given epoch, a set of selected parameters chosen to improve the force model as well as
several geodetic parameters are fitted simultaneously. The geodetic parameters include:
positions of the laser stations and their horizontal and vertical velocities, Earth
orientation parameters (EOP, Le., polar motion and UTI) and zonal harmonics I n and
their time derivative j n for n = 2, 3, 4 and 5.
The force models considered in this analysis are the following: we used the JGM-2
geopotential model (Nerem et aI, 1994) for the Earth's gravity field. This model is
complete up to degree 70. The solid Earth tide model is that recommended by the IERS
(International Earth Rotation Service) standards (1992). For the ocean tides, and their
loading effect, we use the Schwiderski's model (1980) taking into account the eleven
largest tides. A spherical harmonic decomposition is used for each tide, up to degree 19
and order 4. Since the Sa (annual) and 18.6 yr ocean tides are not included in the
Schwiderski's model, we introduce their equilibrium values with amplitudes of 0.216 cm
and 1.23 cm respectively. Only the degree 2 and order 0 harmonic is considered for these
ocean tides. The SI solar tide is introduced as an unknown parameter (degree 2 and order
1 harmonic) with a zero initial value.
The direct as well as reflected (albedo and infrared) radiation pressure is accounted
for. An along-track empirical acceleration is added to account for charged-particle drag.
The force model also includes luni-solar and planets direct gravitational attractions.
Integration of the satellite equations of motion is performed in the instantaneous
celestial reference frame, connected to the 12000 mean equator and equinox through
precession and nutation models of the IERS standards (1992).
The terrestrial reference frame is defmed by the initial coordinates of the laser stations
and Earth orientation parameters. We used as initial station coordinates, values of the
ITRF89 (International Terrestrial Reference Frame for 1989) and for polar motion and
UTI, an homogeneous series computed at IERS.
Station coordinates are assumed time-dependent and their absolute horizonal velocities
(initial values) are from the NUVEL-l geological model (De Mets et al., 1990). Initial
vertical velocities are set to zero.
Basic orbital arcs of 30 days are processed for each Lageos satellite and partial
derivatives of the observables are computed with respect to the unknown parameters
forming a normal equation system.
Computed partial derivatives are related to : 1) orbital parameters at the beginning of
each monthly arc, 2) air drag and radiation pressure empirical coefficients (fortnightly
values), 3) the 18.6-yr ocean tide (degree 2, order 0 harmonic) and SI solar tide (degree
2, order 1 harmonic), 4) daily EOP parameters, 5) stations coordinates at a reference
epoch, 6) absolute horizontal and vertical velocities, 7) corrections to the first five zonal
harmonics and 8) their time derivative jn (assuming purely linear dependence with time).
Normal matrices of each monthly arc are further accumulated over several years
(11 years for Lageos 1 and 2 years for Lageos 2). The weight of each matrix is directly
dependent upon the a priori standard deviation of the laser measurements of each satellite
(assumed equal to 10 cm). Normal matrices of each satellite are then combined and the
total matrix is inverted to derive the solution.
143
several geodetic parameters are fitted simultaneously. The geodetic parameters include:
positions of the laser stations and their horizontal and vertical velocities, Earth
orientation parameters (EOP, Le., polar motion and UTI) and zonal harmonics I n and
their time derivative j n for n = 2, 3, 4 and 5.
The force models considered in this analysis are the following: we used the JGM-2
geopotential model (Nerem et aI, 1994) for the Earth's gravity field. This model is
complete up to degree 70. The solid Earth tide model is that recommended by the IERS
(International Earth Rotation Service) standards (1992). For the ocean tides, and their
loading effect, we use the Schwiderski's model (1980) taking into account the eleven
largest tides. A spherical harmonic decomposition is used for each tide, up to degree 19
and order 4. Since the Sa (annual) and 18.6 yr ocean tides are not included in the
Schwiderski's model, we introduce their equilibrium values with amplitudes of 0.216 cm
and 1.23 cm respectively. Only the degree 2 and order 0 harmonic is considered for these
ocean tides. The SI solar tide is introduced as an unknown parameter (degree 2 and order
1 harmonic) with a zero initial value.
The direct as well as reflected (albedo and infrared) radiation pressure is accounted
for. An along-track empirical acceleration is added to account for charged-particle drag.
The force model also includes luni-solar and planets direct gravitational attractions.
Integration of the satellite equations of motion is performed in the instantaneous
celestial reference frame, connected to the 12000 mean equator and equinox through
precession and nutation models of the IERS standards (1992).
The terrestrial reference frame is defmed by the initial coordinates of the laser stations
and Earth orientation parameters. We used as initial station coordinates, values of the
ITRF89 (International Terrestrial Reference Frame for 1989) and for polar motion and
UTI, an homogeneous series computed at IERS.
Station coordinates are assumed time-dependent and their absolute horizonal velocities
(initial values) are from the NUVEL-l geological model (De Mets et al., 1990). Initial
vertical velocities are set to zero.
Basic orbital arcs of 30 days are processed for each Lageos satellite and partial
derivatives of the observables are computed with respect to the unknown parameters
forming a normal equation system.
Computed partial derivatives are related to : 1) orbital parameters at the beginning of
each monthly arc, 2) air drag and radiation pressure empirical coefficients (fortnightly
values), 3) the 18.6-yr ocean tide (degree 2, order 0 harmonic) and SI solar tide (degree
2, order 1 harmonic), 4) daily EOP parameters, 5) stations coordinates at a reference
epoch, 6) absolute horizontal and vertical velocities, 7) corrections to the first five zonal
harmonics and 8) their time derivative jn (assuming purely linear dependence with time).
Normal matrices of each monthly arc are further accumulated over several years
(11 years for Lageos 1 and 2 years for Lageos 2). The weight of each matrix is directly
dependent upon the a priori standard deviation of the laser measurements of each satellite
(assumed equal to 10 cm). Normal matrices of each satellite are then combined and the
total matrix is inverted to derive the solution.
143