ERS Precise Orbit Determination: Details

Last update: Tue 31 March 1998

Orbit precision

The ERS-1 orbits provided by DEOS are believed to have a radial precision of 5-6 cm. The orbits that feature on the ERS OPR altimeter product are produced by GFZ/D-PAF, are based on the PGM035 and PGM055 gravity model (clones of GRIM 4), and have a radial precision of no better than 12 and 7 cm. For the Tandem Mission, during which solar activity as very low, radial orbit precision is as low as 5 cm. Replacing the GFZ orbits by the DGM-E04 orbits reduces the crossover height difference RMS from approx 18 and 13 to 10 cm. The latter value includes the following altimeter corrections:

  • Atmospheric corrections as provided on the OPR CDROM
  • Inverse barometric correction
  • Grenoble FES95.2.1 ocean tides and ocean loading
  • Sea state bias of 5.5% of SWH [Gaspar et al.]
  • a correction of the altimeter time tags
  • With the Delft DGM-E04 orbits, this makes the ERS crossover height differences to fall within the requirements set for TOPEX/POSEIDON !

    Orbit determination and modelling

    The ERS precise orbit positioning is based on SLR tracking data provided by some 60 stations throughout the world. To aid the orbit determination especially when the laser ranging data are sparse, altimeter crossover height differences and direct altimetric heights are used as additional tracking data. The significant amount of tracking data makes it possible to have a more free adjustment of the orbit to absorb unmodelled or insufficiently modelled forces acting on the huge satellite body.

    DEOS has produced a new gravity field model, DGM-E04, which is especially tuned to ERS and now provides orbits with a radial precision of 5 cm. This was first announced at the European Geophysical Society Assembly in Den Haag, May 1996, and at the Spring Meeting of the American Geophysical Union, June 1996. For details, read the PostScript version of the hand-out.

    A paper is now submitted to Journal of Geophysical Reseach (Oceans) that describes in full the development of the DGM-E04 gravity model and the orbit computation with that model and JGM-3. An abstract is available.

    The remainder of this section summarizes the dynamical and measurement models used for the ERS precise orbit determination with the DGM-E04 gravity field model.

    SLR Measurement model

    Global quick-look SLR data retrieved from Eurolas Data Center (EDC) and and Crustal Dynamics Data Information System (CDDIS), and (if required) converted to 1 per 15 s normal points.
    Data weighting.
    Weight sigma of each system is an rss combination of the assumed overall model accuracy (5 cm) and noise level of the system (1-20 cm).
    Marini-Murray model.
    Geometric correction.
    Offset of LRR optical centre wrt LRR reference point (4.3 cm), and the LRR reference point offset with respect to the spacecraft nominal centre-of-mass.
    Cutoff elevation = 10 deg. Spurious measurements removed.

    Altimeter measurement model

    Global ERS radar altimeter data, retrieved from the ESA ERS OPR products.
    Data corrections.
    The altimeter ranges are corrected for ECMWF dry tropospheric and ionospheric path delays [OPR]; ATSR/M wet tropospheric corrections [OPR]; Schwiderski solid earth tides [OPR]; Grenoble FES95.2.1 ocean tides and tidal loading [Le Provost et al.]; 5.5% sea state bias [Gaspar et al.]; 100% inverse barometric correction; time tag bias [estimated].
    Single altimeter crossovers.
    Crossover height differences between crossing tracks of ERS-1 or ERS-2, spanning the orbital arc.
    Dual altimeter crossovers.
    Crossover height differences between crossing tracks of ERS-1 and ERS-2, spanning the orbital arc. This data type is only used during the ERS Tandem Mission (May 1995-June 1996).
    Altimeter height residuals.
    Altimeter height residuals over the OSU MSS95 mean sea surface model enhanced with an ERS derived seasonal variation. This data type is used only outside the Tandem Mission (May 1995-June 1996)
    Crossover weighting.
    Weight sigma of each crossover measurement is based on the global distribution of the observed crossover RMS coming from an earlier solution.
    Weighting of altimeter residuals.
    Weight sigma of each altimeter residual is based on the global distribution of the observed residuals from an earlier solution, multiplied by 1.5 to downweight this data type.

    Satellite model

    ERS-1: m = 2377.13 kg. ERS-2: m=2502.00 kg.
    Position of LRR and centre-of-mass.
    Conform ESA documents.
    Satellite-specific macro-models, each consisting of 8 fixed and 2 rotating panels.

    Dynamic model

    Gravity model.
    Delft Gravity Model DGM-E04, complete to degree and order 70, including secular C_21 and S_21 and dynamic polar motion. GM = 398600.4415 km3/s2.
    Speed of light.
    c = 299792.458 km/s.
    Reference ellipsoid.
    a_e = 6378.1363 km and 1/f = 298.2564.
    Solid Earth tides.
    Frequency-dependent Wahr model (1981); permanent tide excluded according to IERS Standard (1989).
    Ocean tides.
    JGM-2 ocean tide model.
    Third body attraction.
    Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Neptune, according to JPL DE200 ephemeris.
    Atmospheric drag.
    French Density Model (DTM 87) with daily F_10.7 values and 3-hourly K_p values from NOAA.
    Solar radiation pressure at 1 AU = 4.5783e6 N/m2. Umbra, penumbra, and occultation by Moon modeled. Earth albedo modeled. Solar radiation coefficient fixed at C_R=1.0.
    Pole tide.
    Dynamical effect of pole tide applied.
    Relativistic effects.
    Orbit manoeuvres.
    A priori information according to ESOC predictions. Adjusted during POD. (ERS-1 manoeuvres, ERS-2 manoeuvres).

    Reference frame

    Station coordinates.
    LSC(DUT)95L02 LAGEOS I/II solution (Sep 1983 - Dec 1993, epoch 1 Jan 1988), advanced to epoch by 3-dimensional motions incorporated in the coordinate solution.
    Reference ellipsoid.
    GRS80: a_e = 6378.1370 km and 1/f = 298.257.
    Earth rotation.
    Values from IERS EOP 90 C 04 solution.
    Mean equator and equinox of J2000.0.
    IAU 1976 (Lieske model).
    IAU 1980 (Wahr model).
    Tidal uplift.
    Love model, including frequency dependent and permanent tides (h_2 = 0.609, l_2 = 0.0852).
    Pole tide.
    Geometrical effect of pole tide accounted for.
    Ocean loading.
    not applied.

    Numerical integration

    NASA/GSFC/STX GEODYN orbit determination package, adjusted by DEOS to properly incorporate dual-satellite crossover height differences and PRARE tracking.
    11th-order Cowell prediction correction method for equations of motion and variational equations.
    Step size.
    60 seconds.

    Estimated parameters per orbital arc

    State vector.
    Position and velocity at epoch.
    6-hourly drag coefficients (C_D: 22 parameters per arc).
    Empirical forces.
    22-hourly 1-cpr along-track and cross-track accelerations (6 times 4 parameters per arc).
    Orbit manoeuvres.
    Accelerations in three directions.
    Station coordinates.
    Of some (mobile) stations.
    SLR measurement offsets.
    Range and timing bias for some stations.
    Altimeter measurement offsets.
    Timing bias for both altimeters. Relative range bias between ERS-1 and -2 altimeters.

    Output ephemeris

    Data arcs.
    Arc length of 5.5 days with an epoch spacing of 3.5 days.
    The position of the satellite's nominal centre-of-mass is given in the Conventional Terrestrial Reference System (CTRS) as latitude, longitude, and height above the GRS80 reference ellipsoid, centred around the mean IERS pole origin. This position is obtained from the Inertial True Of Date (ITOD) coordinates after rotation over the Greenwich hour angle and accounting for polar motion. Time-tagging is in the UTC time scale determined by the USNO master clock.
    Step size.
    60 seconds.

    Orbital Data Records (ODR)

    The ERS orbits provided by DEOS are in a binary format particularly useful for altimetric purposes. It contains the longitude, latitude, and altitude of the nominal centre-of-mass of the satellite in the GRS80 reference frame each 60 seconds. These orbit files each span a 5.5-day arc and are displaced by 3.5 days from one arc to the other, such that a 2-day overlap exists between the arcs.

    Recently, the format has been changed to increase the resolution of the latitude and longitude coordinates from 1.0 to 0.1 microdegrees. This should be particularly advantageous for InSAR applications. In order to be ready to use either the old or the new format, download the new supporting software.

    The (binary) format of the ODR files is described separately.

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