2.4 误差方程的组成
按公式Vi?(ajk?ajh)x?j?(bjk?bjh)y?j?ajkx?k?bjky?k?ajhx?h?bjhy?h?li l000i?Li?(ajk?ajh)?Li?Li得：
误差方程系数表和常数项
参数 a b c d ?li 角号 x?i y?i x?j y?j ″ 1 8.4623 14.5660 0.0000 0.0000 0.8 2 -1.1745 -20.2296 0.0000 0.0000 -3.9 3 -13.4603 -1.4653 0.0000 0.0000 0.8 4 6.1725 7.1289 0.0000 0.0000 1.6 5 -6.1725 -7.1289 -1.4888 8.5978 -3.3 6 9.8984 -3.6438 -8.4096 -4.9540 1.8 7 -3.7259 10.7727 9.8984 -3.6438 -2.1 8 18.3607 10.9222 -9.8984 3.6438 5.0 9 -9.8984 3.6438 1.6811 -4.9289 1.6 10 -8.4623 -14.5660 8.2173 1.2851 -5.1 因此误差方程为：
V1?8.4623x?1?14.5660y?1?0.8 V2??1.1745x?1?20.2296y?1?3.9 V3??13.4603x?1?1.4653y?1?0.8 V4?6.1725x?1?7.1289y?1?1.6 V5??6.1725x?1?7.1289y?1?1.4888x?2?8.5978y?2?3.3 V6?9.8984x?1?3.6438y?1?8.4096x?2?4.9540y?2?1.8 V7??3.7259x?1?10.7727y?1?9.8984x?2?3.6438y?2?2.1 V8?18.3607x?1?10.9222y?1?9.8984x?2?3.6438y?2?5.0 V9??9.8984x?1?3.6438y?1?1.6811x?2?4.9289y?2?1.6 V10??8.4623x?1?14.5660y?1?8.2173x?2?1.2851y?2?5.1
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2.5 确定权和组成法方程
因为是等精度观测
???175.593?即：令P?E ， W?BPl???229.854?T??119.7214?? ?25.85921????948.934466.2787?378.85116.28588?N?BTPB??466.27871199.263?73.791?79.3754?BB???378.851?73.791339.2447?41.0007?? ?16.28588?79.3754?41.0007150.9644??由NBBx??W?0得法方程： ?948.9340466.2787?378.851416.2859??x??1???175.593??466.27871199.2630?73.7910?79.3754?????y??1???229.854??=0 ??378.8514?73.7910339.2447?41.0007??16.2859?79.3754?41.0007150.9644????x??-?2?119.7214??y???2??25.85921??2.6 法方程系数阵的逆阵与参数改正数
??0.002492?0.0008070.0026090.000015?N?10.000530?BB???0.0008070.001147?0.000588??0.002609?0.0005880.0058540.000999?? ?0.0000150.0005300.0009990.007173?????x1??0.002492?0.0008070.0026090.000015???y??1??0.0008070.001147?0.000588??175.593??0.06?0.000530???x??=?2??0.002609?0.0005880.0058540.000999????229.854???0.??=?18??cm ?y???2??0.0000150.0005300.0009990.007173???119.7214??0.40??25.85921????0.18??2.7 平差值计算及精度评定 2.7.1 待定点的最或然值为：
X?1?X01?x?1?777.416?0.0006?777.417(m) Y?1?Y01?y?1?320.647?0.0018?320.645(m) X?2?X02?x?2?844.971?0.0040?844.975(m) Y?2?Y02?y?2?504.160?0.0018?504.162(m) 即P1?(777.417,320.645)，P2?(844.975,504.162)。
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2.7.2 观测值的改正数
??l得： 由V?Bx?V1??V??2??V3????V4??V5?????V6??V??7??V8??V??9???V10??14.56600.00000.0000??8.4623??1.1745?20.22960.0000?0.0000????13.4603?1.46530.00000.0000???6.17257.12890.00000.0000????6.1725?7.1289?1.48888.5978???9.8984?3.6438?8.4096?4.9540????3.725910.77279.8984?3.6438???18.360710.9222?9.89843.6438????9.89843.64381.6811?4.9289????1.2851???8.4623?14.56608.2173???0.8???1.29??3.9???0.36???????0.8??0.24??????0.06???1.6??0.70???0.18??3.3???1.45???-??=??（秒） ?0.40???1.8???1.24???????0.18???2.1???0.91???5.0??0.83???1.6??0.14???????5.1????0.54?? 2.7.3 点位中误差：
VTPV7.79?1?0????1.139??，QX?X??NBB
n?t6?x?0Qx?????x??1.139?0.002492?0.06(cm)111?y?0Qy?????y??1.139?0.001147?0.04(cm)111?x?0Qx?????x??1.139?0.005854?0.09(cm)222?y?0Qy?????y??1.139?0.007173?0.10(cm)2222222?P???x?y?P???x?y??0.062?0.042?0.07(cm) ????0.092?0.102?0.13(cm) ??????111222 2.7.4 观测值平差值
??L?V得观测值平差值： 由公式Liii???55?28?11.91????L?V1?1???????V????974153.54L?2????2????93?02?06.24????L?V3?3???????????440352.30L?4????V4??L???50?42?42.85????V5?5?????? 改正数????????L6??595755.96??V6?????69?19?21.19????V?7?L7????????L8??9956?39.03????V8????????V????290551.44L?9????9??????5057?29.54?????V10???L10???
??1.29???0.36????0.24???0.70????1.45???(秒) ?1.24????0.91????0.83??0.14?????0.54??
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第3 章 导线网间接平差
3、有导线网如图所示，A、B、C、D为已知点，P1～P6为待定点，观测了14个角度和9条边长。已知测角中误差σβ=10\，测边中误差σSi=坐标为：
Si（mm）(i=1,2,…,9),Si以m为单位，已知点数据和待定点近似
点号 A B C D X/m 871.1893 632.2173 840.9400 663.4752 角度观测值 o ˊ \301 36 31.0 203 22 35.2 95 41 09.1 224 17 27.4 95 05 02.1 318 16 06.5 53 51 08.7 坐标 Y/m 220.8223 179.4811 533.4018 570.7100 点号 P 1 2 3 4 5 6 观测数据为： 编号 1 2 3 4 5 6 7
坐标 X/m 825.810 740.107 768.340 732.041 681.630 674.567 Y/m 272.250 312.579 392.230 470.885 279.300 506.177 编号 8 9 10 11 12 13 14 角度观测值 o ˊ \145 58 18.1 125 09 37.5 118 35 26.3 131 18 15.2 68 22 31.6 146 19 37.1 139 09 15.9 编号 1 2 3 4 5 6 7 8 9 边长观测值/m 68.582 94.740 84.523 86.668 125.651 111.449 67.289 67.456 65.484 13
设待定点坐标为参数，试按间接平差法求： （1） 误差方程；
（2） 待定点坐标平差值及点位中误差。
解：n=23,有23个误差方程，其中14个角度误差方程，9个边长误差方程，必要观测数t=2×6=12，r=n-t=11,现选取待定点坐标平差值为参数，即：
??X?Y?XP1P1???XYP2P2?Y?XP3P3??XYP4P4?Y?XP5P5??XYP6P6?
T3.1 计算各边坐标方位角改正数方程的系数 见表3-1：
表3-1 坐标方位角改正数方程系数计算表
边号 ?Y 方向 0?X 0(s0)2 (m)2 4704.089196 8971.43245 7141.38409 7504.2264 近似边长 (m) (m) s0 m 近似坐标方位角 ° ˊ \a (\?X0?0 S?Y0?0 S0.7498 -0.4258 -0.9425 -0.9080 -0.4979 0.8962 0.4946 -0.5233 -0.9855 S?S0(mm) -4.36 22.35 16.29 41.06 82.92 69.34 5.63 11.31 4.72 ????Y0b(\?1000?S??02????X0 02 -2.2550 0.9272 2.3006 2.1620 0.8178 -1.6597 -1.5163 1.6003 3.1046 1000?S??S1 S2 S3 S4 S5 S6 S7 S8 S9
p1A -51.4277 45.3793 40.329 79.651 78.655 62.5168 -85.703 28.233 -36.299 108.899 68.58636 311 25 29.52 -0.6616 94.71765 154 47 59.55 84.50671 0.9048 -1.9898 1.9704 -0.8155 0.9977 -1.4246 0.8216 2.6644 2.6062 0.5336 14
p1p2 p2p3 p3p4 p4C 70 28 57.64 -0.3341 0.4190 86.62694 114 46 23.35 15767.34248 125.56808 29 51 33.47 -0.8673 p5B -99.8189 -49.4127 12405.42772 111.37966 243 39 48.63 0.44360 p2p5 -33.279 p4p6 p6D 35.292 64.533 -58.477 -57.474 4527.05137 4548.78594 67.28337 209 38 38.44 67.44469 148 26 52.55 65.47928 99 45 09.32 0.8691 0.8522 0.1694 -11.0918 4287.536116