# how to go from NED to ECI frame?

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Khang Nguyen on 21 Feb 2021
Hello! I am wondering how do you go from NED frame to ECI frame?
I got a NED frame from the WMM block but it say that the dimention of matrix multiplication is not complete.
also I got an error say that the built in fuction ecef2eci does't exist
function ECI = NEDtoECI(mu, l, NED)
DCM = [-sin(mu)*cos(l) -sin(mu)*sin(l) cos(mu) ; -sin(l) cos(l) 0 ; -cos(mu)*cos(l) -cos(mu)*sin(l) -sin(mu)];
dcmtran = DCM.';
ECEF = NED*dcmtran;
utc = [2019 1 4 12 0 0];
ECI = ecef2eci(utc,ECEF);
end
Khang Nguyen on 20 Apr 2023
Edited: Khang Nguyen on 20 Apr 2023
Probally, since this project wes too long ago, I can't remember much! (I wrote this in my first year at University)
But I belive NED (North East Down frame) is a local frame which define by a possition vector in the Geocentric Coordinate. We will need to convert it into the ECEF (Earth Center Earth Fixed frame) frame and then again to the ECI (Earth Center Inertial frame).
Since ECI frame x-direction point torward the vernal equinox and ECEF x-direction point torward the Prime Meridian. Therefore, there is a time dependent component. Since the ECEF is a non-inertial reference frame and ECI is an "Inertial Frame", you will need to do some dynamic math to convert between ECEF and ECI. The code is currently assume that ECI and ECEF at a certain time, and rotate about the ECEF z-axis. This is a good approx, but to be more accurate, the z axis of both frame are slightly not align, therefore you have to rotate the y-axis by a little bit. I am happy to rewrite and update the code after my exam season.
IDK what is your background in dynamic, hope that this make sense.
Oh I see, that makes sense Khang, thank you very much!

Alan Moses on 25 Feb 2021
Hi Khang,
The “ecef2eci” is part of the set of functions that require the ‘Aerospace Blockset CubeSat Simulation Library’ Add-on support package. You could download this from the Add-ons manager.
Alternatively, you may also check out the function here in the MathWorks File Exchange.
Hope it helps!