GPS Solutions (2003) 7:23–32

The right expression for Eq. (10) is as follows:

$$ {\matrix{ {{\{ v_{x} \} _{{ITRFyy}} } \hfill} & { = \hfill} & {{\{ \dot{T}_{x} \} } \hfill} & {{ + [\kern-0.15em[ (1 + s(t_{k} ))\,\underline{{[\dot{\varepsilon }]}} ^{t} + \dot{s}\,[\delta {\Re }] ]\kern-0.15em] \,\{ x(t)\} _{{ITRF00}} } \hfill} \cr {{} \hfill} & {{} \hfill} & {{} \hfill} & {{ + [\kern-0.15em[ (1 + s(t_{k} ))\,[\delta {\Re }] + (2t_{D} - (t_{k} + t))} \hfill} \cr {{} \hfill} & {{} \hfill} & {{} \hfill} & {{ \times [(1 + s(t_{k} ))\,\underline{{[\dot{\varepsilon }]}} ^{t} + \dot{s}\,[\delta {\Re }]]\, ]\kern-0.15em] \,\{ v_{x} \} _{{ITRF00}} } \hfill} \cr {{} \hfill} & {{} \hfill} & {{} \hfill} & {{ + \dot{s}\,\underline{{[\dot{\varepsilon }]}} ^{t} \{ 2(t_{D} - t_{k} )\,\{ x(t)\} _{{ITRF00}} } \hfill} \cr {{} \hfill} & {{} \hfill} & {{} \hfill} & {{ + (3t^{2}_{D} + t^{2}_{k} - 4t_{D} t_{k} + 2t(t_{k} - t_{D} ))\,\{ v_{x} \} _{{ITRF00}} \} } \hfill} \cr } } $$
(10)

The previously published Table 2 was not properly aligned and contained some errors. Replace Table 2 by the following table:

Table 2. Transformation parameters and their rates from ITRF00 to other frames
Full size table

The following two equations should be replaced in Appendix B.

$$ \eqalign{ & \partial {\cal A}/\partial \{ \varepsilon (t_{k} )\} = \partial [\partial \varepsilon ]/\partial t_{D} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = (1 + s(t_{k} ))\,\underline{{[v_{x} ]}} \, \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \dot{s}\, [\kern-0.15em[ \underline{{[x]}} + (2t_{D} - (t_{k} + t))\,\underline{{[v_{x} ]}} ]\kern-0.15em] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = [\bar{\partial }\varepsilon ] \cr} $$
$$ \eqalign{ & \partial {\cal A}/\partial \{ \dot{\varepsilon }\} = \partial [\partial \dot{\varepsilon }]/\partial t_{D} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = (1 + s(t_{k} ))\, [\kern-0.15em[ \underline{{[x]}} + (2t_{D} - (t_{k} - t))\,\underline{{[v_{x} ]}} ]\kern-0.15em] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \dot{s}\, [\kern-0.15em[ 2(t_{D} - t_{k} )\,\underline{{[x]}} + (3t^{2}_{D} + t^{2}_{k} - 4t_{D} t_{k} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + 2t(t_{k} - t_{D} ))\,\underline{{[v_{x} ]}} ]\kern-0.15em] = [\bar{\partial }\dot{\varepsilon }] \cr} $$