Table 1.

Studies related to attitude determination (simulation and in-orbit observations).

Reference	Method (Instruments)	Goal	Results/Remarks
[4]	Simulation	Attitude determination (AD) based solely on magnetometer	Converges from initial attitude errors of maximum 60${}^{°}$ and with an attitude accuracy of 1${}^{°}$ (1$\sigma$) or better
[5]	Observation (Rossi X-ray Timing Explorer satellite calibration maneuvers, Terra and Wide-Field Infrared Explorer mission, Upper Atmosphere Research Satellite (UARS))	On-orbit calibration of satellite gyroscopes	Methods comparison (attitude accuracy below 1${}^{°}$). The Delta-bias algorithm gives slightly less accurate results than the Davenport and BICal algorithms
[6]	Simulation	Absolute alignment calibration of a system comprising two star trackers, an inertial sensor assembly (ISA) of three fiber-optic gyros, and an imaging instrument based on Alignment Kalman Filter (AKF)	AKF is effective to estimate absolute misalignments and gyro calibration parameters
[7]	Simulation	AD using an Extended Kalman Filter (EKF), which applies the albedo model with a magnetometer and sun sensor	Attitude accuracy below 1${}^{°}$
[8]	Simulation and Observation (Total Ozone Mapping Spectrometer (TOMS))	Modeling the albedo for Sun/Earth sensor used in attitude determination	Albedo compensation in attitude estimation, improves the maximum error from 9.9${}^{°}$ to 1.9${}^{°}$
[9]	Simulation	AD using Unscented Kalman Filter (UKF) based only on magnetometer	The attitude estimation accuracies are below 0.5${}^{°}$ after convergence
[10]	Simulation (PROBA-2 Spacecraft scenarios)	Navigation system for magnetic-only orbit and attitude estimation using the square-root Unscented filter (MAGSURF)	RSS attitude error of less than 1.4${}^{°}$ and a time of convergence of less than 2 orbits
[11]	Simulation	Attitude and rate estimation algorithm using EKF based only on geomagnetic field data	Filter converges within the +/−8${}^{°}$ range for any initial attitude error
[12]	Simulation (Radio Aurora Explorer satellites (3U CubeSat))	AD based on gyros, magnetometers, coarse sun sensors, and an EKF	In the sun, the angular uncertainty is between 2${}^{°}$ and 3${}^{°}$, and in eclipse, the uncertainty increases to between 7${}^{°}$ and 8${}^{°}$
[13]	Simulation	AD using two-step EKF based on a magnetometer only	Attitude accuracies of less than 1${}^{°}$
[3]	Observation (Radio Aurora Explorer satellites (3U CubeSat))	Photodiodes calibration and AD from EKF/UKF with albedo model based on the calibrated photodiodes, three-axis magnetometer and gyrometer	Angular improvement of 10${}^{°}$ in sun vector from the photodiodes, and below 1${}^{°}$ accuracy on the attitude determination
[14]	Simulation	AD via a robust Adaptive Kalman Filter based on magnetometer and gyro measurement	Precision of traditional EKF is about 0.2${}^{°}$, and the maximum estimate error of the robust adaptive filter is 0.1${}^{°}$
[15]	Simulation and Observation (experimental data with on-ground nano-satellite)	Gain-scheduled EKF (GSEKF) to reduce the computational requirement in the nanosatellite attitude determination process	Attitude accuracy below 0.2${}^{°}$ during the entire orbital period. Computation time could be reduced by 86.29% and 89.45%
[16]	Simulation	Magnetometer calibration with Hyper least square (HyperLS) estimator for ellipsoid fitting, then utilized for attitude determination via non-linear colored noise filters of EKF, simplex UKF and cubature Kalman filter	Attitude accuracy below 1${}^{°}$ for simplex UKF
[17]	Observation (images taken from International Space Station (ISS))	AD utilizing color earth images taken with visible light camera	Attitude accuracy is about few degrees or less
[18]	Simulation	Heat attitude model for satellite attitude determination	Attitude accuracy between 0.2 ${}^{°}$ to 5${}^{°}$
[19]	Simulation	AD method based on an UKF, using a gyrometer, a magnetometer and solar panels as a sun sensor	The UKF has shown precision in Euler angles of about 1.1${}^{°}$, which is better than for EKF. UKF has a considerably longer processing time compared to EKF
[20]	Simulation and Observation (experimentation on-ground set up)	Thermal imaging sensors to determine attitude of the Sun and the horizon by employing a homogeneous array of such detectors	Angular accuracy below 1${}^{°}$