平差课程设计.docx

1、平差课程设计误差理论与测量平差实习报告班级:滨江2013级测绘工程组别：第一组组长：杜迎，范璐（副）组员：任蔚，单煜，戴展鹏，欧宇杰，于纹鉴，高英杰 本题n=17，有17给误差方程，其中14个角度误差方程，3个边长误差方程，必要观测数t=2*4+6=14,现取定带定点坐标和测站定向角为参数，即X= X3 Y3 X4 Y4 X5 Y5 X6 Y6 Z1 Z2 Z3 Z4 Z5 Z6一求待定点坐标值：1.计算近似坐标 近似坐标通过已知坐标点1 2, 和观测方位角和方向观测值求近似坐标和近似边长。 已知坐标点 X1=121088.500; Y1=259894.000; X2=127990.100;

2、Y2=255874.600; 方向观测值 L1=72+10/60+28.4/3600=72.1746; L2=66+27/60+28.9/3600=66.4580; L3=123+11/60+34.1/3600=123.1928; L4=85+13/60+37.4/3600=85.2271; L5=79+9/60+48.7/3600=79.1635; L6=72+24/60+56.4/3600=72.4157; L7=88+58/60+29.5/3600=88.9749; L8=132+23/60+35.2/3600=132.3931; 边长观测值s1=4451.417; s2=5564.59

3、2;s3=5569.269; 方向角确定 f1=atand(Y2-Y1)/(X2-X1)+360=329.784; f2=f1-L2-180=83.326; f3=f2-L8+180=130.9329; f4=f3-L4=45.7058; f5=f4+180-L6=153.2901; f6=f5+180-L5=254.1266; f7=f6-L7-L3+180=221.9589; 近似坐标求取x4=s2*cos(f2)+X2=128636.8171;y4=s2*sin(f2)+Y2=261401.4835;x6=s1*cos(f4)+x4=131745.4323;y6=s1*sin(f4)+y

4、4=264587.645;x5=s3*cos(f5)+x6=126770.4392;y5=s3*sin(f5)+x6=267090.883;x3=125972.6859y3=264285.4008近似边长s13=sqrt(y3-Y1)2+(x3-X1)2)=6568.0798;s24=sqrt(y4-Y2)2+(x4-X2)2)=5564.5920;s46=sqrt(y6-y4)2+(x6-x4)2)=4451.417;s56=sqrt(y6-y5)2+(x6-x5)2)=5569.269;s35=sqrt(y5-y3)2+(x5-x3)2)=2916.7003;s43=sqrt(y4-y3)

5、2+(x4-x3)2)=3926.13984;s2-s24=0s3-s56=0s1-s46=02.计算方位角改正数系数 (单位:分米）a=206264.8sin(f)/(s*10);b=-206264.8cos(f)/(s*10);a12=-1.2997 a21=1.2997b12=2.232 b21=-2.232a13=2.1 a31=-2.1b13=2.335 b31=-2.335a24=3.682 a42=-3.682b24=0.431 b42=-0.431a34=-3.969 a43=3.969b34=3.442 b43=-3.442a46=3.317 a64=-3.317b46=3.

6、236 b64=-3.236a35=6.802 a53=-6.802b35=1.934 b53=-1.934a56=-1.665 a65=1.665b56=3.308 b65=-3.3083.确定角和边的权设单位权中误差0=1.2，角度观测值的权为Pl=02/l2=1;导线边的权Ps=02/12=0.01 单位：秒平方比上毫米平方1. 常数项边长误差方程的常数项l方向观测值（）近似坐标方位角（）L（）l=LZ()120.0000329.784329.784-0.612372.174641.9589329.784340.612Z1329.78417240.000083.32683.3260.05

7、4166.4580149.778483.32597-0.054Z283.325985310.0000221.9589221.95891.08488.9749310.9329221.95804-2.0165212.167774.1266221.95891.08Z3221.9586460.000045.705845.70580385.2271130.932945.705802217.6202263.32645.70580Z445.70580560.0000333.2901254.1248-3.24379.1635254.1266254.12663.24Z5254.1257640.0000225.7

8、058153.29010572.4157153.2901153.29010Z6153.2901边长误差方程边4-6 V1=-0.698x4-0.7158y4+0.698x6-0.7158y6-l1边2-4 V2=0.116x4+0.993y4-l2边6-5 V3=0.893x6-0.449y6-0.893x6+0.449y6-l3B=0 0 0 0 0 0 0 0 - 1 0 0 0 0 0;-2.1 -2.335 0 0 0 0 0 0 -1 0 0 0 0 0; 0 0 -3.682 -0.431 0 0 0 0 0 -1 0 0 0 0;0 0 0 0 0 0 0 0 0 -1 0 0

9、0 0;-2.1 -2.335 0 0 0 0 0 0 0 0 -1 0 0 0;-3.969 3.442 3.969 -3.442 0 0 0 0 0 0 -1 0 0 0;6.802 1.934 0 0 -6.802 -1.934 0 0 0 0 -1 0 0 0; 0 0 3.317 3.236 0 0 - 3.317 3.236 0 0 0 -1 0 0;3.969 3.442 3.969 -3.442 0 0 0 0 0 0 0 -1 0 0; 0 0 -3.682 -0.431 0 0 0 0 0 0 0 -1 0 0; 0 0 0 0 -1.665 3.308 1.665 3.3

10、08 0 0 0 0 -1 0; 6.802 1.934 0 0 -6.802 -1.934 0 0 0 0 0 0 -1 0; 0 0 3.317 3.236 0 0 -3.317 -3.236 0 0 0 0 0 -1; 0 0 0 0 -1.665 3.308 1.665 -3.308 0 0 0 0 0 -1; 0 0 -0.698 -0.716 0.698 0.716 0 0 0 0 0 0 0 0; 0 0 0.116 0.993 0 0 0 0 0 0 0 0 0 0;0 0 0 0 -0.873 0.449 0.893 -0.449 0 0 0 0 0 0; l=0.612;-

11、0.612;-0.054;0.054;-1.08;2.016;-1.08;0;0;0;3.24;-3.24;0;0;0;0;0 ;p=1;1;1;1;1;1;1;1;1;1;1;1;1; 1;0.01;0.01;0.01;P=diag(p);NBB=B*P*B;W=B*P*l;x=inv(NBB)*W;v=B*x-l;结果：由于我们系数a b 用的单位是分米所以结果应该缩小100倍所以x3=0.002726y3=0.001911x4= -0.009433y4= -0.018437x5= 0.012872y5= -0.028742x6=0.006453Y6=0.048204平差值X3=x3+x3

12、=125972.6886Y3=y3+y3=264285.4027X4=128636.8077Y4=261401.4651X5=126770.4521Y5=267090.8543X6=131745.4388Y6=264587.6932二精度评定：单位权方差公式求得单位权中误差（此处用m0表示）m0=0.3401根据矩阵，得Qx4=0.5226，Qy4=3.6605Qx5=19.0276，Qy5=266.4110点位中误差公式： 代入公式得：点4的中误差m4=0.6956；点5的中误差m5=5.746。三误差椭圆：根据Q矩阵可知Qx4y4=1.27，Qx5y5=-70.8276（1）根据位差极值公

13、式可求得 K4=4.0370，K5=285.0681E42=0.4754,E52=32.9947,E4 =0.6894,E5=5.744F42=8.4495*10-3，F52=0.0214,F4=0.092,F5=0.146QEE4=(QXX+QYY+K)/2=4.11005,QFF4=0.07305根据tanE=(QEE-QXX)/QXY可求得：tanE4=2.8248 进而求得E4=79.5或250.5tanF4=-0.354，F4=-19.5或160.5QEE5=(QXX+QYY+K)/2=285.25335,QFF4=0.18525 TanE5=-321.684，tanF5=0.266

14、E5=-89.8或90.2，F5=14.9或194.94、相对误差椭圆（4和5点）X45=(X4+X5)=127703.6299Y45=(Y4+Y5)=264246.1597x45=x4-x5y45=y4-y5由协因数阵可以得到Qx5x4=1.9217Qy5y4=-16.6602Qx5y4=4.6722Qx4y5=-7.1571Qxx=Qx5x5+Qx4x4-2Qx5x4=15.7068Qyy=Qy5y5+Qy4y4-2Qy5y4=303.3919Qxy=Qx5y5+Qx5y4-Qx4y5+Qx4y4=-67.0727由上面的公式（1）得到E2=108.2412 E=40.4038F=0.53

15、38tanE=(QEE-QXX)/QXY=-4.5108进而求得E4=-77.5或102.4998tanF4=0.8376，F4=39.9495或219.9495 4点的误差椭圆 5点的误差椭圆 4,5点相对误差椭圆代码(4点）:function varargout = untitled5_OutputFcn(Xcenter,Ycenter,LongAxis,ShortAxis,Angle) Xcenter=128636.8077;Ycenter=261401.4651;LongAxis=0.6894;ShortAxis=0.092;Angle=79.5;t1=0:.02:pi;t2=pi:.02:2*pi;z1=exp(1i*t1);z2=exp(1i*t2);z1=(LongAxis*real(z1)+1i*ShortAxis*imag(z1)*exp(1i*(-Angle);z2=(LongAxis*real(z2)+1i*ShortAxis*imag(z2)*exp(1i*(-Angle);z1=z1+Xcenter+Ycenter*1i;z2=z2+Xcenter+Ycenter*1i; plot(z1,r); hold on plot(z2,r) hold offgrid on