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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_126</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_125.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_126</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_127.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 126</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">mechanism for detecting candidate measurements for exclusion. Let the state error covariance be P</font><font face="Times New Roman, Times, Serif" size="2"><sup>-</sup></font><font face="Times New Roman, Times, Serif" size="2"><sup></sup></font><font face="Times New Roman, Times, Serif" size="3"> before the incorporation of the measurement <img src="62824df0ccce6fe865dcadfcfd0fcca5.gif" border="0" alt="YTILDEHX.GIF" width="76" height="19" />. Then the measurement residual <img src="7ccaadef6bf9682cd61eb71617cb8319.gif" border="0" alt="C0126-01.GIF" width="54" height="15" /> is a scalar Gaussian random variable with zero mean and 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="a224d3b1cbf0c625aea7b008f668f67f.gif" border="0" alt="0126-01.GIF" width="129" height="18" /></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>R</i> = var(</font><font face="Symbol" size="3"><i>n</i></font><font face="Times New Roman, Times, Serif" size="3">). The designer can select a threshold </font><font face="Symbol" size="3">l</font><font face="Times New Roman, Times, Serif" size="3"> such that</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="c1a02e0aeaa3dc14236103698415b451.gif" border="0" alt="0126-02.GIF" width="189" height="18" /></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">m</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Symbol" size="3">脦</font><font face="Times New Roman, Times, Serif" size="3"> (0, 1) is usually quite small. Then if the condition <i>r</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2 </sup></font><font face="Times New Roman, Times, Serif" size="3">> </font><font face="Symbol" size="3">l</font><font face="Times New Roman, Times, Serif" size="3">(HP</font><font face="Times New Roman, Times, Serif" size="2"><sup>-</sup></font><font face="Times New Roman, Times, Serif" size="3">H</font><font face="Times New Roman, Times, Serif" size="3"></font><font face="Times New Roman, Times, Serif" size="2"><sup><i>T</i></sup></font><font face="Times New Roman, Times, Serif" size="3"> + <i>R</i>) is satisfied, the measurement is declared invalid and the corresponding measurement update (state and covariance) are skipped. Repeated violations of the test condition can be used to declare the sensor invalid.</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>4.5.4<br />Divergence</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">Section 4.4 provided two methods for analyzing the performance of a filter design relative to a truth model. Even when these analysis techniques predict that the system will achieve a desired level of performance, the actual implementation may not. Assuming that the algorithm is implemented correctly, the divergence of the actual performance from the predicted performance indicates that some important aspect of the system model has been neglected. Typical causes of divergence are the model neglecting unstable or marginally stable states or the process noise being too small. Both of these effects result in the calculated error variance being too small. Therefore the calculated Kalman gain is too small and the measurements are not weighted enough. It is important to emphasize that the Kalman filter is the optimal filter <i>for the modeled process</i>. If the model is an inaccurate representation of the physical system, the optimal filter for the model cannot be expected to be optimal for the actual system.</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">Analysis of the effects of and sensitivity to modeling errors is one of the main objectives of covariance analysis. Covariance analysis for which the system state and parameters {</font><font face="Symbol" size="3">F</font><font face="Times New Roman, Times, Serif" size="3">, Q</font><font face="Times New Roman, Times, Serif" size="1"><sub>d</sub></font><font face="Times New Roman, Times, Serif" size="3">, H, R, P</font><font face="Times New Roman, Times, Serif" size="3">(0)} are identical to those of the design model are only useful for demonstrating the optimal performance that can be achieved under perfect modeling conditions. A good analyst will follow this optimal analysis with a study to determine a set of filter parameters that results in near-optimal performance while being robust to expected ranges of model uncertainty.</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 To illustrate various ways that the actual and the predicted filter performances might not match, consider the example of estimating the state of the random-walk plus random-constant system described by</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="e23ed8f2cb36285149fa2d23def82bd3.gif" border="0" alt="0126-03.GIF" width="261" height="13" /></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">with <i>P</i>(0) = var[<i>x</i>(0)] = 10 and <i>Q(t)</i> = var[</font><font face="Symbol" size="2">w</font><font face="Times New Roman, Times, Serif" size="2">(<i>t</i>)] = </font><font face="Symbol" size="2">s</font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup> from discrete measurements occurring at 2-s intervals:</font><font face="Times New Roman, Times, Serif" size="2" 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"><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="b35f2e2ad02ad85460aa147c676292a0.gif" border="0" alt="0126-04.GIF" width="101" height="14" /></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_125.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_126</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_127.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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