## 1 Introduction  
Available on the market for over three decades, modern navigation systems include inertial navigation systems (INSs) and satellite-based navigation systems such as global positioning systems (GPSs) as key positioning technologies in most of the developed applications. INS is a completely autonomous device for positioning and attitude estimation, which since the 1940s has established itself as an important component in navigation systems for military and civil applications, but it had a significant contribution that is also growing strongly in positioning and space navigation applications, especially due to this advantage offered by its autonomy. Actually, INSs are now found as standard components in the navigation systems that equip satellites, launch vehicles, space rovers, space robots, aircrafts, ships, and submarines, having the great quality to provide attitude, speed and position of the monitored vehicle with an adaptable higher rate and a very good short term performance [1; 2; 3]. A very interesting application of the INSs is the relative navigation of spacecraft vehicles, especially of small satellites, where these systems play a very important role in two configurations considered traditional for this kind of navigation: GNSS/INS and INS/vision-based synergic systems [4; 5; 6; 7; 8; 9; 10]. On the other hand, the literature, as well as the websites of the specialized companies producing equipment for navigation, reveals a lot of applications involving the use of INS in space applications [11; 12; 13; 14; 15; 16; 17; 18]. For example, iXblue in partnership with Airbus Defence & Space designed and manufactured for over two decades the Astrix gyroscopes used in a lot of space applications, from low Earth orbit (LEO) to geostationary Earth orbit (GEO) and even Lagrange points [11]. Safran produces SPACENAUTE, an ultra-compact inertial measurement unit for space launchers, selected and qualified for the Ariane 6 European launcher [12]. Advanced Navigation in partnership with the Space Machines Company equipped Optimus (an orbital service vehicle (OSV) that will provide on-demand orbital services, such as repairing, refueling and upgrading space infrastructure) with a space-grade inertial navigation system (INS) called Boreas X90; Optimus is expected to be launched from Vandenberg Space Force Base aboard a SpaceX Falcon 9 rocket [13]. Also, the Australian Space Agency announced that, on the Moon to Mars initiative, Advanced Navigation in collaboration with Q+CTRL developed quantum-enhanced inertial navigation solutions for space launch vehicles, satellites, and landers. This new inertial navigation technology will be an important element in the Artemis Lunar Exploration Program of NASA [14; 15; 16]. Fully benefiting from the advantage of its total autonomy, but also from the complementary with the GPS system or with other navigation systems, INS was maintained as an indispensable component of the navigation systems and was strongly developed in trend with the new technologies in the fields of the inertial sensors and of the computing equipment with boarding capabilities on various aerospace systems. Therefore, the INS structure has changed over time, passing from the gimbaled INS to strap-down INS (SDINS), and currently aims more and more at low-cost and small-size structures, sometimes packaged with GPS receivers for everyday use such as phone/vehicle location, asset tracking and even new applications such as simultaneous location and mapping [19]. An important current application of these low-cost and small-size structures SDINS is the attitude evaluation of spacecraft, with a special impact on the small satellites' attitude control. In this kind of application, an important role is played by the first calculation floor of a classic SDINS component, the floor that allows attitude determination, which uses IMUs based especially on the gyroscopic component.