Convert ECI to ECEF Coordinates

Transform ECI position, velocity and acceleration to ECEF position, velocity & acceleration.

Description

Convert ECI (CIS, Epoch J2000.0) Coordinates to WGS 84 (CTS, ECEF) Coordinates. This function has been vectorized for speed.

Example Function Call:
>> [r_ECEF v_ECEF a_ECEF] = ECItoECEF(JD,r_ECI,v_ECI,a_ECI);

Where:
JD is the Julian Date vector [1 x N] (units are in days)
r_ECI is the position vector [3 x N] (any units are permitted)
v_ECI is the velocity vector [3 x N] (any units are permitted)
a_ECI is the acceleration vector [3 x N] (any units are permitted)

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Julian Date to Greenwich Mean Sidereal Time

• MATLAB release: MATLAB 7.5 (R2007b)

[Ismail]

Hello,

Is it normal to obtain six values in the r_ECEF and v_ECEF matrices instead of just 3 ?

** Example **
******************************
r_ECI
    10.7148713368681e+003 -7.10368453661470e+003 -22.0702973475812e+003

JD
    2.45215900000000e+006

r_ECEF
   -7.72362036417280e+003 5.12056195755438e+003 15.9089729291096e+003
   -13.0369714274984e+003 8.64317726477505e+003 26.8533169340802e+003
    10.7148713368681e+003 -7.10368453661470e+003 -22.0702973475812e+003

v_ECEF
   -3.39040857672452e+000 86.2958941276462e-003 1.16863824970067e+000
   -3.55490372276425e+000 -1.29159124693780e+000 -2.49278765365527e+000
    3.38461399614162e+000 754.648420343670e-003 1.09531334972829e+000

******************************

[Darin Koblick]

Ismail,

You are more than likely using the wrong dimensions for r_ECI.
This is specified in my input requirements as [3 x N].

Try:
r_ECI = [10.7148713368681e+003; ...
 -7.10368453661470e+003; ...
 -22.0702973475812e+003]

In other words, transpose the r_ECI input for the correct answer.

[Ismail]

Ok .. now it works fine !
Thanks Darin !

[7ate9]

Excellent function - fast, and I verified a limited number of test cases. Thank you!

[lin yue]

 

[Syed Zohaib Ali]

Hi

I am facing problem in converting 1441 values of position and velocity vectors from ECI to ECEF. It seems that function works fine. When 93 out of 1441 values were passed to the function it gave values for x,y & z components which I thought are correct but when 186 out of 1441 values were passed to the function, the initial 93 x & y values were different from the one that I got by passing only 93 values, z components were the same. similarly when more values were passed the x&y were different except the z-component.
can you please guide what could be the problem?

[Darin Koblick]

Syed,

Send me your test case and I will take a look at it.

Thanks,
-Darin

[Syed Zohaib Ali]

Hi Darin

Now its working fine. I was passing JD argument in a wrong way.

Thanks
Zohaib

[Martin Fuchs]

Could you also provide accelerations ?

[Martin Fuchs]

Maybe something like this but I am not sure ???

if (~isempty(a_ECEF) && (~isempty(r_ECEF)) a_ECI = MultiDimMatrixTranspose(T3D(THETA))*a_ECEF' + 2*MultiDimMatrixTranspose(Tdot3D(THETA,omega_e))*v_ECEF' + MultiDimMatrixTranspose(Tdotdot3D(THETA,omega_e))*r_ECEF'; else a_ECI = []; end

function Tdot = Tdotdot3D(THETA,omega_e)
Tdot = zeros([3 3 length(THETA)]);
Tdot(1,1,:) = -omega_e^2.*cosd(THETA);
Tdot(1,2,:) = -omega_e^2.*sind(THETA);
Tdot(2,1,:) = -Tdot(1,2,:);
Tdot(2,2,:) = Tdot(1,1,:);

[Muhammad Shaikh]

I am having some problems in calculating ECEF data. In my calculations, the satellite positions are calculated at the wrong side of Earth (globe) in the same plan they are now being calculated. Can you guide me for this please? Note, the data I am giving to the function is verified and I can easily say that my calculations can wrong, the data can't be. Please help.

[Darin Koblick]

Check to make sure your time vector is in J2000 format, not Unix Time (epoch should be starting 01/01/2000 12:00:00).

[Muhammad Shaikh]

Thanks Darin for your reply.
I am using matlab function 'juliandate' to convert my time to julian date format. I have searched whether it is a J2000 format but could not find anything on Mathworks page. Can you please help me for this as well.

[Darin Koblick]

The MATLAB function juliandate.m should be fine. Can you please post the epoch, the position/velocity vector in ECI coordinates, and your ECF solution?

[Muhammad Shaikh]

I am only posting here first five values of each of the vectors you asked for. They are actually long arrays of more than 1000 values.

GPS XYZ Position in ECI:
 -0.239211241452386 -1.707812336086469 1.994541959448508
  -0.238883560243254 -1.707992218920763 1.994429990702043
  -0.238555873840528 -1.708172064621368 1.994317978585847
  -0.238228182457349 -1.708351873071436 1.994205923172916
  -0.237900485894857 -1.708531644380220 1.994093824395386

GPS XYZ Velocity in ECI:
 3.276820540573197 -1.799032931682451 -1.119482444956503
   3.276872512702608 -1.798661610033275 -1.119916159551723
   3.276924413465574 -1.798290250160732 -1.120349848764825
   3.276976242828717 -1.797918852306742 -1.120783512313681
   3.277028000823877 -1.797547416246293 -1.121217150461423

GPS XYZ Position in ECEF:
2.486257771277870 -0.525992080845330 1.796962071713202
   2.486219408921021 -0.526173379273422 1.796962071713202
   2.486181033343849 -0.526354674903637 1.796962071713202
   2.486142644546566 -0.526535967734976 1.796962071713202
   2.486104242529370 -0.526717257766510 1.796962071713202

GPS XYZ Velocity in ECEF:
 -1.932463623657266 -1.485322200484253 -1.119482444956503
  -1.933172003035996 -1.485054282646371 -1.119916159551723
  -1.933880318496407 -1.484786276830892 -1.120349848764825
  -1.934588569639623 -1.484518183130969 -1.120783512313681
  -1.935296756821210 -1.484250001479990 -1.121217150461423

Juliandate Vector:
2.453937827777778
   2.453937827789352
   2.453937827800926
   2.453937827812500
   2.453937827824074

[Darin Koblick]

The following ECI coordinate information

rECI = [-2392.11241452386
       -17078.1233608647
        19945.4195944851];

vECI = [3.27682054057320
       -1.79903293168245
       -1.11948244495650];

t = 2453937.82777778;

Will yield an ECEF position and velocity of

rECEF = [-15615.6915464865
         -7322.85945823539
           19943.173494021];

vECEF = [-0.253618011215938
          -2.5887912909949
          -1.1194824449565];

This was obtained using the routines provided by CelesTrak found from http://www.celestrak.com/software/vallado-sw.asp

The ECItoECEF.m routine I posted on the FileExchange comes very close to this with the following vectors:

rECF = [ -15618.7911316673
         -7310.12058163083
          19945.4195944851];

vECF = [-0.253618011215938
          -2.5887912909949
          -1.1194824449565];

The problem is your ECEF position and velocity vectors do not correspond to each other.

A very easy way to check this is to compute the magnitude of your position vectors.

The magnitude of the first ECI position vector you have provided is: 26,366.726420485 km

The magnitude of the ECEF solution should be exactly the same as the magnitude in the ECI reference frame.

The magnitude of your ECEF position vector is 31,124.2960748149 km.

Hopefully this solves your problem.

[Johan]

This function is great.
Although i think i found a mistake in your JD2GAST file.
When calculating the EPSILONm shouldn't the first number be 84381.448 and not 84381448 to make sure EPSILONm is calculate in arcseconds.
Shouldn't you convert EPSILONm from arcseconds to degrees like you did with dPSI and dEPSILON?

[Darin Koblick]

Johan,

You are correct, thank you for spotting that mistake. I should have left everything in degrees since the mean obliquity of the ecliptic is referenced directly in the final computation.
The new parameters for the mean obliquity should be:

EPSILONm = 23.439291-0.0130111.*T - 1.64E-07.*(T.^2) + 5.04E-07.*(T.^3);

This corresponds to the estimates contained in Vallado, Fundamentals of Astrodynamics and Applications, Second edition, (EQ 3-53). 2001.

Thank you again for double checking my work.