Browsing by Author "Friederichs, Thomas"

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Analysis of geodetic time series using allan variances
(2010) Friederichs, Thomas
The Allan variance is a statistical measure, developed in the 1960’s by the American physicist David W. Allan. With its aid, data series measured by devices like oscillators or gyroscopes can be analyzed with regard to their stability. In contrast to the Allan variance, the standard variance as a measure of total signal power, is not able to characterize signal stability. There exist further developments of the Allan variance. This student research project considers mainly non-overlapping, overlapping and modified Allan variances. The result of an Allan variance computation is the so-called sigma-tau-diagram. This diagram provides information about the stability and beyond, it allows identification of various random processes that exist in the series of measurement. The Allan variance may be computed directly in the time domain as well as via the frequency domain using the power spectral density of the time series and a transfer function. A domain conversion between the Allan variance and the power spectral density is only unidirectional. More precisely, one can compute the Allan variance by means of the power spectral density, but not vice versa. This student research project takes up the challenge of applying the concept of the Allan variance to geodetic time series (pole coordinates as part of the Earth orientation parameters, GPS measured coordinates of one position, Scintrex CG-5 gravimeter data and GOCE gravity gradients, in addition to oscillator frequencies). The Allan variance turns out to be a reasonable statistical measure for analysis of geodetic time series. The Allan variance, or better the Allan deviation, especially in an entire diagram, can be considered as a form of spectral analysis. Having said this, it is possible to consider the averaging interval tau as the inverted frequency.