大地测量工具高程-最小二乘

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计算软件: 平差之星网络版(水准网数据处理)
计算时间: 2021/12/10 8:07:22

观测等级: 2 ; 观测值总数: 48 ; 总点数: 23 ; 已知点数: 2
是否为往返观测高差: True; 指定路线数: 2 ; 标尺数: 1
水准面不平行性改正:True; 重力异常改正:False
验前单位权中误差: 0.00500 ; 显著水平因子: 0.00300

已知高程:

1 23 331.9760
2 24 335.9620

高差观测值:

1 23 09 1.0096 0.830
2 09 15 0.0963 0.900
3 15 16 0.0244 1.210
4 16 22 -2.3854 1.590
5 22 27 4.2147 1.740
6 27 26 0.2589 1.240
7 09 23 -1.0106 0.860
8 15 09 -0.0943 0.900
9 16 15 -0.0229 1.200
10 22 16 2.3864 1.580
11 27 22 -4.2133 1.780
12 26 27 -0.2587 1.240
13 04 08 1.3867 3.360
14 08 23 -7.2887 1.310
15 08 04 -1.3827 3.360
16 23 08 7.2897 1.260
17 26 25 0.2888 1.350
18 25 24 0.4831 2.670
19 24 17 -4.3457 1.450
20 17 11 0.2168 1.260
21 11 18 0.2332 2.830
22 18 12 -0.4511 1.400
23 12 02 1.0046 1.200
24 02 03 0.0346 3.150
25 03 04 5.2299 1.710
26 25 26 -0.2875 1.330
27 24 25 -0.4825 2.670
28 17 24 4.3467 1.450
29 11 17 -0.2171 1.260
30 18 11 -0.2288 2.800
31 12 18 0.4500 1.430
32 02 12 -1.0032 1.200
33 03 02 -0.0323 3.120
34 04 03 -5.2274 1.740
35 26 21 -3.0666 1.390
36 21 20 -0.8835 1.420
37 20 14 4.2209 1.660
38 14 19 -3.2726 1.880
39 19 13 0.7952 1.770
40 13 01 -0.5731 1.100
41 01 04 5.4681 1.170
42 21 26 3.0688 1.300
43 20 21 0.8824 1.410
44 14 20 -4.2212 1.640
45 19 14 3.2701 1.870
46 13 19 -0.7961 1.770
47 01 13 0.5718 1.110
48 04 01 -5.4673 1.230

经纬度列表:

1 23 343623.1000 1150848.000
2 24 343806.0000 1150700.000
3 09 343636.0000 1150900.000
4 15 343653.1000 1150912.000
5 16 343700.0000 1150948.000
6 22 343736.0000 1151018.000
7 27 343811.1000 1151024.000
8 26 343811.1000 1150936.000
9 04 343530.0000 1150700.000
10 08 343630.0000 1150811.100
11 25 343818.0000 1150842.000
12 17 343730.0000 1150635.100
13 11 343648.0000 1150624.000
14 18 343717.1000 1150648.000
15 12 343636.0000 1150641.100
16 02 343617.1000 1150630.000
17 03 343542.0000 1150630.000
18 21 343741.1000 1150942.000
19 20 343736.0000 1150842.000
20 14 343653.1000 1150823.100
21 19 343724.0000 1150748.000
22 13 343630.0000 1150718.000
23 01 343600.0000 1150706.000

尺长改正计算结果:
No. P1 P2 h12 δ(mm) h12+δ

1 23 09 1.0096 0.0050 1.0096
2 09 23 -1.0106 -0.0051 -1.0106
3 09 15 0.0963 0.0005 0.0963
4 15 09 -0.0943 -0.0005 -0.0943
5 15 16 0.0244 0.0001 0.0244
6 16 15 -0.0229 -0.0001 -0.0229
7 16 22 -2.3854 -0.0119 -2.3854
8 22 16 2.3864 0.0119 2.3864
9 22 27 4.2147 0.0211 4.2147
10 27 22 -4.2133 -0.0211 -4.2133
11 27 26 0.2589 0.0013 0.2589
12 26 27 -0.2587 -0.0013 -0.2587
13 04 08 1.3867 0.0069 1.3867
14 08 04 -1.3827 -0.0069 -1.3827
15 08 23 -7.2887 -0.0364 -7.2887
16 23 08 7.2897 0.0364 7.2897
17 26 25 0.2888 0.0014 0.2888
18 25 26 -0.2875 -0.0014 -0.2875
19 25 24 0.4831 0.0024 0.4831
20 24 25 -0.4825 -0.0024 -0.4825
21 24 17 -4.3457 -0.0217 -4.3457
22 17 24 4.3467 0.0217 4.3467
23 17 11 0.2168 0.0011 0.2168
24 11 17 -0.2171 -0.0011 -0.2171
25 11 18 0.2332 0.0012 0.2332
26 18 11 -0.2288 -0.0011 -0.2288
27 18 12 -0.4511 -0.0023 -0.4511
28 12 18 0.4500 0.0022 0.4500
29 12 02 1.0046 0.0050 1.0046
30 02 12 -1.0032 -0.0050 -1.0032
31 02 03 0.0346 0.0002 0.0346
32 03 02 -0.0323 -0.0002 -0.0323
33 03 04 5.2299 0.0261 5.2299
34 04 03 -5.2274 -0.0261 -5.2274
35 26 21 -3.0666 -0.0153 -3.0666
36 21 26 3.0688 0.0153 3.0688
37 21 20 -0.8835 -0.0044 -0.8835
38 20 21 0.8824 0.0044 0.8824
39 20 14 4.2209 0.0211 4.2209
40 14 20 -4.2212 -0.0211 -4.2212
41 14 19 -3.2726 -0.0164 -3.2726
42 19 14 3.2701 0.0164 3.2701
43 19 13 0.7952 0.0040 0.7952
44 13 19 -0.7961 -0.0040 -0.7961
45 13 01 -0.5731 -0.0029 -0.5731
46 01 13 0.5718 0.0029 0.5718
47 01 04 5.4681 0.0273 5.4681
48 04 01 -5.4673 -0.0273 -5.4673

指定路线的偶然中误差:
No. P1 P2 h12 h21 Δ [Δ] [S]

1 23 09 1.0096 -1.0106 -0.9300 -0.9300 0.8450
1 09 15 0.0963 -0.0943 1.9800 1.0500 1.7450
1 15 16 0.0244 -0.0229 1.5200 2.5700 2.9500
1 16 22 -2.3854 2.3864 0.9700 3.5400 4.5350
1 22 27 4.2147 -4.2133 1.3600 4.9000 6.2950
1 27 26 0.2589 -0.2587 0.2700 5.1700 7.5350
MΔ = 0.6124 M允 = 1.0000 [Δ] = 5.1700

2 04 08 1.3867 -1.3827 4.0000 4.0000 3.3600
2 08 23 -7.2887 7.2897 1.0200 5.0200 4.6450
MΔ = 0.8345 M允 = 1.0000 [Δ] = 5.0200

正反向高差之差值、高差中数计算结果:
No. P1 P2 h12 h21 h12+h21 限差(等级) 限差(指定Miu) 高差中数

1 23 09 1.0096 -1.0106 -0.9300 3.6770 13.0000 1.0101
2 09 15 0.0963 -0.0943 1.9800 3.7947 13.4164 0.0953
3 15 16 0.0244 -0.0229 1.5200 4.3909 15.5242 0.0236
4 16 22 -2.3854 2.3864 0.9700 5.0359 17.8045 -2.3859
5 22 27 4.2147 -4.2133 1.3600 5.3066 18.7617 4.2140
6 27 26 0.2589 -0.2587 0.2700 4.4542 15.7480 0.2588
7 04 08 1.3867 -1.3827 4.0000 7.3321 25.9230 1.3847
8 08 23 -7.2887 7.2897 1.0200 4.5343 16.0312 -7.2892
9 26 25 0.2888 -0.2875 1.2600 4.6303 16.3707 0.2882
10 25 24 0.4831 -0.4825 0.6000 6.5361 23.1084 0.4828
11 24 17 -4.3457 4.3467 1.0700 4.8166 17.0294 -4.3462
12 17 11 0.2168 -0.2171 -0.3000 4.4900 15.8745 0.2169
13 11 18 0.2332 -0.2288 4.3500 6.7112 23.7276 0.2310
14 18 12 -0.4511 0.4500 -1.1500 4.7582 16.8226 -0.4505
15 12 02 1.0046 -1.0032 1.4000 4.3818 15.4919 1.0039
16 02 03 0.0346 -0.0323 2.3000 7.0824 25.0400 0.0334
17 03 04 5.2299 -5.2274 2.5500 5.2536 18.5742 5.2287
18 26 21 -3.0666 3.0688 2.1500 4.6390 16.4012 -3.0677
19 21 20 -0.8835 0.8824 -1.1200 4.7582 16.8226 -0.8829
20 20 14 4.2209 -4.2212 -0.3300 5.1381 18.1659 4.2210
21 14 19 -3.2726 3.2701 -2.4700 5.4772 19.3649 -3.2713
22 19 13 0.7952 -0.7961 -0.9000 5.3217 18.8149 0.7957
23 13 01 -0.5731 0.5718 -1.2800 4.2048 14.8661 -0.5724
24 01 04 5.4681 -5.4673 0.8000 4.3818 15.4919 5.4677

按往返高差不符值计算的全区每公里高差中数的偶然中误差: 0.6584(mm)

正常水准面不平行改正(正高改正)计算结果:
No. P1 P2 h(m) ε(mm) h+ε

1 23 09 1.0101 -0.0957 1.0100
2 09 15 0.0953 -0.1438 0.0951
3 15 16 0.0236 -0.0479 0.0236
4 16 22 -2.3859 -0.2867 -2.3862
5 22 27 4.2140 -0.2875 4.2137
6 27 26 0.2588 0.0000 0.2588
7 04 08 1.3847 -0.4873 1.3842
8 08 23 -7.2892 0.0483 -7.2892
9 26 25 0.2882 -0.0483 0.2881
10 25 24 0.4828 0.0967 0.4829
11 24 17 -4.3462 0.2883 -4.3459
12 17 11 0.2169 0.3343 0.2172
13 11 18 0.2310 -0.2389 0.2307
14 18 12 -0.4505 0.3344 -0.4502
15 12 02 1.0039 0.1434 1.0041
16 02 03 0.0334 0.2872 0.0337
17 03 04 5.2287 0.0965 5.2287
18 26 21 -3.0677 0.2402 -3.0675
19 21 20 -0.8829 0.0478 -0.8829
20 20 14 4.2210 0.3359 4.2214
21 14 19 -3.2713 -0.2403 -3.2716
22 19 13 0.7957 0.4309 0.7961
23 13 01 -0.5724 0.2394 -0.5722
24 01 04 5.4677 0.2412 5.4680

=== 环闭合差计算 ===

环闭合差： 23 - 08 - 04 - 01 - 13 - 19 - 14 - 20 - 21 - 26 - 27 - 22 - 16 - 15 - 09 - 23
[S]= 22.5400(km); W = -1.4044(mm)
按指定等级(2等)计算的限差为: 18.991 ; 按指定Sigma计算的限差为:47.476 )

环闭合差： 26 - 21 - 20 - 14 - 19 - 13 - 01 - 04 - 03 - 02 - 12 - 18 - 11 - 17 - 24 - 25 - 26
[S]= 27.3700(km); W = 1.9365 (mm)
按指定等级(2等)计算的限差为: 20.927 ; 按指定Sigma计算的限差为:52.316 )

=== 路线闭合差计算 ===
附合路线： 24 - 25 - 26 - 27 - 22 - 16 - 15 - 09 - 23
[S] = 11.5450(km); W = -0.1117 (mm)
按指定等级( 2等)计算的限差为: 13.591 , 按指定Sigma计算的限差为:33.978 )

最小二乘平差结果：
[pvv]=0.00000016
μ=±0.00023234

==== 高程平差值及其精度 ====

点名近似高程改正数高程平差值中误差

23 331.9760 0.0000 331.9760 0.0000
24 335.9620 0.0000 335.9620 0.0000
09 332.9860 0.0000 332.9860 0.0002
15 333.0811 -0.0001 333.0811 0.0003
16 333.1047 -0.0001 333.1046 0.0003
22 330.7186 -0.0002 330.7184 0.0004
27 334.9323 -0.0003 334.9320 0.0004
26 335.1911 -0.0003 335.1908 0.0003
04 337.8804 0.0008 337.8812 0.0004
08 339.2652 0.0000 339.2652 0.0002
25 335.4792 -0.0002 335.4789 0.0003
17 331.6161 0.0001 331.6162 0.0003
11 331.8333 0.0002 331.8335 0.0003
18 332.0641 0.0003 332.0644 0.0004
12 331.6139 0.0004 331.6143 0.0005
02 332.6179 0.0005 332.6184 0.0005
03 332.6516 0.0007 332.6523 0.0004
21 332.1236 -0.0004 332.1232 0.0004
20 331.2407 -0.0006 331.2402 0.0004
14 335.4621 -0.0007 335.4614 0.0005
19 332.1905 -0.0009 332.1897 0.0005
13 332.9866 -0.0010 332.9856 0.0004
01 332.4144 -0.0012 332.4133 0.0004

==== 观测值平差值及其精度 ====

No. 起点终点观测高差ｖ高差平差值观测权中误差

1 23 09 1.0100 0.0000 1.0100 1.18 0.0002
2 09 15 0.0951 0.0000 0.0951 1.11 0.0002
3 15 16 0.0236 0.0000 0.0235 0.83 0.0002
4 16 22 -2.3862 -0.0001 -2.3862 0.63 0.0003
5 22 27 4.2137 -0.0001 4.2137 0.57 0.0003
6 27 26 0.2588 -0.0001 0.2587 0.81 0.0002
7 04 08 1.3842 -0.0001 1.3841 0.30 0.0004
8 08 23 -7.2892 0.0000 -7.2892 0.78 0.0002
9 26 25 0.2881 0.0001 0.2882 0.75 0.0002
10 25 24 0.4829 0.0001 0.4831 0.37 0.0003
11 24 17 -4.3459 0.0001 -4.3458 0.69 0.0003
12 17 11 0.2172 0.0001 0.2173 0.79 0.0003
13 11 18 0.2307 0.0002 0.2309 0.36 0.0004
14 18 12 -0.4502 0.0001 -0.4501 0.71 0.0003
15 12 02 1.0041 0.0001 1.0041 0.83 0.0002
16 02 03 0.0337 0.0002 0.0339 0.32 0.0004
17 03 04 5.2287 0.0001 5.2289 0.58 0.0003
18 26 21 -3.0675 -0.0001 -3.0676 0.74 0.0003
19 21 20 -0.8829 -0.0001 -0.8830 0.71 0.0003
20 20 14 4.2214 -0.0002 4.2212 0.61 0.0003
21 14 19 -3.2716 -0.0002 -3.2717 0.53 0.0003
22 19 13 0.7961 -0.0002 0.7959 0.56 0.0003
23 13 01 -0.5722 -0.0001 -0.5723 0.90 0.0002
24 01 04 5.4680 -0.0001 5.4679 0.83 0.0002