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Fast error analysis of continuous GPS observations |
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| Authors: | M S Bos R M S Fernandes S D P Williams L Bastos |
| Institution: | 1. University of Porto, Monte da Virgem, 4430-146, Vila Nova de Gaia, Portugal 2. University of Beira Interior, CGUL, IDL, R. Marquês d’ávila e Boloma, 6201-001, Covilh?, Portugal 3. Delft University of Technology, DEOS, Kluyverweg 1, 2629 HS, Delft, The Netherlands 4. Proudman Oceanographic Laboratory, 6 Brownlow Street, Liverpool, L3 5DA, UK |
| Abstract: | It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white
noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods
require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years
of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD AthlonTM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead
of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE
computations can be simplified to a  process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations
that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number
of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction
factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit
assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for
the uncertainty of the estimated trend if the data only contains power-law noise.
Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users. |
| Keywords: | GPS Power-law Correlated noise Time-series analysis |
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