# Perform Calculations in Cartesian Frame (NED/ECEF) Vs. Geodetic Frame

I'm recording robot's path (using INS) in Cartesian frame coordinates (x,y,z) relative to origin point. So essentially I've created NED coordinate system.

Origin point has exact (in advance measured) geodetic location (LLA: Latitude, Longitude, Altitude).

The calculation I apply for each NED (x,y,z) robot's location to get geodetic position:

1. Represent the origin point in ECEF.
2. Because relationship between the origin point to robot's location (x,y,z) is in Cartesian coordinates (NED), and from previous step I have origin point in ECEF, which is also Cartesian. Using well known geometry I can represent robot's location - NED (x,y,z) in ECEF.
3. Using well known equations I can convert that ECEF location to LLA (geodetic coordinates), for example in WGS84 standard.

Moreover - I can perform spatial calculations in my Cartesian frame coordinates using simple geometry, instead of getting used to complex geodetic calculations.

Question- It sounds too good to be true that one can just using simple geometry and having closed form ECEF to LLA equations to transform into geodetic locations. Assuming perfect transformations (with only numeric errors) and no "Great Circle" issues, where this mode of operation will not be good? For example, if in Cartesian frame the robot moved 100m in X direction, If I transform start & end locations from Cartesian to geodetic, it will still keep 100m distance in WGS84 system?