TABLE 3

Estimation Parameters and GNSS Measurements used for Real-Time Processing

ItemDescription
Estimation
    FilterExtended Kalman filter
    Estimation parametersEpoch state vector, empirical accelerations, epoch-wise residual phase offset and fractional frequency offset, inter-system bias, phase ambiguities
    Stochastic modelsWhite observation noise, elevation-independent weighting, zero a-priori values, and configurable standard deviation of empirical accelerations
    AmbiguityFloat
GNSS Measurements
    GNSS ObservationsUndifferenced GPS L1 C/A / L2C, L1/L2 P(Y), and Galileo E1/E5a pseudorange and carrier phase (Table 4)
    Sampling rate30 s
    GNSS data arcContinuous from January 17 to January 30, 2021; telemetry data gap on January 25 between 02:29 and 02:46
    GNSS satellite biasesGPS C1C/C2L timing group delay (TGD) and inter-signal corrections from CNAV; Galileo C1C/C5Q neglected
    Phase windupNeglected
    S6A GNSS antennaConstant antenna offset in satellite body frame; zero antenna phase center offset
    S6A attitudeQuaternions (measured)
    Reference frameGPS: WGS84(1762’) (Malys et al., 2016); Galileo: GTRF19v01
Orbit Model
    Earth gravity fieldGOCO03S (Tapley et al., 2004) up to order and degree 50, rate terms Ċ20, Ċ21, Ṡ21
    Third-body gravityPoint-mass model; truncated analytical series of luni-solar coordinates (Montenbruck & Gill, 2000)
    Solid Earth tidesK2 tides (Rizos & Stolz, 1985)
    Ocean tidesNeglected
    RelativityNeglected
    Solar radiation pressureCannonball model
    Earth radiation pressureNeglected
    Atmospheric forcesCannonball model; Harris-Priester model for medium-solar flux (Harris & Priester, 1962)
    Empirical accelerationEpoch-wise approximation; three components in radial, tangential, normal direction; constant during propagation step
    Reference frameITRF
    Earth orientationGPS CNAV Earth Orientation Parameters (EOP; GPS ICD, 2020)
    Numerical integration4th-order Runge-Kutta