Allan Variance Tools

The avar library provides tools for Allan variance analysis, a statistical method used to quantify the stability of time series data, particularly in the context of noise characterization for signals. The library includes functions to compute Allan variances, generate various types of noise, and interactively fit Allan variance curves. It is built using Python with dependencies on NumPy, Matplotlib, and SciPy.

Window Generation

M = avar.windows(K, min_size=1, density=64)

Generates an array of integer averaging window sizes for Allan variance analysis. It creates logarithmically spaced window sizes between min_size and K/2, with approximately density sizes per decade. It ensures unique integer values.

Allan Variance Calculation

va = avar.variance(y, M)

Computes Allan variance for a time series y over specified window sizes M. Supports both 1D arrays (single time series) and 2D arrays (multiple time series). Uses cumulative sums to calculate variance efficiently, handling overlapping windows.

Ideal Allan Variance

va = avar.ideal_variance(tau, ks, T=None)

Calculates theoretical Allan variance curves for various noise types. Supports quantization, white, first-order Gauss-Markov (FOGM), Brownian, and ramp noises. Parameter ks defines noise slopes and variances, and T specifies the sampling period (required for FOGM).

Noise Generation

The library provides functions to generate different types of noise, each with specific statistical properties:

y = avar.noise_quantization(var, T, K)
y = avar.noise_white(var, T, K)
y = avar.noise_fogm(var, tau, T, K, y0=None)
y = avar.noise_brownian(var, T, K)
y = avar.noise_ramp(var, T, K)

Interactive Allan Variance Fitting

avar.fit(
    tau: np.ndarray,
    va: np.ndarray,
    T: float = 1.0,
    ks: tuple | list | None = None,
    ax: axes = None,
    truecolor: str = "tab:blue",
    fitcolor: str = "tab:orange")

Provides an interactive Matplotlib-based interface for fitting Allan variance curves. Displays true Allan variance (va) and fitted curves based on noise components (ks).

Supports interactive manipulation via mouse and keyboard:

• Left-click and drag: Move noise components.
• Shift and left-click or middle-click: Pan the view.
• Scroll: Zoom (faster with shift).
• Keys 'q', 'w', 'f', 'b', 'r': Add quantization, white, FOGM, Brownian, or ramp noise components.
• 'Delete', 'backspace', or key 'x': Remove components.
• Key 'o': Optimize component variances using least-squares fitting.
• Key 'h': Reset view to the data limits.
• Key '?': toggle the help menu.

Features log-log scaling, customizable colors, and optimization bounds for fitting. Handles multiple noise types with specific slopes (-2 to +2) and parameters (e.g., time constant for FOGM).