## 1 Introduction  
The scenario of this study considers two actors: an emitter of electromagnetic waves located on the Earth's surface and a set of satellite platforms with receivers acting as sensors to geolocate the emitter. Geolocation is the process of determining the physical location of an entity in geographical coordinates. This process is crucial for many applications, ranging from navigation and communication to surveillance and environmental monitoring [1]. In general, among the cases of interest in which it is important to perform an operation of geolocation, there is the one where the signal is non-cooperative; a signal is said to be non-cooperative when its position (and the signal itself) are not supposed to be known. It can be intentional--for example, it can be the case of illegal activities such as the jamming of signals used by civil aviation--or it can be non-intentional, such as the case of emergency calls from remote locations. In the first case, the interception and geolocation of the signal is used in patrolling activities of spectrum monitoring, while, in the latter case, it is used to coordinate operations of search and rescue to help people in need [2]. This study considers satellite systems with passive payloads, comprising only receivers able to capture electromagnetic waves without the use of onboard transmitters or radars [3; 4]. In general, this kind of geolocation can be accomplished through various methods, one of which is based on the estimation of the Angle of Arrival (AOA) [1; 2; 3; 5], i.e., the angle at which a signal arrives at a receiver. One of the most common techniques for AOA estimation is array beamforming [4]. Other classical sensing techniques are Time Difference of Arrival (TDOA), Frequency Difference of Arrival (FDOA), and Received Signal Strength (RSS) [1; 2; 3; 5]. For antenna array technology, recent trends and interests are on innovative analysis and synthesis considering the minimization of the number of elements [6], beam pattern design and rotating elements [7], error calibration for space applications [8], quantum antenna array [9], and machine learning applied to AOA estimation and processing [10]. By combining AOA measurements from multiple spatially distributed receivers, it is possible to triangulate the precise location of the signal emitter. This method is based on the principle that signals arrive at different angles to different receivers depending on the emitter's location. In general, in order to perform the geolocation of the signal, at least two separate measurement directions are needed. In satellite-based geolocation systems, the measurement is primarily affected by two sources of error. The first source is associated with the individual signal receivers and includes contributions from time delays [11], relativistic effects [12], the presence of the atmosphere [13], satellite attitude, antenna technology [4], and the signal-to-noise ratio (SNR) [5; 14]. Among these, SNR and the electronic performance of the receiver are the most significant contributors and are often modeled using the Cramer-Rao Lower Bound (CRLB) [15]. The second source of error has a geometric origin and it is known as Dilution of Precision (DOP), which arises from the spatial distribution of receivers in space. The minimization of the DOP enhances the overall precision of the geolocation system and improves the services that rely on satellite-based geolocation. The optimization of the spatial distribution of satellites in constellations started in the context of Global Navigation Satellite Systems (GNSSs) [16], although for these kinds of systems, the measurement is based on Time of Arrival. In addition to GNSS studies, some works have focused on terrestrial wireless systems exploring fixed geometries in a plane (e.g., triangular, squared, and hexagonal distributions [17]) as well as optimal geometrical distributions of receivers in two dimensions [18; 19].