Varying measurement error in Kriging predictions

Hello, my question is how can I implement known varying measurement error
in my
Kriging predictions?

I have two separate datasets: the first one is a 2-D dataset that includes
the observations and
the second is the a 2-D dataset that includes the measurement error in each
specific location.
The measurement error dataset follows a structure, it's not random (which
can be characterized via the use of the experimental variogram).

I have searched a lot online on how to incorporate the measurement
uncertainty in
Kriging predictions but it seems to still be an open question in the forums
(a paper solving this issue has been developed by William F. Christensen
titled as: Filtered Kriging for Spatial Data with Heterogeneous Measurement
Error Variances). I have tried to use gstat and incorporate the variances
using the weights functionality but after I do the kriging and visualize
the predicted variance field, even though it qualitatively resembles the
defined one, the values of the variances are magnitudes lower than the ones
proposed.

Does anyone have an idea on how to solve it, or aware of some
software-package that
has already implemented this functionality? (It's quite tough to understand
the stated paper already, rather having to program
its contents) .


Thank you.

Regards,
Antonios.

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