WGS84RPT.tif:Corel PHOTO-PAINT - Henry A. Rowland Department ...

2.2.2.2 Tidal Effects
Tidal phenomena are another source of temporal and
permanent displacement of a station’s coordinates. These displacements can be modeled to
some degree. In the most demanding applications (cm-level or better accuracy), these
displacements should be handled as outlined in the IERS Conventions (1996) [1]. The results
of following these conventions lead to station coordinates in a ‘zero-tide’ system. In practice,
however, the coordinates are typically represented in a ‘tide-free’ system. This is the procedure
followed in the NIMA GPS precise ephemeris estimation process. In this ‘tide-free’ system,
both the temporal and permanent displacements are removed from a station’s coordinates.
Note that many practical geodetic surveying algorithms are not
equipped to rigorously account for these tidal effects. Often, these effects are completely
ignored or allowed to ‘average-out’. This approach may be adequate if the data collection
period is long enough since the majority of the displacement is diurnal and semi-diurnal.
Moreover, coordinates determined from GPS differential (baseline) processing would typically
contain whatever tidal components are present in the coordinates of the fixed (known) end of
the baseline. If decimeter level or better absolute accuracy is required, careful consideration
must be given to these station displacements since the peak absolute, instantaneous effect can
be as large as 42 cm [11]. In the most demanding applications, the rigorous model outlined in
[1] should be applied.
2.3 Mathematical Relationship Between the Conventional Celestial Reference System
(CCRS) and the WGS 84 Coordinate System
Since satellite equations of motion are appropriately handled in an inertial
coordinate system, the concept of a Conventional Celestial Reference System (CCRS)
(alternately known as a Conventional Inertial System (CIS)) is employed in most DoD orbit
determination operations. In practical orbit determination applications, analysts often refer to
the J2000.0 Earth-Centered Inertial (ECI) reference frame which is a particular, widely adopted
CCRS that is based on the Fundamental Katalog 5 (FK5) star catalog. Since a detailed
definition of these concepts is beyond the scope of this document, the reader is referred to [1],
[13], [14] and [15] for in-depth discussions of this topic.
Traditionally, the mathematical relationship between the CCRS and a CTRS (in
this case, the WGS 84 Coordinate System) is expressed as:
CTRS = [A] [B] [C] [D] CCRS (2-1)
where the matrices A, B, C and D represent the effects of polar motion, Earth rotation, nutation
and precession, respectively. The specific formulations for the generation of matrices A, B, C
and D can be found in the references cited above. Note that for near-real-time orbit
determination applications, Earth Orientation Parameters (polar motion and Earth rotation
2-8