实验三 利用matlab程序设计语言完成某工程导线网平差计算.docx
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实验三 利用matlab程序设计语言完成某工程导线网平差计算.docx
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实验三利用matlab程序设计语言完成某工程导线网平差计算
实验三利用matlab程序设计语言完成某工程导线网平差计算
实验数据;
某工程项目按城市测量规范(CJJ8-99)不设一个二级导线网作为首级平面控制网,主要技术要求为:
平均边长200cm,测角中误差±8,导线全长相对闭合差<1/10000,最弱点的点位中误差不得大于5cm,经过测量得到观测数据,设角度为等精度观测值、测角中误差为m=±8秒,鞭长光电测距、测距中误差为m=±0.8√smm,根据所学的‘误差理论与测量平差基础’提出一个最佳的平差方案,利用matlab完成该网的严密平差级精度评定计算;
平差程序设计思路:
1采用间接平差方法,12个点的坐标的平差值作为参数.利用matlab进行坐标反算,求出已知坐标方位角;根据已知图形各观测方向方位角;
2计算各待定点的近似坐标,然后反算出近似方位角,近似边.计算各边坐标方位角改正数系数;
3确定角和边的权,角度权Pj=1;边长权Ps=100/S;
4计算角度和边长的误差方程系数和常数项,列出误差方程系数矩阵B,算出Nbb=B’PB,W=B’Pl,参数改正数x=inv(Nbb)*W;角度和边长改正数V=Bx-l;
6建立法方程和解算x,计算坐标平差值,精度计算;
程序代码以及说明:
s10=238.619;s20=170.759;
s30=217.869;s40=318.173;
s50=245.635;s60=215.514;
s70=273.829;s80=241.560;
s90=224.996;s100=261.826;
s110=279.840;s120=346.443;
s130=312.109;s140=197.637;%已知点间距离
Xa=5256.953;Ya=4520.068;
Xb=5163.752;Yb=4281.277;
Xc=3659.371;Yc=3621.210;
Xd=4119.879;Yd=3891.607;
Xe=4581.150;Ye=5345.292;
Xf=4851.554;Yf=5316.953;%已知点坐标值
a0=atand((Yb-Ya)/(Xb-Xa))+180;
d0=atand((Yd-Yc)/(Xd-Xc));
f0=atand((Yf-Ye)/(Xf-Xe))+360;%坐标反算方位角
a1=a0+(163+45/60+4/3600)-180
a2=a1+(64+58/60+37/3600)-180;
a3=a2+(250+18/60+11/3600)-180;
a4=a3+(103+57/60+34/3600)-180;
a5=d0+(83+8/60+5/3600)+180;
a6=a5+(258+54/60+18/3600)-180-360;
a7=a6+(249+13/60+17/3600)-180;
a8=a7+(207+32/60+34/3600)-180;
a9=a8+(169+10/60+30/3600)-180;
a10=a9+(98+22/60+4/3600)-180;
a12=f0+(111+14/60+23/3600)-180;
a13=a12+(79+20/60+18/3600)-180;
a14=a13+(268+6/60+4/3600)-180;
a15=a14+(180+41/60+18/3600)-180;%推算个点方位角
aa=[a1a2a3a4a5a6a7a8a9a10a12a13a14a15]'
X20=Xb+s10*cosd(a1);
X30=X20+s20*cosd(a2);
X40=X30+s30*cosd(a3);
X50a=X40+s40*cosd(a4);
X60=Xd+s50*cosd(a5);
X70=X60+s60*cosd(a6);
X80=X70+s70*cosd(a7);
X90=X80+s80*cosd(a8);
X100=X90+s90*cosd(a9);
X50c=X100+s100*cosd(a10);
X130=Xf+s110*cosd(a12);
X140=X130+s120*cosd(a13);
X150=X140+s130*cosd(a14);
X50e=X150+s140*cosd(a15);%各点横坐标近似值
X0=[X20X30X40X60X70X80X90X100X130X140X150X50aX50cX50e]'
Y20=Yb+s10*sind(a1);
Y30=Y20+s20*sind(a2);
Y40=Y30+s30*sind(a3);
Y50a=Y40+s40*sind(a4);
Y60=Yd+s50*sind(a5);
Y70=Y60+s60*sind(a6);
Y80=Y70+s70*sind(a7);
Y90=Y80+s80*sind(a8);
Y100=Y90+s90*sind(a9);
Y50c=Y100+s100*sind(a10);
Y130=Yf+s110*sind(a12);
Y140=Y130+s120*sind(a13);
Y150=Y140+s130*sind(a14);
Y50e=Y150+s140*sind(a15);%个点从坐标近似值
Y0=[Y20Y30Y40Y60Y70Y80Y90Y100Y130Y140Y150Y50aY50cY50e]'
P=[X0Y0];
X50=(X50a+X50c+X50e)/3
Y50=(Y50a+Y50c+Y50e)/3
s4=sqrt((Y40-Y50)^2+(X40-X50)^2);
s1=sqrt((Y100-Y50)^2+(X100-X50)^2);
s14=sqrt((Y150-Y50)^2+(X150-X50)^2);
A1=[cosd(a1)cosd(a2)cosd(a3)cosd(a4)cos(a5)cosd(a6)cosd(a7)cosd(a8)cosd(a9)cosd(a10)cosd(a12)cosd(a13)cosd(a14)cosd(a15)]';
B11=[sind(a1)sind(a2)sind(a3)sind(a4)sin(a5)sind(a6)sind(a7)sind(a8)sind(a9)sind(a10)sind(a12)sind(a13)sind(a14)sind(a15)]';
s=blkdiag(s10,s20,s30,s4,s50,s60,s70,s80,s90,s10',s110,s120,s130,s14);
a=206.2648026*inv(s)*B11
b=-206.2648026*inv(s)*A1
ab4=atand((Y50-Y40)/(X50-X40))+180;
ab10=atand((Y50-Y100)/(X50-X100));
ab14=atand((Y50-Y150)/(X50-X150))+360;
m4=ab4-a3+180;
m10=ab10-a9+180;
m11=ab4-ab10;
m15=ab14-a14+180;
m16=ab10-ab14+360;
m04=103+57/60+34/3600;
m010=98+22/60+4/3600;
m011=94+53/60+50/3600;
m015=180+41/60+18/3600;
m016=ab10-ab14+360;
l=[000m4-103-57/60-34/360000000m10-98-22/60-4/3600m11-94-53/60-50/3600000m15-180-41/60-18/3600m16-103-23/60-8/3600000s40-s400000s100-s1000s140-s14]';
e1=(abs(X20-Xb))/s10;e2=(abs(X30-X20))/s20;e3=(abs(X40-X30))/s30;e4=(abs(X50-X40))/s4;e5=(abs(X60-Xd))/s50;e6=(abs(X70-X60))/s60;e7=(abs(X80-X70))/s70;
e8=(abs(X90-X80))/s80;e9=(abs(X100-X90))/s90;e10=(abs(X50-X100))/s1;e11=(abs(X130-Xf))/s110;e12=(abs(X140-X130))/s120;e13=(abs(X150-X140))/s130;e14=(abs(X50-X150))/s14;
e=[e1e2e3e4e5e6e7e8e9e10e11e12e13e14]'
m1=(abs(Y20-Yb))/s10;m2=(abs(Y30-Y20))/s20;m3=(abs(Y40-Y30))/s30;m4=(abs(Y50-Y40))/s4;m5=(abs(Y60-Yd))/s50;m6=(abs(Y70-Y60))/s60;m7=(abs(Y80-Y70))/s70;
m8=(abs(Y90-Y80))/s80;m9=(abs(Y100-Y90))/s90;m10=(abs(Y50-Y100))/s1;m11=(abs(Y130-Yf))/s110;m12=(abs(Y140-Y130))/s120;m13=(abs(Y150-Y140))/s130;m14=(abs(Y50-Y150))/s14;
m=[m1m2m3m4m5m6m7m8m9m10m11m12m13m14]'%以上为求得误差方程系数
B=[-0.68510.52710000000000000000000000
0.38720.0289-1.0723-0.55600000000000000000000
000.94531.49420.127-0.9382-0.938200000000000000000
000.127-0.93820.47561.1776-0.6026-0.23940000000000000000
000000000.8256-0.153600000000000000
00000000-0.6191-0.7809-0.20650.9345000000000000
00000000-0.20650.93450.9518-1.0435-0.74530.1090000000000
0000000000-0.74530.1091.55160.1722-0.8063-0.281200000000
000000000000-0.8063-0.28121.71320.4151-0.9069-0.1339000000
000000-0.24910.8277000000-0.90690.13391.156-0.6938000000
00000.60260.23940.8517-0.586300000000-0.24910.8277000000
0000000000000000000.7111-0.1940000
000000000000000000-0.75880.78750.0477-0.593500
0000000000000000000.0477-0.5935-0.70780.62460.6601-0.0311
0000001.0417-0.06160000000000000.6601-0.0311-1.70180.0927
000000-1.28090.7661000000000.2491-0.827700001.0417-0.066616
0.60970.79260000000000000000000000
-0.4603-0.88780.46030.887800000000000000000000
00-0.991-0.13420.9910.1342000000000000000000
0000-0.3692-0.92930.36920.92930000000000000000
000000000.39960.916700000000000000
00000000-0.9764-0.21580.97640.2158000000000000
0000000000-0.1447-0.98950.14470.98950000000000
000000000000-0.3293-0.94420.32930.944200000000
00000000000000-0.1461-0.98930.14610.9893000000
0000000.95740.288800000000-0.9574-0.2888000000
0000000000000000000.26310.96480000
000000000000000000-0.9968-0.08010.99680.080100
00000000000000000000-0.047-0.99890.0470.9989
0000000.05940.998200000000000000-0.0594-0.9982]%系数矩阵B
P=blkdiag(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,100/s10,100/s20,100/s30,100/s40,100/s50,100/s60,100/s70,100/s80,100/s90,100/s100,100/s110,100/s120,100/s130,100/s140);%定义权矩阵
Nbb=B'*P*B
W=B'*P*l;
x=inv(Nbb)*W
V=B*x-l;
inv(Nbb);
Y=V'*P*V;
O=sqrt(Y/6)*3600%精度评定
计算结果:
平差值坐标X:
1.0e+003*
5.01825825621441
4.09214051058779
4.93966691935177
4.24372266973269
4.72376669705670
4.21449589983501
4.60629216903406
4.51018726572495
4.21804227380177
3.66643202793325
4.42847073890118
3.71293519499601
4.46807141156653
3.98387916563715
4.38851642122011
4.21197375648003
4.35564105689259
4.43455120690799
4.92518731972161
5.04699037092905
4.57985606835358
5.01925382686518
4.59452770624570
4.70750589265634
点名
坐标(m)
X
Y
2
5018.2582
4092.1405
3
4939.6669
4243.7227
4
4723.7667
4214.4959
5
4606.2921
4510.1872
6
4218.0423
3666.4320
7
4428.4707
3712.9352
8
4468.0714
3983.8792
9
4388.5164
4211.9738
10
4355.6411
4434.5512
13
4925.1873
5046.9904
14
4579.8561
5019.2538
15
4595.5277
4707.5059
Qx1=1.488Qy1=1.5596Qx2=2.2058Qy2=5.1342……Qx15=1.1836Qy15=4.9268
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