# EPSG:1054

## Time-dependent Position Vector tfm (geog2D)

### Attributes

Data source: EPSG

Information source: EPSG guidance note #7-2, http://www.epsg.org

Revision date: 2019-02-21

Remarks: Note the analogy with the Time-dependent Coordinate Frame rotation (code 1057) but beware of the differences! The Position Vector convention is used by IAG. See method codes 1053 and 1055 for similar methods operating between other CRS types.

### Formula

```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.

Transformation of coordinates from one geographic coordinate reference system into another is often carried out as a concatenation of the following operations:

(geographical to geocentric) + (geocentric to geocentric) + (geocentric to geographic)

The Time-dependent Position Vector transformation (geog2D domain) has 5 steps:

(i) geographic 2D coordinates are converted to 3D using EPSG coordinate operation method code 9659;

(ii) geographic 3D coordinates are converted to geocentric coordinates using EPSG coordinate operation method code 9602;

(iii) the middle step of the concatenated transformation, from geocentric coordinates to geocentric coordinates, uses the Time-dependent Position Vector (geocentric domain) method, EPSG method code 1053;

(iv) the geocentric coordinates are converted to geographic 3D using EPSG coordinate operation method code 9602;

(v) finally the geographic 3D coordinates are converted to geographic 2D using EPSG coordinate operation method code 9659.```

### Example

```Input point:
Coordinate reference system: WGS 84 (G1674) = ITRF08 (geographic 2D)
Latitude  =  15 deg 28 min 32.368 sec S
Longitude = 128 deg 02 min 56.198 sec E
at epoch 2013.90

This is taken to be geographic 3D with an assumed ellipsoidal height hs  =  46.244 m

This transforms to WGS 84 (G1674) = ITRF2008 Cartesian geocentric coordinates:
Xs = -3789470.702 m
Ys =  4841770.411 m
Zs = -1690893.950 m
(at epoch 2013.90)

Transformation parameters ITRF08 to GDA94:
tX = –84.68 mm
dtX = +1.42 mm/yr
tY = –19.42 mm
dtY = +1.34 mm/yr
tZ = +32.01 mm
dtZ = +0.90 mm/yr
rX = 0.4254 msec
drX = -1.5461 msec/yr
rY = -2.2578 msec
drY = -1.1820 msec/yr
rZ = -2.4015 msec
drZ = -1.1551 msec/yr
dS = +0.00971 ppm
ddS = +0.000109 ppm/yr
t0 = 1994.00

Corrections due to rate of change to each of the 7 transformation parameters for the period (t-t0), taking care to convert the translations to the same units as the source CRS (in this case metres) and the rotations to radians:
tX' = –84.68  + [(1.42 * (2013.90-1994.00)] =  –56.42 mm =  –0.056m
tY' = +0.007 m
tZ' = +0.050 m
rX' = –0.4254  + [(1.5461 * (2013.90-1994.00)] =  +30.3420 msec =  1.471021E-07rad
dS' = 0.00971 + [0.000109 * (2013.90-1994.00)] = 0.01188 ppm

from which M' = 1.00000001188

Using these parameter values, application of the 7 parameter Coordinate Frame transformation results in:
Xt = -3789470.008 m
Yt =  4841770.685 m
Zt = -1690895.103 m
on the GDA94 geocentric coordinate reference system.

This converts into:
Latitude  =  15 deg 28 min 32.406 sec S
Longitude = 128 deg 02 min 56.174 sec E
Ellipsoidal height =  +46.244m
on the GDA94 geographic 3D coordinate reference system. For the 2D equivalent the height is ignored.```