## 2 Methods and Materials
### Alfacrux Digital Twin Architecture  
One of the main innovative contributions of the AlfaCrux mission is concerned with the development of a digital twin model, see Figure 7. The DT can be defined as a high-fidelity and up-to-date digital representation of an physical counterpart. This representation is achieved by combining different models (physics-based and data-driven models), simulations, sensor updates and historical data [21]. Although this topic has been studied in the aerospace field [22], the use and applications of digital twin in the context of small satellites are still incipient, with very few examples and systems implemented so far [23; 24]. In this first approach, the goal is to set the start point and the guidelines to establish the concept and a methodology to build a reliable framework for the operation and main services of nanosatellites, in a first moment CubeSat standard, fulfilling the necessary space standards (such as health checks, dynamic characteristics, and safety mechanisms, among others) and conforming to the necessary payload requirements. By innovative framework, we mean a new architecture in which the development of a digital model of the nanosatellite is considered. In this innovative approach, the digital model is constantly under improvements based on the data collection system (laboratory tests, computer simulations, and in-orbit data), and more than that, the digital model can improve and update the physical entity, i.e., the satellite in orbit). In other words, we are proposing a digital twin framework for nanosatellite mission applications. The digital twin can be modeled in a five-dimensional architecture composed of the physical entity (PE), the virtual entity (VE), the DT data (DD), the system services provided (SS) and the connections between the parts (CN) [25]. Figure 7 provides a conceptual model of the DT specifically for the AlfaCrux. The sensors in the PE gather data that will be used as input for the analysis, models, and simulations of the VE. In this way, the VE can mirror the physical geometry, physical properties, behaviors, and rules of the PE. The SS consists  
Figure 7: Five-dimensional architecture for the CubeSat digital twin framework. of the services for the physical and virtual entities, and for the project stakeholders. These services include the scheduling of the payload services, the change in operational mode, the telemetry viewer, and firmware updates. The DD is composed of data collected from the PE, VE, and SS through the connections. The connections are also used to link the PE, VE, and SS among themselves [25]. In the center of the five-dimensional architecture is the digital twin data, due to their critical role in the DT as the knowledge representation [26]. The process of creating the knowledge involves, among other things, the data collection and pre-processing of different sources. These sources can be divided into three main categories: synthetic data (computer simulation), experimental data (laboratory tests and validation), and in-operation data (satellite telemetry) [22]. Specifically, the synthetic data are generated by simulations in the virtual world, the experimental data are gathered through experiments conducted in the physical entity, and the last category, the in-operation data, are collected during regular operation of the physical entity, in our case the AlfaCrux CubeSat. The first part of the DT that has been developed is dedicated to kinematic reconstruction, as seen in Figure 8. The models were initially validated with simulated and real telemetry data. This pilot DT is explained below, considering the five dimensions shown in Figure 7.  
1. Physical entity: acquires measurements of the magnetometer, solar panels, and gyroscope, and the two-line elements (TLE);
2. Virtual entity: uses the Sun, Geomagnetic, and Albedo models; the orbit propagation; and the telemetry data to reconstruct the satellite attitude;
3. Connection: responsible for the data collection and management system;
4.