ROBUST PROCEDURES FOR DATA PREPROCESSING, 
TESTING AND ARCHIVING 
Tamara Bellone* 
Bruno Crippa** 
wire «Xk 
Luigi Mussio 
* DIGET - Politecnico di Torino (Italy) 
Corso Duca degli Abruzzi, 24 - 10129 Torino, Italy 
** DIIAR - Politecnico di Milano (Italy) 
Piazza Leonardo da Vinci, 32 - 20133 Milano, Italy 
bruno@ipmtf4.topo.polimi.it 
Commission I, Working Group 6 
Keywords: Accuracy, reliability, robustness. 
Abstract 
Robust estimation techniques are essentially downweighting methods and, among them, redescending estimators are the 
most promising ones, because their breakdown point is often very high. A method, recently proposed by Rousseeuw and 
Leroy, is here presented and applications to outlier identification in photogrammetry are discussed. 
1. The problem 
Outlier identification and solution methods insensitive to 
outliers are a main topic in the photogrammetric and gen- 
erally survey and mapping community and many significant 
results have been established. The fundamental concepts 
of internal and external reliability introduced by Baarda 
(Baarda '67 et ’68) received a widespread acknowledgment 
and provide guidelines in network design as well as in out- 
lier identification. Many testing strategies have been sug- 
gested to improve the efficiency of data snooping and reduce 
masking effects: some are based on still unidimensional test 
statistics and look for a satisfactory backward and/or for- 
ward elimination procedure. In the last decade also ro- 
bust estimation procedures became part of the mathemat- 
ical background of photogrammetric and generally survey 
and mapping community; further achievements are com- 
ing out in robust testing. This might lead in the future 
to a decline of the fortune of the least squares principle; 
at present, nevertheless, robust estimation methods heavy 
rely on least squares since, as outlined above, their compu- 
tational scheme is based on iterative least squares adjust- 
ments. 
“Robustness is insensitivity against small deviations from 
assumptions” (Huber ’81): it is looked for an estimator 
being perhaps less efficient when all model hypothesis are 
satisfied, but which is still capable, to the contrary, of 
identifying the kernel of consistent observation. Among 
144 
model assumption violations, the more understood is per- 
haps the shape of the true underlying distribution deviating 
slightly from the assumed (usually the gaussian distribu- 
tion). According to (Hampel et al. ’86), “robust statis- 
tics are the statistics of the approximate parametric mod- 
els”; this means robust estimators are derived under a dis- 
tributional model more flexible than the maximum likeli- 
hood estimators: more precisely they provide an infinite di- 
mensional neighbourhood of a specified parametric model. 
Contaminations of the basic distribution are explicitly ac- 
counted for. The estimation procedure is designed to pro- 
vide a screening among the observations, taking a priori 
into account that not all of them should be given the same 
role in determining the solution. This does not happen 
to least squares estimates, where all observations equally 
contribute, on the basis of their a priori variance, to the 
solution. 
Most robust estimation techniques are basically down- 
weighting methods where in an iterative least squares 
scheme suspicious observations undergo to a decrease of 
their role in determining the solution, through the modifi- 
cation of their weights according to some specified criterion. 
The amount of the weight change is generally determined on 
the basis of the (standardized) residual of the observation 
and may involve from a theoretical point of view all obser- 
vations. Following a more pratical approach (Bucciarelli et 
al. ’92), changes to the weights will be assumed to be signif- 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996 
  
ican! 
and 
the « 
to ei 
ical 
chan 
quer 
outli 
ing 1 
with 
Sec 
tech 
inst: 
whe! 
in re 
gres: 
signi 
obse 
tion. 
In | 
the : 
dire 
nity 
iden 
Man 
this 
mati 
ular, 
trian 
Ro 
ful v 
ics v 
may 
tion 
ods) 
for | 
Dig 
intei 
(e.g. 
trac 
reco 
and 
who. 
tion. 
proc 
The 
the 
the 1 
ital 
emp