Math

`calculate_adev_errors(tau, adev, tau0, N, alpha=0, d=2, overlapping=True, modified=False)`

Calculate non-naive Allan deviation errors. Equivalent to Stable32.

Ref

https://github.com/aewallin/allantools/blob/master/examples/ci_demo.py https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050061319.pdf

Parameters:

Name	Type	Description	Default
`tau`	`list of floats`	list of tau_values for which deviations were computed	required
`adev`	`list of floats`	list of ADEV (or another statistic) deviations	required
`tau0`	`float`	averaging factor; average interval between measurements	required
`N`	`int`	number of frequency observations	required
`alpha`	`int`	+2,...,-4 noise type, either estimated or known	`0`
`d`	`int`	statistic code: 1 first-difference variance, 2 allan variance, 3 hadamard variance	`2`
`overlapping`	`bool`	True if overlapping statistic used. False if standard statistic used	`True`
`modified`	`bool`	True if modified statistic used. False if standard statistic used.	`False`

Returns:

Name	Type	Description
`err_lo`	`list of floats`	non-naive lower 1-sigma confidence interval for each point over which deviations were computed
`err_high`	`list of floats`	non-naive higher 1-sigma confidence interval for each point over which deviations were computed

`calculate_allan_dev(ds, taus='octave', measurement_rate=None)`

Calculate the overlapped Allan deviation of a time series.

Parameters:

Name	Type	Description	Default
`ds`	`Series`	Time series of frequency input data.	required
`taus`	`array or str`	Time differences (tau), in seconds, for which the Allan deviation is calculated. Specify "all", "octave" or "decade" for automatic generation. See `allantools.oadev` documentation.	`'octave'`
`measurement_rate`	`float`	Sampling rate of the input data, in Hz. Specify None to calculate from average interval.	`None`

Returns:

Type	Description
`Series`	Allan deviation at different taus

`get_adev_wn_range(adev_data, n_tau_min=3)`

Find averaging time range of white noise section of Allan Deviation data.

Using a simple bruteforce method, the RMSE error between the Allan Deviation data and a fitted line with slope -0.5 is computed for many possible sections of varying length of the Allan Deviation data. Longer sections are favored by normalization of the RMSE using squared length of the section. Finally the white noise section is defined via the minimum normalized RMSE value.

Parameters:

Name	Type	Description	Default
`adev_data`	`DataFrame`	Dataframe of computed Allan Deviation data including averaging time `tau` as index and Allan Deviation values as `adev` column.	required
`n_tau_min`	`int`	Minimum number of datapoints to use for fitting of the line.	`3`

Returns:

Name	Type	Description
`wn_tau0`	`float`	Averaging time at start of white noise section.
`wn_tau1`	`float`	Averaging time at end of white noise section.

`interval_means(series, interval, min_count=None, name=None, err='sem')`

Calculate interval means of a time series

See pandas.DataFrame.resample.

Parameters:

Name	Type	Description	Default
`series`	`Series`	Input time series.	required
`interval`	`str`	Resampling interval, e. g. "1h".	required
`min_count`	`int \| float`	Minimum number of samples required in each interval. For intervals with fewer samples, the mean value is set to NaN. A fractional value `0 < min_count < 1` is interpreted as a fraction of the maximum number of samples.	`None`
`name`	`str`	Prefix of the output dataframe's columns. If unspecified, the input series' `name` attribute is used, or "y", if it does not have a name.	`None`
`err`	`str`	Statistical function to use for error column. Options are "sem" (standard error of the mean) and "std" (standard deviation).	`'sem'`

Returns:

Type	Description
`DataFrame`	Time series of mean value, standard error of the mean (SEM), and count of samples per interval.

`truncate(x, digits=0)`

Truncate a float number to specified digits

`weighted_mean(values, errors)`

Weighted mean, standard deviation and standard error of the mean