ample
ction in an engineer-
on method described
norm data snooping
nge photogrammetric
in Figure 8.
etry Example. Photo
rity.
cluded four exposure
d seven unknown ob-
rk redundancy of 35.
ocus of this example,
rbed by 50m (noted
ations were randomly
of this limited exam-
lay be correctly iden-
jon whereas repeated
ify multiple blunders
of observations with
int which is observed
. It appears that the
ih the intentional er-
In addition to the
l, a compelling rea-
ease with which large
a visual examination
10.
,» norm residuals
L1 La
p-value | p-value :
0.00005 | 0.01097
0.32227 | 0.00470
0.06923 | 0.00001
0.05638 | 0.01420
0.01854 | 0.00001
0.19880 | 0.25638
0.30007 | 0.22081
0.00001 | 0.00001
e initial network un-
stations which were
utions containing un-
Adding a fourth ex-
] thereby increasing
a 1996
Figure 9: Lj Norm Residual Plot: Data Contains Two
50um Blunders
40 T T T T T T T
30 3
10 © 0°
o
Q9 9 oo e o o
0-0 ¢, 00 0x0 - 0000 “ao 0 © 0 0.9 0000 qo0o oc0oo oooco ood" oo C0 -
5.0 o co 9. 9
-10Fr- -— e o. 9 cis CY 4
Residual Magnitude (um)
o
1 1 L
10 20 30 40 50 60 70 80
Observation Number
Figure 10: L5 Norm Résidual Plot: Data Contains Two
50um Blunders
20 T T T T T T T
-5r ; Qi on
Residual Magnitude (um)
©
T
©
1 L 1
10 20 30 40 50 60 70 80
Observation Number
network redundancy) eliminated the “spike-only” residual
sampling distributions.
8 Conclusions
Based on these preliminary investigations and numerical
examples, it appears that analysis of L; residuals can be
put on a sound statistical footing by Monte Carlo gener-
ation of sampling distributions. This together with the
robust character of Li estimation makes it worthy of con-
sideration for analysis of photogrammetric and geodetic
networks. As pointed out, however, there are some po-
tential pitfalls to avoid in network design when network
redundancy is minimal.
References
[1] Baarda, W., 1968. A Testing Procedure For Use In
Geodetic Networks, Neth. Geod. Comm., Publ. on
Geod., New Series 2, No. 5 Delft.
43
Bassett, G., 1973. Some properties of the Least Ab-
solute Error Estimator. PhD. Dissertation, University
of Michigan.
Kavouras, M., 1982. On the Detection of Outliers
and the Determination of Reliability in Geodetic Net-
works. Technical Report No. 87, University of New
Brunswick, Canada.
Mackenzie, A., 1985. Design and Assessment of Hor-
izontal Survey Networks. Master of Science Thesis,
University of Calgary.
Marshall, J. and Bethel, J., (in press 1996). Basic
Concepts of L1 Norm Minimization for Surveying Ap-
plications. Journal of Surveying Engineering.
Menke, W., 1989. Geophysical Data Analysis: Dis-
crete inverse theory, Academic Press, Inc. San Diego,
CA.
Mikhail, E., 1976. Observations and Least Squares,
IEP, New York.
Pope, A., 1976. The Statistics of Residuals and The
Detection of Outliers, NOAA Technical Report NOS
65 NGS 1, Rockville, Md.
Press, W., et. al 1992. Numerical Recipes in C, the
Art of Scientific Computing, Second Edition, Cam-
bridge University Press.
Zarembka, P. ed., 1974. Frontiers in econometrics.
Academic Press, New York, N.Y.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
