Abstract
The paper presents a summary of research activities concerning theoretical
geodesy performed in Poland in the period of 2011–2014. It contains the results of research on
new methods of the parameter estimation, a study on robustness properties of the
M-estimation,
control network and deformation analysis, and geodetic time series analysis. The main
achievements in the geodetic parameter estimation involve a new model of the
M-estimation
with probabilistic models of geodetic observations, a new Shift-M
split
estimation, which allows
to estimate a vector of parameter differences and the Shift-
M
split
(+)
that is a
generalisation of
Shift-
M
split
estimation if the design matrix
A
of a functional model has not a full column
rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic
coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of
the research of the last four years. New parameter estimation models developed have been
adopted and successfully applied to the control network and deformation analysis.
New algorithms based on the wavelet, Fourier and Hilbert transforms were applied
to find time-frequency characteristics of geodetic and geophysical time series as well as
time-frequency relations between them. Statistical properties of these time series are also
presented using different statistical tests as well as 2
nd
, 3
rd
and 4
th
moments about the mean.
The new forecasts methods are presented which enable prediction of the considered time
series in different frequency bands.
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