the correlation coefficient of the two
ie. the two
weighted zero,
observational residuals must be zero.
residuals are no longer correlated.
1.2.3 For any two observations where residuals are
of strong correlation and weighted zero, the value of
main component coefficient of the standardized residuals
will be decreased evidently.
In the second step, the observation(s) weighted zero
will be decided according to the comprehensive decison
which include the analysed correlation of residuals,
statistical test using standardized residuals and
refered weighted zero residuals.
1.3 The Programm for the Second Step Iterations
1.3.1 Type A observation After the first step
iterations, the observation where standardized residual
is larger than the critical value which is 2.5 in this
paper would be a possible gross error observation and
called Type A observation. The correlation coefficient
of residuals will be calculated and make analysis as
fellows
Calan = ;
Bk pq ,kz1,m kxi
where i = the number of the type A observation
k = the number of another observation
For Type A observations,
if Pix 2%7 pecored p;, and k
if bp, <0.7 , then the observation i to be decided as
contained gross error and always weighted zero in
sequential iterations.
1.3.2 Type B Observation Type B observation is
determined by two factors. The first is the frequency
of correlation coefficient of which value is larger than
0.1. The second is the magnitude of correlation
coefficient.
1.3.3 Assigning Zero Weight to the Pair Observation
of Type A and Type B It is allowable that more one
pair observation of Type A and Type B to be assigned
zero weight in an iteration, if the redundante number of
the adjustment system is large enough.
1.3.4 Transferring the Weighted Zero Residuals to
the Stndardized Residuals We have to transfer weighted
zero residual fo standardized residual, calculate the
main component coefficient of the standardized residuals
as well as make statistical test. In consideration of
the properties of weighted zero residual, We take 1.5
as the critical value in the experiment, when the main
component coefficient is smaller than 0.5.
1.4 The Factors About Comprehensive Decisions
There are five factors have to be considered in the
comprehensive decisions.
1.4.1 Whether the standardized residual is larger
than the critical value.
1.4.2 Checking the correlation of residuals.
1.4.3 Checking the magnitude of the main component
coefficient of standardized residual.
1.4.4 Checking the magnitude of the weighted zero
residual.
1.4.5 If necessary, one have to refer to the data
about the previous iterations.
2. EXAMPLES ABOUT GROSS ERROR LOCATION
BY THE TWO STEP ITERATIONS METHOD
We take the calculation of photo relative orientation
parameters with simulated data as an example for the
discussions.
design matrix A
4 8 1,0 QS 1.0
(D. 2.0 1.0. 71.0 .Ü
071.0... 2.0 JD. -1.9
71.0;,.:0.:.2.0. -1.0 .0
JD 1.0. 2.0 D 71.0
D. .0.2.9..-1.0 .0
9.5: 2.0 7.8 =
Ao: 8.0.04. 0..0 11.0
-.04 -.16 1.04 -.2 -.8
.16 .04 1.04 -.8 7.2
Qvv.P matrix ( as P = I )
84 -.13 -.15 11 -.06...16. .66 -.16 -.31-.16
60 .18 -.12 .13 -.12 -.06 .03 -.17 -.34
7. .02. .06 -.13 -.15. .06 -.16 ..1
43 -.06 .07 -.45 .01 .05 -.03
A1 -.10 -.04 -.45 03 .07
13:.03. 02 11 +15
symmetry 461 ...01. .01. .01
.62 -.08 -.02
.71 -.18
„70
The simulated observationl error vector of vertical
parallax is
E =(-.87 -.39 1.5 7.51 .44 .08 -.87 -.75 2.11 -.75)
2.1 The Capacity of gross Error Location by First Step
Iterations
It is assumed that the observations contain only one
gross error and use the weight function proposed by the
present author. After five times of iterations, the
minimum of gross error which can be located by first
Step iterations is listed in Table 1.
TABLE 1 THE MINIMUM LOCATED GROSS ERROR
Point| 1 “2 3 "4-5 6 T 8 9.10
|--
6G) [^5 14 12^ 9 4^1 235 95 3 5 4 4
| y, > 36
(-) | -4 -5 -9 -5 -5 -17 Z -6 -4 4
Gi 1.6400 .17 43 .41 113 .61 82 .71 .70
The condition of this adjustment system is pretty good
for gross error location, because the average value of
main diagonal element of Qvv.P matrix is egual to 0.5.
The main diagonal elements of Qvv.P matrix related to
observation 1, 2, 8, 9 and 10 are rather big and small
gross error can be located correctly. . However the main
component coefficient of Qvv.P matrix related to
observation 6 is relatively small and only large gross
error can be located. In observation 7 and 4, residuals
are of strong correlation(»^^ - 0.88), both observation
7 and observation 4 are decided as containing gross
error. When point 7 contain gross error in the interval
of 240 -- 350
