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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_120</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_119.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_120</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_121.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 120</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">an analysis of system design tradeoffs, it is usually more useful to be able to calculate the output error variance due to<i> each</i> source independently. The output error variance due to each error source allows the designer to easily determine the dominant error sources and decide whether it is feasible to reduce the error effects (through either better hardware or more detailed modeling) to the point where the design specifications are achieved. This process is referred to as error budgeting.</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">Either Eqs. (4.64)(4.69) or Eqs. (4.71) and (4.72) can be used for error-budgeting analysis. Note that when K is fixed, both sets of equations are linear in P(0), Q</font><font face="Times New Roman, Times, Serif" size="1"><sub>d</sub></font><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, and R [or M(0), Q</font><font face="Times New Roman, Times, Serif" size="1"><sub>d</sub></font><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, and R]. For brevity, this discussion considers only Eqs. (4.71) and (4.72). Since this set of equations is linear in each of the driving-noise terms, the principal of superposition can be applied.</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">Let <img src="06145027d4559b85e7ffda2c204fa512.gif" border="0" alt="C0120-01.GIF" width="317" height="36" />, and <img src="2b0d9b5fe0748c8162c807de950cc8d7.gif" border="0" alt="C0120-02.GIF" width="125" height="33" />, where <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>q</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">, and <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>r</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> denote the number of independent error or noise terms in the matrices M(0), Q, and R. For simplicity of notation, let each of these matrices be diagonal. The design equations (4.54)(4.57) are first simulated once, with all noise sources turned on, to determine the gain sequence K(<i>k</i>). This gain sequence must be saved and used in each of the subsequent component simulations of the error-budget analysis. The components of P that are of interest should be saved at the corresponding times of interest, for later analysis. For the subsequent <i>l =l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font><font face="Times New Roman, Times, Serif" size="3"> + l</font><font face="Times New Roman, Times, Serif" size="1"><sub>q</sub></font><font face="Times New Roman, Times, Serif" size="3"> + l</font><font face="Times New Roman, Times, Serif" size="1"><sub>r</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> simulations of Eqs. (4.71) and (4.72), the gain vector sequence is considered as given.</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">For each independent component of M(0) (i.e., <i>l</i> = 1,聽.聽.聽.聽, <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">), we calculate</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="3f7cc33273d9f93a6aae55702789982f.gif" border="0" alt="0120-01.GIF" width="352" height="19" /></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="ee48703d65de3297d55c95d99126c5a1.gif" border="0" alt="0120-02.GIF" width="313" 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"></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 M</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>l</i></sub></font><font face="Times New Roman, Times, Serif" size="3">(0) is the <i>l</i>th independent component of M(0), as previously defined. This set of simulations produces the error covariance due to each independent source of initial condition uncertainty in the absence of process and measurement noise.</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">For each independent component of Q</font><font face="Times New Roman, Times, Serif" size="1"><sub>d</sub></font><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> [i.e., <i>l</i> = (<i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + 1),聽.聽.聽.聽, (<i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>q</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">)], we calculate</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="d77f749d5041e0fab83e3b9f18babbd3.gif" border="0" alt="0120-03.GIF" width="353" height="19" /></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="b336b4ffb3632fc04720e4dfcd7b270f.gif" border="0" alt="0120-04.GIF" width="312" 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"></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 M</font><font face="Times New Roman, Times, Serif" size="1"><sub><i>l</i></sub></font><font face="Times New Roman, Times, Serif" size="3">(0) is a zero matrix and Q</font><font face="Times New Roman, Times, Serif" size="1"><sub>d</sub></font><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> is the discrete-time equivalent of Q</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">, where <i>i</i> = <i>l</i> - <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">. This set of simulations produces the error covariance due to each independent source of process driving noise in the absence of initial condition errors and measurement noise.</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">For each independent component of R [i.e., <i>l</i> = (<i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>q</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + 1),聽.聽.聽.聽, (<i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>m</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>q</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3"> + <i>l</i></font><i><font face="Times New Roman, Times, Serif" size="1"><sub>r</sub></font></i><font face="Times New Roman, Times, Serif" size="1"><sub></sub></font><font face="Times New Roman, Times, Serif" size="3">)], we calculate</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><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="efd1410d8edca7974fa8a860875b13e4.gif" border="0" alt="0120-05.GIF" width="383" height="19" /></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="a5fe0bf60b91fb6838482fb2c85c5fe0.gif" border="0" alt="0120-06.GIF" width="344" height="20" /></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_119.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_120</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_121.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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