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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_247</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_246.html">< previous page</a></td> <td id="ebook_previous" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_247</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_248.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 247</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="b131714adaf3d646b38c8d5dd9d5fa39.gif" border="0" alt="0247-01.GIF" width="191" height="49" /></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">Figure聽7.1<br />Direct聽GPS聽INS聽integration.</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">of the stand-alone GPS solution were outlined. An additional drawback is the tradeoff between the system bandwidth or response time and the amount of filtering achieved.</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 vehicle accelerates, the GPS-only solution cannot begin to reflect the acceleration until at least the next GPS measurement cycle. Because the Kalman filter weights this next GPS measurement relative to the accuracy of the current state of the filter, as dictated by the error covariance matrices, the filter state is not immediately set equal to the state corresponding to the measurement, but slowly converes to it. The rate of convergence is determined by the accuracy of the state estimate P relative to the measurement R. A higher rate of convergence will normally imply noisier state estimates.</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">To achieve a more responsive estimate of the vehicle state without sacrificing filter performance in steady-state conditions, the system can be augmented with inertial sensors. A direct extension of the approach of Sec. 7.1 would input the inertial measurements (f, </font><font face="Symbol" size="3"><i>w</i></font><font face="Symbol" size="3"></font><font face="Times New Roman, Times, Serif" size="3">) and the GPS data into the Kalman filter, as shown in Fig. 7.1. The Kalman filter model would correspond to the PVA model augmented with states to represent attitude, angular rates, and accelerometer and gyro errors. The Kalman filter would incorporate information from the accelerometers and gyros at high rates and information from GPS measurements at lower rates. The navigation state would be propagated between measurement instants according to the navigation mechanization equations.</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">There are three major drawbacks of this direct-filtering approach. First, the Kalman filter covariance propagation equations would have to be iterated at the high rate of the inertial measurements. The covariance propagation equations are very computationally intensive. This would severely limit the rate at which the inertial measurements could be incorporated. Second, the measurements driving the filter and the filter states have significant deterministic components that have to be represented by ad hoc models in the filter design. Consider the acceleration state of the PVA model. It is modeled as a GaussMarkov process with parameter </font><font face="Symbol" size="3"><i>b</i></font><font face="Times New Roman, Times, Serif" size="3"> = (1/</font><font face="Symbol" size="3"><i>t</i></font><font face="Times New Roman, Times, Serif" size="3">). This parameter reflects the correlation time of the vehicle acceleration. This parameter is not known and is actually time varying. Third, the filter must have high bandwidth, since it is estimating the total navigation state, which may change rapidly.</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 alternative complementary-filter approach [21], the inertial measurements and the INS mechanization equations are processed as a separate system, which provides a reference trajectory to the Kalman filter. Special algorithms, as discussed in the appropriate subsections of this text, are designed to achieve high accuracy and efficient computation at high iteration rates. At</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_246.html">< previous page</a></td> <td id="ebook_next" align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_247</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_248.html">next page ></a></td> </tr> </table> </body> </html>
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