A. Ettlinger, H.-B. Neuner:

"Assessment of inner reliability in the Gauss-Helmert model";

Journal of Applied Geodesy (eingeladen),14(2020), 1; S. 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

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.