I am trying to properly project Latitude and Longitude into cartesian coordinates so that I can use an unscented Kalman filter to smooth out some GPS data. I am using constant jerk newtonian motion as my state transfer matrix. My issue is that I have tried many popular projections(Mercator, etc.) and when I reproject into latitude and longitude, my data is stretched with respect to maps. Any insight on my situation would be greatly appreciated! If you need more information please ask in the comments. Thank you.
Projections into Cartesian Space from Latitude and Longitude for Kalman Filtering
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The stretch factor between longitude and latitude is cos(latitude).
So you can do a local Cyclindrical Equidistant transformation.
this is a simple tranformation, but is only acurate around 10-100km of the center (longitudeCenter, latitudCenter). this kind of projektion needs a (fixed) center.
Look further for "Cyclindrical Equidistant Projection" to get the simple formula.