基于CRLB准则的变速无人机群目标无源定位路径优化

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

    • 摘要: 在利用无人机群进行目标无源定位的应用中,其性能表现极大地取决于无人机集群(Unmanned Aerial Vehicles, UAVs)的空间位置配置,因此,为提升目标无源定位精度,本文提出一种无人机变速路径优化方法。首先,建立基于到达时间差(Time Difference of Arrival, TDOA)定位算法的目标无源定位信号模型,并采用TDOA-Chan-Taylor联合改进算法对其进行优化。此策略可充分发挥Chan算法非迭代、计算量小的优势,同时借助泰勒级数迭代法有效提升算法在非线性、大噪声及非视距场景下的适应性与定位精度,二者互补能够显著改善传统TDOA定位的鲁棒性、收敛性能与工程实用性。其次,推导得到TDOA-Chan-Taylor联合改进算法的克拉美罗下界(Cramér-Rao Lower Bound, CRLB),并将其作为代价函数优化无人机在各时间步长的位置参数。不同于现有研究,本文考虑无人机的变速飞行特性,无人机群搜索下一时刻最优位置时,不仅考虑优化其航偏角同时优化其运动速度大小,使问题优化模型与实际应用情况更相近且获得更优解。然而,由于无人机群下一时刻最优位置的搜索空间增大导致算法效率降低,为解决此问题,本文采用粒子群优化算法(Particle Swarm Optimization, PSO)快速计算寻优。PSO算法采用启发式智能搜索,相较于遍历全域的搜索方式,能够降低求解的计算复杂度,可高效逼近问题的近似最优解,在本文场景下具备良好的收敛性能,相比穷举法显著提升了计算效率。最后,进行数值仿真实验。在目标静止情况下,得到相较于定速飞行,变速方案可使RMSE与CRLB分别降低约35%和约33%,验证了变速飞行提升定位精度的可行性;定速与变速条件下,PSO算法相比穷举法可使RMSE平均降低约26%、CRLB平均降低约57%,证明了PSO算法的精度优势;在计算效率上,PSO算法相比穷举法耗时降低约99%,在目标静止情况下可适度提升定位效率,验证了本文所提方法的可行性与有效性。当目标以匀速直线运动时,在相同仿真场景下,PSO算法的定位精度和每步长耗时相较于穷举法具备一定优势,验证了本文所提方法在动态模型下的可行性。此外,为直观体现本文所提方法的优化效果,分别设置了遗传算法(Genetic Algorithm, GA)、灰狼优化算法(Grey Wolf Optimizer, GWO)与本文算法的对比实验,以及CRLB行列式与本文所用的CRLB迹两种代价函数的对比分析。结果表明,本文方法在定位精度和收敛性能上均优于GWO与 GA算法,且以CRLB迹为优化目标所获得的定位性能在穷举法与PSO算法中均优于CRLB行列式,作证了所提方法及所选代价函数在优化性能方面的优势。

       

      Abstract: 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.

       

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