# Sensitivity of Line-of-Sight Estimation to Measurement Errors in L-Shaped Antenna Arrays for 3D Localization for In-Orbit Servicing

## TL;DR

This paper analyzes how measurement errors affect 3D satellite localization using L-shaped antenna arrays.

## Contribution

The study introduces a sensitivity analysis of line-of-sight estimation in L-shaped antenna arrays for 3D satellite localization.

## Key findings

- Variation in antenna placement affects 3D positioning precision.
- Misplaced antennas increase line-of-sight errors at small distances with range errors.
- Phase measurement errors amplify line-of-sight errors at large distances.

## Abstract

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