observations with zero weight and calculated MCCVi in
Table 1.
TABLE 1 THE MAIN COMPENENT COEFFICIENT OF STANDARDIZED
RESIDUAL
Point | P=I | 8.2.56] 8£5,2.88|P.: z,88,P …w=-.05] Pas =,36
| | P, =P, =0| Ps =P;,=0| p, *P;70]| p, 2P470| p, zP.z0
| | |-- | |
1 4.801 | | | |
2 1.071 04° | | | |
3. | 411: 34. 1 | | |
4 | .65 | | | .30 "4 .65 À
5 | 54 | [ 30 | | |
6 | 36 | | | | | 33
71-1 .78 1 | | 935 1 |
8 1.79] r 0 | | |
9 1.941 | | | + 28
10 | .84 | | | | 83 1
From Table 1, one may find that when correlation
coefficient of residuals is increased the main component
coefficient of standardized residual will be decreased.
4.2.2 The Weighted Zero Residual and Standardized
Residual When Observations without Gross Error We take
design matrix A, error vector E, different weight matrix
P and calculated results listed in Table 2.
TABLE 2 WEIGHTED ZERO RESIDUAL AND STANDARDIZED RESIDUAL
Example 1 | Example 2
|
Point v V € plv V € p
|
1 1.9 717 81. 11] 1.1 -2.1. —971. 1
2 go 71.8. —399 1| 1.8 3.6 ~.39 1
3 2.1 16.0; 1.5 0j 1.0 -7.8 . 1.5 0
4 2.1. z17.0 -.581. 01 1.0 2.6 —.51 Q0
5 oii = A 44. 1] „x. 1.4 Jd4 |
6 „7: - 6.6 9... 4 1. 1.0 -9.8 .08 0
7 2.2. .-17.1., -.87 9| 2.1 $.—16.4 -.81 |
8 o3 4-9. 17 2 =" 4 -.15 À
9 1:0 2-1 2.11 11 2.1 3.1 . 2.11 1
10 .8 8 *.19 lt 1.9 '-1.9 -.15 1
From Table 2, we find that even observations do not
contain any gross error, the magnitude of some weighted
zero residual is still large. However the magnitude of
standardized residual always is not too large. Therefore
using weighted zero residual as statistical quantity may
be possible to get wrong decision about localizing gross
errors.
5. CONCLUSIONS
The approximate expressions of Qvv.P matrix are power
tools for discussion of gross errors localization. The
fast recursive algorithm to be calculated Qvv.P matrix
would be very helpful using standardized residuals as
statistical quantity for statistical test in every
iteration. One should be careful about the limitation of
the fast recursive algorithm in practical adjustment.
From the analysis of the properties about correlation of
residuals and weighted zero residual. We not only have
to further improve the weight function but also have to
from the strategical point review investigate about
gross errors location.
REFERENCES
Shan Jie, 1988. A fast recursive algorithm for
repeated computation of the reliability matrix Qvv.P.
Acta Geodetica et Cartographica Sinica. vol. 17,
No. 4 : 269-227.
Stefanovic, P., 1985. Error treatment in photogra-
mmetric digital techniques. ITC Journal. 1985-2.:
93-95.
Wang Zhizhuo, Theory of gross error detection.
Photogrammetric principle (with remote sensing)
Publishing House of Surveying and Mapping, Bejing, May
1990. chapter 17 : 196-217.
Wang Renxiang, 1986a. Studies on weight function for
robust iterations. Acta Geodetica et Cartographica
Sinica. vol. 15, No. 2 : 91-101.
Wang Renxiang, 1988b. Theoretical capacity and
limitations of localizing gross errors by robust
adjustment. ISPRS, Kyoto, Commission III, July, 1988.
Wang Renxiang, 1989c. Effects of parameters of weihgt
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adjustment. Acta Geodetica et Cartographica Sinica.
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