Formation Control for CRLB-Optimal Cooperative Sensing in Low-Altitude Wireless Networks

Cooperative sensing with uncrewed aerial vehicles (UAVs) is a key enabler for low-altitude wireless networks (LAWNs), where sensing accuracy critically depends on the spatial configuration of the UAV formation. In this paper, we study formation design and control for Cramer-Rao lower bound (CRLB)-optimal cooperative target sensing. We first establish a sensing performance model based on range measurements and derive the Fisher information matrix (FIM) of the target location. By adopting the A-optimality criterion, we analytically characterize the formation geometry that minimizes the CRLB of the estimation error. The optimal formation is shown to exhibit isotropic Fisher information in the horizontal plane, leading to a regular polygon geometry with an elevation angle determined by the tradeoff between path loss and geometric diversity. Building on this result, we further develop a distributed formation control strategy that steers UAVs from arbitrary initial deployments toward the sensing-optimal configuration while maintaining formation motion and obstacle avoidance. Numerical results demonstrate that the proposed scheme consistently outperforms benchmark formations in terms of CRLB and achieves reliable convergence under practical constraints.

💡 Research Summary

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This paper addresses the problem of designing and controlling a formation of unmanned aerial vehicles (UAVs) that cooperatively sense a ground target in a low‑altitude wireless network (LAWN). The authors start by modeling the sensing process as a set of noisy range measurements obtained from round‑trip signal delays. Each UAV measures a distance (d_m) to the target, corrupted by additive white Gaussian noise whose variance (\sigma_m^2) is inversely proportional to the received signal‑to‑noise ratio (SNR). Because the SNR decays with the fourth power of distance in a two‑way radar channel, the measurement noise grows rapidly with range.

From this model the Fisher information matrix (FIM) of the range measurements, (J_d), is derived; it is diagonal because measurement noises are independent. Using the Jacobian (Q = \partial d / \partial s) that relates range to the target coordinates (s =