误差理论与测量平差基础习题集5(参考答案) 下载本文

W4?L4?L10?L11?L12?1800W5?L8?L9?L10?L11?1800

?sin(L6?L7)sinL2sinL13?W6??n?1??sin(L?L)sinLsinL12612? ??sin(L9?L10)sinL5sinL12?W7??n?1??sin(L?L)sinLsinL45911? ?5.2.26 n=8,t=4,r=4;有多种条件方程的列法,其中之一为:

?1?0??0??010001??0??2?110000-1??V????0?-4?0100-110????000-1-101??-4? 00注:常数项单位为mm。 5.2.27 n=4,t=2,r=2。 设

1?1,?2,?3的改正数为V1,V2,V3,S的改正数为V5。

10??cot(180????)?cot(???)V?VS?W1?0 122AB?2??S1?cot(1800??1??2)V1+V1?V3?W2?0

其中:W?1?SAB?sin(?2??AB)

1S?sin(?1??2)?1800 W2??1??35.2.28 n=7,t=4,r=3

V1?V6?V7?3n?0

V2?V3?V4?V5?5n?0

?1.125V1?0.817V3?1.498V4?0.872V6?2n?0 5.2.29 n=8,t=6,r=2

19.52VX1?6.83VY1-19.48VX2-0.06VY2?0.04VX4?6.89VY4?0.73?0 19.54VX1?0.06VY1?19.50VX2?6.83VY2?0.04VX3?6.89VY3?2.39?0 5.2.30

?Yij?Yv?Xv?Yv?Xv?Yv?YH?XHYHv?v?v?v?v?v?v?arctan?arctanjiiHiiiSv2Sv2Sv2Sij2SH2SH2SH2XijXHPA?32 5.3.33 (1)

P'A2?PAP'AP(2)设平差前A角的权为,平差后为,A3

(3)1P??0

5.3.34

1P?AOB?3 2 P??AOB23325.2.35 (1)P?5.3.36 (1)

(2)P?1

PB?1.6,

PC?2.1

PD?2.1,

PE?1.6

(2)5.3.37

PCD?1.8?sinL?sinL? (1)F?CD?ABsinL1313?sinL?sinL?sinL1146 dF??''dCD?cotLv?cotLv?cotLv?cotLv?cotLv?cotLv 1133446611111313CD(2)dF?v8

5.3.38

?sin(L??L?)sinL418F?BD?AC??L?)sinL?sin(L237

dF??''dBD??0.813v1?0.932v2?0.932v3?0.369v4?1.929v7?0.813v8 BD???2.49981.99981.35181.8515?Tm,??0.32(mm) 5.4.42 h?25.4.43

?1?1??0?10110001?1010?V1??V?2 0?????9???V3??9??00???V?????4???6?1??V5???????V6??V??045?4?5?2?mm

T???1.576h2.219?3.7950.867?2.433?1.352?m

T5.4.44

??10.3556m h??15.0028m (1)h12??h3?20.3556m h4?14.5008m

??4.6472mh??5.854hm85 6 ??10.5020m h7?F??2.2mm (2)?5.4.45

(1)各高差的平差值为:

??189.4006m h??273.5108m h15???187.2495mh2?736.9806m h6 ??h3?376.6501m h7?274.0693m ??574.5801m h??86.2612m h48(2)??F??15.6mm

(3)??F2??15.4mm

11?5.5.46 L3?(900?2L3?L1?L2?2L4)5

??45.06(cm)2,??0.67(cm2) 5.5.47 Ss5.5.48

'''???44?5914.5??152.315m (1)?,S1?215.453m,S2??(2)XC?152.3148m,YC?152.3148m

5.5.49

(1)条件方程为:

'' v1?v2?v3?20?0

0.0365v2?0.0186v3?0.832vS1?0.947vS2?3.20cm?0

(2)观测值的平差值为:

??135.6062m,S??119.1487m S12'''?'''??'''??52?3013.61 ?,?2?56?1811.82,?3?711134.5315.4.50

(1)共有4个条件方程:

??SS34??0?????)sin(?????)sin(???12334①正弦条件:

??SS12??0??②正弦条件:sin?3sin?1

?2?S?2?S?2S152??1?arccos?0??2SS15③余弦条件:

④余弦条件:

?2?S?2?S?2S234???3??4?arccos?0?S?2S23

线性条件为:

①0.995vS3?0.640vS4?1.594v?1?1.594v?2?1.467v?3?0.127v?4?2.488?0 ②0.860vS1?0.599vS2?0.522v?1?1.174v?3?1.024?0 ③0.984vS2?0.140vS1?0.788vS5?v?1?0.97?0 ④1.065vS4?0.819vS2?0.757vS3?v?3?v?4?3.53?0

(2)观测值的改正数及平差值为:

VS???14.3V???0.6?9.90.525.313.5?0.4?('')

T?16.1?(cm)

T0.8S1??2107.6853024.6272751.3424278.5013498.951?(m)

TT???? ?1???5916'6.6''4407'56.8''3647'50.5''5840'25.6''??5.5.51 条件方程为:

??SS 1?2?0?sin90?sin?线性条件为:

0.486?s??s2?0.176???1.085?0

1观测值的平差值为: ??416.055m,S??202.110m,???29?03'48.0'' S12????S平差值L?1?S2??的协因数阵与方差阵分别为: ??T1.2015?9.4005??0.78370.1602?1.2534??5.88??1.20151.80986.963? QL0.24130.9284?,D????0.1602??L??????1.25350.92858.7370????9.40056.96365.5275??5.5.52

????1???17?11'19.8''????119?10'37.3''? ??(1)2??????????43?38'03.0''?L?3?????1410.597m???S1????S????1110.0915m??2?????549.314m?XXA?X??A? (2)

????14.493mY??YA??A?87.30292.06?DX(mm2) ???2??92.0629.22?5.5.53

条件方程系数阵:

1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 3.6203 2.6347 1.6723 0.0000 0.1269 0.1272 -0.0356 0.1900 0.0638 -0.0595 0.0000 -0.9919 -0.9919 -0.9994 条件方程常数项阵: -14.00 -30.47 -14.12 法方程系数阵:

4.0000 7.9272 0.1943 7.9272 22.9141 0.3686 0.1943 0.3686 7.4763 法方程常数项阵: -14.00 -30.47