误差理论与测量平差基础习题集5(参考答案)

其中:

7.2.23

未知参数:a,a???ao?δa

平差值的观测方程:

yi = (x,a)1/2 (i=1,2, …,6) 线性化得误差方程:

?1??x1??δa-0??2?a?i12Vil

i0?其中,li????xa?? yi??7.2.24 设三个参数: V1=X1 V2=X2

V3=-X1+X2-5 V4=-X1-X3-4 V5=-X2+X3-3 V6=-X2 V7=X3 7.2.25

有三个条件方程: V1-V3-1=0 V2-V4+2=0 V1-V2-V4-4=0 7.3.29

????0.07?x1x??????? ???1.57???x2???Qx??1.1250.071???? ?0.0710.143?7.3.30

?0?14,?0?3.74 7.3.31

令C=4,Qxp2?0.75, ?0?6mm

??2??xp?2??0Qxp?5.2mm

2?7.3.32

Qx??17?2??171?? ?P?44?7.3.33

Qx??3?5???2??5?23?2????1?115??? ??? Qlx5??11?3???5??32???3?11?1??12??5?1?22??21?12??21? ??1?3?QLV?0 Ql?7.3.35

舍弃h6的结果导致D点的权降至原有值67%。 7.3.36

平差后P1点高程精度最高,精度最高点与最低点精度之比为1:1.37 7.3.37 令Q??I?

QQxC??=4.17×10﹣4,Qy=4.23×10﹣4

CxCyC??=0 (单位:m2/秒2)

7.3.38

NBB?8????2?2?? 7??1?752??22?? 8?QQx???N?1BB?1152 P?? 52117.3.39

设平差后∠BDC=∮,则

? =360°-(L1+L3)

?dd??=﹣dL1-dL5

??权数式为:

??=2.48x0+7.97y0

7.3.40

每千米观测高差中误差应小于3.3mm。 7.3.41

设参数X =[Xc Yc XD YD]t

参数近似值X°= [Xc° Yc° XD° YD°]t

X=X°+ x

??

7.4.43

H?c=11.4251m,

?HD=10.3575m,

?HG=12.5210m

?HC=2.60mm, ?HD=2.35mm, ?HC=2.60mm,

7.4.44

(1)Hc=6.193m,HD=6.688m (2)Q????1, =1.43mm 3??7.4.45

HP=22.456m HP=23.368m HP=20.145m

123????0?3.8mm

?HP=2.6mm ?HP=2.6mm ?HP=2.2mm

123????7.5.47

PX?C*S?SSS1122

7.5.48

(1) HP=55.945m (2) Q=1/4

P?7.5.49

(1) HP=25.4652m (2)

?PHP=1(c=1)

7.5.50

(1) 75°18′10.4″?1.6″ (2)9.2″ 7.6.51 (1)误差方程

?0.6519?0.8397???3.37\????????0.04350.74407.08\xP? ??— ?? V???0.0435?0.7740??????3.79\?y?????P???0.77480.6498?1.79\????法方程:

?1.0290??0.0207???3.02?0.0207??— x??? = 0

2.2346??11.24?(2) x? [ -3.04,5.06 ] Tmm

XP= 4881.267 YP= 346.865mm

??Qx??0.9720?0.0090???? ??0.00900.4476?

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