Article Figures & Data
Figures
- FIGURE 1
Closed-loop ADCS
- FIGURE 2
Flow diagram of A-POD and A-PAD modules implemented in the LeoPod software
- FIGURE 3
Layout of the simulated antenna array
- FIGURE 4
Roll and pitch attitude angles estimated from dual-frequency (left column) and single-frequency (right column) observations for MC A-PAD (top row) and AC A-PAD (bottom row)
- FIGURE 5
Yaw attitude angle, with magnified results shown for a duration of approximately 20 min on the right
- FIGURE 6
Observation residuals from conventional POD with one antenna (top) and A-POD with a full array (bottom); UTC: coordinated universal time
Tables
- TABLE 1
Specifications of ADCS Sensors for CubeSats (Source: https://www.cubesatshop.com/)
Name Sensor Type Accuracy (1σ) Power (W) Weight (g) Cost (USD) Sagitta Star tracker 2 arc seconds <1.4 275 ~45000 Twinkle Star tracker 15 arc seconds <0.6 40 ~45000 NSS Magnetometer 1° <0.7 85 ~15000 NSS Sun sensor <0.5°–0.1° <0.013 5–35 ~12000 Antenna #1 #2 #3 #4 Coordinates (cm) [0, 0, −16.31] [0, 10, −16.31] [−10, 10, −16.31] [−10, 0, −16.31] ID Name COSPAR ID Altitude Orbit Type 099 LEMUR-2-JOHANLORAN 2019-018G 505 km Sun-synchronous orbit (local time of descending node 09:30) Item Description Dynamic models and Stochastic accelerations Gravity field: Earth Gravitational Model (EGM 2008) (Pavlis et al., 2008) Tidal corrections: FES2014b (Lyard et al., 2021) Relativity: International Earth Rotation and Reference Systems Service (IERS 2010) (Petit & Luzum, 2010) Planet ephemeris: Jet Propulsion Laboratory (JPL DE421) (Standish, 1998) Velocity changes (pulses) and piecewise constant accelerations Observation model Observation model: Ionospheric-free linear combination of 1-Hz GPS code (C1, C2) and phase (L1, L2); Stochastic model: SNR-based weighting model (Allahvirdi-Zadeh, El-Mowafy, & Wang, 2022) Eclipsed observations: Removed using the shadow model (Allahverdi-Zadeh et al., 2016) Code and phase standard deviation: 0.1 m and 1 mm (Zenith, L1) Satellite attitude information: Obtained as quaternions Antenna phase center offset: [0.0021, 0.0011, −0.0223] m for L1 [0.0033, 0.0034, −0.0125] m for L2 Antenna phase center variation pattern: Residual approach (Allahvirdi-Zadeh, 2021) Phase ambiguities: Fixed by applying observable-specific signal biases (Schaer et al., 2021) Observations X (m) Y (m) Z (m) 3D One antenna 0.069 0.051 0.081 0.118 A-POD with FOUR antennae 0.022 0.016 0.031 0.041 Symbol size comment pr,f (m −1)× 1 SD code observations of antenna r, frequency f φr,f (m −1)× 1 SD phase observations of antenna 1, frequency f Pr f(m −1)×1 SD code observations of antenna r Φr f(m −1)×1 SD phase observations of antenna r yr 2f(m −1)× 1 All SD observations of antenna r 
f(m −1)×1 DD code observations of antennae 1 and 2 f(m −1)×1 DD phase observations of antennae 1 and 2 Y 2f(m −1)×(a −1) All DD observations of the array vec[yr, Y] 2f(m −1)a × 1 Observation set of the A-POAD model vec(Yr) 2f(m −1)a × 1 All SD observations in vec form 3 × 1 Unit-direction vector to satellite s G = Gr 2f(m −1)× 3 Geometry component of the design matrix A 2f(m −1)× f(m −1) Ambiguity component of the design matrix Qp m × m Covariance matrix of undifferenced code observations Qϕ m × m Covariance matrix of undifferenced phase observations (m −1)×(m −1) Covariance matrix of DD code observations (m −1)×(m −1) Covariance matrix of DD phase observations Qr a × a Covariance matrix of the array (array precision) Qf f × f Contribution of frequencies Qvec[yr, Y] 2f(m −1) a × 2f(m −1)a Covariance matrix of the A-POAD model QY 2f(m −1)(a −1)× 2f(m −1)(a −1) Covariance matrix of DD observations zr f(m −1)×1 All SD observations of antenna r Z f(m −1)×(a −1) All DD observations of the array B 3×(a −1) All baselines (considering one antenna as reference) ∇ (m −1)× 2m DD operator (i+1)× i Differencing matrix ei 1 × i Row vector with elements equal to 1 Ii i × i Identity matrix c1 (i +1)×1 Column vector in which the first element equals 1 and the remainder equal 0
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