七参数计算表格
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利用EXCEL表格解算七参数的方法
误差方程系数矩阵B
100-2.8310-15.83322.703
010 4.68315.833013.726
001 3.266-22.703-13.7260
100-2.8640-15.76322.656
010 4.67315.763013.884
001 3.251-22.656-13.8840
100-2.870-15.95422.504
010 4.64215.954013.912
001 3.291-22.504-13.9120
100-2.8820-15.87822.519
010 4.64515.878013.974
001 3.275-22.519-13.9740
100-2.8770-15.9122.514
010 4.64415.91013.946
001 3.282-22.514-13.9460
100-2.8680-16.06422.429
010 4.62616.064013.905
001 3.313-22.429-13.9050
18×7
B矩阵的转置矩阵B T由TRANSPOSE(A3:G20)得到10010010
01001001
00100100 -2.831 4.683 3.266-2.864 4.673 3.251-2.87 4.642 015.833-22.703015.763-22.656015.954
-15.8330-13.726-15.7630-13.884-15.9540
22.70313.726022.65613.884022.50413.912
7×18
法方程组成B T B
600-17.1920-95.402135.325
06027.91395.402083.347
00619.678-135.325-83.3470
-17.19227.91319.678243.66020.0050520.008174-0.007087
095.402-135.3250.0050524569.17341879.78891325.2593
-95.4020-83.3470.0081741879.78892674.8021-2151.666
135.32583.3470-0.007091325.2593-2151.6664210.0211
法方程B T B的逆矩阵
22984.591814.03211755.53464.503247.22132554.53045-569.1299
1814.0327480.84292.5959-752.623-117.928534.843924-151.4806
11755.53292.595916381.71-527.099381.94202434.69752-281.7222
464.503-752.623-527.099161.5650.10649860.0272444-0.050205
247.2213-117.929381.9420.10649912.3809247.4183752-5.717858
554.530434.84392434.69750.0272447.418375219.254797-11.00882
-569.13-151.481-281.722-0.0502-5.717858-11.0088217.466494
七参数计算结果的精度评定
V=BY-L
单位权中误差Q20=V T V/3N-7Q2Y=Q20(B T B)-1
-20.5052-20.5080.0028228
-116.909-116.9130.0042437
-45.3784-45.3830.0046311
-21.4521-21.452-0.000136
-116.646-116.636-0.00988
BY=-44.717 L=-44.710 V=-0.006996
-20.9457-20.941-0.00474
-116.873-116.8740.001371
-43.9377-43.9420.004288
-21.4682-21.4710.0028119
-116.705-116.7090.0040715
-43.8348-43.8370.0022114
-21.2453-21.239-0.006259
-116.777-116.7810.0037419
-43.8854-43.8890.0036197
-20.5455-20.5510.0055
-117.043-117.039-0.003548
-43.6328-43.625-0.007755
V T=0.0028230.0042440.004631-0.000136-0.00988-0.006996-0.00474
V T V=0.0004354
Q20=VTV/3N-7=0.0004354/3×6-7=0.0000396
0.91米
0.296米
Q2Y=0.649米
0.00639ppm
0.00049
0.9540.5440.8050.07990.022
米 米 米 ppm 秒
常数项矩阵L
-20.508
-116.913
-45.383
-21.452
-116.636
-44.71
-20.941
-116.874
-43.942
-21.471
-116.709
-43.837
-21.239
-116.781
-43.889
-20.551
-117.039
-43.625
18×1
由TRANSPOSE(A3:G20)得到
01001001
00100100
10010010
3.291-2.882
4.645 3.275-2.877 4.644 3.282-2.868
-22.504015.878-22.519015.91-22.5140
-13.912-15.8780-13.974-15.910-13.946-16.064 022.51913.974022.51413.946022.429
B T L
-126.162
-700.952
-265.386
-3769.743467
-5159.53205
5692.165705
-12582.504
七参数计算结果
-129.221⊿X
-227.833⊿Y
-148.557⊿Z
13.50878M
0.59732Εx