误差理论与测量平差基础

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1、误差理论与测量平差基础实习报告王驩裕1420501201420050135东华理工大学测绘学院测量系水准网间接平差function V,ZL,SIGMA1,SIGMA2,SIGMA3=math(B,s,l,L,r)P=diag(1./s);NBB=B*P*B;W=B*P*l;x=inv(NBB)*W;V=B*x-l;ZL=L+V;SIGMA=sqrt(V*P*V/r);E=inv(NBB);SIGMA1=SIGMA*sqrt(E(1);SIGMA2=SIGMA*sqrt(E(2,2);D=B*E*B;SIGMA3=SIGMA*sqrt(D(5,5);end导线网间接平差1. 按间接平差法完成一

2、导线网的平差计算。function ZX,v,J,H=nc(s,X,l,beta)L=dms2degrees(beta);alpha0=dms2degrees(226 44 59);alpha1=alpha0+L(1)-180;alpha2=alpha1+L(2)-180;alpha3=alpha2+L(3)-180;alpha4=alpha3+L(4)-180;alpha=alpha1;alpha2;alpha3;e=alpha;c=180*3600*sind(e)/(pi*100);d=-180*3600*cosd(e)/(pi*100);a=c./s;b=d./s;f=cosd(e);g

3、=sind(e);B=a(1) b(1) 0 0;a(2) b(2) -a(1) -b(1); a(3) b(3) -a(2) -b(2);0 0 -a(3) -b(3); f(1) g(1) 0 0;-f(1) -g(1) f(2) g(2);0 0 -f(3) -g(3);P1=diag(1 1 1 1);SIGMA0=5;SIGMAS=0.5*sqrt(s);D=1./SIGMAS;T=(SIGMA0*D).2;P2=diag(T);P=blkdiag(P1,P2);NBB=B*P*B;W=B*P*l;x=inv(NBB)*W;ZX=X+x;v=B*x-l;ZL=L;s+v/3600;J

4、=degrees2dms(ZL(1:4,:);H=ZL(5:7,:);end2.求各导线点的坐标平差值极其点位中误差。function ZX,SIGMA1,SIGMA2,SIGMA3,SIGMA4,SIGMA5=pa(B,S,l,X)P1=eye(10);P2=diag(100000./S);P=blkdiag(P1,P2);NBB=B*P*B;W=B*P*l;x=inv(NBB)*W;ZX=X+x;E=inv(NBB);V=B*x-l;SIGMA0=sqrt(V*P*V/7);G=diag(E);SIGMA1=SIGMA0*sqrt(G(1)+G(2);SIGMA2=SIGMA0*sqrt(

5、G(3)+G(4);SIGMA3=SIGMA0*sqrt(G(5)+G(6);SIGMA4=SIGMA0*sqrt(G(7)+G(8);SIGMA5=SIGMA0*sqrt(G(9)+G(10);end三角网的间接平差function ZX,SIGMA1,SIGMA2=CH(B,l,X)P=eye(18);NBB=B*P*B;W=B*P*l;x=inv(NBB)*W;ZX=X+x;Q=inv(NBB);E=diag(Q);V=B*x-l;SIGMA0=sqrt(V*P*V/12);SIGMA1=SIGMA0*sqrt(E(1)+E(2);SIGMA2=SIGMA0*sqrt(E(3)+E(4)

6、;end测量平差软件的使用 1. TXT导入控 制 网 平 差 报 告控制网概况计算软件：南方平差易2005网名：bjw3计算日期：1970-01-01观测人：SOUTH记录人：计算者：SOUTH检查者：测量单位：SOUTH SURVEY备注：BJW平面控制网等级：城市二级，验前单位权中误差：2.50(s)已知坐标点个数：2未知坐标点个数：3未知边数：8最大点位误差5 = 0.0080 (m)最小点位误差3 = 0.0045 (m)平均点位误差 = 0.0066 (m)最大点间误差 = 0.0114(m)最大边长比例误差 = 693250平面网验后单位权中误差 = 0.57 (s)边长统计总边

7、长：24226.019(m),平均边长：3028.252(m),最小边长：2115.919(m),最大边长：4363.611(m)闭合差统计报告序号:中点多边形路径：极条件闭合差=0.9,限差=5.3序号:大地四边形序号:闭合导线路径:2-3-4-1极条件闭合差=1.4,限差=6.8路径：2-3-1角度闭合差=0.30(s),限差=12.99(s)fx=-0.002(m),fy=-0.006(m),fd=0.007(m)总边长s=4415.979(m),全长相对闭合差k=1/669040,平均边长=1471.993(m)序号:闭合导线路径：2-4-1角度闭合差=2.10(s),限差=12.99

8、(s)fx=-0.029(m),fy=-0.007(m),fd=0.030(m)总边长s=7453.964(m),全长相对闭合差k=1/249836,平均边长=2484.655(m)序号:闭合导线路径：3-4-1角度闭合差=1.60(s),限差=12.99(s)fx=-0.011(m),fy=0.015(m),fd=0.018(m)总边长s=8011.322(m),全长相对闭合差k=1/445509,平均边长=2670.441(m)序号:闭合导线路径：3-5-2角度闭合差=-1.71(s),限差=12.99(s)fx=-0.013(m),fy=0.014(m),fd=0.019(m)总边长s=

9、7928.226(m),全长相对闭合差k=1/425564,平均边长=2642.742(m)序号:闭合导线路径：4-5-2角度闭合差=-0.60(s),限差=12.99(s)fx=0.000(m),fy=0.022(m),fd=0.022(m)总边长s=11929.705(m),全长相对闭合差k=1/548892,平均边长=3976.568(m)起算点数据表点名X(m)Y(m)H(m)备注131250.250011500.4100233256.570010900.8400方向观测成果表测站照准方向值(dms)改正数(s)平差后值(dms)备注120.000000357.203210-0.105

10、7.2032004113.1406351.70113.140805250.000000332.1222920.1332.122305457.501530-0.4457.501486198.2612730.8398.261356310.000000256.253779-0.3156.2537485172.5339440.55172.5339994282.295383-0.18282.295365410.000000226.095412-0.8726.095325346.361798-0.3846.361760577.5946710.0677.594677540.000000339.001779-

11、0.6239.001717270.1951510.1170.195162距离观测成果表测站照准距离(m)改正数(m)平差后值(m)方位角(dms)132300.06000.00112300.061140.421418143090.35300.00333090.356396.355023253643.2340-0.01023643.223864.552862232115.91900.00392115.922997.075166244363.6110-0.00814363.6029122.454348352169.07300.00342169.076433.355417342620.9090-0.

12、00032620.9087143.120783453922.8600-0.00193922.8581354.353700点名长轴(m)短轴(m)长轴方位(dms)点位中误差(m)备注30.00380.0025161.0149440.004540.00660.003324.2748780.007450.00720.0036140.0635520.0080 平面点位误差表平面点间误差表点名点名长轴MT(m)短轴MD(m)D/MD长轴方位T(dms)平距D(m)备注130.00450.0029805056161.0149442300.0611140.00740.003783302824.274878

13、3090.3563250.00800.0039932724140.0635523643.2238230.00450.0028764259161.0149442115.9229240.00740.0034129591024.2748784363.6029350.00450.0029805056161.0149442169.0764340.00450.0028764259161.0149442620.9087450.00610.0031693250165.5934563922.8581控制点成果表点名X(m)Y(m)H(m)备注131250.250011500.4100已知点233256.5700

14、10900.8400已知点332993.902113000.3960430895.198714570.3026534800.605914200.69352.直接输入方向改化概算成果表测站 照准 角度(dms) 改正数(s) 改正后角度(m)-A A 0.000000 0.00 0.000000 A A 85.302110 -0.48 85.302062 C C 0.000000 0.00 0.000000 C C 244.183000 -2.87 244.182713 2 2 0.000000 0.00 0.000000 2 2 254.323220 -0.69 254.323151 3 3

15、0.000000 0.00 0.000000 3 3 131.043330 -1.52 131.043178 4 4 0.000000 0.00 0.000000 4 4 272.202020 -2.54 272.201766 边长改化概算成果表测站 照准 边长(m) 改正数(m) 改正后边长(m)-A B 1000.0000 3.0112 1003.0112 A 2 1474.4440 4.4319 1478.8759 C D 1000.0000 2.9698 1002.9698 2 3 1424.7170 4.2682 1428.9852 3 4 1749.3220 5.2123 1754

16、.5343 4 C 1950.4120 5.7869 1956.1989 边长气象改正成果表测站 照准 边长(m) 改正数(m) 改正后边长(m)-A B 1003.0112 0.2758 1003.2871 A 2 1478.8759 0.4067 1479.2826 C D 1002.9698 0.2758 1003.2456 2 3 1428.9852 0.3930 1429.3782 3 4 1754.5343 0.4825 1755.0169 4 C 1956.1989 0.5380 1956.7368闭合差统计表=序号:几何条件:附合导线路径:D-C-4-3-2-A-B角度闭合差=3.90(s),限差=11.18(s)fx=0.014(m),fy=0.054(m),fd=0.056(m)总边长s=6598.895(m),全长相对闭合差k=1/118203,平均边长=1649.724(m)=