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Imagine I have two samples of XY points, lets call them A and B, distributed across the same area/extent:

Points A and B

Points A have an attribute, lets call it N. I’d like to estimate (i.e. interpolate) attribute N for points B.

I could simply “copy across” the value from the nearest corresponding points in A to B, but this is no good for the use case I have in mind. Instead I need to interpolate the value, e.g. using IDW or kriging. So far all tools I can think of take point attributes and interpolate them to a new raster (i.e. continuous surface, which I do not want), rather than interpolating to existing points. Does anyone know of any way to accomplish the latter please?

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There are many ways to tackle this problem.

An easy path

The simplest i can think is to use any point-to-raster interpolation followed by raster-sampling. Any Gis software should do it. I would say SAGA is a good choice for this process.

Saga can make ordinary krigging (under "geoprocessing" -> "spatial and geostatistics" menu), and raster sampling (under "geoprocessing" -> "shapes" -> "point cloud").

You may want also to look the "geoprocessing" -> "spatial and geostatistics" -> "Regression" menu, i think there can be some usefull tools for your case.

If you feel comfortable with programming

Give a shot to the R programming language, in combination with jupyter-lab it can be very easy to get up and running.

This link explains kriging on r: https://rpubs.com/nabilabd/118172. It is all built around the "krige" function, from the package gstat. Documentation Here: https://www.rdocumentation.org/packages/FeedbackTS/versions/1.5/topics/krige

There you build the variogram and make the regression on separate steps, which is very instructive.

Note that interpolation points are explicit, and can be arbitrary, despite the fact that you will find that every example around there uses grids.

More About kriging for a single point

I've found some time ago a very interesting piece of software: E{Z}-kriging. I think this software is a good place to start if you want to learn how is kriging done point by point. You can find it here: https://wiki.52north.org/AI_GEOSTATS/SWEZKriging

For a further look

I suggest searching the internet for spatial regression problems or multiple regression problems. You will find plenty of statistical learning or machine learning sites with theory and examples on cases very similar to that of yours.

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