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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_129</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_128.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_129</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_130.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 129</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">this occurs, the Kalman filter gains for the corresponding states have the wrong sign, and the state may temporarily diverge. Even if the sign eventually corrects itself, subsequent performance will suffer since the covariance matrix is no longer accurate. In addition, the interim divergence can be arbitrarily bad.</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">Any symmetric matrix, in particular P, can be factorized 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="e43162aa26f70cdc6843a45592adbc48.gif" border="0" alt="0129-01.GIF" width="72" height="15" /></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">Special-purpose algorithms have been derived that propagate the factors U and D instead of P itself. The factors contain the same information as P, the factorized algorithms can be shown to be theoretically equivalent to the Kalman filter, and the algorithms automatically maintain both the positive definiteness and the symmetry of the covariance matrix. The main drawbacks of square-root algorithms are that they are more complex to program and usually require more computation (i.e., flops). So-called <i>square-root implementations</i> are discussed in depth in Refs. 58 and 109.</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="17"></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<br />Suboptimal Filtering</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">When the <i>cost function</i> involves only the mean-square estimation error and the system is linear, the Kalman filter provides the optimal estimation algorithm. In many applications, the actual system is often nonlinear. Suboptimal filtering methods for nonlinear systems are discussed in Sec. 4.7.5. In addition, more factors may have to be considered in the overall filter optimization than the mean-square error alone. For example, the complete Kalman filter may have memory or computational requirements beyond those feasible for a particular project. In this case, the system engineer will attempt to find an implementable suboptimal filter that achieves performance as close as possible to that of the benchmark optimal Kalman filter algorithm. Dual-state covariance analysis (see Sec. 4.4.2) is the most common method used to analyze the relative performance of suboptimal filters. A few techniques for generating suboptimal filters within the Kalman filter framework are discussed in the following subsections.</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>4.7.1<br />Deleting States</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 best model available to represent the actual system, referred to as the <i>truth model</i>, will usually be high dimensional. In INS applications, the number of states can be near 100. GPS error states can add on the order of six states per satellite. Since the number of flops required for implementing a Kalman filter is of the order of <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>, where <i>n</i> is the state dimension and <i>m</i> is the measurement dimension, the question arises of whether some of the states can be removed or combined in the implemented filter. For each hypothesized filter model, Monte Carlo or covariance studies can be performed to determine the performance of the designed filter relative to the truth model. Several rules have been developed through analysis and experience to guide the designer in the choice of states to combine or eliminate.</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_128.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_129</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_130.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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