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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_7</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_6.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_7</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_8.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 7</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">Applying Taylor's theorem to the function on the right-hand side of Eq. (1.4) and dropping all error terms greater than first order yields</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="3d2e3bc463cb229878198ce7d0ae469e.gif" border="0" alt="0007-01.GIF" width="480" height="40" /></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="87501aced13176a498e7bfdc4a291383.gif" border="0" alt="0007-02.GIF" width="419" height="96" /></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">Differencing Eqs. (1.1) and (1.6) results in the linear differential equations for the error variables <img src="4ca040a7b4652077995ba55849df5d53.gif" border="0" alt="C0007-01.GIF" width="65" height="13" /> and <img src="647076493ee08e325a1936333e5924c9.gif" border="0" alt="C0007-02.GIF" width="61" height="13" />:</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="343c6f6bcad5d19221380621f224555e.gif" border="0" alt="0007-03.GIF" width="451" height="106" /></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">Linear error differential equations such as Eq. (1.7) are very useful for analysis. For example, because of the single integration in the error differential equations, a constant value for any of the sensing errors under consideration results in a linear growth in position error. For the heading bias and speed scale-factor errors, the rate of linear error growth is a function of the speed. In addition, as previously stated, initial position errors (</font><font face="Symbol" size="3"><i>d</i></font><i><font face="Times New Roman, Times, Serif" size="3">n</font></i><font face="Times New Roman, Times, Serif" size="3">, </font><font face="Symbol" size="3"><i>d</i></font><i><font face="Times New Roman, Times, Serif" size="3">e</font></i><font face="Times New Roman, Times, Serif" size="3">) result in constant position offsets for all future times. Systematic techniques for error analysis are required for the more complicated navigation systems that result from three-dimensional applications on the round, rotating earth.</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">Note a couple of characteristics of this example. First, errors in position cannot be detected or corrected without additional sensors. In the terminology of systems theory, the position errors are not <i>observable</i> with the given set of sensors. Observability is a critical issue that is defined in Sec. 3.3.6. Second, error analysis, as exemplified above, is only as accurate as the assumed form of the system model allows. In particular, any errors that are not modeled cannot be analyzed, even though the unmodeled errors may still exist in the implemented system. Third, the size and the nature of the sensor errors in this example are not easy to characterize, are time variable, and can be affected by events outside the sensor itself. For example, the magnetic heading bias can change because of location, tilt, or externally generated fields. Such factors complicate the error analysis and call into question the robustness of the navigation system. Fourth, the inevitable growth of errors within the navigation system motivates the need for on-line calibration (i.e., error-estimation) methods.</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_6.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_7</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_8.html">next page ></a></td> </tr> </table> </body> </html>⌨️ 快捷键说明
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