IERS4m

These classes facilitates the CIO based celestial to terrestrial transformation. The main function is GCRS2ITRS which provides the 3x3 celestial to terrestrial transformation matrix. In order to obtain the necessary EOP information use helper object USNO.m.

There is a detailed writeup (docs/README.pdf) which explains this transformation in more detail as well as explains the matrix formulation implemented in MATLAB. Most relevant references are listed in the References section below. Select papers are avaliable in the docs/refs folder.

Default 2010 IERS convention.

Contents

• Example Usage
• Notes on Transforming Velocity and Acceleration
• References

Example Usage

This example is taken from David Vallado's paper listed in the References section.

% date time UTC: 2004/04/06 07:51:28.386
fMJD_UTC = 53101.3274118751;
% init EOP object
eopobj = USNO();
% pull latest EOP data from USNO servers
eopobj = eopobj.initWithFinalsHttp();
% interpolate EOP information for date and time
[xp,yp,du,dt] = eopobj.getEOP(fMJD_UTC);
% Vallado et al. 2006, AIAA                        [meters]
X_itrs = [-1033.4793830, 7901.2952754, 6380.3565958]';
% dx,dy = 0                                        [meters]
X_gcrs = [5102.5089592, 6123.0114033, 6378.1369247]';
% compute the 3x3 transformation matrix
GC2IT = IERS.GCRS2ITRS(fMJD_UTC,dt,du,xp,yp);
% perform the coordinate/position conversion: C -> T
X = GC2IT*X_gcrs;
% compute the error in meters
err = sum(sqrt((X-X_itrs).^2))

err =

0.00038976917267064

Notes on Transforming Velocity and Acceleration

Use IERS.wrot(w,GC2IT) to if velocity and accelerations are present to account for the relative rotation of the inertial and noninertial frames. Generally speaking can simply use the nominal earth rotation rate in radians per second (IERS.DS2R).

% define earth rotation rate in radians per second about the z-axis (GCRS -> ITRS)
w = [0,0,IERS.DS2R];

% expand to 9x9 matrix to accomodate X = [pos, vel, acc]
GC2IT = IERS.wrot(w,GC2IT);
% reduce transformation matrix to 6x6 for state vectors of position and velocity
GC2IT = GC2IT(1:6,1:6);

Finally keep in mind that when going in the opposite direction from ITRS to GCRS, the rotation is in the opposite direction and thus must negate the z-axis rotation rate so that w = [0,0,-IERS.DS2R];

References

  IERS 2010
www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html

  IERS 2003
www.iers.org/IERS/EN/Publications/TechnicalNotes/tn32.html

  IERS FTP
ftp://tai.bipm.org/iers/conv2010/chapter5/
ftp://maia.usno.navy.mil/conv2010/chapter5/

  SOFA Library

    Main:
http://www.iausofa.org

    Time Reference Cookbook:
http://www.iausofa.org/2012_0301_C/sofa/sofa_ts_c.pdf

    Validation Routines:

      C:
http://www.iausofa.org/2012_0301_C/sofa/t_sofa_c.c

      FORTRAN:
http://www.iausofa.org/2012_0301_F/sofa/t_sofa_f.for

    Tutorial:
www.iausofa.org/publications/sofa_pn.pdf

    NOVAS Comparison:
www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA543243

  David Vallado, Seago J., Seidelmann P., Implementation Issues
Surrounding the New IAU Reference Systems for Astrodynamics,
AIAA, AAS 06-134, 2006

Published with MATLAB® R2015a