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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_252</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_251.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_252</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_253.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 252</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">of additive zero-mean Gaussian white noise. Therefore the equations of motion for the vehicle are</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="cfe047bbb8c5f54f167e13eff4597a12.gif" border="0" alt="0252-01.GIF" width="69" height="39" /></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">or</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="6f9c099370e8532ef56e590d6773003b.gif" border="0" alt="0252-02.GIF" width="440" height="37" /></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 acceleration is measured as</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="041bdeac3e06d14386a0e007556e594a.gif" border="0" alt="0252-03.GIF" width="273" height="16" /></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 a is the actual acceleration and </font><font face="Symbol" size="3">n</font><font face="Times New Roman, Times, Serif" size="3"> is measurement noise. For this example the spectral density of the additive accelerometer white noise is assumed to be </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup></font><font face="Times New Roman, Times, Serif" size="3">, where <img src="c25803f7ab7940faea62c9d8a82e0f37.gif" border="0" alt="C0252-01.GIF" width="108" height="20" />, which corresponds to an inexpensive solid-state accelerometer. Therefore <img src="9f7fbbcbfc4640077fc17f72ecef4117.gif" border="0" alt="C0252-02.GIF" width="169" height="19" />.</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>7.3.1<br />Receiver Kalman Filter</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">As is typical when the GPS receiver is bought off the shelf, this analysis assumes that the receiver Kalman filter is fixed except for a few design parameters that are user selectable. Therefore it is assumed that the GPS receiver uses the PVA dynamic model described in Sec. 7.1:</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="9945beb8848045fa5e20835a7100ac31.gif" border="0" alt="0252-04.GIF" width="398" height="55" /></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 subscript <i>r</i> denotes receiver variables and x</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> = [P</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3">, v</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3">, a</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3">]. The variable <i>p</i> is a design parameter selected by the manufacturer to model the reciprocal of the expected correlation time of the vehicle acceleration. The value of this parameter for this analysis is <i>p</i> = 0.333.</font><font face="Times New Roman, Times, Serif" size="2"><sup>**</sup></font><font face="Times New Roman, Times, Serif" size="3"> The vector </font><font face="Symbol" size="3"><i>w</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"> has nine elements. The first six elements of </font><font face="Symbol" size="3"><i>w</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"> are zero. The last three elements of </font><font face="Symbol" size="3"><i>w</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"> are assumed to be white noise with spectral density <img src="84879642540f63dd111806b2dc44f956.gif" border="0" alt="C0252-03.GIF" width="17" height="19" />. The user normally has some freedom in the selection of the </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3"> value depending on the application. The results of this analysis are presented as functions of </font><font face="Symbol" size="3">s</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3">. The spectral density of </font><font face="Symbol" size="3"><i>w</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 denoted as <img src="30cce381d4d7aebcdc19890de2e5b063.gif" border="0" alt="C0252-04.GIF" width="58" height="19" />.</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">Based on the receiver state dynamics defined by Eq. (7.17), the receiver Kalman filter tries to estimate the receiver state x</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>r</i></sub></font><font face="Times New Roman, Times, Serif" size="3">. The actual receiver Kalman</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><table border="0" cellspacing="0" cellpadding="0" width="100%"><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" height="1"><table cellpadding="0" cellspacing="0" border="0"><tr><td></td></tr></table></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2"><sup>** </sup>This value is not critical to the results presented, since no matter what value is selected for <i>p</i> the remaining parameters can be adjusted to produce results similar to those presented.</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_251.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_252</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_253.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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