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.

This letter addresses joint localization of 3D mobile networks with asynchronous clocks, where both relative distance and relative velocity measurements are used. Clock offsets and drifts are explicitly modeled, and an anchor-based compensation term is introduced to fully exploit anchor information and resolve translation ambiguity. A block majorization–minimization algorithm, termed vBMM, is proposed to jointly estimate node positions and clock parameters. Simulation results show that vBMM achieves position accuracy close to the Cramér–Rao lower bound and remains stable under different clock conditions. Compared with the state-of-the-art algorithm, vBMM achieves higher localization accuracy when clock asynchrony is significant and maintains robustness across clock conditions and measurement noise levels.

Directed inter-UAV Time-Differenced Carrier Phase (TDCP) couples an inter-node distance increment with a relative clock-bias increment, while phase differencing produces temporally correlated noise and near-planar formations retain a weak relative-height mode. We formulate a fixed-lag factor graph that combines reciprocal TDCP, Time-of-Arrival (TOA), Global Positioning System (GPS), clock dynamics, and calibrated navigation-frontend motion and altitude outputs. An invertible sum-and-difference transformation exposes geometry and clock-bias-increment-rate channels while full covariance propagation preserves the reciprocal-pair likelihood. Local information analysis shows that the reverse observation removes the single-direction geometry–clock-increment rank deficiency, and phase-level modeling yields the first-order moving-average covariance retained by block whitening. A causal motion-consistency test (MCT) compares the whitened geometry channel with an independent motion prediction before the current pair enters optimization; a flagged pair is assigned negligible information and its detector–estimator phase arc is reset. Implementation checks verify the exact four-bias-state residual, covariance-normalized reciprocal innovations, and operation under sparse single-direction ambiguity changes. Across ten paired runs at $p_s=5\%$, MCT detected all 770 injected events with a pair-level false-alarm rate of 0.169% and reduced the mean position RMSE by 96.6% relative to DCS.

This paper investigates joint deployment of unmanned aerial vehicle (UAV)-borne linear-array angle-of-arrival (AOA) sensors for localizing a target UAV in three-dimensional space. Since each sensing UAV carries a lightweight one-dimensional (1-D) AOA array, each measurement provides only one angular constraint, and its information contribution depends jointly on the UAV waypoint and array pointing direction. This leads to a coupled coordinate–orientation design problem that differs from conventional full-AOA deployment. We formulate a Cramér–Rao lower bound (CRLB)-based framework under A- and D-optimality criteria, covering both free-flight and constrained hovering regions. By exploiting the structure of the 1-D AOA Fisher information matrix, we show that, for fixed UAV coordinates, the orientation block can be exactly eliminated through a low-dimensional eigenproblem. The resulting reduced coordinate problem is then solved by a geometry-structured sequential quadratic programming (SQP) method, whose curvature model captures the radial and tangential sensitivities induced by line-of-sight geometry. Numerical simulations further validate the effectiveness of the proposed approach.