Error calibration of quasi-geoidal, normal and ellipsoidal heights of Sweden using variance component estimation

Mehdi ESHAGH

doi:10.2478/v10126-010-0001-9

Mehdi ESHAGH Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden

DOI: https://doi.org/10.2478/v10126-010-0001-9

Keywords: combined adjustment, error calibration, singularity, stochastic model

Abstract

Errors of estimated parameters in an adjustment process should be scaled
according to the size of the estimated residuals or misclosures. After computing a quasigeoid
(geoid), its biases and tilts, due to existence of systematic errors in the terrestrial
data, are removed by fitting a corrective surface to the misclosures of the differences
between the GNSS/levelling data and the quasi-geoid (geoid). Variance component estimation
can be used to re-scale or calibrate the error of the GNSS/levelling data and the
quasi-geoid (geoid) model. This paper uses this method to calibrate the errors of the recent
quasi-geoid model, the GNSS and the normal heights of Sweden. Different stochastic
models are investigated in this study and based on a 7-parameter corrective surface model
and a three-variance component stochastic model, the calibrated error of the quasi-geoid
and the normal heights are 6 mm and 5 mm, respectively and the re-scaled error of the
GNSS heights is 18 mm.