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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_125</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_124.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_125</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_126.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 125</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">The total number of computations for the <i>m</i> scalar measurement updates is <img src="950ff88b82b0523f4ee047f72a43ed88.gif" border="0" alt="C0125-01.GIF" width="77" height="20" /> plus <i>m</i> scalar divisions. Thus it can be seen that <i>m</i> scalar updates are computationally cheaper for all <i>m</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">At the completion of the <i>m</i> scalar measurements, <img src="4a62a256968c6e12657d88efb704a24f.gif" border="0" alt="C0125-02.GIF" width="34" height="15" /> and P</font><font face="Times New Roman, Times, Serif" size="2"><sup>+</sup></font><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>) will be identical to the values that would have been computed by the corresponding vector measurement update. The state-feedback measurement vectors K</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"> corresponding to the scalar updates are <i>not</i> equal to the columns of the state-feedback gain matrix that would result from the corresponding vector update. This is due to the different ordering of the updates affecting the error covariance matrix P</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"> at the intermediate steps during the scalar updates.</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>4.5.2<br />Correlated Measurements</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 scalar measurement processing algorithm is valid only in situations in which the measurement-noise corrupting the set of scalar measurements is uncorrelated (i.e., R is a diagonal matrix). In situations in which this assumption is not satisfied, the actual measurements can be transformed into an equivalent set of measurements v(<i>k</i>) with uncorrelated measurement noise. The transformed set of measurements can then be incorporated by the scalar processing algorithm.</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">With <img src="62824df0ccce6fe865dcadfcfd0fcca5.gif" border="0" alt="YTILDEHX.GIF" width="76" height="19" />, let</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="e8979f8534546b631cb98f07472f2902.gif" border="0" alt="0125-01.GIF" width="134" height="17" /></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 U is an orthonormal matrix (i.e., U</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">U = I). The UDU decomposition is possible for any symmetric matrix. If v is defined 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="8579b2df618267a09739a017b5226332.gif" border="0" alt="0125-02.GIF" width="55" 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">then the equivalent additive noise on the measurement <img src="849e4aeb8cefccd1184a524659460145.gif" border="0" alt="c0125-03.GIF" width="11" height="12" /> is U</font><font face="Times New Roman, Times, Serif" size="2"><sup><i>T</i></sup><i></i></font><i><font face="Symbol" size="3">n</font></i><font face="Symbol" size="3"></font><font face="Times New Roman, Times, Serif" size="3"> with 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="6fd788d1aac229b8d30f888580a635dd.gif" border="0" alt="0125-03.GIF" width="193" height="17" /></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">Therefore the scalar processing algorithm can be used with v, D, and U</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">H in place of y, R, and H, respectively.</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>4.5.3<br />Bad or Missing Data</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">In many applications, a measurement expected at the <i>k</i>th sample time may occasionally be missing. Such instances have no effect on the Kalman filter algorithm, as long as the missing measurement is ignored correctly. When a measurement is missing, the corresponding measurement update (both state and covariance) must not occur. In addition, the state estimate and the error covariance must be propagated through time to the time of the next expected measurement.</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">Even when a measurement is available, it is sometimes desirable to reject certain measurements as faulty or erroneous. The Kalman filter provides a</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_124.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_125</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_126.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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