The study focuses on the determination of the conditions of the divergence of the variance of the measurement for antenna array able to perform measurements of direction of electromagnetic waves.

The payload of the study is a cross array of antennas, able to perform measurements of direction through array beamforming and Angle of Arrival (AOA) technology.

In particular, starting from the modeling of satellite kinematics in terms of position and attitude combined with its relative position with respect to an emitter of electromagnetic waves located on the surface of the Earth, the study gives the mathematical fundamentals to determine potential cases that lead to the divergence in the variance of the estimation of the position of the emitter of signal.

The numerical predictions, conducted through the evaluation of the metrics of Cramér-Rao Lower Bound (CRLB), are on the angles of Azimuth, Elevation, and broadside through the generation of errors in the attitude with Monte Carlo simulations.

Recent advanements on the miniaturization of the electronics make these studies of particular interest for a new set of technological demonstrators equipped with payloads composed of antenna array. Applications of interest are on Earth-scanning missions with exemplary cases of search and rescue or spectrum monitoring of jamming in E1/L1 band for GNSS.