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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_257</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_256.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_257</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_258.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 257</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">standard deviation to the navigation system predicted value of the position error standard deviation. The relative velocity error is defined similarly. Since actual </font><font face="Symbol" size="3"><i>s</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>a</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>s</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"> values do not affect the navigation system's prediction of its own performance, the steady-state INS prediction of its position and velocity error variance result in the values 2.23 and 0.17 in all cases.</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">Figures 7.6 and 7.7 show the computed relative position and velocity error performance as functions of </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>a</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> for <img src="110ecb73185c26d313dd37a724c1cc40.gif" border="0" alt="C0257-01.GIF" width="196" height="21" />. In each figure, the top curve corresponds to <img src="3292198215bd89a35c485ddb9577c270.gif" border="0" alt="C0257-02.GIF" width="65" height="20" /> and the bottom curve to <img src="921b3493f029ca323463e85fc8c81ab5.gif" border="0" alt="C0257-03.GIF" width="73" height="19" />. At best, the actual position and velocity error standard deviation are, respectively, four and five times worse than the navigation systems self-predicted accuracy.</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 best overall relative performance occurs when the receiver Kalman filter is designed based on the highest acceleration. Effectively, this tells the receiver Kalman filter to ignore its past velocity and acceleration estimates in predicting the current position. Therefore the current receiver position estimate is formed as the least-squares estimate to the measured pseudoranges. This effectively eliminates the time correlation from the receiver position error. The remaining factor-of-four relative difference between actual and predicted position error performances is due to the neglected off-diagonal structure of the R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>i</i></sub></font><font face="Times New Roman, Times, Serif" size="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">For each curve, the best relative performance occurs for actual vehicle accelerations below that expected based on the design value of the receiver acceleration PSD. Again, this corresponds to the receiver Kalman filter's overweighting the current pseudorange measurements relative to the present filter state. The navigation systems self-predicted performance is still overly optimistic because of the neglected off-diagonal structure of the R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>i</i></sub></font><font face="Times New Roman, Times, Serif" size="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">In some early GPS applications that used position aiding, R</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>i</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> was made an increasing function of vehicle acceleration. This effectively discarded the GPS position estimates during periods of high acceleration, but did not address the underlying problem. In applications in which this cascading of Kalman filters cannot be avoided, appropriate design and analysis techniques are discussed, in, e.g., Refs. 29 and 132.</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">7.4<br />Carrier-Smoothed Code</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">Given that the GPS code and phase measurements (L1, L2, or wide lane) contain essentially the same information and error sources, it is natural to consider methods of combining the two measurements to achieve higher-accuracy range information. To use the phase measurement for ranging purposes, the integer ambiguity must be estimated. This estimation can be implemented as a search of integer values, as in Sec. 5.7.3, or as part of a stochastic estimation process wherein the estimated ambiguity is allowed to assume real values. Generically, the latter methods are referred to as <i>carrier-smoothed-code</i> techniques for reasons that will become apparent in the following discussion. Several methods have been suggested. In this section various techniques are presented in a unified framework, which simplifies comparison of the techniques.</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_256.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_257</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_258.html">next page ></a></td> </tr> </table> </body> </html>
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