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

Jun Wu, Haijia Jin, Nanchi Su, Jinna Li, Haoyuan Pan, Tse-Tin Chan

TL;DR

A distributed formation control strategy is developed that steers UAVs from arbitrary initial deployments toward the sensing-optimal configuration while maintaining formation motion and obstacle avoidance and achieves reliable convergence under practical constraints.

Abstract

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.

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

TL;DR

A distributed formation control strategy is developed that steers UAVs from arbitrary initial deployments toward the sensing-optimal configuration while maintaining formation motion and obstacle avoidance and achieves reliable convergence under practical constraints.

Abstract

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.
Paper Structure (6 sections, 1 theorem, 19 equations, 4 figures)

This paper contains 6 sections, 1 theorem, 19 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. CRLB-Optimal Formation Geometry
  4. Distributed Formation Control
  5. Numerical Results
  6. Conclusion

Key Result

Proposition 1

For any fixed $w_m$, the trace of the inverse FIM, $\text{tr}(\mathbf{J}_{\mathbf{s}}^{-1})$, reaches its global minimum if and only if $\mathbf{J}_{\mathbf{s}}$ is a scalar matrix.

Figures (4)

  • Figure 1: The considered LAWN system where a formation is dispatched to sense the target cooperatively.
  • Figure 2: The CRLB vs. flight altitudes under various formation configurations.
  • Figure 3: The formation evolution behavior and UAV trajectory in the presence of obstacles.
  • Figure 4: The evaluation of CRLB and cost function \ref{['costfun']}.

Theorems & Definitions (1)

  • Proposition 1