误差理论与测量平差基础习题集5(参考答案)

???Y???Y??0?Y122313

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???X???X??0?X133414

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???Z???Z??0?Z133414

5.2.17 n=11,t=6,r=5

共有5个条件方程,其中有4个图形条件

??L??L??L??1800?0L1238 ??L??L??L??1800?0L2345 ??L??L??L??1800?0L4567 ??L??L??1800?0L91011

1个极条件(以

P2点为极)

??L?)sinL?sinL?sin(L1246?1?0?sin(L??L?)sinL?sinL3161 5.2.18 n=13,t=6,r=7

共有7个条件方程,其中有3个图形条件:

??L??L??L??L??1800?0L1251112 ??L??L??L??L??1800?0L25678 ??L??L??L??L??1800?0L678910

2个极条件: 大地四边形

AP2P3B以B点为极:

??L?)sinL?sinL?sin(L1269?1?0?????sinL5sin(L7?L8?L9)sinL1 扇形

PP12P3BA以

P1点为极:

??L??L?)sinL?sinL?sin(L??L?)sin(L123471011?1?0???????sinL3sin(L4?L5?L6)sin(L8?L9)sinL12 2个边长条件:

?SS1AB?S1:?AB?0??L?)sinL?sin(L11125

S1?S2:S1S?2?0??L?)sinL?sin(L782

5.2.19 n=10,t=6,r=4

v1?v5?v8?L1?L5?L8?1800?0

v1?v6?v7?L1?L6?L7?1800?0?v2?v3?v7?v8?L7?L8?L2?L3?1800?0?sinLsinL?sinL135?sinL?sinL?sinL246=1(以D点为极) 5.2.20

(1)n=22,t=10-1=9,r=13;图形条件7个,圆周条件1个,极条件2个,边长条件2个,基线条件1个。

??L??L??1800?0L128(2) ??L??L??1800?0L379 ??L??L??1800?0L41314

??L??L??L??1800?0L11171819

??L??L??L??1800?0L561016

??L??L??L??1800?0L6101119

??L??L??L??L??3600?0L910111213

?sinL?sinL?sinL?sinL5101719?sinL?sinL?sinL?sinL6111620=1(以大地四边形中点为极)

?sinL?sinL?sinL?sinL361418=1?sinL?sinL?sinL?sinL471519(以中点四边形D点为极)

?SFCS2???sinL??sinL?S?SsinLsinL2的边长条件) 11151217(FC??SS12???S?????SsinL13sinL18sinL12sinL2的边长条件) 4(1?sinL?sinL?sinL?sinLS13611?FC?sinL?sinL?sinL?SABsinL891719(基线条件)

5.2.21 n=5,t=2,r=3

v1?v2?v3?L1?L2?L3?1800?0

v3?v4?v5?L3?L4?L5?0

v2?v4??BA?L2?L4??CP??1800?05.2.22 n=13,t=6,r=7

图形条件4个,极条件1个,固定角条件1个,固定边条件1个。

?sin(L??L?)sinL?sinL79103?1????Psin(L2?L3)sinL6sinL9(以1点为极)

?sin(L??L??L?)sinL?SsinL12373?BC??SBAsinL7sinL13(固定边条件)

5.2.23 n=16,t=8,r=8;5个图形条件,1个圆周条件,2个极条件。

v1?v2?v13?L1?L2?L13?1800?0

v3?v8?v14?L3?L8?L14?1800?0v4?v5?v6?v7?L4?L5?L6?L7?1800?0v9?v10?v15?L9?L10?L15?1800?0

v11?v12?v16?L11?L12?L16?1800?0v13?v14?v15?v16?L13?L14?L15?L16?3600?0?sin(L??L?)sinL?sinL5873?1??L?)sinL?sinL?sin(L4368(以大地四边形F点为极)

线性化的条件方程为:

?cotL3?cot(L3?L4)?v3?cot(L3?L4)v4?cotL5v5?cotL6v6?cot(L7?L8)v7?[cot(L7?L8)?cotL8]v8??n?1???sinL5sin(L8?L7)sinL3???0sin(L4?L3)sinL6sinL8?

sinL1sinL3sinL9sinL11?1sinL2sinL8sinL10sinL12(以中点四边形F点为极)

线性化的条件方程为:

?sinL2sinL8sinL10sinL12?cotL1v1?cotL2v2?cotL3v3?cotL8v8?cotL9v9?cotL10v10?cotL11v11?cotL12v12+?n?1???0?sinL1sinL3sinL9sinL11?

5.2.24 n=11,t=6,r=5;有4个图形条件,1个极条件。

V1?V9?V10?V11?W1?0

V2?V3?V8?W2?0

V4?V5?V6?V7?W3?0V6?V7??V8?V9?V10?W4?0cotLV11?cotL2V2?cotL3V3?cotL4V4?cot(L5?L6)V5??cot(L5?L6)?cotL6?V6??cotL10?cot(L10?L11)?V10?cot(L10?L11)V11?W5?0

其中:

W1?L1?L9?L10?L11?1800

W2?L2?L3?L8?1800

W3?L4?L5?L6?L7?1800W4?L6?L7?L8?L9?L10?1800n?sinL2sinL4sinL6sin(L10?L11)?W5???1??sinL1sinL3sinL10sin(L5?L6)??

5.2.25 n=13,t=6,r=7;5个图形条件,2个极条件。

V1?V2?V3?V13?W1?0

V4?V5?V6?V7?V12?W2?0V1?V7?V12?V13?W3?0

V4?V10?V11?V12?W4?0V8?V9?V10?V11?W5?0

cot(L1?L2)V1??cot(L2)?cot(L1?L2)?V2??cot(L6?L7)?cotL6?V6?cot(L6?L7)V7?cotL12V12?cotL13V13?W6?0(以 P1 点 为 极)cot(L4?L5)V4??cot(L4?L5)?cotL5?V5??cot(L9)?cot(L9?L10)?V9?cot(L9?L10)V10

?cotL11V11?cotL12V12?W7?0(以B 点为极)

W1?L1?L2?L3?L13?1800其中:

W2?L4?L5?L6?L7?L12?1800W3?L1?L7?L12?L13?1800

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