2.3 The Example about Gross Errors Location by Two Step
Iterations Method
We give a brief note in Table 4 about gross errors
localization.
TABLE 4 GROSS ERRORS LOCATION BY TWO STEP ITERATIONS METHOD
Point [ 1 2 3 4 5 6 7 8 9 10 | Noted in comprehehsive desions ‘
| | 77] 8.1 2.4 . | observational error vector = E
First | | 4 12.5 2.8 . | gross error V,= 6, V.= -6
Step | it=6! * | : . : : . . | point 5 as Type A observation
| Pel 0.8: .- 3.0 . | point 8 as Type B observation
| aede . | point 5, 8 strong correlation
| | point 9 with good observation
Second| tv "| 24 >. «" 1,6 ”. ’, | point 5,8 weighted zero
Step | it:11 9 ] . : . = gui -. . -4.4 . . | point 5, 8 contained gross error
| |MCCV| 30 «37 |
| | observational error vector = E
| [+ 43.9 2.9 3.6 2:1 533.4 2.7 . . «| gross error V,= -12, V:s-12
litsl[s 1-48 3.7 8.4 4.1 8.9 -3.4 | point 1, 2, 3, 5, 6 and 7 are
First | | | Type A observations
Step ------------------------ T-------------------
| | | after five iterations only
| Iv 13.7 2.2 2.3 | point 1 as Type A observation
| it=6 | ¢ |-4.6 | 33 . 3.6 . . + | point 5, 7 near Type A obs.
| Pau Î d. d. : . . | residual of point 4 is strong
| Foon Fb 7-3. | correlation with point 1, 7
| | point 4 as Type B observation
| Iv | 1.9 1.1 1.3 1.7 | pointi,4, 5, 7 weighted zero
l'it:11*$? 1331 -5.4 2.4 -7.0 | point 4, 7 need further
Second | IMCCV| 0.6 0.2 .55 0.24 | detection
Step ------------------------------------------------- ——
| [v 4 3.9 4.7 | point 4, 7 weighted zero
t'it=i te | -13.0 -13.1 | point 4, 7 contained gross error
| |MCCV| 0.30 0.35 |
From Table 3 and Table 4, we find that when weighted
zero is assigned a pair observation in which residuals
Comparasion of the observations in which residuals are
are of strong correlation after iteration, the not correlated shows that the capability of localizing
correlation of residuals have been disspated and have grvss : errors would decrease even if the critical value
made convenient condition for decision of gross errors is 1.5 instead of 2.5.
localization, because the magnitude of main component
coefficient of standardized residual is decreased.
conclusions
Gross error location, especially for more one gross
error, is a problem that has not been completely solved
in adjustment. From the strategical point review, to
develop the iterated weighted least squares method to
two step iterations method is a powerful way to improve
the capability and relibility for gross errors location.
After the first step iterations, the searching gross
error observations is in a comparatively limited area.
The experiment proved that the second step iterations
play an important part in correcting the mistakes of
decision about gross error observation(s) in the first
step iterations. In the second step, the decision about
gross error observation(s) are concerned with the
magnitude of of standardized residuals and weighted zero
residuals, the correlation of residuals as well as the
main component of standardized residual MCCV. When the
value of MCCV is very small, the comprehensive decisions
will be particulary difficult. One has to further
investigate in gross errors locationin order to get more
knowledges about comprehensive decisions.