EPSG guidance note #7-2, http://www.epsg.org
Note the analogy with the Time-specific Position Vector method (code 1065) but beware of the differences!
Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided. The time-specific ooordinate transformation is an alternative approach to the time-dependent coordinate transformation. In this method the transformation parameter values are declared for a specified transformation reference epoch (an additional parameter for the transformation) and coordinates are adjusted to this epoch before the transformation is applied. This requires that the velocities for points whose coordinates are to be transformed are available. The time-specific transformation may then be applied as part of a concatenated coordinate operation in conjunction with one or two point motion operations (see EPSG Guidance Note 7-3 section 3) in two or three steps: i) change the source CRS Cartesian coordinates from their dataset coordinate epoch to the transformation reference epoch at which the time-specific transformation is valid; ii) apply the Time-specific Coordinate Frame rotation transformation; iii) change the target CRS Cartesian coordinates from the transformation reference epoch at which the time-specific transformation is valid to any other desired coordinate epoch. The transformation reference epoch of the Time-specific Coordinate Frame rotation transformation is used as the target epoch (t2) in step (i) and as the source epoch (t1) in step (iii). It is not used in step (ii).
Initial coordinates are referenced to the ITRF2008 CRS (EPSG code 5332) at coordinate epoch 2005.00. (Note: this happens to be the frame reference epoch for ITRF2008 but in other circumstancs the coordinate set could be referenced to a coordinate epoch different from the CRS's frame reference epoch). Coordinates are required to be referenced to the PZ-90.11 CRS (EPSG code 7679) at coordinate epoch 2013.90. Input point geocentric Cartesian coordinates and linear velocities: XS = 2845 456.0813 m VX = –0.0212 m/yr YS = 2160 954.2453 m VY = +0.0124 m/yr ZS = 5265 993.2296 m VZ = +0.0072 m/yr t = 2005.00 (years) These are referenced to ITRF2008 at coordinate epoch 2005.00 Step 1: convert the coordinates in the source CRS from the dataset coordinate epoch (2005.00) to the epoch of validity of the time-specific transformation (2010.00) using the Point Motion (geocentric Cartesian) method described in EPSG Guidance Note 7-2. XS(t=2010.00) = 2845456.0813 + (–0.0212) * (2010.0 - 2005.0) * 2845455.9753 m YS(t=2010.00) = 2160954.2453 + (+0.0124) * (2010.0 - 2005.0) * 2160954.3073 m ZS(t=2010.00) = 5265993.2296 + (+0.0072) * (2010.0 - 2005.0) * 5265993.2656 m Step 2: transform the coordinates in the source CRS at coordinate epoch 2010.00 to the target CRS at coordinate epoch 2010.00 using the Coordinate Frame Rotation (geocentric domain) method described in EPSG Guidance Note 7-2. The time-specific transformation from PZ-90.11 to ITRF2008 (EPSG Dataset transformation code 7960) parameter values are: tX = –0.003 m tY = –0.001 m tZ = 0.000 m rX = 0.019 msec rY = –0.042 msec rZ = 0.002 msec dS = 0.000 ppm from which M = 1.0 t = 2010.00 years This uses the Coordinate Frame rotation convention. Because the transformation is required in the reverse direction to that defined, the relevant parameters need to have their signs reversed. Transformation parameter values (from ITRF2008 to PZ-90.11) then are: tX = 0.003 m tY = 0.001 m tZ = 0.000 m rX = –0.019 msec = –9.21145994108117E-11 radians rY = 0.042 msec = 2.03621746066005E-10 radians rZ = –0.002 msec = –9.69627362219071E-12 radians M = 1.0 t = 2010.00 (years) Then: XT(t=2010.00) = 2845455.9772m YT(t=2010.00) = 2160954.3078m ZT(t=2010.00) = 5265993.2652m Step 3: convert the coordinates in the target CRS from epoch 2010.00 to the required coordinate epoch 2013.90 using the Point Motion (geocentric Cartesian) method: XT(t=2013.90) = 2845455.9772 + [–0.0212 * (2013.90 - 2010.00)] = 2845455.8945m YT(t=2013.90) = 2160954.3078 + [+0.0124 * (2013.90 - 2010.00)] = 2160954.3562m ZT(t=2013.90) = 5265993.2652 + [+0.0072 * (2013.90 - 2010.00)] = 5265993.2945m