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).

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.

Installation

Windows

Pre-built wheels are available for Python 3.10–3.13. FFTW3 is bundled inside the wheel, so no separate installation is needed:

pip install hector-ts

macOS (Intel and Apple Silicon)

Install FFTW3 via Homebrew, then install Hector:

brew install fftw
pip install hector-ts

Hector is compiled from source during pip install, so Xcode Command Line Tools must be present (xcode-select --install). If the build fails for any reason, conda provides a self-contained alternative:

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

Linux

Install the FFTW3 development package for your distribution, then install Hector:

# 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

Pre-built manylinux wheels are available for Python 3.10–3.13 on x86_64, so pip install may use a wheel directly without needing the FFTW3 headers. The development package is only required when building from source (e.g. on ARM64 or other architectures).

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

Recommended directory structure

obs_files/    raw time series (mom or NCF format)
pre_files/    after outlier removal
fin_files/    fitted model output from estimatetrend

Run estimate_all_trends in a directory that follows this layout to process all files in obs_files/ automatically.

Examples

Eight worked examples are bundled with the package. Copy them to your working directory with:

hector-examples                  # creates ./hector-examples/
hector-examples my_examples_dir  # or choose a name
Example Topic
ex1 Synthetic GNSS: removeoutliers → estimatetrend → PSD
ex2 Monthly sea-level data from Cascais tide gauge
ex3 Synthetic coloured noise with simulatenoise
ex4 Post-seismic relaxation
ex5 Offset detection on a real GNSS station
ex6 Multi-station offset detection from NGL tenv files
ex7 Piecewise linear (multi-trend) estimation
ex8 Toeplitz factorisation: Levinson vs. Generalised Schur (Jupyter notebook)

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).

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-3.0.1-cp310-cp310-macosx_14_0_arm64.whl:

Publisher: release.yml on machielbos8/hector-ts

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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

3.0.3

17 files

3.0.2

17 files

This release

3.0.1 This release

17 files

3.0

12 files

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