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
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_v3.1.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 ~27× 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% | 1.11 | 2.9 | 2.6× |
| 20 yr | 0% | 1.60 | 6.6 | 4.1× |
| 30 yr | 0% | 2.32 | 21.8 | 9.4× |
| 40 yr | 0% | 2.58 | 68.7 | 26.6× |
| 10 yr | 10% | 2.36 | 4.5 | 1.9× |
| 20 yr | 10% | 4.36 | 16.5 | 3.8× |
| 30 yr | 10% | 9.16 | 51.7 | 5.6× |
| 40 yr | 10% | 14.44 | 150.1 | 10.4× |
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.
1 maintainer
Metadata
1 maintainer
Release files for hector-ts 3.1.2
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47a87a926734dcec0a96ef79b65371897447ccd712447d37e4342f46bae0991c
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twine/7.0.0 CPython/3.13.14
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