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I have a set of ~20 Landsat images acquired with sensor version varying from LT5 up to L8, downloaded from EarthExplorer. Many of them do not align to the most current images, they are shifted by a distance between 100m (what is understantable) to 500m or a few kilometers. But the older ones have the misplacement even bigger - one of the LT5 images is shifted by 40 km! (though the corelation between error scale and Landsat version is none for me, I also have LT5 images with a very small displacement)

Using ArcMap, how can I fix this to have all images in the same place? I need to be 15m precise in my analysis (pansharpened 30m).

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In ArcMap you can use Shift tool:

Moves (slides) the raster to a new geographic location, based on x and y shift values. This tool is helpful if your raster dataset needs to be shifted to align with another data file.

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