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

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.

💡 Research Summary

The paper addresses the problem of accurately localizing maritime targets and a cooperating surface vessel (USV) in environments where GPS signals are unavailable or denied. Traditional approaches rely on UAVs equipped with gimballed electro‑optical (EO) cameras, which provide flexible bearing measurements but introduce mechanical complexity, higher cost, and a single‑point failure risk. The authors propose an estimation‑aware trajectory optimization framework that enables a team of low‑cost fixed‑wing UAVs carrying only fixed‑field‑of‑view (FFOV) cameras to perform cooperative bearing‑only localization together with a USV.

Key contributions include: (1) Formulating the trajectory design as a nonlinear programming (NLP) problem that simultaneously minimizes the trace of the posterior Cramér‑Rao lower bound (PCRLB) – a scalar measure of the expected estimation error – and satisfies a comprehensive set of realistic constraints; (2) Incorporating operational constraints such as sensor FOV limits, bank‑to‑turn (BTT) dynamics of fixed‑wing aircraft, no‑fly zones (NFZ) around hostile targets, bounded UAV‑USV communication ranges, and a constant low‑altitude flight envelope to reduce detection risk; (3) Demonstrating that Bernstein‑polynomial‑based discretization provides uniform time sampling and avoids the “Runge” phenomenon, making it better suited than traditional pseudospectral collocation for handling the visibility constraints; (4) Extending previous single‑UAV work to multi‑UAV cooperation in three dimensions, showing that a modest team (three to five UAVs) equipped with FFOV cameras can match or surpass the localization performance of a single UAV with a gimballed camera while offering far lower SWaP‑C (size, weight, power, cost) and higher mission resilience.

The dynamics model assumes constant airspeed and altitude, reducing the problem to planar motion with heading ψ and roll angle ϕ as the control input. The roll angle governs the heading rate through the BTT relationship ψ̇ = g·tan(ϕ)/V, where g is gravity and V is airspeed. Roll limits (ϕ_min, ϕ_max) and rate limits are enforced to respect structural and actuator capabilities. For gimballed sensors, additional control variables (camera azimuth ψ_g and elevation θ_g) and their rate limits are introduced, but the primary focus is on the FFOV case where the camera points along the aircraft body axis.

The objective function integrates the PCRLB trace over the planning horizon, encouraging trajectories that produce geometrically favorable bearing measurements. The PCRLB captures prior uncertainty, process noise, and the information gain from each new bearing, providing a Bayesian lower bound on estimator covariance. Minimizing its trace is analogous to reducing position dilution of precision (PDOP) in GNSS, and is more numerically stable than maximizing the determinant of the Fisher information matrix.

Numerical results are presented for two case studies. In the first, a single FFOV UAV’s optimized trajectory reduces the average localization error by more than a factor of two compared with heuristic circular or straight‑line paths, confirming the value of the information‑driven design. In the second, a coordinated team of three to five FFOV UAVs is shown to achieve localization accuracy comparable to, or better than, a single UAV equipped with a gimballed camera. The multi‑UAV solution also offers redundancy: loss of one platform does not catastrophically degrade performance, enhancing survivability in contested airspace.

The authors conclude that incorporating realistic mission constraints into bearing‑only localization planning yields dynamically feasible, operationally compliant paths that dramatically improve estimator performance while enabling low‑cost, low‑signature UAV swarms to operate effectively in GPS‑denied maritime scenarios. Future work is suggested on real‑time re‑planning, extension to multiple moving targets, and hardware‑in‑the‑loop flight tests.