Hector v3.1
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
Hector has no graphical installer and no icon to click — everything happens in a terminal. Open one (Windows: Command Prompt or PowerShell; macOS: Terminal; Linux: any shell), then type each of the two commands below and press Enter, waiting for the first to finish before starting the second:
Step 1 — install Hector (requires Python 3.10 or newer with pip;
on macOS install FFTW first, see Installation below):
pip install hector-ts
Nothing works until this step has completed successfully.
Step 2 — get the examples and the manual:
hector-examples
This copies eight worked examples, the PDF user manual, and the
paper_scripts directory into a new hector-examples directory in your
current location (give a different name as argument if you prefer, e.g.
hector-examples my_dir). If the command is not found, step 1 did not
finish successfully — read its error messages.
The paper_scripts directory contains the numerical experiments of the
paper "Faster analysis of GNSS time series" (Journal of Geodesy),
together with the raw results measured for the paper, so every figure
can be re-created directly and every benchmark re-run:
cd hector-examples/paper_scripts
python3 run_all.py # smoke tests + all paper figures (~5 min)
python3 run_all.py --full # regenerate the raw results (hours)
See paper_scripts/README.md for details.
Open hector_manual_v3.1.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 v3.1 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 exactly with an FFT-based conjugate-gradient solver. The speedup over C++ v2.2 grows with series length — up to ~24× at 40 years without gaps, and ~10× with 10% gaps:
| Series | Gaps | Hector v3.1 (s) | Hector C++ v2.2 (s) | Speedup |
|---|---|---|---|---|
| 10 yr | 0% | 1.13 | 3.0 | 2.7× |
| 20 yr | 0% | 1.54 | 7.0 | 4.5× |
| 30 yr | 0% | 2.32 | 25.3 | 10.9× |
| 40 yr | 0% | 2.73 | 64.8 | 23.8× |
| 10 yr | 10% | 2.32 | 4.5 | 1.9× |
| 20 yr | 10% | 4.44 | 16.4 | 3.7× |
| 30 yr | 10% | 9.73 | 60.5 | 6.2× |
| 40 yr | 10% | 14.22 | 146.3 | 10.3× |
Median of ten realisations on Apple M4 Pro, GGM+White noise model,
including offset estimation — the same run as Table 2 of the paper.
Reproduce with hector-examples → paper_scripts/run_all.py.
License
Free for academic, research, and educational use. Commercial use requires a separate license from TeroMovigo – Earth Innovation Lda. See LICENSE for full terms.
1 maintainer
Metadata
1 maintainer
Release files for hector-ts 3.1.11
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twine/7.0.0 CPython/3.13.14
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Transparency logRelease files / hector_ts-3.1.11-cp310-cp310-macosx_14_0_arm64.whl
| Download URL | hector_ts-3.1.11-cp310-cp310-macosx_14_0_arm64.whl |
|---|---|
| Size | 13.1 MB |
| Tags | CPython 3.10 macOS 14.0+ ARM64 |
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b199e3f061ce49a141753b8a713876b9bd5d4121f985587df7c2cbe77f5875df
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bac751772032d382beae9e451f156bbbe55a0a875c7f971877f9cabd2249c62a
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twine/7.0.0 CPython/3.13.14
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