avar 0.1.3

Allan variance tools

Allan Variance Tools

Array of Windows

avar.windows(K, density=64)

This will create an array M of integer window sizes. The averaging period tau would equal M*T, where T is the sampling period. The density is the target number of window sizes in the array per decade. Obviously, in the first decade it is not possible to have more than 9 window sizes: 1 through 9.

Signal Allan Variance

avar.variance(y, M)

To get the actual Allan variance of a signal y, use this function. You must supply the array of window sizes M for which to calculate the Allan variance values. This function can take for y either a one-dimensional array or a two-dimensional array in which each row will be treated as a data set.

Ideal Allan Variance

avar.ideal(tau, p)

The ideal function will calculate the ideal Allan variances over an array of averaging periods tau. For any noise components you wish not to be included, set their corresponding variances to zero.

This function make use of the params class. Objects of this type store the five basic component noise variances (quantization, white, flicker, walk, and ramp), vc, any first-order, Gauss-Markov (FOGM) noise variances, vfogm, and the corresponding FOGM time constants, tfogm. The p parameter is one such object. You can define it as shown in the following example:

p = avar.params(
        vc=np.array([0.5, 1.0, 0, 0.5, 0.1]) * 1e-9,
        vfogm=[1e-8, 1e-7],
        tfogm=[0.1, 1.0])

The ideal function will return the total Allan variance curve, va, as well as a matrix, vac, whose rows represent the component Allan variances over tau.

Fitting to Signal Allan Variance

avar.fit(tau, va, mask=None, fogms=0, tol=0.007, vtol=0.0)

Given the Allan variance curve of some signal, va, at various averaging periods tau, you can get the best fit using the five basic component noises and fogms number of first-order, Gauss-Markov (FOGM) noises. By default, this function will automatically attempt to determine if certain component noises are even at play based on the tolerance value tol. However, you can directly control which component noises you wish to include or exclude with the mask array. For each element of mask that is False the corresponding component noise will be excluded. This function will iterate through the various permutations of component noises, starting with 0 FOGMs. If a fit satisfies the specified tol tolerance, the search will end. Otherwise, the best fit will be used. The vtol parameter is the minimum allowed variance for any fitted component noise variance.

The return values are the fitted Allan variance curve, vf, and a params object, p (see the section on Ideal Allan Variance), containing the variances of the basic component noise variances (quantization, white, flicker, walk, and ramp), vc, any first-order, Gauss-Markov (FOGM) noise variances, vfogm, and the corresponding FOGM time constants, tfogm.

Noise Generation

avar.noise(K, T, p)

Generate a noise signal of length K, sampling period T, and parameters p. Parameter p is a params object (see the section on Ideal Allan Variance).

This function returns the noise signal y.

For flicker (bias-instability) noise, multiple, balanced FOGMs are used.