Geography Reference
In-Depth Information
Table 24.4
Residual from a Balanced Least Absolute Value fit (LESS)
No.
ry
1
(m)
ry
2
(m)
ry
3
(m)
1
−
0.0419930
0.0000000
+0.1886574
2
+0.2921596
0.0000000
−
0.0788454
3
−
0.1511354
−
0.5772763
+0.5135602
4
+0.0000000
+0.2632668
−
0.2783069
5
+0.4943256
+0.0149275
+0.0000000
6
−
0.0322810
−
0.1844494
+0.0000000
7
+0.9364496
+0.0000000
+0.4995037
8
+0.0000000
+0.2710426
+0.0365388
9
+0.6029285
−
1.2504552
−
0.1811957
10
−
0.0381260
+0.0000000
+0.0000000
11
+1.1150286
+0.0000000
−
0.4470969
12
−
0.0271904
+0.2160558
+0.1043160
−
−
−
13
0.0595793
0.2013183
0.1691942
14
+0.7286051
+0.4248259
+0.6807238
15
+0.6027258
−
0.1983727
−
0.0931333
Table 24.5
Residual from a Minimax fit (MINIMAX)
No.
ry
1
(m)
ry
2
(m)
ry
3
(m)
1
−
0.6914626
+0.0615821
+0.2846016
2
−
0.5232632
+0.2105376
+0.2030011
3
−
0.6914626
−
0.2812702
+0.6414800
4
−
0.6914626
+0.6779095
+0.0221739
5
−
0.0606393
+0.4210982
+0.2376789
6
−
0.5898076
+0.2813725
+0.2573426
7
+0.3744737
+0.4550569
+0.6914626
8
−
0.5190582
+0.6914626
+0.2043970
9
+0.1094704
+0.6914626
−
0.0879036
10
−
0.6593011
+0.3076530
+0.1412971
11
+0.6914626
+0.6914626
−
0.6914626
12
−
0.4712279
+0.5630593
+0.0311289
13
−
0.6914626
−
0.1424975
−
0.2271799
14
+0.3596312
+0.6914626
+0.3268494
15
+0.1433850
−
0.1146535
−
0.3755350
number 1 and point number 15 from 834km to 8.34cm. Now as being documented by Tables
24.9
and
24.10
the parameters 7, 8, 9 occur to be significantly large in size compared to the other
parameters.
Because of a priori linearity the ten parameter transformation group
C
10
(3)
close to the iden-
tity
reveals some benefits in practice. Usually three-dimensional Cartesian coordinate transfor-
mations suffer from their necessity to work out iterations due to nonlinearity, a fact which makes
blunder detection
by statistical means dicult. Here the assumption of “small” rotation angles
is widely met in practice. Alternatively large orientation parameters could be determined by a
pre-transformation fit. A report of such a procedure will be given elsewhere.
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