sid — Open-Source System Identification¶

sid is a free, open-source toolbox for system identification — covering both non-parametric frequency response estimation and time-varying state-space identification. All implementations share a single mathematical specification and cross-language reference test vectors to ensure numerical consistency.

Get started¶

:material-language-python: Python
```
pip install -e "./python[plot]"
```
Install guide :material-arrow-right:
:simple-mathworks: MATLAB / Octave
```
run('/path/to/sid/matlab/sidInstall.m')
```
Install guide :material-arrow-right:

Features¶

Blackman-Tukey spectral analysis — frequency response and noise spectrum estimation with configurable window size.
Frequency-dependent resolution — vary the smoothing bandwidth across the frequency axis.
Empirical transfer function estimate — maximum resolution via FFT ratio, with optional smoothing.
Time-varying frequency maps and spectrograms — sliding-window analysis for non-stationary signals.
LTV state-space identification (COSMIC) — identify time-varying A(k), B(k) with O(N) complexity, automatic regularization, and Bayesian uncertainty.
Partial-observation identification (Output-COSMIC) — identify dynamics from output-only measurements.
Multi-trajectory support — ensemble averaging for frequency estimates; pooled least-squares for state-space.
Asymptotic uncertainty estimates — confidence bands for all estimation functions.
SISO, MIMO, and time-series modes — unified API across all estimation functions.

Two paths, one specification¶

sid provides a frequency-domain path (Blackman-Tukey, ETFE) and a time-domain state-space path (COSMIC). The two are derived from a single mathematical specification and validated against shared test vectors so that both implementations agree to floating-point tolerance.

Read the overview :material-arrow-right: