Sensitivity to Measurement Errors of an L-Shaped Phase Array for 3D Localization in Inter-Satellite Links

The sensitivity analysis of the L-shaped phase array contributes to the deeper understanding of how the measurement errors affects a 3D localization system. First, the proposed 3D localization model in Cartesian coordinate system is given, where for simplicity the origin of the coordinate system is the origin of the L-shaped phase array. The proposed localization method relies on three measurements: range measurement, and line-of sight angles with the x, respectively y axis. The sensitivity analysis revealed that the variation of the L-shaped phase array geometry (variation of the antennas placements) has an impact on the 3D positioning accuracy: a misplaced antenna - placed closer then intended - will have larger line-of-sight error for small distances/ranges in the presence of range measurement errors. Notably, a misplaced antenna will result larger line-of-sight error for large distances/ranges when phase measurement errors occur.