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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_108</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_107.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_108</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_109.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 108</font></td></tr></table><table cellpadding="0" cellspacing="0" border="0" width="100%"><tr><td height="12"></td></tr><tr><td><table cellspacing="0" width="490" cellpadding="4"><tr><td colspan="2" valign="top"><font face="Times New Roman, Times, Serif" size="2">TABLE 4.3 Discrete Kalman Filter Equations</font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Initialization</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="1003e3614147deed65ea732d108a424b.gif" border="0" alt="0108-01.GIF" width="98" height="33" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Gain calculation</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="57a67c930a742b4fae245bf8e4d60b41.gif" border="0" alt="0108-02.GIF" width="226" height="17" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Measurement update</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="3845f12684a9de89f718baa620322672.gif" border="0" alt="0108-03.GIF" width="155" height="15" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Covariance update (choose one)</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="c8028d14c19f90753eb8b793a79675b1.gif" border="0" alt="0108-04.GIF" width="294" height="68" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Time propagation</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="2"><img src="86aadf1e3e4ef63112ce70d364a9fae9.gif" border="0" alt="0108-05.GIF" width="198" height="33" /></font></td></tr></table></td></tr></table><br /><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">It is important that the reader remember that although the Kalman filter can be implemented by a variety of techniques, the techniques are equivalent theoretically. However, some of the implementation techniques require less computation while others have better numeric properties. These issues and additional Kalman filter implementation approaches are discussed in Sec. 4.5.</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 Consider the common situation in which <i>m</i> measurements <img src="2c7860047dab2c27ec7d777f34e06733.gif" border="0" alt="C0108-01.GIF" width="95" height="13" /> of a time-invariant quantity are available. The objective is to provide the optimal estimate of the unknown quantity. It is well known that the solution is the average of the <i>m</i> measurements, but the above mathematics may be clarified by determination of this solution by use of the least-squares and the Kalman filter techniques.</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="10" 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">The measurements are related to the actual value according to</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="c2c86b31219b09190d5ec524e2390efc.gif" border="0" alt="0108-06.GIF" width="124" height="20" /></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">where <i>H</i>(<i>k</i>) = 1 and <i>n</i>(<i>k</i>) is a normal random variable with zero mean and variance <img src="069944fbaff0dd45019ca30ba4e5cdce.gif" border="0" alt="C0108-02.GIF" width="15" height="17" />. Therefore the R and H of Eq. (4.1) 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"><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="96215461e11dbc8e1b196025291516c0.gif" border="0" alt="0108-07.GIF" width="108" height="42" /></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">Computing the estimate and the estimate error variance with Eqs. (4.10) and (4.11) gives</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="9b0ef8f269e9207e0fdd9cfa86721a8c.gif" border="0" alt="0108-08.GIF" width="122" height="173" /></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_107.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_108</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_109.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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