误差理论与测量平差基础习题集5(参考答案)

(1)条件方程:

v1 + v2 + v3 + 11″ = 0 v4 + v5 + v6﹣20″ = 0

﹣0.081v1+0.945 v2+0.663 v3-5.890 = 0

1.190v1+0.325 v2+0.663 v3-0.981x -10.779 = 0 (2)V = [﹣7° 2″ ﹣6″ 7″ 7″ 7″ 6]T(mm)

85°22′58″,L2 = 46°37′12″,L3 = 47°59′50″,L4 = 40°L1 = 00′57″,

?????L5= 67°59′38″,L6 = 71°59′26″

??S?310.935m

(3)σ = 11.7″ (4)S

?CD

?= 210.240 - 0.001 = 210.239 m

Qx?= ﹣0.627,σCD = 9.2 mm

相对中误差: 6.3.23

1 22000条件方程系数列: A=

?1.00001.00001.00001.00001.00000.00000.00000.00000.0000????1.8235?1.5253?0.9777?0.42040.00000.7129?0.15860.3812?0.5317???0.1810?0.1221?0.0342?0.26400.00000.70130.98730.92450.8469????0.8457?0.54800.00000.00000.00000.7129?0.15860.00000.0000???0.2151?0.08800.00000.00000.00000.70130.98730.00000.0000???

?00???00??B = ?00?

??-10???0?1???法方程系数阵:

?? 5.0000 ﹣4.7469 ﹣0.2393 ﹣1.3937 0.127100?? ﹣4.7469 8.2603 0.3700 3.1194 0.147216???? ﹣0.2393 0.3700 5.3427 0.3191 2.465811?? ﹣1.3937 3.1194 0.3191 1.7569 0.271539? ??? 0.1271 0.1472 2.4658 0.2715 2.470145?? 改正数:

V = [ 4″ 4″ 2″ 2″ 0 ﹣4mm ﹣3mm ﹣6mm ﹣1mm] 观测值平差值:

?β? [73°56′25″ 234°35′44″ 148°27′59″ 234°31′45″46′29″]t

S?? [ 87.768 114.385 124.329 102.396 ]T(m)

参数改正数:x = ﹣7.6mm,y = ﹣5.9mm 参数平差值:X = 779.434m,Y = 446.687m

第七章

7.1.04

??h1= 1.356m,h2 =﹣0.822m,?h3 =﹣0.534m

7.1.05

??α? 78°23′16″,β?85°30′08″

?γ? 16°06′36″,δ = 343°53′24″

7.1.06

?H = h1 + S1/(S1+S2)·(HB-HA-h1+h2) 7.1.07

???αB = 53°35′32.7″,αC = 114°50′08″,αD = 208°59′53″

7.2.13

独立参数的个数等于9

°

767.2.14

独立参数有6个,可以有48组组合,其规律是:△AP1P2中的任意两个角加上构成大地四边形P2P3BA的四个三角形中的每一个内角(不算复全角),如:L1、L2、L4、L5、L7、L11。 7.2.15

?V1??1???V?2??1(1)?V3? = ??1????V4??0???0V???5??0??0?1??1?1???100????l1?110?????010?????l2????x1? - ?l? (2)V = ??01?1?x - l ????3??001???l4??x2??????110????l5???-1-11?????110???0?10???100??(3)V =??x - l

??101??0?11????01??0?7.2.16 设X1? X1=

?0L1,X02??L3

0?X?01?x1,X2=X2?x2

?误差方程:

V1=x1-l1 V2=

?X???X?0212?X0102??X???X?0212X0202x2?l?2

V3=x3-l3 其中:

l1=0,l1=L2?7.2.17

?X???X?,l=0

0202212

a°=1.26cm,b°=2.04cm;a=a°+ζa、b=b°+ζb 7.2.18

?????Z?\?????18.37?7.98???2.8?????????V31???111.340.50??xP(cm)???3.4??\?

???113.438.87????5.9????y(cm)???p????7.2.19

?10.837.65?????????x???10.632.13?P???(cm)???V41???10.63?2.13??????y???p???5.029.23??????2??5??\? 5??28?7.2.20

????0.93670.3502?????5.22???xP??V31(cm)???0.1960?0.9806????(cm)??5.56??\?

???0.9189??yp??6.47??0.3945??????7.2.21

误差方程系数阵: 误差方程常数项阵:

?0.9107 ﹣1.1670  ﹣0.7652 0.2583??3.01\?????0.0000  0.0000  0.7652 ﹣0.2583 ?1.31\?????0.0785  0.8140  0.0000  0.0000 ???0.47\?????﹣0.0785 ﹣0.8140 ﹣0.4060 0.68490.69\?? ?? ?0.0000  0.0000  0.4060  ﹣0.6849 ???0.09\??????0.6074  0.4962  0.0000  0.0000 ??0.07\??﹣0.6074 0.4962  0.4583  1.3359???2.55\??????(mm)??0.1777  ﹣0.9841 ﹣0.1777 0.9841 ????63.93?7.2.22

设椭圆的误差方程为x2/a2+y2/b2=1 独立参数:[Xa Xb]T=[a2 b2]

参数近似值为xa、xb,改正数为 Va、Vb,椭圆的误差方程为: V1=a1Va+b1Vb-l1(i=1,2,…,10)

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