Model Evaluation – Sensitivity Analysis

Aim:

Analysis of non-linear and non-additive models using by further development and adaption of the variance-based sensitivity.

Procedure:

As a rule in geodesy linear or linearised models are assumed to analyse the sensitivity of models with respect to disturbances as gross errors.

In the meantime non-linear and non-additive models gain importance due to more complex measurement systems as well as faster movement processes. Hence the methods of sensitivity analysis have to be enhanced especially for the evaluation of kinematic measurements.

A method of sensitivity analysis independent of the model characteristics (model-free) is called variance-based sensitivity analysis. Using special methods for sample generation and special transformations into the frequency domain (FAST) the dependencies of the output variances on the input variances may be determined. The results are model-free meaning that non-additive models may be analysed too.

Results:

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The proceeding example presents the results of a variance-based sensitivity analysis of the state variable “orientation” of a Kalman filter for positioning. The individual columns represent the different driving scenarios not discussed at this place. The deviation of the height of each column form 1 illustrates the deviation from the additivity of the model. The different colours represent the respective input quantities (e.g. da-Odo = orientation change measure be odometer, Y-DGPS = measured DGPS co-ordinate).

The individual colour shares specify the impact in percentage of the respective input variance on the variance of the state variable “grid bearing”. Thus the exemplary figure shows on the one hand the non-additive character of the model and on the other hand the dominating influence of the measured DGPS co-ordinates (blue and violet colour).

References:

  • Schwieger, V.: Sensitivity Analysis as a General Tool for Model Optimisation – Examples for Trajectory Estimation. Journal of Applied Geodesy, Walter de Gruyter, Berlin – New York, Volume 1, Heft 1, 2007.
  • Ramm, K.: Evaluation von Filter-Ansätzen für die Positionsschätzung von Fahrzeugen mit den Werkzeugen der Sensitivitätsanalyse. Bayerische Akademie der Wissenschaften, Verlag C. H. Beck, DGK, Reihe C, Nr. 619, 2007.
  • Ramm, K.: Enhanced Kinematic Positioning Methods by Shaping Filter Augmentation, Proceedings on 3rd IAG International Symposium on Geotechnical and Structural Engineering and 12th International Symposium on Deformation Measurements, Baden, Österreich, 22.-24.05.2006.
  • Schwieger, V.: Sensitivity Analysis as a General Tool for Model Optimisation – Examples for Trajectory Estimation. Proceedings on 3rd IAG International Symposium on Geotechnical and Structural Engineering and 12th International Symposium on Deformation Measurements, Baden, Österreich, 22.-24.05.2006.
  • Schwieger, V.: Nicht-lineare Sensitivitätsanalyse, gezeigt an Beispielen zu bewegten Objekten. Deutsche Geodätische Kommission, Reihe C, Heft 581, 2005.
  • Schwieger, V.: Variance-based Sensitivity Analysis for Model Evaluation in Engineering Surveys. Proceedings on 3rd International Conference on Engineering Surveying, Bratislava, Slowakei, 11.-13.11.2004.

Contact:

Prof. Dr.-Ing. habil. Volker Schwieger