Journal of Geodesy

, Volume 76, Issue 9, pp 483-494

First online:

The effect of coloured noise on the uncertainties of rates estimated from geodetic time series

  • S. D. P. WilliamsAffiliated withProudman Oceanographic Laboratory, Bidston Observatory, Merseyside CH43 7RA, UK e-mail:; Tel.: +44-151-653-8633; Fax: +44-151-653-6269

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


 Until recently, it was typically assumed that only white noise was present in geodetic time series. However, several data sets have now provided evidence for the presence of power-law noise. The uncertainty of any rates estimated from such data sets is dependent on the error model assumed for the data. Here a general form for the covariance matrix for any power-law noise model is introduced and simple equations that relate the rate uncertainty to the noise amplitude, sampling frequency and length of the time series are empirically derived. In addition, equations to analyse data sets and obtain a rate uncertainty when computational speed is at a premium are provided. These equations are tested against previously published geodetic data sets.

Keywords: Time series analysis – Power-law noise – Error analysis