NATIONAL REPORT OF THE FEDERAL REPUBLIC OF ... - IAG Office

162 Inter-commission committees (ICC) – ICC on Theory (ICCT)
In order to find an optimal solution to the unknown parameters
of the gravity field model, the reliable weighting
factor between SGG and SST must be estimated. In order
to overcome the ill-condition of the normal equation
system, a positive definite regularization matrix (scaled by
unknown regularization parameter) must be added to the
combined normal equation system. To select both the
optimum weighting factors and the optimum regularization
parameter KOCH and KUSCHE (2002) demonstrated the
Monte Carlo variance component estimation to be a suitable
procedure in large-scaled least-squares problems. This
procedure for obtaining the variance components was
developed by ALKHATIB (2007) to be integrated into the
Preconditioned Conjugate Gradients Multiple Adjustment
(PCGMA) algorithm of BOXHAMMER and SCHUH (2006),
BOXHAMMER (2006).
Fuzzy Data Analysis
Systematic effects play a key role in the error budget of
many geodetic applications. Typically, the arising errors
are modeled in terms of random variables and random
distributions. If such an approach is chosen, the data
analysis can be completely based on the theory of stochastics.
As this procedure shows some shortcomings in
terms of inconsistency with practical experiences like, e.g.,
the reduction of systematic effects just by averaging of
observations, a thorough discussion of uncertainty measures
in geodesy is urgently needed; KUTTERER and SCHÖN
(2004) as well as HENNES (2007) discuss some options in
this context. In order to overcome some of the inconsistencies,
an alternative methodology has been proposed by
KUTTERER (2002) which is based on fuzzy data analysis.
The use of interval mathematics (SCHÖN, 2003) can be
considered as a special case. This approach was already
presented in the previous National Report. It has been
extended significantly during 2003-2007 in the following
way. Fuzzy intervals can be used to model the uncertainty
caused by remaining systematic effects in the observations
(NEUMANN and KUTTERER, 2006, 2007). The respective
uncertainty measures (spread, interval radius) can be
quantified based on a sensitivity analysis with respect to
some originary influence parameters (SCHÖN, 2003). This
has been realized for all relevant terrestrial observations
and for GPS phase observations (SCHÖN and KUTTERER,
2005, 2006a, b, 2007). The corresponding mathematical
propagation of uncertainty is available; the effects of data
processing techniques such as observation averaging or
differencing are treated in a consistent way. In case of
vector-valued quantities the derived multidimensional
uncertainty measures are a special case of polyhedrons
(zonotopes); see SCHÖN and KUTTERER (2005). Significant
progress was also achieved for statistical hypotheses tests
for multidimensional fuzzy test statistics (KUTTERER and
NEUMANN, 2007). Ongoing work is on a proper extension
of the Kalman filter for fuzzy data.
Soft computing techniques
In case of complex applications such as in global geodynamics
or the monitoring of large structures it is typically
not possible to describe the considered system or object in
sufficient detail by mathematical equations which are
physically meaningful (structural models). At least to some
part the system’s or object’s behavior has to be modeled
in a more or less descriptive manner using regression or
comparable models. In the last years neuro-fuzzy approaches
such as ANFIS have shown their ability to compete
with other methods just as Artificial Neural Networks
(ANN). For the prediction of Earth Orientation parameters
results were obtained by ANFIS which are similar to ANN
but based on a better computer performance (AKYILMAZ
and KUTTERER, 2004, 2005). A further comparison of ANN
and fuzzy logic has been published by MIIMA and NIEMEIER
(2004a, b). At present, the use of ANFIS in causal inputoutput
models is studied for various modeling purposes
(BOEHM and KUTTERER, 2006). In this modeling context
SCHWIEGER (2004a, b, 2006) is mentioned who has studied
a Monte-Carlo based sensitivity analysis of dynamic models
which allows to manifest the input-output relation mathematically,
and to identify the dominating variables. It is
possible to analyse nonlinear and non-additive relations and
models in a quantitatively correct way. The particular
application was the motion of vehicles.
Extended modeling of quality
Quality in geodesy is typically restricted to modeling and
quantifying the uncertainty of estimated parameters of
interest based on the concept of mean quadratic deviations
or variances, respectively. From a more general point of
view additional features have to be taken into account.
WILTSCHKO (2004) presents a quality model for applications
of geo-data in telematics which comprises measures
for integrity consisting of completeness, consistency and
correctness, reliability (in a more general meaning as usual)
consisting of availability and up-to-dateness, and precision
consisting of metric and semantic precision. It is based on
fault-tree analysis and failure mode and effect analysis. This
extended process-oriented quality model is formulated in
a probabilistic framework and can be subject to optimized
data acquisition and processing. It has been applied to
advanced driver assistance systems.
References
AKYLIMAZ O., KUTTERER H.: Soft Modelling of Possible Blunders
in Geodetic Networks. ARI – The Bulletin of the Istanbul
Technical University, Vol. 54, no. 1, 2003
AKYLIMAZ O., KUTTERER H.: Prediction of Earth Orientation
Parameters by Fuzzy Inference Systems. DGFI Report, No.
75, München, 2003
AKYILMAZ O., KUTTERER H.: Prediction of Earth rotation parameters
by fuzzy inference systems. Journal of Geodesy 78
(2004): 82-93, 2004
AKYILMAZ O., KUTTERER H.: Fuzzy Inference Systems for the
Prediction of Earth Rotation Parameters. In: Sansò F. (Ed.):
A Window on the Future of Geodesy. IAG Symposia, Vol.
128, Springer, pp. 582-587, 2005