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A Horizon Tracking Algorithm for Chang’E-4 Lunar Surface Penetrating Radar Based on Dynamic Search Center
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摘要: 月球浅表层结构是理解月球地质演化、物质组成及空间风化过程的重要窗口。随着嫦娥工程等国内外探月任务获得大量雷达数据，月壤层状结构与物性特征的精细刻画成为月球科学研究的重点与难点之一。鉴于现有雷达层位识别与追踪方法在复杂散射环境下易受噪声和非均一性地质条件的影响，该文提出一种基于动态搜索中心的层位自动追踪算法。该算法引入高斯加权预测机制实现历史趋势与当前信号间的平衡，并采用多特征融合决策函数增强噪声环境下的追踪鲁棒性。模拟实验结果表明，当搜索半径l = 20、历史窗口n = 20 时，算法在浅层(<140 ns)层位识别误差小于2%；针对深层(>170 ns)信号衰减问题，引入边缘方向权重可将追踪误差降低30%以上。将所提算法应用于嫦娥四号实测数据，实现了测月雷达剖面层位的自动拾取，所得分层结果与前人研究高度吻合。算法在数值模拟与任务实测穿透雷达数据中均表现优异，能够准确识别不同介质与复杂形态下的真实层位，抑制噪声并保持路径平滑。综上，该文提出的算法实现了低人工依赖、高鲁棒性与高精度的层位自动追踪，对精确识别未来嫦娥七号月球任务与火星浅表层雷达数据中的地下结构，具有重要参考价值。Abstract: The Moon’s shallow subsurface structure provides crucial insights into its geological evolution, material composition, and space weathering processes. With the acquisition of extensive radar datasets from recent lunar exploration programs, such as the Chang’E missions, high-resolution characterization of the lunar regolith’s stratigraphic and physical properties has become a focus and challenge in lunar science. Conventional radar layer identification and tracking methods often suffer from instability in complex scattering environments, because of their sensitivity to noise and subsurface heterogeneity. To address these limitations, this study proposes an automatic layer-tracking algorithm based on a Dynamic Search Center (DSC) approach. This algorithm employs a Gaussian-weighted prediction mechanism to balance historical trajectory trends with local signal responses and uses a multifeatured fusion decision scheme to enhance tracking robustness under noisy conditions. Numerical simulations demonstrate that, with a search radius l = 20 and a historical window n = 20, the algorithm achieves a layer identification error of less than 2% for shallow strata (<140 ns). Meanwhile, for deep layers (>170 ns), with considerable signal attenuation, incorporating an edge-direction weighting term reduces the tracking error by over 30%. When applied to lunar penetrating radar data from the Chang’E-4 mission, the proposed method successfully realizes automatic stratigraphic tracing in lunar radar profiles, producing layer boundaries that are highly consistent with previous interpretations. Simulation and in-situ results confirm that the DSC-based algorithm accurately delineates real subsurface interfaces across media and structural morphologies, effectively suppressing noise, while maintaining smooth trajectories. Overall, the proposed method achieves low manual dependence, high robustness, and high precision in automatic radar layer tracking, thereby providing a valuable reference for analyzing radar data from upcoming missions such as Chang’E-7 and Martian shallow-subsurface explorations.
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图 1 基于高斯分布的动态搜索更新机制示意图
Figure 1. Schematic of the dynamic search-center update mechanism based on a Gaussian distribution
图 2 基于 FDTD 的雷达响应正演与合成数据生成
Figure 2. FDTD forward radar response modeling and synthetic data generation
图 3 动态搜索中心算法在模拟数据的层位追踪结果
Figure 3. Horizon tracking results of the dynamic search center algorithm on simulated data
图 4 不同参数下算法的层位追踪结果
Figure 4. Horizon tracking results of the algorithm under different parameter settings
图 5 嫦娥四号月球雷达高频通道实测数据
Figure 5. Measured high-frequency channel data from the Chang’E-4 lunar penetrating radar
图 6 玉兔二号行进路线600～800 m处测月雷达CH-2数据，绿色虚线为算法追踪得到的层位分界线
Figure 6. CH-2 lunar penetrating radar data from the 600～800 m segment of the Yutu-2 traverse route, where the green dashed lines indicate the horizon boundaries identified by the algorithm.
1 逆序分布介电常数模型及其正演雷达响应示意
1. Schematic of a dielectric constant reverse-distribution model and the corresponding forward radar response
2 逆序分布介电常数模型的层位追踪结果对比
2. Comparison of horizon tracking results for the reverse distribution dielectric constant model (solid lines: algorithm results; dashed lines: true horizons)
3 噪声扰动下层位拾取算法的鲁棒性评估
3. Robustness evaluation of horizon picking under noise perturbations
4 噪声扰动下层位拾取算法的鲁棒性评估
4. Robustness evaluation of horizon picking under noise perturbations
1 动态搜索中心层位追踪算法
1. Dynamic search center horizon tracking algorithm
输入：处理完成的雷达剖面矩阵，搜索半径$ {l} $，历史窗口长度
$ {n} $，权重$ {\lambda } $，${\alpha } $输出：层位轨迹 1. 初始化首道层位位置 $ {{{{y}}_{{1}}}}_{\leftarrow }{\arg } {\max } {{E}}_{{1}}\left({t}\right) $ 2. for $ {j}={2} $ to $ {N} $ do 3. 提取第$ {j} $道信号 $ {{s}}_{{j}}\left({t}\right) $，计算包络$ {{E}}_{{j}}\left({t}\right) $ //式4—式5 4. 计算动态搜索中心$ {\bar{{y}}_{{j}}} $ //式6 5. 确定搜索窗口$ \left[{\max } \left({0},{\bar{{y}}_{{j}}}-{l}\right),{\min } \left({T},{\bar{{y}}_{{j}}}+{l}\right)\right] $ //确保搜索
窗口在雷达数据矩阵的范围内6. 检测局部极大值点集$ {\mathcal{C}}_{j}={c}_{m}|{E}_{j}\left({c}_{m}\right)\geq {E}_{j}\left({c}_{m}\pm 1\right) $ 7. if $ {\mathcal{C}}_{\boldsymbol{j}}={\varnothing } $ then 8. $ {{y}}_{{j}}\leftarrow {\overline{{y}}}_{{j}} $ //无候选点时继承预测值 9. else 10. for 每个$ {{c}}_{{m}}\in {{C}}_{{j}} $ do 11. 计算$ {{S}}_{{s}}\left({{c}}_{{m}}\right) $ $ {{S}}_{{g}}\left({\boldsymbol{c}}_{{m}}\right) $ $ {{S}}_{{e}}\left({{c}}_{{m}}\right) $ 12. 计算综合得分 $ {{S}}_{\text{total}}\left({{c}}_{{m}}\right) $ //式7 13. end for 14. $ {{y}}_{{j}}\leftarrow {{\mathrm{arg}}} {\max}\left({{c}}_{{m}}\right){{S}}_{\text{total}}\left({{c}}_{{m}}\right) $ 15. end if 16. 更新轨迹$ {Y}\leftarrow {Y}\cup {{y}}_{{j}} $ 17. end for 
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表 1 二维分层模型中各单元的物性参数
Table 1. The physical property parameters of each unit in the layered model
单元 介电常数 密度
(g/cm3)损耗角正切 平均电导率
(S/m)平均厚度(m) 下界面平均
双程时延(ns)1 1 0 0 0 0.6 0 2 2 1.05 0.0033 0.00018 6 64.17 3 3 1.67 0.0062 0.00 046 6 139.01 4 4 2.11 0.0097 0.00087 3.4 171.50 5 5 2.45 0.0136 0.00139 3 \
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表 2 第4复杂层位自动追踪的参数敏感性分析结果
Table 2. Results of parameter sensitivity analysis for automatic tracking of layer4
组合与对应结果 搜索半径 历史窗口 平滑因子 边缘权重与方向 双程平均时延(ns) 误差(%) 相关系数 均方根误差(ns) 1-图2 20 20 0 0, 0 175.01 2.26 0.84 4.7029 2-图3(a) 10 20 0 0, 0 172.00 1.87 0.63 3.7701 3-图3(b) 30 20 0 0, 0 175.31 2.63 0.76 5.5295 4-图3(c) 20 10 0 0, 0 177.86 3.77 0.79 7.8661 5-图3(d) 20 30 0 0, 0 174.96 2.23 0.84 4.6408 6-图3(e) 20 20 0.3 0, 0 174.73 2.05 0.86 4.2807 7-图3(f) 20 20 0 0.3, –1 172.97 1.55 0.85 3.4284
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