The Allan variance (AVAR) was introduced 50 years ago as a statistical tool
for assessing of the frequency standards deviations. For the past decades, AVAR
has increasingly being used in geodesy and astrometry to assess the noise
characteristics in geodetic and astrometric time series. A specific feature of
astrometric and geodetic measurements, as compared with the clock measurements,
is that they are generally associated with uncertainties; thus, an appropriate
weighting should be applied during data analysis. Besides, some physically
connected scalar time series naturally form series of multi-dimensional
vectors. For example, three station coordinates time series X, Y, and Z
can be combined to analyze 3D station position variations. The classical AVAR
is not intended for processing unevenly weighted and/or multi-dimensional data.
Therefore, AVAR modifications, namely weighted AVAR (WAVAR), multi-dimensional
AVAR (MAVAR), and weighted multi-dimensional AVAR (WMAVAR), were introduced to
overcome these deficiencies. In this paper, a brief review is given of the
experience of using AVAR and its modifications in processing astro-geodetic
time series
