# An Effective Sensor Architecture for Full-Attitude Determination in the HERMES Nano-Satellites
## 1 Introduction  
Multi-messenger astrophysics is a novel scientific field that uses information carried by various and diverse cosmic messengers, electromagnetic waves, neutrinos, and gravitational waves, to observe and understand astrophysical phenomena. In order to effectively collect the multiple sources, distributed space systems are becoming extremely popular and useful, either as primary detectors or as localization sentinels to subsequently alert other instruments and observatories. In all these cases, the benefits guaranteed by miniaturized spacecraft are evident. In fact, these small platforms allow an easier and cost-effective access to space, with a reduced time scale from design to operations and with a pragmatic possibility to implement distributed space missions. Nano-satellites have lowered by several orders of magnitude the difficulties and the costs to realize orbital constellations or multi-element space observatories. In this way, they have facilitated and have made more accessible astrophysical studies from space that require an observation baseline, such as interferometry or localization by triangulation. The positive influence of miniaturized space platforms on the multi-messenger astrophysics field has been deeply exploited by the High Energy Rapid Modular Ensemble of Satellites (HERMES) mission [1]. HERMES is based on a constellation of nano-satellites in low-Earth orbit (LEO). The constellation is composed of 3U CubeSats, and it is built upon a twin project: the HERMES Technological Pathfinder (HERMES-TP), funded by the Italian Ministry for University and Research (MUR) and the Italian Space Agency (ASI); and the HERMES Scientific Pathfinder (HERMES-SP), funded by the European Union's Horizon 2020 Research and Innovation Programme. Both the HERMES-TP and HERMES-SP projects provide three complete satellites to the constellation, for a total of six 3U CubeSats composing the space segment. The mission aims at the fast detection and localization of energetic astrophysical transients, such as gamma-ray bursts (GRBs), which are the electromagnetic counterparts of gravitational wave events, thanks to novel miniaturized detectors sensitive to X-rays and gamma-rays [2]. The astrophysical events' localization has to be accomplished with an accuracy level ranging from a few degrees to arcminutes, as a function of the number of spacecraft composing the full HERMES constellation. This is achieved in a field of view of several steradians exploiting the triangulation technique [3]. In doing so, at least three spacecraft, separated by a minimum baseline of 1000 km, shall observe the same region of the sky by co-aligning the detectors' lines of sight [4]. This is achieved by maneuvering the individual elements of the constellation to orient their fields of view in the desired directions with an autonomous attitude determination and control subsystem (ADCS) [5; 6]. Then, any HERMES spacecraft shall estimate its full orbital and attitude states on-board. The first is needed to understand if the minimum baseline requirement is respected and to feed the environment models used in the attitude determination functions [7]. The latter is globally needed to have the ADCS properly working, achieving the expected mission goals. Specifically, the scientific requirements impose:  
* A maximum attitude knowledge error of 1 deg at 1\(\sigma_{a}\);
* A maximum orbital position knowledge error of 10 m at 1\(\sigma_{o}\). Therefore, despite the specific mission scenario analyzed, this research work can be applied and generalized to any spacecraft mission with similar attitude determination requirements, which are becoming common in complex and advanced nano-satellites. However, this class of required performances is quite demanding for a nano-satellite because of its stringent mass, volume, power, and computation constraints. Moreover, the cost budget imposes a further difficulty to achieve the desired mission objectives.