Hector v3.0

Hector estimates trends, periodic signals, and offsets in geodetic time series with correlated noise. It uses Restricted Maximum Likelihood Estimation (RMLE) and supports several noise models (GGM/flicker, power-law, AR(1), Matérn, white noise and combinations thereof).

Quick start

pip install hector-ts
hector-examples          # creates ./hector-examples/ with examples + manual PDF

hector-examples copies eight worked examples and the PDF user manual into a directory of your choice. Open hector_manual_v3.0.pdf first — it explains the workflow, all control-file parameters, and walks through every example step by step. The examples are self-contained: each has its own data and control files ready to run.

Installation

Windows

Pre-built wheels are available for Python 3.10–3.14. FFTW3 is bundled inside the wheel, so no separate installation is needed:

pip install hector-ts

macOS (Apple Silicon — M1 and later)

Pre-built wheels are available for Python 3.10–3.14. Install FFTW3 via Homebrew first (it is not bundled in the macOS wheel):

brew install fftw
pip install hector-ts

macOS (Intel)

Hector is compiled from source during pip install, so Xcode Command Line Tools must be present (xcode-select --install):

brew install fftw
pip install hector-ts

If the build fails, conda provides a self-contained alternative:

conda install -c conda-forge fftw
pip install hector-ts

Linux

Pre-built manylinux wheels are available for Python 3.10–3.14 on x86_64 — no FFTW3 headers needed for those platforms. For other architectures (ARM64 etc.) Hector builds from source; install the FFTW3 development package first:

# Ubuntu / Debian
sudo apt install libfftw3-dev

# CentOS / RHEL / Fedora
sudo yum install fftw-devel        # or: sudo dnf install fftw-devel

pip install hector-ts

Programs

Name Description
estimatetrend Estimate trend, seasonal signals, and offsets using RMLE
estimatespectrum Welch periodogram of the residuals
removeoutliers Flag and remove outliers before trend estimation
findoffsets Automated forward search for offset epochs
find_all_offsets Multivariate (E+N+U) offset search on NCF files
simulatenoise Generate synthetic coloured-noise time series
estimate_all_trends Batch trend estimation on all files in obs_files/
ncfgen Create a multi-channel NCF (NetCDF4) time-series file
ncfdump Inspect or export an NCF file
plot_ts Quick time-series plot from a mom file
date2mjd Convert calendar date to Modified Julian Date
mjd2date Inverse of date2mjd
convert_rlrdata2mom Convert PSMSL RLR data to mom format
predict_error Predict trend uncertainty as a function of series length

Reference

If you use Hector in your research, please cite:

Bos, M.S. (2026). Fast noise analysis and offset detection for continuous GNSS time series. Journal of Geodesy (submitted).

Performance

Hector v3.0 is a Python/Cython rewrite of Hector C++ v2.2. The core Toeplitz factorisation uses the Generalised Schur Algorithm (O(n log²n)) instead of Durbin-Levinson (O(n²)), and data gaps are handled with an FFT-based spectral approximation. The result is 6–27× faster for typical GNSS series lengths:

Series Gaps Hector v3.0 (s) Hector C++ v2.2 (s) Speedup
10 yr 0% 0.45 5.2 11.6×
20 yr 0% 1.7 14.4 8.5×
30 yr 0% 3.2 30.9 9.7×
40 yr 0% 4.4 91.9 20.7×
10 yr 10% 1.3 7.3 5.8×
30 yr 10% 14.2 85.4 6.0×
40 yr 10% 24.0 220.1 9.2×

Benchmarked on Apple M4 Pro, GGM+White noise model, including offset estimation.

License

Free for academic, research, and educational use. Commercial use requires a separate license from TeroMovigo – Earth Innovation Lda. See LICENSE for full terms.

Project links

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Newer release available (3.1.1)

1 maintainer

PyPI data
Data sourced directly from PyPI's database.
Avatar for msbos from gravatar.com msbos

Credits

Author: Machiel Bos

License

Free for non-commercial use

Requires

Python >=3.6

Tags

geodesy GNSS GPS time series trend estimation noise analysis maximum likelihood power-law noise offset detection Toeplitz

Classifiers

Report project as malware

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The following attestation bundles were made for hector_ts-3.0.3-cp310-cp310-macosx_14_0_arm64.whl:

Publisher: release.yml on machielbos8/hector-ts

Attestations: Values shown here reflect the state when the release was signed and may no longer be current.

Release history Release notifications | RSS feed

3.1.1

17 files

3.1.0

17 files

3.0.10

17 files

3.0.9

17 files

3.0.8

17 files

3.0.7

17 files

3.0.6

17 files

3.0.5

17 files

3.0.4

17 files

This release

3.0.3 This release

17 files

3.0.2

17 files

3.0.1

17 files

3.0

12 files

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