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A. Ettlinger, H.-B. Neuner:
"Assessment of inner reliability in the Gauss-Helmert model";
Journal of Applied Geodesy (invited), 14 (2020), 1; 13 - 28.

In this contribution, the minimum detectable
bias (MDB) as well as the statistical tests to identify disturbed
observations are introduced for the Gauss-Helmert
model. Especially, if the observations are uncorrelated,
these quantities will have the same structure as in the
Gauss-Markov model, where the redundancy numbers
play a key role. All the derivations are based on onedimensional
and additive observation errors respectively
offsets which are modeled as additional parameters to be
estimated. The formulas to compute these additional parameters
with the corresponding variances are also derived
in this contribution. The numerical examples of
plane fitting and yaw computation show, that the MDB is
also in the GHM an appropriate measure to analyze the
ability of an implemented least-squares algorithm to detect
if outliers are present. Two sources negatively influencing
detectability are identified: columns close to the
zero vector in the observation matrix B and sub-optimal
configuration in the design matrix A. Even if these issues
can be excluded, it can be difficult to identify the correct
observation as being erroneous. Therefore, the correlation
coefficients between two test values are derived and analyzed.
Together with the MDB these correlation coefficients
are an useful tool to assess the inner reliability - and therefore
the detection and identification of outliers - in the
Gauss-Helmert model.

Least-Squares Adjustment, Gauss-Helmert model, Inner Reliability

http://dx.doi.org/10.1515/jag-2019-0013