Multi-UAV Trajectory Optimization for Bearing-Only Localization in GPS Denied Environments

TL;DR

This work tackles bearing-only localization of maritime targets in GPS-denied environments by introducing an estimation-aware trajectory optimization framework. It uses Bernstein polynomial parameterization to generate dynamically feasible paths that respect NFZ, communication, and area constraints while maximizing localization accuracy via minimizing the trace of the PCRLB, with PCRLB computed from bearing measurements and sensor geometry. A federated fusion scheme with local EKFs and a final FKF aggregates estimates, enabling low-bandwidth collaboration across UAVs. Results show that optimized trajectories substantially improve estimation performance over heuristic paths, and coordinated teams of FFOV UAVs can match or exceed a single gimballed system’s localization accuracy with reduced time and SWaP-C, highlighting scalability, resilience, and practical applicability in contested settings.

Abstract

Accurate localization of maritime targets by unmanned aerial vehicles (UAVs) remains challenging in GPS-denied environments. UAVs equipped with gimballed electro-optical sensors are typically used to localize targets, however, reliance on these sensors increases mechanical complexity, cost, and susceptibility to single-point failures, limiting scalability and robustness in multi-UAV operations. This work presents a new trajectory optimization framework that enables cooperative target localization using UAVs with fixed, non-gimballed cameras operating in coordination with a surface vessel. This estimation-aware optimization generates dynamically feasible trajectories that explicitly account for mission constraints, platform dynamics, and out-of-frame events. Estimation-aware trajectories outperform heuristic paths by reducing localization error by more than a factor of two, motivating their use in cooperative operations. Results further demonstrate that coordinated UAVs with fixed, non-gimballed cameras achieve localization accuracy that meets or exceeds that of single gimballed systems, while substantially lowering system complexity and cost, enabling scalability, and enhancing mission resilience.

Figures (6)

• Figure 1: Reference frame depiction for a strap-down gimballed camera system relative to the UAV.
• Figure 2: Smooth approximation of FOV constraints using overlapping sigmoid functions.
• Figure 3: Heuristic UAV racetrack trajectory vs optimized Bernstein trajectory.
• Figure 4: Histograms for the combined RMSE for the target and collaborating USV positions. The optimized trajectory consistently reduces RMSE and eliminates large outliers while reducing mission time. The racetrack trajectory exhibits high variance and occasional severe localization failures.
• Figure 5: Optimized UAV equipped with a gimballed camera trajectory. The UAV localizes a stationary target and a collaborating USV in minimum time while adhering to mission flight constraints. FOV segmentation along the UAV trajectory - Red: target USV in FOV. Blue: collaborating USV in FOV. Purple: both USVs visible. Gray: both USVs out of view.