[转帖]投影坐标转换

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<P >摘自武测毕业论文（赖增先）——我也是从网上弄来，转载时请务必保留此此信息。</P>
<P  align=center><FONT face="Times New Roman">第二节 平面坐标基准转换<p></p></FONT></P>
<P >由于海上和陆地上在测量时，使用不同的坐标系和不同参考椭球，而且采用的投影也不同，使得我们获得的数据不统一，必须进行坐标转换。<p></p></P>
<P  align=center><FONT face="Times New Roman">§3·2·1 欧拉角<p></p></FONT></P>
<P >设有两个空间直角坐标系，分别为<FONT face="Times New Roman">O-XYZ</FONT>和<FONT face="Times New Roman">O-X</FONT><v:shapetype><FONT face="Times New Roman"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></FONT></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>，为了便于讨论其相应坐标轴间的变换，设其原点相同如图所示，选择<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>为欧拉角，又称旋转参数，经过三次旋转，使两个坐标系重合，既：（图见下页<FONT face="Times New Roman">A</FONT>）<p></p></P>
<P >首先，绕<FONT face="Times New Roman">O Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴，将<FONT face="Times New Roman">O X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴旋转到<FONT face="Times New Roman">OX</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>轴，所转的角为<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>；<p></p></P>
<P >其次，绕<FONT face="Times New Roman">OY</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴，将<FONT face="Times New Roman">O Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴旋转到<FONT face="Times New Roman">OZ</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴，所转的角为<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>；<p></p></P>
<P >最后，绕<FONT face="Times New Roman">OX</FONT>轴，将<FONT face="Times New Roman">O Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>轴旋转到<FONT face="Times New Roman">OZ</FONT>轴，所转的角为<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>；<p></p></P>
<P ><v:line><v:stroke endarrow="block"></v:stroke></v:line><FONT face="Times New Roman">                            Z<p></p></FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                             Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">   Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                        <p></p></FONT></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">       X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">             O <p></p></FONT></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">             X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><p></p></P>
<P ><FONT face="Times New Roman">          X                   Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">  Y<p></p></FONT></P>
<P ><FONT face="Times New Roman">                 <p></p></FONT></P>
<P ><v:shapetype><v:formulas><v:f eqn="val #2"></v:f><v:f eqn="val #3"></v:f><v:f eqn="val #4"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" extrusionok="f" connectlocs="0,0;21600,21600;0,21600" arrowok="t"></v:path><v:handles><v:h polar="@0,@1" position="@2,#0"></v:h><v:h polar="@0,@1" position="@2,#1"></v:h></v:handles></v:shapetype><v:shape><FONT face="Times New Roman"></FONT></v:shape><FONT face="Times New Roman">                                  Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman"> <p></p></FONT></P>
<P ><FONT face="Times New Roman">                   </FONT>图<FONT face="Times New Roman">A <p></p></FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P >因此有<FONT face="Times New Roman">   <p></p></FONT></P>
<P ><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="0,0;0,21600;21600,10800" arrowok="t" textboxrect="0,@2,15274,@3"></v:path><v:handles><v:h position="bottomRight,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="21600,0;0,10800;21600,21600" arrowok="t" textboxrect="6326,@2,21600,@3"></v:path><v:handles><v:h position="topLeft,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:shape><FONT face="Times New Roman"></FONT></v:shape><FONT face="Times New Roman">        X                                   X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman"> <p></p></FONT></P>
<P ><FONT face="Times New Roman">        Y    = R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>）<FONT face="Times New Roman">R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>）<FONT face="Times New Roman">R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>）<FONT face="Times New Roman">  Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><FONT face="Times New Roman">        Z                                   Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P >式中<FONT face="Times New Roman"> R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>）、<FONT face="Times New Roman">R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>）、<FONT face="Times New Roman">R</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>（<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>）为旋转矩阵，其表达式在<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>很小时可以最终表示为：<p></p></P>
<P ><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><FONT face="Times New Roman">        X         1       </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">      </FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">        X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><FONT face="Times New Roman">        Y    =   -</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">       1      </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">        Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">         </FONT>公式<FONT face="Times New Roman">1<p></p></FONT></P>
<P ><FONT face="Times New Roman">        Z         </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">     - </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">     1         Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P  align=center><FONT face="Times New Roman">§3·2·2 不同三维空间直角坐标系的变换模型<p></p></FONT></P>
<P >GPS测量的WGS—84属地心坐标系，而1980年国家大地坐标系和1954年北京坐标系属参心坐标系，他们所对应得空间直角坐标系是不同的，这里将讨论不同空间直角坐标系的变换模型。<p></p></P>
<P >如图B两个空间直角坐标系分别为<FONT face="Times New Roman">O-XYZ</FONT>和<FONT face="Times New Roman">O</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">-X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>，其坐标系原点不同则存在三个平移参数<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>，他们表示<FONT face="Times New Roman">O</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">- X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>坐标系原点<FONT face="Times New Roman">O</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>相对于<FONT face="Times New Roman">O-XYZ</FONT>坐标系原点<FONT face="Times New Roman">O</FONT>在三个坐标轴上的分量；又当各坐标轴相互不平行时，既存在三个旋转参数<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>。<FONT face="Times New Roman">                     Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="val #1"></v:f><v:f eqn="val #2"></v:f><v:f eqn="sum #0 width #1"></v:f><v:f eqn="prod @3 1 2"></v:f><v:f eqn="sum #1 #1 width"></v:f><v:f eqn="sum @5 #1 #0"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="mid width #0"></v:f><v:f eqn="ellipse #2 height @4"></v:f><v:f eqn="sum @4 @9 0"></v:f><v:f eqn="sum @10 #1 width"></v:f><v:f eqn="sum @7 @9 0"></v:f><v:f eqn="sum @11 width #0"></v:f><v:f eqn="sum @5 0 #0"></v:f><v:f eqn="prod @14 1 2"></v:f><v:f eqn="mid @4 @7"></v:f><v:f eqn="sum #0 #1 width"></v:f><v:f eqn="prod @17 1 2"></v:f><v:f eqn="sum @16 0 @18"></v:f><v:f eqn="val width"></v:f><v:f eqn="val height"></v:f><v:f eqn="sum 0 0 height"></v:f><v:f eqn="sum @16 0 @4"></v:f><v:f eqn="ellipse @23 @4 height"></v:f><v:f eqn="sum @8 128 0"></v:f><v:f eqn="prod @5 1 2"></v:f><v:f eqn="sum @5 0 128"></v:f><v:f eqn="sum #0 @16 @11"></v:f><v:f eqn="sum width 0 #0"></v:f><v:f eqn="prod @29 1 2"></v:f><v:f eqn="prod height height 1"></v:f><v:f eqn="prod #2 #2 1"></v:f><v:f eqn="sum @31 0 @32"></v:f><v:f eqn="sqrt @33"></v:f><v:f eqn="sum @34 height 0"></v:f><v:f eqn="prod width height @35"></v:f><v:f eqn="sum @36 64 0"></v:f><v:f eqn="prod #0 1 2"></v:f><v:f eqn="ellipse @30 @38 height"></v:f><v:f eqn="sum @39 0 64"></v:f><v:f eqn="prod @4 1 2"></v:f><v:f eqn="sum #1 0 @41"></v:f><v:f eqn="prod height 4390 32768"></v:f><v:f eqn="prod height 28378 32768"></v:f></v:formulas><v:path connecttype="custom" extrusionok="f" connectlocs="@8,0;@11,@2;@15,0;@16,@21;@13,@2" textboxrect="@41,@43,@42,@44" connectangles="270,270,270,90,0"></v:path><v:handles><v:h position="#0,topLeft" xrange="@37,@27"></v:h><v:h position="#1,topLeft" xrange="@25,@20"></v:h><v:h position="bottomRight,#2" yrange="0,@40"></v:h></v:handles><complex v:ext="view"></complex></v:shapetype><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                       Z<p></p></FONT></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                                  O</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman"> <p></p></FONT></P>
<P ><v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="val #1"></v:f><v:f eqn="val #2"></v:f><v:f eqn="sum #0 width #1"></v:f><v:f eqn="prod @3 1 2"></v:f><v:f eqn="sum #1 #1 width"></v:f><v:f eqn="sum @5 #1 #0"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="mid width #0"></v:f><v:f eqn="sum height 0 #2"></v:f><v:f eqn="ellipse @9 height @4"></v:f><v:f eqn="sum @4 @10 0"></v:f><v:f eqn="sum @11 #1 width"></v:f><v:f eqn="sum @7 @10 0"></v:f><v:f eqn="sum @12 width #0"></v:f><v:f eqn="sum @5 0 #0"></v:f><v:f eqn="prod @15 1 2"></v:f><v:f eqn="mid @4 @7"></v:f><v:f eqn="sum #0 #1 width"></v:f><v:f eqn="prod @18 1 2"></v:f><v:f eqn="sum @17 0 @19"></v:f><v:f eqn="val width"></v:f><v:f eqn="val height"></v:f><v:f eqn="prod height 2 1"></v:f><v:f eqn="sum @17 0 @4"></v:f><v:f eqn="ellipse @24 @4 height"></v:f><v:f eqn="sum height 0 @25"></v:f><v:f eqn="sum @8 128 0"></v:f><v:f eqn="prod @5 1 2"></v:f><v:f eqn="sum @5 0 128"></v:f><v:f eqn="sum #0 @17 @12"></v:f><v:f eqn="ellipse @20 @4 height"></v:f><v:f eqn="sum width 0 #0"></v:f><v:f eqn="prod @32 1 2"></v:f><v:f eqn="prod height height 1"></v:f><v:f eqn="prod @9 @9 1"></v:f><v:f eqn="sum @34 0 @35"></v:f><v:f eqn="sqrt @36"></v:f><v:f eqn="sum @37 height 0"></v:f><v:f eqn="prod width height @38"></v:f><v:f eqn="sum @39 64 0"></v:f><v:f eqn="prod #0 1 2"></v:f><v:f eqn="ellipse @33 @41 height"></v:f><v:f eqn="sum height 0 @42"></v:f><v:f eqn="sum @43 64 0"></v:f><v:f eqn="prod @4 1 2"></v:f><v:f eqn="sum #1 0 @45"></v:f><v:f eqn="prod height 4390 32768"></v:f><v:f eqn="prod height 28378 32768"></v:f></v:formulas><v:path connecttype="custom" extrusionok="f" connectlocs="0,@17;@2,@14;@22,@8;@2,@12;@22,@16" textboxrect="@47,@45,@48,@46" connectangles="180,90,0,0,0"></v:path><v:handles><v:h position="bottomRight,#0" yrange="@40,@29"></v:h><v:h position="bottomRight,#1" yrange="@27,@21"></v:h><v:h position="#2,bottomRight" xrange="@44,@22"></v:h></v:handles><complex v:ext="view"></complex></v:shapetype><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                          X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman"> <p></p></FONT></P>
<P ><v:shape><FONT face="Times New Roman"></FONT></v:shape><FONT face="Times New Roman">                                 <p></p></FONT></P>
<P ><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><v:line><v:stroke endarrow="block"><FONT face="Times New Roman"></FONT></v:stroke></v:line><FONT face="Times New Roman">                    O                 Y      <p></p></FONT></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P >            X                                                                                              <p></p></P>
<P >      考虑到两个坐标系的平移和旋转以及尺度参数可得公式如下：<p></p></P>
<P ><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>       <FONT face="Times New Roman"> X                X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">       1       </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">      </FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">       X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><FONT face="Times New Roman">        Y    =</FONT>（<FONT face="Times New Roman">1+m</FONT>）<FONT face="Times New Roman">   Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">      -</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">      1       </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">       Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">         <p></p></FONT></P>
<P ><FONT face="Times New Roman">        Z                Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">       </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">     - </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">     1         Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:shape><FONT face="Times New Roman"></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P ><FONT face="Times New Roman">+    </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">         </FONT>公式一<p></p></P>
<P ><FONT face="Times New Roman">      </FONT><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P>
<P >式中共有七个变换参数<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>、<FONT face="Times New Roman">m,</FONT>简称此公式为布尔莎七参数变换公式，是坐标变换中一个非常重要的公式。七参数变换公式，除了布尔莎公式外，还有莫洛琴斯基公式和范氏公式。这三种公式，它们之间的七个参数相差很大，但各自构成完整的数学模型，参数间存在着明确的解析关系，可以相互间转换。分别用它们来换算点的坐标时，其结果是完全相同的。因此，这三个公式是等价的。我国的地心坐标变换参数地心二号是七个变换参数，既采用布尔莎公式。<p></p></P>
<P >当公式一中<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><v:shape><v:imagedata><FONT face="Times New Roman"></FONT></v:imagedata></v:shape><FONT face="Times New Roman">=</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">=</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">=m=0,</FONT>既称之为三参数公式。三参数公式表明两个空间直角坐标系尺度一致，且两个坐标轴相互平行。我国地心坐标变换参数地心一号系三个变换参数。同理在公式一中，略去某些参数，可分别得到四参数、五参数、六参数等坐标变换参数。公式一中的变换参数，一般利用公共点上的两套空间直角坐标系坐标值（<FONT face="Times New Roman">X</FONT>，<FONT face="Times New Roman">Y</FONT>，<FONT face="Times New Roman">Z</FONT>）<v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman"> </FONT>和<FONT face="Times New Roman">(X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">,Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">, Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">)</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape>即可采用最小二乘法解得。<p></p></P>
<P >应该指出，当进行两种不同空间直角坐标系变换时，坐标变换的精度除取决于坐标变换的数学模型和求解变换参数的公共点坐标精度外，还和公共点的多少、几何形状结构有关。鉴于地面网可能存在一定的系统误差，且在不同区域并非完全一样，所以采用分区变换参数，分区进行坐标转换，可以提高坐标变换精度。无论是从我国的多普勒网还是<FONT face="Times New Roman">GPS</FONT>网，利用布尔莎公式求解和地面大地网间得变换参数，分区变换均较明显地提高了坐标变换的精度。<p></p></P>
<P ><p><FONT face="Times New Roman"> </FONT></p></P>
<P ></FONT></P>

<P 0cm 0cm 0pt; TEXT-INDENT: 30pt; TEXT-ALIGN: center" align=center><FONT face="Times New Roman">§3·2·3 不同三维大地坐标系的变换模型<p></p></FONT></P><P 0cm 0cm 0pt; TEXT-INDENT: 30pt">对于不同的三维大地坐标系的变换模型，除了上节的七个变换参数外，还应增加两个变换参数，，这就是两个大地坐标系所对应的地球椭球参数的不同。不同大地坐标的变换公式，又称大地坐标微分公式或变换椭球微分公式。当包括旋转参数和尺度参数时，称为广义大地坐标微分公式或广义变换椭球微分公式。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 30pt">空间一点的空间直角坐标与大地坐标关系式是：<p></p></P><P 0cm 0cm 0pt"><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="0,0;0,21600;21600,10800" arrowok="t" textboxrect="0,@2,15274,@3"></v:path><v:handles><v:h position="bottomRight,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape></v:shape><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="21600,0;0,10800;21600,21600" arrowok="t" textboxrect="6326,@2,21600,@3"></v:path><v:handles><v:h position="topLeft,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>         X       (N+H)cosBcosL  <p></p></P><P 0cm 0cm 0pt">         <p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 48pt"> Y   =   (N+H)cosBsinL           公式二<p></p></P><P 0cm 0cm 0pt">         Z       [N (1-e<v:shapetype> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape>)+H]sinB           <p></p></P><P 0cm 0cm 0pt">式中N为卯酉圈曲率半径。在这个公式中当已知L，B，H时，求X，Y，Z是非常简单的，只要代入公式即可。当已知X，Y，Z时反求L，B，H则可以采用直接解或迭代解法，解算时对公式做些变化即可。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">由公式二最终我们可以得到不同三维大地坐标系的变换公式；<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">      <v:shape><v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm 0cm 0pt"><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>    dL       -<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>   <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>   0           <v:shape><v:imagedata></v:imagedata></v:shape><FONT face="Times New Roman">X</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P><P 0cm 0cm 0pt">    dB   =   -<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>      -<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>     <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>   <v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">Y</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><FONT face="Times New Roman">   +</FONT><p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt"><p> </p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">dH       cosBcosL           cosBsinL          sinB        <v:shape><v:imagedata></v:imagedata></v:shape><FONT face="Times New Roman">Z</FONT><v:shape><FONT face="Times New Roman"> <v:imagedata></v:imagedata></FONT></v:shape><p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt"><p> </p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt"><p> </p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt"><p> </p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt"><p> </p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt"><p> </p></P><P 0cm 0cm 0pt"><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>       <v:shape><v:imagedata></v:imagedata></v:shape>       -1      <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm 0cm 0pt">-<v:shape> <v:imagedata></v:imagedata></v:shape>    <v:shape><v:imagedata></v:imagedata></v:shape>   0       <v:shape><v:imagedata></v:imagedata></v:shape><FONT face="Times New Roman">    +</FONT><p></p></P><P 0cm 0cm 0pt">-<v:shape> <v:imagedata></v:imagedata></v:shape>         <v:shape><v:imagedata></v:imagedata></v:shape>        0       <v:shape><v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 42pt"><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>0                            0                       <p></p></P><P 0cm 0cm 0pt">-<v:shape> <v:imagedata></v:imagedata></v:shape>   m+   <v:shape><v:imagedata></v:imagedata></v:shape>  <p></p></P><P 0cm 0cm 0pt">N+H-Ne<v:shape> <v:imagedata></v:imagedata></v:shape>sin<v:shape> <v:imagedata></v:imagedata></v:shape>            -<v:shape> <v:imagedata></v:imagedata></v:shape>      <p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 42pt"><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>0                  da<p></p></P><P 0cm 0cm 0pt"><v:shape><v:imagedata></v:imagedata></v:shape>               公式三<p></p></P><P 0cm 0cm 0pt"><v:shape><v:imagedata></v:imagedata></v:shape>       df   <p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 27.75pt">式中dL、dB以弧度秒为单位，等式右端L、B、H均以换算前坐标值代入。公式三也就是顾及七个参数和椭球大小变化的广义大地坐标微分公式或广义变换椭球微分公式。略去旋转参数和尺度变化参数的影响，即为一般的大地坐标微分公式或椭球微分公式。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 27.75pt">利用一些公共点上两套大地坐标系坐标值，采用最小二乘法可解得变换参数。<p></p></P>

<P 0cm 0cm 0pt; TEXT-INDENT: 27.75pt"><FONT face="Times New Roman">§3·2·4 不同两维大地坐标系的变换模型 <p></p></FONT></P><P 0cm 0cm 0pt"><FONT face="Times New Roman">   </FONT>在三维不同大地坐标系的变换模型中，当进行WGS—84和我国参心大地坐标系的变换时，由于后者大地高的精度不高（一般在<st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="False" SourceValue="3" UnitName="m">3m</st1:chmetcnv>左右的误差），加之又难以确定其方差和协方差，因此，也可以考虑选择二维大地坐标系的变换模型。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">所谓二维大地坐标系，即当大地高H为零时的椭球面上的大地坐标系。其变换模型，只要在公式三中，将H=0代入即可得到。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">将此公式用于GPS网和地面网联合平差时，如果顾及地面网的系统性观测误差对网的定向的影响时，则可在椭球面上引入一个附加旋转参数dA,以使两网更好的配合。由于dA产生的对dL、dB的影响加于公式右端。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">为了便于比较GPS网和地面网的大地坐标，若在将GPS网的X、Y、Z反算L、B、H时，采用了地面网的椭球参数，即两网相应的椭球参数已化为一致，则公式中不再有 da、df项。<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt"><FONT face="Times New Roman">§3·2·5 不同二维高斯投影平面坐标系的坐标转换<p></p></FONT></P><P 0cm 0cm 0pt; TEXT-INDENT: 27pt">由高斯投影正算公式可得：<p></p></P><P 0cm 0cm 0pt 27pt; TEXT-INDENT: 36pt"><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="0,0;0,21600;21600,10800" arrowok="t" textboxrect="0,@2,15274,@3"></v:path><v:handles><v:h position="bottomRight,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape></v:shape><v:shapetype><v:formulas><v:f eqn="val #0"></v:f><v:f eqn="sum 21600 0 #0"></v:f><v:f eqn="prod #0 9598 32768"></v:f><v:f eqn="sum 21600 0 @2"></v:f></v:formulas><v:path connecttype="custom" gradientshapeok="t" connectlocs="21600,0;0,10800;21600,21600" arrowok="t" textboxrect="6326,@2,21600,@3"></v:path><v:handles><v:h position="topLeft,#0" yrange="0,10800"></v:h></v:handles></v:shapetype><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>dx         <v:shapetype><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape>     <v:shape> <v:imagedata></v:imagedata></v:shape>      dL<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 60pt">dy    =     <v:shape><v:imagedata></v:imagedata></v:shape>      <v:shape> <v:imagedata></v:imagedata></v:shape>    dB       公式四<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">式中等号右端偏导数由高斯投影正算公式得：<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">      <v:shape><v:imagedata></v:imagedata></v:shape>=NsinBcosBl<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">      <v:shape><v:imagedata></v:imagedata></v:shape>=M[1+<v:shape> <v:imagedata></v:imagedata></v:shape>(1-2sin<v:shape> <v:imagedata></v:imagedata></v:shape> B)l<v:shape> <v:imagedata></v:imagedata></v:shape>]<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">      <v:shape><v:imagedata></v:imagedata></v:shape> =NcosB[1+<v:shape> <v:imagedata></v:imagedata></v:shape>(1-2sin<v:shape> <v:imagedata></v:imagedata></v:shape> B) l<v:shape> <v:imagedata></v:imagedata></v:shape>]       公式五<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">      <v:shape><v:imagedata></v:imagedata></v:shape>=-MsinBl<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">上式中，l=L-L<v:shape> <v:imagedata></v:imagedata></v:shape>, L<v:shape> <v:imagedata></v:imagedata></v:shape>为中央子午线得大地经度，公式五中dB、dL见公式三。对于不同二维高斯投影平面坐标系坐标差的模型，可以由公式三和公式四给出。<p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 30pt; TEXT-ALIGN: center" align=center><FONT face="Times New Roman">§3·2·6     同一参考系统下的高斯直角坐标、              大地坐标、空间直角坐标之间的相互转换<p></p></FONT></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt; TEXT-ALIGN: center" align=center>当运用了§3·2·1～§3·2·5后，我们就可以将一个系统的坐标，转化到另一个系统的对应结果。可以完成对应之间的坐标转化，但是，如果高斯直角坐标、<p></p></P><P 0cm -4.3pt 0pt 0cm">大地坐标、空间直角坐标之间的相互转换就需要用本节的内容。<p></p></P><P 0cm -4.3pt 0pt 0cm">3·2·6·1 高斯直角坐标同大地坐标之间的转化<p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">完成两者之间的转化，要用高斯正、反算方法。这里并不详细介绍，只给出其数学模型： <p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">正算公式：x=X+<v:shape> <v:imagedata></v:imagedata></v:shape>N*t*cos<v:shape> <v:imagedata></v:imagedata></v:shape>B*l<v:shape> <v:imagedata></v:imagedata></v:shape>+<v:shape> <v:imagedata></v:imagedata></v:shape>N*t(5- t<v:shape> <v:imagedata></v:imagedata></v:shape>+9<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>+4<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>)cos<v:shape> <v:imagedata></v:imagedata></v:shape>B*l<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">            +<v:shape> <v:imagedata></v:imagedata></v:shape>N*t(61-58 t<v:shape> <v:imagedata></v:imagedata></v:shape>+ t<v:shape> <v:imagedata></v:imagedata></v:shape>+270 <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>-330 <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>t<v:shape> <v:imagedata></v:imagedata></v:shape>)cos<v:shape> <v:imagedata></v:imagedata></v:shape>* l<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">          y=N*cosB*l+<v:shape> <v:imagedata></v:imagedata></v:shape>N(1-t<v:shape> <v:imagedata></v:imagedata></v:shape>+<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>)cos<v:shape> <v:imagedata></v:imagedata></v:shape>B* l<v:shape> <v:imagedata></v:imagedata></v:shape>+<v:shape> <v:imagedata></v:imagedata></v:shape>N(5-18 t<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 96pt">+ t<v:shape> <v:imagedata></v:imagedata></v:shape>+14<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>-58 <v:shape><v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>t<v:shape> <v:imagedata></v:imagedata></v:shape>)cos<v:shape> <v:imagedata></v:imagedata></v:shape>B*l<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">反算公式：B=B<v:shape> <v:imagedata></v:imagedata></v:shape>-<v:shape> <v:imagedata></v:imagedata></v:shape>-y<v:shape> <v:imagedata></v:imagedata></v:shape>+24<v:shape> <v:imagedata></v:imagedata></v:shape>(5+3t<v:shape> <v:imagedata></v:imagedata></v:shape>+<v:shape> <v:imagedata></v:imagedata></v:shape>-9t<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>)y<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">            -<v:shape> <v:imagedata></v:imagedata></v:shape>(61+90t<v:shape> <v:imagedata></v:imagedata></v:shape>+45t<v:shape> <v:imagedata></v:imagedata></v:shape>)y<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">          l=<v:shape> <v:imagedata></v:imagedata></v:shape>-<v:shape> <v:imagedata></v:imagedata></v:shape>(1+2t<v:shape> <v:imagedata></v:imagedata></v:shape>+<v:shape> <v:imagedata></v:imagedata></v:shape>)y<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">            +<v:shape> <v:imagedata></v:imagedata></v:shape>(5+28t<v:shape> <v:imagedata></v:imagedata></v:shape>+24t<v:shape> <v:imagedata></v:imagedata></v:shape>+6<v:shape> <v:imagedata></v:imagedata></v:shape>+8t<v:shape> <v:imagedata></v:imagedata></v:shape><v:shape><v:imagedata></v:imagedata></v:shape>) y<v:shape> <v:imagedata></v:imagedata></v:shape><p></p></P><P 0cm -4.3pt 0pt 0cm; TEXT-INDENT: 24pt">通过高斯正、反算，可以将高斯直角坐标化算为大地坐标，或将大地坐标化算为高斯直角坐标。<p></p></P><P 0cm -4.3pt 0pt 0cm">3·2·6·2 大地坐标同空间直角坐标的化算<p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">空间一点的空间直角坐标与大地坐标关系式是：<p></p></P><P 0cm 0cm 0pt"><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape><v:shape></v:shape>         X       (N+H)cosBcosL  <p></p></P><P 0cm 0cm 0pt">         <p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 48pt"> Y   =   (N+H)cosBsinL          <p></p></P><P 0cm 0cm 0pt">         Z       [N (1-e<v:shape> <v:imagedata></v:imagedata></v:shape>)+H]sinB           <p></p></P><P 0cm 0cm 0pt">式中N为卯酉圈曲率半径。在这个公式中当已知L，B，H时，求X，Y，Z是非常简单的，只要待入公式即可。当已知X，Y，Z时反求L，B，H则可以采用直接解或迭代解法，解算时对公式做些变化即可。<p></p></P><P 0cm 0cm 0pt">3·2·6·3高斯直角坐标与空间直角坐标的相互转换 <p></p></P><P 0cm 0cm 0pt; TEXT-INDENT: 24pt">关于这两者的转换关系并没有直接给出，但是，我们可以利用两者同大地坐标的转换关系，先把其中的一种化算成大地坐标，然后再由大地坐标转换成另一种坐标。<p></p></P>

<P 0cm 0cm 0pt; TEXT-INDENT: 24pt; TEXT-ALIGN: center" align=center><FONT face="Times New Roman">§3·2·7 不同投影之间的转换<p></p></FONT></P><P 0cm 0cm 0pt"><FONT size=3>陆地地形图采用高斯投影系统，而海图采用的是墨卡托投影系统，这使得两种地形图不能拼接。在此以由高斯投影系统转化到墨卡托投影系统，给出转化的思路和过程：<p></p></FONT></P><P 0cm 0cm 0pt"><FONT size=3>首先利用<B normal">布</B><B normal">尔莎七参数变换公式</B>（公式一）将一参考系内的高斯坐标转换为另一参考系内的高斯坐标；再利用<B normal">高斯反算公式，</B>将转换后的高斯直角坐标换算为大地坐标；然后在同一参考系内进行<B normal">墨卡托投影</B>将大地坐标化算为该平面内的平面坐标。这里考虑的是高斯坐标同墨卡托平面坐标不在同一参考椭球上，如果在同一参考椭球内，则第一步化算可以省略。<p></p></FONT></P>

<P>有谁知道BJ54---西安80的转换参数嘛</P>
<P>中央子午线是114</P>
<P>有的话请帮帮忙</P>
<P>谢谢了</P>

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