Time-of-Arrival and Angle-of-Arrival Measurement-Assisted 3D Inter-Unmanned Aerial Vehicle Relative Localization Under Distance-Dependent Noise Model

This paper addresses the 3D relative localization problem for two unmanned aerial vehicles (UAVs) using a combination of time-of-arrival (TOA) and angle-of-arrival (AOA) measurements across varied flight trajectories. We commenced by examining the problem of relative attitude estimation using only time-of-arrival (TOA) measurements, taking into account a distance-dependent noise model. To address this issue, we constructed a constrained weighted least squares (CWLS) problem and applied semidefinite relaxation (SDR) techniques for its resolution. Furthermore, we extended our analysis to incorporate AOA measurements and scrutinize the Cramer–Rao Lower Bound (CRLB) to illustrate enhanced localization accuracy through TOA-AOA integration compared to TOA alone under stable trajectory conditions. Ultimately, numerical simulations substantiate the efficacy of the proposed methodologies.