Hector is an open-source academic software package that can be used to estimate a trajectory model, for example a linear trend with an annual signal, in time-series with temporal correlated noise. Trajectory estimation is a common task in geophysical research where one is interested in phenomena such as the increase in temperature, sea level due to climate change and position over time due to vertical land and tectonic plate motion. It is well known that in most geophysical time-series the noise is correlated in time and this has a significant influence on the accuracy by which the linear trend can be estimated. Therefore, the use of a computer program such as Hector is advisable.

Hector assumes that the user knows what type of temporal correlated noise exists in the observations and estimates both the linear trend and the parameters of the chosen noise model using the Maximum Likelihood Estimation (MLE) method.

TeroMovigo members are the main authors of Hector and continue its development and maintenance in the hope that it continues to serve the academic community. More details about the underlying method can be found in the following book: “Geodetic Time Series Analysis in Earth Sciences“.  Other good programs that can be used for this task are CATS and est_noise. Especially with est_noise many intercomparisons with Hector have been made, demonstrating that both software packages produce the same results. If you use Hector in your publications, please cite the following reference:

Bos, M.S., Fernandes, R.M.S., Williams, S.D.P., and Bastos, L. (2013). Fast Error Analysis of Continuous GNSS Observations with Missing Data. J. Geod., Vol 87(4), 351-360, doi:10.1007/s00190-012-0605-0.

Main features

  • Correctly deals with missing data. No interpolation or zero padding of the data nor an approximation of the covariance matrix is required (as long the noise is, or has been made, stationary).
  • Allows yearly, half-yearly and other periodic signals to be included in the estimation process of the linear trend.
  • Allows the option to estimate offsets at given time epochs.
  • Includes power-law noise, ARFIMA, generalized Gauss-Markov and white noise models. Any combination of these models can be made.
  • Allows taking the first difference of the data if power-law noise model is chosen (including combination of white, flicker and random walk).
  • Comes with programs to remove outliers and to make power spectral density plots.
  • Provides a program + script to automatically detect offsets.

Requirements and Download

The hector software package is mainly intended to be run on computers with Unix-like operating systems. If you don’t want to use the static executables you can compile the source code. In this case one should also install the boost, FFTW3 and OpenBLAS  libraries. For Mac users, one can use X-code (clang) and homebrew to compile the source code.

To download the latest version (2.0) of the statically compiled executables (for various flavours of the operating Linux operating system), the source code + examples, Python 3 scripts or the manual, click on the following links:

hector_2.0_OL8.tar.bz2 (Oracle Linux 8)

hector_2.0_SL7.tar.bz2 (Scientific Linux 7)

hector_2.0_Ubuntu18.04.tar.bz2 (Ubuntu 18.04 LTS)

hector_2.0_Ubuntu20.04.tar.bz2 (Ubuntu 20.04 LTS)

hector_2.0_Ubuntu21.04.tar.bz2 (Ubuntu 21.04)

hector_2.1_Ubuntu20.04.tar.bz2 (Ubuntu 20.04 LTS)

hector_2.1_Ubuntu21.04.tar.bz2 (Ubuntu 21.04)

hector_2.1_Ubuntu22.04.tar.bz2 (Ubuntu 22.04 LTS)

source code hector-2.0

source code hector-2.1 (added missing file on 28/7/23)

Python3 scripts hector-2.0

Python3 scripts hector-2.1


manual hector-2.0

manual hector-2.1


Hector is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

This page was updated on 21 October 2022.