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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_153</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_152.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_153</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_154.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 153</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">To complete the clock error model, the spectral densities of the driving-noise processes must be specified. This can be accomplished by fitting the clock error variance</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="5bf822db2a2c99d9b87d075ea41d2420.gif" border="0" alt="0153-01.GIF" width="281" height="35" /></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 specified in Eq. (5.18) to the Allan clock error variance specified in Refs. 23 and 143 to be</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="fbfb0bfed61f59654cb79913305cd39e.gif" border="0" alt="0153-02.GIF" width="327" height="36" /></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 <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>0</sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>-1</sub></font><font face="Times New Roman, Times, Serif" size="3">, and <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>-2</sub></font><font face="Times New Roman, Times, Serif" size="3"> are Allan variance parameters. Since the second-order error model cannot fit the Allan variance exactly (in fact, no finite-order state model can [22]), the parameters <i>S</i></font><i><font face="Symbol" size="1"><sub>f</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> and <i>S</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>f</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> can be selected to optimize the fit in the vicinity of the known value of <i>T</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>s</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">. This method and the tradeoffs involved are thoroughly discussed in Refs. 22, 23, and 143. One approach is to select <i>S</i></font><i><font face="Symbol" size="1"><sub>f</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> and <i>S</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>f</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> so that Eqs. (5.19) and (5.20) match for two time intervals denoted as <i>T</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="3"> and <i>T</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="3">. By use of least squares, this approach results in the formula</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="b8808012d973483839902fce506c993d.gif" border="0" alt="0153-03.GIF" width="411" height="65" /></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"><img src="f7703d30723feae8ee39d997c6419c20.gif" border="0" width="24" height="1" alt="f7703d30723feae8ee39d997c6419c20.gif" /></td></tr><tr><td colspan="3"></td></tr><tr><td></td> <td><font face="Times New Roman, Times, Serif" size="2">Example For a temperature-compensated crystal, the Allan variance parameters are <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>0</sub></font><font face="Times New Roman, Times, Serif" size="2"> = 2 脳 10<sup>-19</sup>(sec<sup>2</sup>/<i>s</i>), <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>-1</sub></font><font face="Times New Roman, Times, Serif" size="2"> = 7 脳 10<sup>-21</sup>(sec<sup>2</sup>/<i>s</i><sup>2</sup>), and <i>h</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>-2</sub></font><font face="Times New Roman, Times, Serif" size="2"> = 2 脳 10<sup>-20</sup>(sec<sup>2</sup>/<i>s</i><sup>3</sup>), where the units sec and <i>s</i> have been used to distinguish between the two meanings of time in this example. Let <i>T</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>1</sub></font><font face="Times New Roman, Times, Serif" size="2"> = 1<i>s</i> and <i>T</i></font><font face="Times New Roman, Times, Serif" size="1"><sub>2</sub></font><font face="Times New Roman, Times, Serif" size="2"> = 10<i>s</i> for an application in which GPS measurements will be taken with <i>T</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>s</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="2"> = 1<i>s</i>. Then Eq. (5.21) results in <i>S</i></font><i><font face="Symbol" size="1"><sub>f</sub></font></i><font face="Symbol" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="2"> = 1.1 脳 10<sup>-19</sup>(sec<sup>2</sup>/<i>s</i>) and <i>S</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>f</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="2"> = 4.3 脳 10<sup>-20</sup>(sec<sup>2</sup>/<i>s</i><sup>3</sup>) which can be converted to estimate clock bias in meters by multiplication by the square of the speed of light. The resulting value of the discrete time process noise matrix, scaled to meters, is</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"><img src="4b3cfdfd41a41eee088770b3b012bded.gif" border="0" alt="0153-04.GIF" width="302" height="36" /></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 last receiver clock issue to be addressed is the detection and accommodation of clock resets (i.e., the epochs at which the clock bias estimate jumps by 0.001c). This is a real issue only when a Kalman filter, including a state-space clock model, is being used. A filtering approach that does not accommodate these discrete jumps before residual processing will not yield accurate position or clock bias estimates.</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">Since the magnitude of the discrete jumps in the clock estimate (i.e., range measurements) is highly predictable, it is straightforward to detect and remove them from the residuals before residual processing. In a state-estimation approach, the filter residual (which is usually small, e.g., <1000) at the epoch including a clock reset would be extremely large (e.g., 卤 0.001<i>c</i>). The knowledge of the magnitude of the clock reset can be used to detect the clock reset, while</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_152.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_153</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_154.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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