平差课设报告Word下载.docx
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平差课设报告Word下载.docx
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算出参数近似值改正数
4、由
算出V;
5、由
算出高程平差值;
6、由
算出单位权中误差
7、由
算出各高程平差值的中误差;
最后结果:
1、1公里高差平差值中误差:
mo=0.0011mm;
2、P1到P9平差后高程为:
H1
H2
H3
H4
H5
H6
H7
H8
H9
146.3587
148.1490
145.5285
146.0641
148.6502
144.9991
142.4870
145.9069
144.5285
3、P1到P9高程平差值中误差:
P1
P2
P3
P4
P5
P6
P7
P8
P9
0.0006183
0.0006225
0.0007011
0.0005095
0.0007502
0.0009930
0.0010206
0.0008769
0.0008248
加测5段高差后
4、平差后各待定点精度:
0.0005315
0.0004855
0.0005497
0.0004682
0.0006488
0.0009154
0.0009161
0.0008100
0.0008052
5、精度最弱点没有变化,仍为P7、P8;
6、P3点精度提高最多;
计算源程序:
%*****************************TESTONE*****************************
clear
fidResultInfo=fopen('
resultsONE.txt'
'
wt'
);
fprintf(fidResultInfo,'
\n\n'
********************TESTONE*******************\n\n'
%HA,HB,BC为已知高程点高程
HA=151.5664;
HB=144.5684;
HC=144.3194;
%Î
ª
1~15号水准路线观测高差
L1=1.4957;
L2=1.7892;
L3=5.2062;
L4=2.0853;
L5=3.4175;
L6=1.2080;
L7=6.0373;
L8=4.3307;
L9=3.6510;
L10=2.5120;
L11=2.0416;
L12=1.5355;
L13=1.7450;
L14=2.7434;
L15=1.3785;
%1~15号水准路线长度(/km)
S1=0.4;
S2=0.5;
S3=0.7;
S4=0.9;
S5=0.4;
S6=1.0;
S7=0.6;
S8=0.6;
S9=0.6;
S10=0.3;
S11=0.8;
S12=0.7;
S13=0.8;
S14=0.4;
S15=0.5;
S16=0.6;
S17=0.6;
S18=1.8;
S19=0.8;
S20=1.2;
%观测数n¡
必要观测数t¡
多余观测数r
n=15;
t=9;
r=6;
%待定点高程近似值(估值)
X1=HB+L2;
X2=HA-L5;
X3=HA-L7;
X4=HB+L1;
X5=HC+L8;
X6=HC+L8-L9;
X7=HC+L8-L9-L10;
X8=HC+L8-L14;
X9=HB+L1-L12;
X=[X1;
X2;
X3;
X4;
X5;
X6;
X7;
X8;
X9;
];
%l为误差方程常数项,是观测值与近似值之差
l1=L1-X4+HB;
l2=L2-X1+HB;
l3=L3+X1-HA;
l4=L4-X2+X4;
l5=L5+X2-HA;
l6=L6-X3+HC;
l7=L7+X3-HA;
l8=L8-X5+HC;
l9=L9-X5+X6;
l10=L10-X6+X7;
l11=L11-X9+X7;
l12=L12-X4+X9;
l13=L13-X4+HC;
l14=L14-X5+X8;
l15=L15-X8+X9;
%l为1行1列矩阵
l=[l1;
l2;
l3;
l4;
l5;
l6;
l7;
l8;
l9;
l10;
l11;
l12;
l13;
l14;
l15];
%下面计算P(权阵),设一公里的权为单位权观测值
P1=1/S1;
P2=1/S2;
P3=1/S3;
P4=1/S4;
P5=1/S5;
P6=1/S6;
P7=1/S7;
P8=1/S8;
P9=1/S9;
P10=1/S10;
P11=1/S11;
P12=1/S12;
P13=1/S13;
P14=1/S14;
P15=1/S15;
P16=1/S16;
P17=1/S17;
P18=1/S18;
P19=1/S19;
P20=1/S20;
P=[P1P2P3P4P5P6P7P8P9P10P11P12P13P14P15];
P=diag(P);
%B矩阵
B=[000100000;
100000000;
-100000000;
010-100000;
0-10000000;
001000000;
00-1000000;
000010000;
00001-1000;
000001-100;
000000-101;
00010000-1;
000100000;
0000100-10;
00000001-1];
%改正数x
NBB=B'
*P*B;
W=B'
*P*l;
Q=inv(NBB);
x=Q*W;
%****1~9点高差平差值***
tX=X+x;
1~9º
Å
µ
ã
¸
ß
²
î
Æ
½
Ö
£
º
H1=%8.4fH2=%8.4fH3=%8.4fH4=%8.4fH5=%8.4fH6=%8.4fH7=%8.4fH8=%8.4fH9=%8.4f\n'
tX
(1),tX
(2),tX(3),tX(4),tX(5),tX(6),tX(7),tX(8),tX(9));
%观测值改正数V
V=B*x-l;
%***一公里高差平差值中误差mo***
mo=V'
*P*V/r;
mo=sqrt(mo);
Ò
»
¹
«
À
ï
Ð
Î
ó
%8.4f\n'
mo);
%***待定点中误差m***
m=mo*sqrt(Q);
´
ý
¶
¨
point1=%8.7fpoint2=%8.7fpoint3=%8.7fpoint4=%8.7fpoint5=%8.7fpoint6=%8.7fpoint7=%8.7fpoint8=%8.7fpoint9=%8.7f\n'
m(1,1),m(2,2),m(3,3),m(4,4),m(5,5),m(6,6),m(7,7),m(8,8),m(9,9));
7µ
¾
È
×
Í
¬
4µ
\n'
%加测16~20
Bn=[000100000;
00000001-1;
-110000000;
01-1000000;
00-1100000;
000-110000;
000000-110];
Pn=[P1P2P3P4P5P6P7P8P9P10P11P12P13P14P15P16P17P18P19P20];
Pn=diag(Pn);
NBBn=Bn'
*Pn*Bn;
Qn=inv(NBBn);
%新的改正后高程协因数阵
mn=mo*sqrt(Qn);
加测16~20后待定点中误差:
mn(1,1),mn(2,2),mn(3,3),mn(4,4),mn(5,5),mn(6,6),mn(7,7),mn(8,8),mn(9,9));
%对比可知原精度最弱点为7,8号点,加测后精度最弱点仍为7,8号点,3号点精度提高最多
对比可知原精度最弱点为7,8号点,加测后精度最弱点仍为7,8号点,3号点精度提高最多\n'
第二题
由题可知,n=24,t=14,r=10,选取7个待定点坐标X1,Y1到X7,Y7为参数,根据间接平差模型来平差。
1、计算待定点近似坐标:
根据AB边的坐标求出AB的方位角,再由边长观测值以及角度观测值求出各点近似坐标值
、
到
2、据测角误差公式
测边网误差公式
=
-(
-
)和
列出24个误差方程;
3、由近似坐标值算出各边近似方位角、近似边长值及坐标增量,将误差方程整理线性化为
形式;
4、由测角次数和边长观测值得出权阵P;
算出参数近似改正数
计算出V;
8、由
9、由
最后结果:
1、平差后单位权中误差:
9.99602;
2、7个待定点的坐标平差值:
1
2
3
4
5
6
7
X
627.0885
674.7909
847.7214
974.4849
971.9237
859.4469
747.8589
Y
290.7425
447.5555
531.6769
358.6551
171.5669
213.2901
317.0324
3、7个待定点坐标平差值中误差:
4.9770
8.4523
11.1029
7.5221
3.7591
4.0762
6.1599
5.1303
5.7558
5.6548
6.3152
4.4510
4.3940
5.4476
4、平差后S4的边长相对中误差(mm):
0.0225;
5、精度最弱点误差椭圆:
E=11.1152F=5.6305angle_E=-0.0546;
计算源程序:
%**************************TESTTWO********************************
resultsTWO.txt'
********************TESTTWO*******************\n\n'
%起算数据:
已知坐标;
角观测值b(/rad);
各边坐标方位角近似值(/rad)(其中A0为真值);
边长观测值S(/m)
%´
待定点坐标估值X边长估值S0
p=206265/1000;
n=24;
t=14;
r=10;
XA=897.950;
YA=74.629;
XB=676.583;
YB=136.123;
所用数据为9班的7号:
XA=%f;
YA=%f\n\n'
XA,YA);
S=[162.351;
163.910;
192.306;
214.493;
187.109;
121.940;
143.901;
152.356;
149.626;
angle=[1231631;
%1
1451948;
%2
1325131;
%3
1001706;
%4
1425936;
%5
1432611;
%6
1114921;
%7
460932;
%8
1975047;
%9
1482553;
%10
585724;
%11
2481048;
%12
525157;
%13
864150;
%14
2270818];
%15
%将角度转化为弧度
angle_degrees=dms2degrees(angle);
angle_rad=zeros(15,1);
fori=1:
15
angle_rad(i,1)=angle_degrees(i,1)*pi/180;
end
A0=atan((YB-YA)/(XB-XA))+pi;
%AB坐标方位角
A(1,1)=A0+angle_rad(1,1)-pi;
fori=2:
A(i,1)=A(i-1,1)+angle_rad(i,1)-pi;
A(6,1)=A0-angle_rad(7,1);
A(5,1)=A(6,1)-angle_rad(6,1)-pi;
A(7,1)=A0-angle_rad(11,1);
A(8,1)=A(7,1)-angle_rad(10,1)+pi;
A(9,1)=A(8,1)-angle_rad(9,1)+pi;
9
ifA(i,1)<
A(i,1)=A(i,1)+2*pi;
ifA(i,1)>
2*pi
A(i,1)=A(i,1)-2*pi;
X(1,1)=XB+S(1,1)*cos(A(1,1));
X(1,2)=YB+S(1,1)*sin(A(1,1));
X(2,1)=X(1,1)+S(2,1)*cos(A(2,1));
X(2,2)=X(1,2)+S(2,1)*sin(A(2,1));
X(3,1)=X(2,1)+S(3,1)*cos(A(3,1));
X(3,2)=X(2,2)+S(3,1)*sin(A(3,1));
X(5,1)=XA+S(6,1)*cos(A(6,1));
X(5,2)=YA+S(6,1)*sin(A(6,1));
X(4,1)=X(5,1)+S(5,1)*cos(A(5,1));
X(4,2)=X(5,2)+S(5,1)*sin(A(5,1));
X(6,1)=XA+S(7,1)*cos(A(7,1));
X(6,2)=YA+S(7,1)*sin(A(7,1));
X(7,1)=X(6,1)+S(8,1)*cos(A(8,1));
X(7,2)=X(6,2)+S(8,1)*sin(A(8,1));
So(1,1)=sqrt((X(1,1)-XB)^2+(X(1,2)-YB)^2);
So(i,1)=sqrt((X(i,1)-X(i-1,1))^2+(X(i,2)-X(i-1,2))^2);
fori=6:
So(i,1)=sqrt((X(i-1,1)-XA)^2+(X(i-1,2)-YA)^2);
So(8,1)=sqrt((X(7,1)-X(6,1))^2+(X(7,2)-X(6,2))^2);
So(9,1)=sqrt((X(2,1)-X(7,1))^2+(X(2,2)-X(7,2))^2);
%计算B矩阵
B=zeros(24,14);
a(i,1)=p*sin(A(i,1))/S(i);
b(i,1)=p*cos(A(i,1))/S(i);
B(1,1)=-a
(1);
B(1,2)=b
(1);
B(2,1)=a
(2)+a
(1);
B(2,2)=-b
(2)-b
(1);
B(2,3)=-a
(2);
B(2,4)=b
(2);
B(3,1)=-a
(2);
B(3,2)=b
(2);
B(3,3)=a(3)+a
(2);
B(3,4)=-b(3)-b
(2);
B(3,5)=-a(3);
B(3,6)=b(3);
B(4,3)=-a(3);
B(4,4)=b(3);
B(4,5)=a(4)+a(3);
B(4,6)=-b(4)-b(3);
B(4,7)=-a(4);
B(4,8)=b(4);
B(5,5)=-a(4);
B(5,6)=b(4);
B(5,7)=-a(5)+a(4);
B(5,8)=b(5)-b(4);
B(5,9)=a(5);
B(5,10)=-b(5);
B(6,7)=a(5);
B(6,8)=-b(5);
B(6,9)=-a(6)-a(5);
B(6,10)=b(6)+b(5);
B(7,9)=a(6);
B(7,10)=-b(6);
B(8,1)=-a
(2);
B(8,2)=b
(2);
B(8,3)=-a(9)+a
(2);
B(8,4)=b(9)-b
(2);
B(8,13)=a(9);
B(8,14)=-b(9);
B(9,3)=a(9);
B(9,4)=-b(9);
B(9,11)=a(8);
B(9,12)=-b(8);
B(9,13)=-a(8)-a(9);
B(9,14)=b(8)+b(9);
B(10,11)=-a(7)-a(8);
B(10,12)=b(7)+b(8);
B(10,13)=a(8);
B(10,14)=-b(8);
B(11,11)=a(7);
B(11,12)=-b(7);
B(12,9)=-a(6);
B(12,10)=b(6);
B(13,9)=a(6);
B(13,10)=-b(6);
B(13,11)=-a(7);
B(13,12)=b(7);
B(14,3)=a(3)+a(9);
B(14,4)=-b(3)-b(9);
B(14,5)=-a(3);
B(14,6)=b(3);
B(14,13)=-a(9);
B(14,14)=b(9);
B(15,1)=a
(2);
B(15,2)=-b
(2);
B(15,3)=-a
(2)-a(3);
B(15,4)=b
(2)+b(3);
B(15,5)=a(3);
B(15,6)=-b(3);
B(16,1)=(X(1,1)-XB)/S
(1);
B(16,2)=(X(1,2)-YB)/S
(1);
B(17,1)=-(X(2,1)-X(1,1))/S
(2);
B(17,2)=-(X(2,2)-X(1,2))/S
(2);
B(17,3)=(X(2,1)-X(1,1))/S
(2);
B(17,4)=(X(2,2)-X(1,2))/S
(2);
B(18,3)=-(X(3,1)-X(2,1))/S(3);
B(18,4)=-(X(3,2)-X(2,2))/S(3);
B(18,5)=(X(3,1)-X(2,1))/S(3);
B(18,6)=(X(3,2)-X(2,2))/S(3);
B(19,5)=-(X(4,1)-X(3,1))/S(4);
B(19,6)=-(X(4,2)-X(3,2))/S(4);
B(19,7)=(X(4,1)-X(3,1))/S(4);
B(19,8)=(X(4,2)-X(3,2))/S(4);
B(20,7)=-(X(5,1)-X(4,1))/S(5);
B(20,8)=-(X(5,2)-X(4,2))/S(5);
B(20,9)=(X(5,1)-X(4,1))/S(5);
B(20,10)=(X(5,2)-X(4,2))/S(5);
B(21,9)=-(XA-X(5,1))/S(6);
B(21,10)=-(YA-X(5,2))/S(6);
B(22,11)=(X(6,1)-XA)/S(7);
B(22,12)=(X(6,2)-YA)/S(7);
B(23,11)=-(X(7,1)-X(6,1))/S(8);
B(23,12)=-(X(7,2)-X(6,2))/S(8);
B(23,13)=(X(7,1)-X(6,1))/S(8);
B(23,14)=(X(7,2)-X(6,2))/S(8);
B(24,3)=-(X(2,1)-X(7,1))/S(9);
B(24,4)=-(X(2,2)-
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