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.

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hector-ts 3.1.0

Hector v3.1

Quick start

Installation

Windows

macOS (Apple Silicon — M1 and later)

macOS (Intel)

Linux

Programs

Reference

Performance

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1 maintainer

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