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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_137</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_136.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_137</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_138.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 137</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="535" cellpadding="4"><tr><td colspan="2" valign="top"><font face="Times New Roman, Times, Serif" size="2">Table 4.5 Approximation to Optimal Nonlinear Estimation 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="3"><img src="08d36981eb87df5cc508303a2717b5b9.gif" border="0" alt="0137-01.GIF" width="100" height="32" /></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="3"><img src="ed820310c292dc1d40f859c39f26e939.gif" border="0" alt="0137-02.GIF" width="223" 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="3"><img src="de27755df205b7c1568acec28b456803.gif" border="0" alt="0137-03.GIF" width="173" height="34" /></font></td></tr><tr><td valign="top"><font face="Times New Roman, Times, Serif" size="2">Definitions</font></td><td valign="top"><font face="Times New Roman, Times, Serif" size="3"><img src="45fcc054ab2576b601bf7d3321f61e6d.gif" border="0" alt="0137-04.GIF" width="254" height="114" /></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">where</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="5de557c8072848dc5ebb3c0f273028ae.gif" border="0" alt="0137-05.GIF" width="298" 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">Two examples of this linearization process were presented in Chap. 1. Several additional examples are discussed in subsequent chapters. In navigation applications, the F matrix is typically not asymptotically stable. Therefore the trajectory perturbation typically diverges with time. For the linearized error dynamics to remain accurate, either the time interval of interest should be short or some mechanism should be used to ensure that <img src="23d6d5a09ea288522074f5b273e001c1.gif" border="0" alt="C0137-01.GIF" width="74" height="15" /> remains small.</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 the linearized error dynamics defined in Eqs. (4.124), (4.126), an approximation to the optimal nonlinear estimator can be defined with the linear Kalman filter equations. The implementation equations are accumulated for ease of reference in Table 4.5. The matrix </font><font face="Symbol" size="3">F</font><font face="Times New Roman, Times, Serif" size="3">(<i>k</i>) is the state-transition matrix corresponding to <img src="ee9e6b67c97ae3473e49a036815c4877.gif" border="0" alt="C0137-02.GIF" width="174" height="15" /> (see Sec. 3.3.3).</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 matrix P is only an approximation to the actual error covariance matrix. Therefore Monte Carlo simulations should be used in addition to covariance analysis to ensure that the results of the covariance analysis are accurate.</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">4.7.5.1<br />Linearized Kalman Filter</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 the case in which <img src="b904ecb50eac864b3ea8501ff07436aa.gif" border="0" alt="C0137-03.GIF" width="23" height="13" /> is a predetermined trajectory, the approximate optimal estimation equations are referred to as a <i>linearized Kalman filter</i>. In this case, the on-line calculations can be significantly simplified since the on-line measurements do not affect the calculations of F, </font><font face="Symbol" size="3">F</font><font face="Times New Roman, Times, Serif" size="3">, H, P, or K. Table 4.6 organizes the calculations of Table 4.5 into on-line and off-line calculations. The estimate of the filter can be interpreted as the</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_136.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_137</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_138.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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