When I try to correlate the gps coordinates among points obtained from field and satellite for the same location there is a big difference among the two. I assume that this is partly due to the satellite image shift. Can anyone tell me how to correlate the two datasets that are actually same but have difference in coordinates?
Some satellite images may differ from the actual coordinate system, so you can first try placing your GPS points in Google Earth. (Usually, the deviation between the display of points on Google Earth and GPS values is small.) If there is a significant deviation, please check the accuracy of your GPS positioning points to see if there is a significant error or gross error caused by poor GNSS observation data quality. If there is no problem, it is a problem with the satellite image. Please check if the satellite image is calibrated.
My answers support the first answer from Jens Kleb above. I do not want to repeat it.
But if you need to correlate for other purposes try to investigate the differences in coordinates between GPS measurements in other image points. If they nearly look the same so that difference can be used for georeferencing the satellite image to be in the same GPS reference frame (datum- transformation parameters). These transformation parameters can be used also if you need to keep the satellite image as reference to layout your collected data to match with the image.
"there is a big difference among the two" - how big?
If just a few hundred meters (in case of some older terrestrial geodetic networks, up to 1-2 kilométeres) it is the obvious effect of different geodetic datums (geodetic datum == an ellipsoid and its spatial position; in practice, the 3D location of its geometric centre from the mass center of the Earth, which is more or less the geometric centre of the WGS84 ellipsoid/datum).
Chapter 3 of my book:
Book Map grids and datums
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