Fast error analysis of continuous GPS observations

Bos, M. S.; Fernandes, R. M. S.; Williams, S. D. P. ORCID: https://orcid.org/0000-0003-4123-4973; Bastos, L.. 2008 Fast error analysis of continuous GPS observations. Journal of Geodesy;, 82 (3). 157-166. https://doi.org/10.1007/s00190-007-0165-x

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Abstract/Summary

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

Item Type:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.1007/s00190-007-0165-x
Programmes:	Oceans 2025 > Climate, ocean circulation and sea level
ISSN:	0949-7714
Additional Keywords:	POWER LAW; CORRELATED NOISE; TIME SERIES ANALYSIS; GPS; GEODETIC TIME SERIES; COLORED NOISE; VELOCITIES
NORA Subject Terms:	Marine Sciences
Date made live:	13 Jan 2009 16:09 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/5375

Item Type:

Publication - Article

Digital Object Identifier (DOI):

https://doi.org/10.1007/s00190-007-0165-x

Programmes:

Oceans 2025 > Climate, ocean circulation and sea level

ISSN:

0949-7714

Additional Keywords:

POWER LAW; CORRELATED NOISE; TIME SERIES ANALYSIS; GPS; GEODETIC TIME SERIES; COLORED NOISE; VELOCITIES

NORA Subject Terms:

Marine Sciences