MatLab测量平差实习讲义_matlab讲义实习题

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MatLab测量平差实习讲义

一、误差传播定律

1）非线性间接函数误差传播定律

A,边长bb,cc,试求三角形面积中误差

syms A;syms b;syms c;sigmaA=6;sigmab=2;sigmac=4;pmiao=206265;syms Area;Area = b*sin(A)*c/2;difA = diff(Area,A);difb = diff(Area,b);difc = diff(Area,c);sigmaArea sqrt(difA*difA*(sigaA/pmiao)*(sigaA/pmiao)+difb*difb*sigmab*sigmab+difc*difc*sigmac*sigmac);

= 2）平差方程到误差方程

syms X1 Y1 X2 Y2 XA YA XB YB XC YC XD YD L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 l1 l2 l3 l4 l5 l6 l7 l8 l9 l10 l11 l12 l13 l14 l15 l16 l17 l18;syms difL1X1 difL1Y1 difL1X2 difL1Y2;syms L10 L20 L30 L40 L50 L60 L70 L80 L90 L10 L110 L120 L130 L140 L150 L160 L170 L180;L1='atan((YB-Y1)/(XB-X1))-atan((YA-Y1)/(XA-X1))';l1='L10-atan((YB-Y1)/(XB-X1))-atan((YA-Y1)/(XA-X1))';difL1X1=diff(L1,X1);difL1Y1=diff(L1,Y1);difL1X2=diff(L1,X2);difL1Y2=diff(L1,Y2);a1=subs(difL1X1,{XA,YA,XB,YB,X1,Y1},{9684.28,43836.82,10649.55,31996.50,13188.61,37334.97})*206265;a2=subs(difL1Y1,{XA,YA,XB,YB,X1,Y1},{9684.28,43836.82,10649.55,31996.50,13188.61,37334.97})*206265;a3=difL1X2;a4=difL1Y2;l1r=subs(L1,{XA,YA,XB,YB,X1,Y1},{9684.28,43836.82,10649.55,31996.50,13188.61,37334.97})*180/pi;l10=24.1-((l1r-fix(l1r))*60-fix((l1r-fix(l1r))*60))*60;

二、条件平差

1、定义并输入初始值

Step 1: 在Workspace中定义初始值变量

Step 2: 给初始值变量赋值

（1）双击变量，得到如图变量赋值表

（2）分别给其赋值

2、定义给系数阵A,L0,W并赋值

3、计算W W=A*L+L04、计算Naa Q=inv(P);Naa=A*Q*A' K=-inv(Naa)*W5、计算改正数

V=Q*A'*K6、计算平差值及单位权方差 LL=L+V sigma0=sqrt(V'*P*V/r)

7、计算QLˆLˆ

QVV=Q*A'*inv(Naa)*A*Q QLL=Q-QVV9、计算点的高程

三、间接平差