[SciPy-Dev] Adding algorithm for automatic differentiation of noisy data to SciPy

[Siva Sankar]

Hello,

Automatic differentiation of noisy data has not been very accurate and does
not have a lot of different algorithms that give consistent and accurate
results.

I have added an algorithm that estimates the derivative of noisy data using
linear Gaussian state-space smoothing and square root formulas.

Link to the pull request. https://github.com/scipy/scipy/pull/9004

The algorithm in its current state provides the smoothed signal from the
noisy measurements, estimation of the first and second order derivatives
and optionally also provides the dense output for the same. It accepts
non-equally spaced data abscissas and is able to compute the state
parameters between the abscissas, hence being able to provide the dense
output.

The algorithm was tested with data from bioanalytics and provides equal or
better accuracy of the derivatives compared to the other automatic
derivative algorithms.

Real life readings and measurements of data in any field are prone to
noise, thereby making the normal differentiation algorithms less reliable.
Having an algorithm like this can significantly help users from a variety
of fields where they need a good differentiation estimation without having
to tweak with the parameters to differentiate data.

Best Regards,
Siva Sankar Kannan.
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