Variable-speed UAVs Path Optimization Based on the CRLB Criterion for Target Passive Localization

The performance of target passive localization is significantly influenced by the positions of the Unmanned Aerial Vehicles (UAVs) swarms. In this paper, we investigate the problem of UAVs variable-speed path optimization to enhance the accuracy of passive target localization. Firstly, a passive target localization signal model based on the Time Difference of Arrival (TDOA) positioning algorithm which is then improved by the TDOA-Chan-Taylor Joint algorithm is established. This strategy can fully exploit the advantages of the Chan algorithm, such as non-iterative nature and low computational complexity, while effectively improving the adaptability and positioning accuracy of the algorithm in nonlinear, high-noise, and non-line-of sight scenarios by means of the Taylor series iterative method. The complementarity between the two significantly enhances the robustness, convergence performance, and engineering practicability of the traditional TDOA localization. Secondly, the Cramér-Rao Lower Bound (CRLB) of the TDOA-Chan-Taylor Joint algorithm is derived and adopted as the evaluation criterion to optimize the position parameters of the UAVs at each time step. Different from the existed works, in this paper, we consider the UAVs are with variable speed. When searching for the optimal positions at the next moment, we optimized not only the heading angles of the UAVs but also the movement speed, making the optimization model more aligned with practical applications and producing better solutions. However, the expanded search space for the optimal positions of the UAVs at the next moment leads to reduced algorithm efficiency. To address this issue, the Particle Swarm Optimization (PSO) algorithm is employed for rapid computation and optimization. By adopting heuristic intelligent search, the PSO algorithm reduces the computational complexity of solution compared with the full-space ergodic search method, which can efficiently approximate the near-optimal solution of the problem and exhibits favorable convergence performance under the scenario studied in this paper, thus significantly improving the computational efficiency compared with the exhaustive method. Finally, for a stationary target, numerical simulation experiments are conducted, from which we can know that compared with the constant-speed flight scheme, the variable-speed flight scheme can reduce RMSE and CRLB by at least approximately 35% and 33%, respectively, verifying the feasibility of variable-speed flight in improving positioning accuracy. Under both constant-speed and variable-speed conditions, the PSO algorithm reduces the average RMSE and CRLB by approximately 26% and 57%, respectively, compared with the exhaustive method, which validates the accuracy superiority of the PSO algorithm. In terms of computational efficiency, the PSO algorithm reduces the computation time by approximately 99% compared with the exhaustive method, which can moderately improve positioning efficiency under stationary target conditions, verifying the validity and effectiveness of the proposals in this paper. Moreover, when the target moves with uniform linear velocity under the same simulation scenario, the PSO algorithm still notably outperforms the exhaustive method in both positioning accuracy and per-step computation time, confirming the feasibility of the proposed method in dynamic environments. To intuitively reflect the optimization performance of the method proposed in this paper, comparative experiments are conducted against the GA and the GWO, and the determinant of the CRLB is compared with the trace of the CRLB adopted in this work as the cost function. The results show that the proposed method surpasses both GA and GWO in positioning accuracy and convergence performance, Moreover, within the exhaustive search and PSO algorithm, the positioning performance achieved by optimizing the trace of the CRLB is also better than that obtained with the determinant of the CRLB, which corroborates the relative performance gains of the proposed method and the selected cost function.