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

160
Quality Measures and Control
(Stochastic and Non-Stochastic Methods of Data Evaluation)
Introduction and overview
Talking about quality in geodesy is a very heterogeneous
task with many different aspects. As the spectrum of
methods in geodetic data analysis covers estimation,
filtering, testing, and other techniques it is rather hard to
provide a clear and unique picture. In all fields a proper
modeling is mandatory. This compilation is dedicated to
relevant scientific work in Germany within the period 2003-
2007. As there has not been much work which was free of
applications the following overview presents both the
theoretical aspects and the applications in the field of data
processing. Most of the presented methods are based on the
theory of probability. Some of them have a different
background such as fuzzy theory. Nevertheless, all of them
can be considered as statistical methods.
The core item of this report is quality. Without doubt,
uncertainty can be identified as the main component of
quality in geodesy. However, this point of view is incomplete
as today’s data shows more features of interest than
a pure repeatability of the observed (metric) values. The
complete process starting with data acquisition and ending
with the provision of defined results has to be considered
and studied. For this reason an extended quality modeling
will become more and more meaningful. First successful
steps into this direction are mentioned at the end.
New developments in parameter estimation
It is well known that for many reasons mathematical models
in geodesy are only approximate to some extent. There are
various strategies to handle this problem. One of them, the
so called Total Least-Squares (TLS) approach can be
considered as a regression with errors in the variables. Its
most significant aspect is the modeling of errors of the
design matrix in adjustment models such as the Gauss-
Markov model. These model errors are added to the observation
errors. KUPFERER (2005) studies some applications
of the TLS approach in geodesy.
In case of singular or only weakly regular adjustment
problems regularization strategies are required. Some work
was dedicated to the optimal determination of the regularization
parameter in Uniform Tykhonov-Phillips regularization
(CAI et al., 2004). CAI (2004) considered the statistical
inference of the eigenspace components of a symmetric
H. KUTTERER 1 , W.-D. SCHUH 2
random deformation tensor; see also CAI and GRAFAREND
(2007).
A prominent quality issue in the derivation of terrestrial and
celestial reference frames is the calculation of meaningful
uncertainty measures based on the variance-covariance
matrix of the estimated parameters. KUTTERER et al. (2007)
study a model which takes both the equality of observation
values used at different analysis centers and impact of the
individual Operator-Software into account. The present
continuation focuses on the provision of consistent estimators
for the parameters of the reference frames and of the
variance of the unit weight.
Further work has to be mentioned on robust estimation
where NEITZEL (2003, 2004) studied a combinatorial
approach in order to determine maximal point groups which
are consistent with respect to congruence transformations.
The well-known Gauss-Helmert model has recently received
some new attraction regarding the correct way of
treating non-linearities; see, e.g., LENZMANN and LENZ-
MANN (2004) or KUPFERER (2004).
Filtering techniques and stochastic modeling
The work on filtering techniques has covered two main
topics: colored noise and decorrelation strategies as well
as the treatment of instationary time series. Extension and
refinement of the stochastic modeling of space-geodetic
techniques are also mentioned in this context.
The great amount of data generated by sensors (e.g., during
satellite missions) will allow for a precise modelling of the
deterministic and stochastic model. To capture the detailed
correlation structures present in the sensor signals, complex
stochastic models have to be built. Such models are implemented
in an efficient manner by means of digital filters
with tailored stop and band-pass regions; see SCHUH (2003).
Special hypothesis test strategies are necessary to compare
the filtered residuals with white noise behaviour to get
objective criteria of the quality of the filter process (SCHUH
and KARGOLL, 2004). Also the influence of robust parameter
estimation procedures was investigated in this
context; see KARGOLL (2005). Unfortunately, the computational
costs grow considerably when the filter captures more
and more details. The question to be addressed will be,
whether the quality of the parameter estimates justifies the
use of an exact filter (SCHUH et al., 2007).
1 Hansjörg Kutterer: Geodätisches Institut, Universität Hannover, Nienburger Straße 1, D - 30167 Hannover, Germany, Tel. +49 -
511 - 762-2461/-2462(Secr.), Fax +49 - 511 - 762-2468, e-mail kutterer@gih.uni-hannover.de
2 Wolf-Dieter Schuh: Institut für Theoretische Geodäsie, Universität Bonn, Nußallee 17, D - 53115 Bonn, Germany, Tel. +49 - 228 -
73 33 95, Fax +49 - 228 - 733 029, e-mail schuh@theor.geod.uni-bonn.de