Trajectory estimation for geophysical research

What is Hector?

Hector is an open-source academic software package designed for estimating trajectory models, such as linear trends with annual signals, in time-series data with temporally correlated noise. Trajectory estimation plays a crucial role in geophysical research, where phenomena like temperature increase, sea level rise due to climate change, and positional changes caused by vertical land and tectonic plate motion are of interest. In geophysical time-series, noise is typically correlated over time, which significantly impacts the accuracy of linear trend estimation. Therefore, utilizing a computer program like Hector is advisable.
Hector assumes that users have prior knowledge of the type of temporal correlated noise present in their observations. It employs the Maximum Likelihood Estimation (MLE) method to estimate both the linear trend and the parameters of the chosen noise model.
TeroMovigo members are the main authors of Hector, overseeing its development and maintenance, with the aim of providing ongoing support to the academic community. For more details about the underlying methodology, refer to the book titled 'Geodetic Time Series Analysis in Earth Sciences .' There are other notable programs available for similar tasks, such as CATS and est_noise . Extensive comparisons between Hector and est_noise have been conducted, demonstrating that both software packages yield identical results. If you utilize Hector in your publications, kindly cite the following reference to acknowledge its contribution:
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 handles missing data. It eliminates the need for data interpolation, zero padding, or approximation of the covariance matrix. As long as the noise is, or has been made, stationary, Hector effectively manages missing data without compromising the estimation process.
  • 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 selected (including combination of white, flicker, and random walk).
  • Includes 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 (2.1) 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)
hector-2.1_CentOS7.tar.bz2 (CentOS7)
hector-2.1_CentOS9.tar.bz2 (CentOS9)
source code hector-2.0
source code hector-2.1
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.

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