武汉大学误差理论与测量平差基础2002-2003学年度第二学期期末考试B

武汉大学 测绘学院

2002-2003学年度第二学期期末考试 误差理论与测量平差基础 课程试卷（B 卷）

出题者：黄加纳 审核人：邱卫宁

班级： 学号： 姓名： 分数：

一. 已知观测值向量21

L 的协方差阵为??

????--=31

14LL

D ，又知协因数11

411=

Q ，

试求观测值的权阵LL P 及观测值的权1

L P 和2

L P 。（10分）

二. 在相同观测条件下观测A 、B 两个角度，设对A ∠观测4测回的权为1，

则对B ∠观测7个测回的权为多少？（10分） 三. 在图一所示测角网中，A 、B 、C 为已知点，P 为待定点，721,,,L L L 为

同精度观测角值。

若按条件平差法对该网进行平差：

有多少个条件方程？各类条件方程各有多少

个？

试列出全部条件方程（非线性条件方程不必

线性化）。（15分）

图一

四. 在图二所示水准网中，A 、B 为已知点，已知m H A 00.1=，m H B 00.10=，P 1、P 2为待定点，设各线路等长。观测高差值m h 58.31=，m h 40.52=，

m

h 11.43=，m h 85.44=，m h 50.05=，现设1

?P

H X =，试问：(1).应按何种平差方法进行平差？(2).试列出其函数模型。(10分)

五. 在图三所示测角网中，已知A 、B 两点的坐标和P 1、P 2两待定点的近似坐

标值（见图三，以“km ”为单位），以及00002250

01

'''=B P α，

00001800

2

1'''=P P α，

320

1=

B P S km ，

km S P P 0.40

2

1=，

8

21,,,L L L 为同精度观测值，其中

2000450

4'''=L 。若按坐标平差法对该网

进行平差，试列出观测角4L 的误差方程

图三 (设5102?=ρ，x ?、y ?以dm 为单位)。(10

分)

六. 有水准网如图四所示，网中A 、B 为已知点，C 、D 为待定点，51~h h 为高差观测值，设各线路等长。已知平差后算得)(752mm V V T =，试求平差后C 、

D 两点间高差5

?h 的权及中误差。（10分）

七. 在间接平差中，参数1

?t X 与改正数1

n V 是否相关？试证明之。（10分）

八. 某平差问题有以下函数模型)(I Q =

??????++=

+=--=-=2

??1?2??1?214

2331211

x

x v x v x

x

v x v

03???321=++-x x x

试问：

(1). 以上函数模型为何种平差方法的模型？

(2). 本题中，=n ，=t ，=r ，

=c ，=u ，=s 。(10分)

九. 已求得某控制网中P 点误差椭圆参数03670'=E ?、dm E 57.1=和

dm

F 02.1=，已知PA 边坐标方位角03970'=PA α，km S PA 5=，A 为已知

点，试求方位角中误差PA

ασ?和边长相对中误差

PA

S S PA

σ

?。(15分)

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