实验二 利用平差易软件完成某工程工程控制网的平差计算.docx
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实验二利用平差易软件完成某工程工程控制网的平差计算
实验二利用平差易软件完成某工程工程控制网的平差计算
本题有已知点2个,4个未知点,14个方向观测值,3个边长观测值,方向观测值验前中误差为1.2秒,边长固定误差5mm,求个位置点的坐标,以及点位精度。
平差程序设计思路
间接平差法是通过选定t个独立未知量作为参数,将每个观测值分别表达成这t个参数的的函数,建立数学模型,按最小二乘原理,用求自由极值的方法解出参数的最或然值,从而求得各观测值的平差值。
1.计算待定点计算坐标:
各点近似坐标按坐标计算
p3的近似值,由p1、p2点的近似坐标和推算:
2.求得近似坐标以及近似坐标方位角以及近似距离,求得误差方程系数a、b.
3.列立误差方程
定权:
角度定权为1,边长定权100/s。
数学模型:
Nbb=B’PB,W=B’Pl.X=inv(Nbb)W,V=BX-L
4.求中误差:
单位权中误差δ0,协因数阵Nbb^-1.求得中误差δ
5.误差椭圆和相对误差椭圆的参数:
程序代码以及说明:
X1=121088.500;
Y1=259894.000;
X2=127990.100;
Y2=255874.600;%已知坐标点
p1=72+10/60+28.4/3600;
p2=66+27/60+28.9/3600;
p3=123+11/60+34.1/3600;
p4=85+13/60+37.4/3600;
p5=79+9/60+48.7/3600;
p6=72+24/60+56.4/3600;
p7=88+58/60+29.5/3600
p8=132+23/60+35.2/3600;%各测站方向观测角
s1=4451.417;
s2=5564.592;
s3=5569.269;%3个边长观测值
f1=atand((Y2-Y1)/(X2-X1))+360;%坐标反算起始方位角
f2=f1-p2;
f3=f2-p8;
f4=f3-p8-p4+360;
f5=f4-p5;
f6=f5-p6;
f7=f6-p7-p3;%由起始方位角算得各方向角
x4=s2*cosd(f2)+X2
y4=s2*sind(f2)+Y2
x5=s1*cosd(f4)+x4
y5=s1*sind(f4)+y4
x6=s3*cosd(f5)+x5
y6=s3*sind(f5)+y5
x3=126064.323
y3=264367.747%各点近似坐标
s13=sqrt((y3-Y1)^2+(x3-X1)^2)
s24=sqrt((y4-Y2)^2+(x4-X2)^2)
s45=sqrt((y5-y4)^2+(x5-x4)^2)
s43=3926.376
s36=3449.208
s56=sqrt((y6-y5)^2+(x6-x5)^2)%两点之间近似距离
F1=[sind(f2)sind(f4)sind(f5)]'
F2=[cosd(f2)cosd(f4)cosd(f5)]'
S=blkdiag(s24,s45,s56)
a=206.2648*inv(S)*F1
b=206.2648*inv(S)*F2
b13=-2.293
a13=2.061
b24=-0.431
a24=3.682
b45=-3.236
a45=3.317
b43=3.442
a43=3.969
b36=-1.794
a36=5.705
b56=3.090
a56=2.042%误差方程系数a、b
B=[-2.0612.293000000;00-3.6820.4310000;
003.317-3.236-3.3173.23600;
-3.969-3.4423.9693.4420000;
5.705-1.7940000-5.7051.794;
00002.0423.090-2.042-3.090;
00-0.698-0.7160.6980.71600;
000.1160.9930000;
00000.843-0.551-0.8430.551]
%系数矩阵B
P=blkdiag(1,1,1,1,1,1,100/s1,100/s2,100/s3)%权矩阵
Nbb=B'*P*B
W=B'*P*l
x=inv(Nbb)*W
h3=-154.4041
g3=-115.3208
h4=-29.9042
g4=-258.7939
h5=86.9634
g5=-139.4339
h6=453.0739
g6=-381.1782
X3=x3+h3/1000
Y3=y3+g3/1000
X4=x4+h4/1000
Y4=y4+g4/1000
X5=x5+h5/1000
Y5=y5+g5/1000
X6=x6+h6/1000
Y6=y6+g6/1000%各点坐标值
V=B*x-l%误差方程(mm)
Qxx=inv(Nbb)%观测值协因数阵
Qo=sqrt(V'*P*V/9)%单位权中误差
Q=Qo*sqrt(Qxx)%各点精度
Q4=sqrt(19.797^2+159.0323^2)%p4点中误差
Q5=sqrt(112.2654^2+210.1904^2)%p5点中误差
K4=sqrt((19.797-159.0323)^2+4*54.4667^2)%求p4点位差极大值和极小值
Qee4=0.5*(19.797+159.0323+k4)
Qff4=0.5*(19.797+159.0323-k4)
E4=Qo*sqrt(Qee4)%p4点位差最大值
F4=Qo*sqrt(Qff4)%p4点位差极大值
k5=sqrt((112.2654-210.1904)^2+4*135.7331^2)
Qee5=0.5*(112.2654+210.1904+k5)
Qff5=0.5*(112.2654+210.1904-k5)
E5=Qo*sqrt(Qee5)%p5点位差极大值
F5=Qo*sqrt(Qff5)%p5点位差极小值
程序运行结果;
B=
-2.06102.2930000000
00-3.68200.43100000
003.3170-3.2360-3.31703.236000
-3.9690-3.44203.96903.44200000
5.7050-1.79400000-5.70501.7940
00002.04203.0900-2.0420-3.0900
00-0.6980-0.71600.69800.716000
000.11600.99300000
00000.8430-0.5510-0.84300.5510
P=
1.000000000000
01.00000000000
001.0000000000
0001.000000000
00001.00000000
000001.0000000
0000000.022500
00000000.01800
000000000.0180
Nbb=
52.5477-1.2993-15.7530-13.661300-32.547010.2348
-1.299320.3236-13.6613-11.84740010.2348-3.2184
-15.7530-13.661340.32381.3538-11.013410.722600
-13.6613-11.84741.353822.534110.7226-10.483200
00-11.013410.722615.1960-4.4211-4.1825-6.3014
0010.7226-10.4832-4.421120.0368-6.3014-9.5536
-32.547010.234800-4.1825-6.301436.7295-3.9333
10.2348-3.218400-6.3014-9.5536-3.933312.7720
l=1.0e+003*0.0515
0
0.0002
-0.0005
-3.9440
0
0
0
0
W=1.0e+004*-2.2605
0.7195
-0.0001
-0.0002
-0.0001
0.0001
2.2501
-0.7076
x=-154.4041
-115.3208
-29.9042
-258.7939
86.9634
-139.4339
453.0739
-381.1782
X3=1.2606e+005
Y3=2.6437e+005
X4=1.2734e+005
Y4=2.5035e+005
X5=1.2760e+005
Y5=2.4590e+005
X6=1.2220e+005
Y6=2.4454e+005
V=2.2962
-1.4328
-1.6008
0.8053
1.3898
-0.6078
167.0354
-260.4513
-441.8323
Qxx=13.045911.66012.792023.44915.920026.642215.716620.1735
11.660110.61112.515121.12495.304823.972614.041818.2036
2.79202.51510.65764.97761.30935.64293.35044.2952
23.449121.12494.977642.435810.617748.193228.281536.5296
5.92005.30481.309310.617721.147330.912515.209534.8332
26.642223.97265.642948.193230.912574.128940.431567.8434
15.716614.04183.350428.281515.209540.431522.525235.6282
20.173518.20364.295236.529634.833267.843435.628267.4052
Qo=24.4129
Q=88.177383.362440.7923118.217659.3993126.009796.7827109.6503
83.362479.524338.7167112.206156.2282119.530091.4809104.1591
40.792338.716719.797054.466727.934657.992444.685750.5952
118.2176112.206154.4667159.032379.5488169.4774129.8287147.5509
59.399356.228227.934679.5488112.2654135.733195.2087144.0840
126.0097119.530057.9924169.4774135.7331210.1904155.2312201.0819
96.782791.480944.6857129.828795.2087155.2312115.8653145.7189
109.6503104.159150.5952147.5509144.0840201.0819145.7189200.4314
Q4=160.2598
Q5=238.2929
K4=176.7851
Qee4=177.8072
Qff4=1.0221
E4=325.5320
F4=24.6815
E5=426.7174
F5=208.3484