Faculty of Spatial Information

Advanced methods of geodetic statistics

As soon as we assign standard deviations to geodetic measurement values, we use, maybe unknowingly, the theoretical concept of mathematical statistics. Fortunately, this concept is meanwhile highly developed. If we would consequently use this concept , we could extract the optimal information from geodetic measurements. Based on those measurements, we could make correct decisions with highest probability.

In the 20th century this goal was not achieved due to the considerable computational workload, such that only very simple statistical models were used. Since the advent of powerful computers there is no justification to use them anymore. However, they are used almost exclusively in practical geodetic work.

Existing models should be extended into the following directions:

1. The classical reliability theory of Baarda (1968) always assumes that the data may be contaminated by only one outlier. It is better to use a concept, which can take into account multiple outliers.

2. In classical geodetic models only the measurement values are permitted to be random numbers. In EIV models (errors in variables) there may be further random numbers without resorting to pseudo measurements.

3. Geodetic models are often non-linear and must be linearised. There is the belief that (a) this is unavoidable and (b) this is in general harmless. Both is wrong. It is possible to work with non-linear models directly.

4. Besides the few classical hypothesis tests, which can be done without computer assistance, there is a just about infinite multitude of further possibilites to make decision based on geodetic measurements. They can be adapted to the practical case arbitrarily close and consequently yields better results.

This list is yet incomplete.

Publications of R. Lehmann for this research project


►On the consideration of combined measurement uncertainties in relation to GUM concepts in adjustment computations
Journal of Applied Geodesy DOI: 10.1515/jag-2021-0043 (together with Frank Neitzel and Michael Lösler)


►Mean Shift versus Variance Inflation Approach for Outlier Detection – a Comparative Study
Mathematics 2020, 8(6), 991 (together with Michael Lösler and Frank Neitzel)


Bias in least-squares adjustment of implicit functional models
Survey review DOI: 10.1080/00396265.2020.1715680 (together with M. Lösler, F. Neitzel, C. Eschelbach)


Type-Constrained Total Least Squares Fitting of Curved Surfaces to 3D Point Clouds
Journal of Mathematical and Statistical Analysis, Volume 2 - Issue 1 (2019)


Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations
Journal of Geodetic Science, Volume 8, Issue 1, Pages 98–114 (2018) DOI:10.1515/jogs-2018-0009 (together with M. Lösler)

A half-century of Baarda’s concept of reliability: a review, new perspectives, and applications
Survey Review 2018: ahead of print (together with Vinicius Francisco Rofatto, M. T. Matsuoka, I. Klein, M. R. Veronez, M. L. Bonimani)

A universal and robust computation procedure for geometric observations
Survey Review, Volume 50, Issue 361, Pages 364-372 (2018). DOI 10.1080/00396265.2017.1279844


Congruence analysis of geodetic networks – hypothesis tests versus model selection by information criteria
Journal of Applied Geodesy, Volume 11, Issue 4, Pages 271–283 (2017). DOI: 10.1515/jag-2016-0049 (together with M. Lösler)

Modellselektion mittels Akaike-Informationskriterium – Anwendung in der Kongruenzanalyse
Allgemeine Vermessungs-Nachrichten 05/2017 (zusammen mit M. Lösler und C. Eschelbach)

On the statistical power of Baarda’s outlier test and some alternative
Journal of Geodetic Science, Volume 7, Issue 1, Pages 68–78 (2017). DOI:10.1515/jogs-2017-0008 (together with A. Voß-Böhme)


Epochenvergleiche von Präzisions-EDM-Messungen zur Untersuchung der Punktstabilität auf einer EDM-Basislinie
Schriftenreihe des Instituts für Markscheidewesen und Geodäsie an der Technischen Universität Bergakademie Freiberg 2016-1

Multiple outlier detection: hypothesis tests versus model selection by information criteria
Journal of Surveying Engineering, Volume 142, Issue 4 (2016) (together with M. Lösler)
OPEN ACCESS of original via Qucosa


Observation error model selection by information criteria vs. normality testing
Studia Geophysica et Geodetica, Volume 59, Issue 4, Pages 489-504 (2015), DOI: 10.1007/s11200-015-0725-0
►OPEN ACCESS of postprint via Qucosa


Detection of a sinusoidal oscillation of unknown frequency in a time series - a geodetic approach
Journal of Geodetic Science, Volume 4, Issue 1, ISSN (Online) 2081-9943 (2014), DOI: 10.2478/jogs-2014-0015 (OPEN ACCESS)

Transformation model selection by multiple hypotheses testing
Journal of Geodesy, Volume 88, Issue 12, Pages 1117-1130 (2014), DOI:10.1007/s00190-014-0747-3
OPEN ACCESS of postprint via Qucosa

The usage of recursive parameter estimation in automated reference point determination
Geophysical Research Abstracts Vol. 16, EGU2014-11215, 2014 (together with T. Lossin, M. Lösler, A. Neidhardt, S. Mähler, and Th. Klügel)

Geodetic investigation of accuracy and reliability of INS/GNSS system iTraceRT-F200-E for navigation in tunnels
IEEE Xplore 2014, DOI 10.1109/WPNC.2014.6843285 (together with A. Bilajbegovic)

The usage of recursive parameter estimation in automated reference point determination
General Meeting of the International VLBI Service for Geodesy and Astrometry (IVS) Shanghai March 2-7, 2014 (together with T. Lossin, M. Lösler, A. Neidhardt, S. Mähler)

Ausreißererkennung in geodätischen Zeitreihen
Beitrag zum 129. DVW-Seminar "Zeitabhängige Messgrößen – Ihre Daten haben (Mehr-)Wert" am 26. und 27. Februar 2014 in Hannover, DVW-Schriftenreihe Band 74, Wissner Verlag


The 3sigma-rule for outlier detection from the viewpoint of geodetic adjustment
Journal of Surveying Engineering, Volume 139, Issue 4, Pages 157–165 (2013), DOI 10.1061/(ASCE)SU.1943-5428.0000112
OPEN ACCESS of postprint via Qucosa

Testing the compatibility of constraints for parameters of a geodetic adjustment model
Journal of Geodesy, Volume 87, Issue 6, Pages 555-566 (2013), DOI: 10.1007/s00190-013-0627-2 (together with F. Neitzel)
►OPEN ACCESS of postprint via Qucosa

On the formulation of the alternative hypothesis for geodetic outlier detection
Journal of Geodesy, Volume 87, Issue 4, Pages 373-386 (2013), DOI: 10.1007/s00190-012-0607-y
OPEN ACCESS of postprint via Qucosa


Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models
Journal of Geodesy, Volume 86, Issue 12, Pages 1137–1146 (2012), DOI: 10.1007/s00190-012-0569-0
OPEN ACCESS of postprint via Qucosa

Geodätische Fehlerrechnung mit der skalenkontaminierten Normalverteilung
Allgemeine Vermessungsnachrichten 5/2012. VDE-Verlag Offenbach
OPEN ACCESS of postprint via Qucosa


Monte Carlo based data snooping with application to a geodetic network (together with T. Scheffler)
Journal of Applied Geodesy, Volume 5, Issue 3-4, Pages 123–134 (2011), DOI: 10.1515/JAG.2011.014


Im Schwerpunkt der Anschlusspunkte – Zur Genauigkeit geodätischer Koordinatentransformationen
Allgemeine Vermessungsnachrichten 4/2010. VDE-Verlag Offenbach.
►OPEN ACCESS of postprint via Qucosa

Normierte Verbesserungen – wie groß ist zu groß?
Allgemeine Vermessungsnachrichten 2/2010. VDE-Verlag Offenbach