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Transformation GPS - Map coordinates

Thanks for the nice paper. I have a question regarding the mapping phase.
How do you keep the correspondence for any location between the GPS coordinates and the map points which is in local coordinates by definition?
Do you only use the initial pose transform GPS-map frame and use it all along the path?
If you apply SLAM algorithm, it means the point clouds from lidars are optimized and aligned at each time step using gmapping i suppose.
So, how to you keep trace of the transform global coordinate / local coordinate for the complete map?
Thanks!

GPS Recommendation

Hello. I wanted to ask you for some help. We also have a wide area and we want to increase our success in amcl. We work with an industrial robot. However, we are looking for a GPS that is small in size. Can you recommend a GPS that will work properly?

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