## 1 Introduction
The provided attitude solution is then fused with the solutions provided by other complementary systems on board the satellite, astro-observers (sun sensors, horizon sensors, star sensors, Earth sensors), and magnetometers, each of these having their own advantages and limitations [20]. The literature reveals a lot of applications for the development of attitude determination and control system (ADCS) equipping pico-satellites [21], nano-satellites [22; 23; 24; 25], and micro-satellites [26; 27; 28] by using inertial techniques. Another perspective for a complementary system for attitude evaluation was opened by the architecture of GOMX-4A and GOMX-4B nano-satellites launched in the GOMX-4 mission of GomSpace from Denmark [29]. Starting from this architecture, a new attitude estimation solution was proposed, integrating the Automatic Dependent Surveillance-Broadcast (ADS-B) receiver and MEMS gyro by using a multiplicative extended Kalman filter (MEKF) [30]. Related to the attitude detection and control system (ADCS) for small satellites, it supposes the presence of a detection system able to measure/estimate vehicle angular orientation, an actuation system able to generate torques to change the angular position of the vehicle, and a control system that includes some algorithms, which control the actuation system based on the current attitude data provided by the detection system and on the desired attitude data. The attitude sensors included by the detection system can be of two types: (1) relative attitude sensors, which need an initialization of the attitude information to be able to estimate the current attitude (gyroscopes and IMUs); (2) absolute attitude sensors, which use various objects or phenomena outside the satellite to determine the attitude (sun sensors, horizon sensors, star sensors, magnetometers, GPS, etc) [20, 31, 32, 33, 34, 35]. The literature shows that there are some issues that need to be overcome at the level of the sensors in the small satellite attitude determination systems: (1) the impossibility of having the full attitude solution from all sensors; (2) the exchange of light and the eclipse, which produces intermittences in providing the attitude data by star and sun sensors; (3) the limited accuracy of some sensors (i.e., the magnetometers, based on the measurement of the Earth magnetic field, which has an accuracy no better than 1 deg); (4) the very low available space which limits the redundancy; and also (5) the accuracy in the use of performing architectures, which need special geometries (i.e., in certain situations, the use of a multi-antenna GPS receiver able to produce an accurate attitude solution) [20, 26]. The horizon sensors are used to measure roll and pitch angles, as they are not able to provide the yaw angle, while the sun and star sensors offer directions. Because the star sensors and sun sensors are not able to offer continuous attitude data, many architectures have added an IMU to provide attitude data between the valid measurements of the other sensors. From a different perspective, the inertial sensors in IMU are affected by various errors and they need to be corrected starting from the valid data delivered in the system by the complementary attitude sensors [35]. All these shortcomings led to the conception of attitude determination methods, which combine the data from the sensors included in the detection unit.