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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_101</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_100.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_101</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_102.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 101</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="3"><img src="b28abd1dbdd919894e1ad42f6fe457c7.gif" border="0" alt="0101-01.GIF" width="407" height="127" /></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" width="100%"><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 align="center"><font face="Times New Roman, Times, Serif" size="2">Table聽4.2<br />Computational聽and聽Memory聽Requirements聽for聽the聽RLS聽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">where <img src="b86beba3b5e556c4f8a5fc22b8da481c.gif" border="0" alt="C0101-01.GIF" width="148" height="26" />. Although a linear estimator is the desired form, a linear relationship was never assumed. The linear update relationship of Eq. (4.22) is a natural consequence of the problem formulation.</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">Equations (4.19) and (4.22) provide the RLS estimate of the vector x. With proper initialization, the estimate is exactly the same as that attained by use of a batch approach for <i>m </i>+ 1 measurements with Eq. (4.10). Table 4.1 shows that the memory and the computational requirements of the batch algorithm for <i>m</i> measurements are <i>O</i>(<i>n</i></font><font face="Times New Roman, Times, Serif" size="2"><sup>2</sup></font><font face="Times New Roman, Times, Serif" size="3"><i>m</i>) and <i>O</i>(<i>nm</i>), respectively. These requirements are necessary even if the estimate is known for (<i>m </i>- 1) measurements before the <i>m</i>th measurement. The computational and the memory requirements for incorporating a single additional scalar measurement with the recursive algorithm are evaluated in Table 4.2. For the RLS algorithm, the memory and the computational requirements for incorporating each measurement are determined by only the dimension of the estimated vector.</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 addition to requiring smaller amounts of memory and computation, the RLS algorithm provides iterative estimates immediately following the measurement time. This has the potential of providing estimates with reduced delay over an approach that waits to accumulate a fixed-sized batch of <i>m</i> samples before calculating an estimate.</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">Equation (4.19) is not in a convenient form for calculation because of the necessity to invert the information matrix. In Sec. 4.2 alternative algorithms for the covariance measurement update are derived that are suitable for online implementation. The following subsection extends the present analysis of least-squares estimation to the derivation of the 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"><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 Continuing with the double-differencing example of Sec. 4.1.1, consider the situation in which a new set of range measurements is received every second and the GPS antenna location is fixed. The data processing for the first data set (see the previous example) required the inversion of a 3 脳 3 matrix and three differential range measurements. At the <i>m</i>th iteration, the batch least-squares implementation of Eqs. (4.10) and (4.11) would involve manipulation of 3<i>m</i> 脳 3 matrices and 3<i>m</i> range measurements. Therefore both the computation time and the memory requirements grow with each iteration. Alternatively, the recursive approach of Eqs. (4.19)(4.22) have fixed memory and computational requirements per iteration. Since the algorithms</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></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_100.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_101</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_102.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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