag could be detrimental in a high-accuracy INS GPS implementation (see Sec. 7.3).</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">3. Although the noise on each of the individual pseudorange measurements is uncorrelated with the noise on other pseudorange measurements at a given time instant, the inversion process of the pointwise least-squares approach or the Kalman filter estimation process results in correlation between the state estimates. This is an important issue that is considered more fully in Sec. 7.3.</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">4. The least-squares analysis of Chap. 5 showed that at least four linearly independent pseudorange measurements were required for determine a full position and clock estimate. If fewer measurements were available at a given instant, then a complete GPS solution could not be provided by the pointwise techniques of that chapter. Alternative solution approaches in this circumstance include</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">(<i>a</i>) Finding a constrained solution. For example, in marine-vehicle applications, the altitude could be defined as sea level.</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_244.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_245</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_246.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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