基于IHHO-LSSVM的区域GNSS高程异常拟合方法
doi: 10.11728/cjss2026.01.2024-0180 cstr: 32142.14.cjss.2024-0180
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何广焕 男, 1997年03月出生于广西梧州市, 现为广西建设职业技术学院市政与交通学院专任教师, 硕士研究生, 主要研究方向为GNSS数据处理及应用、无人机数据处理与应用. E-mail: 503871493@qq.com -
任超 男, 1974年05月出生于河南周口市, 现为桂林理工大学测绘与地理信息学院教授, 博士生导师, 主要研究方向为GNSS数据处理与应用、遥感技术应用研究. E-mail: 2707814165@qq.com
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Regional GNSS Elevation Anomaly Fitting Method Based on IHHO-LSSVM
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摘要: 针对当前复杂区域难以获取较高精度的高程异常值问题, 提出一种基于IHHO-LSSVM的高程异常拟合方法. 采用具有非线性的收敛因子、跳跃距离和自适应权重对哈里斯鹰优化算法(Harris Hawk Optimization, HHO)进行改进; 利用改进后的HHO算法为最小二乘向量机(Least Squares Support Vector Machine, LSSVM)高程异常拟合模型提供更为精确的正则化参数和核函数; 为验证高程异常组合模型在复杂地形中的适应性, 以高程异常值的均方根误差作为评判依据, 并结合两组不同地形的工程实例数据进行试验. 结果表明, 在桥梁带状区域和喀斯特面状区域, 相比于HHO-LSSVM法和LSSVM法, IHHO-LSSVM拟合模型的外符合精度更高、稳定性更强、适应性更广, 其中桥梁带状区域精度达到0.0101 m, 喀斯特面状区域达到0.0125 m, 可为GNSS高程异常拟合模型的建立提供一定的参考价值.Abstract: In order to effectively address the challenge of obtaining high-precision elevation outliers in complex geographical areas, this paper proposes an innovative elevation anomaly fitting method based on IHHO-LSSVM. The study begins with an improved Harris Hawk Optimization (HHO) algorithm through the implementation of nonlinear convergence factors, optimized jump distances, and adaptive weights. These improvements significantly enhance the algorithm’s ability to escape local optima and improve convergence efficiency, thereby providing a more robust optimization framework for subsequent model parameter tuning. Subsequently, the improved HHO algorithm is employed to determine more accurate regularization parameters and kernel functions for the Least Squares Support Vector Machine (LSSVM) elevation anomaly fitting model. This optimization process ensures that the LSSVM model achieves higher precision and better generalization capabilities in elevation anomaly fitting tasks. To thoroughly validate the adaptability and robustness of the proposed elevation anomaly combination model in complex terrains, extensive experiments were conducted using engineering case data from two distinct geographical regions: a bridge strip area and a karst surface area. The evaluation was based on the Root Mean Square Error (RMSE) of the elevation anomaly values as the primary metric, with additional consideration given to computational efficiency and model stability. The experimental results demonstrate that in both the bridge strip area and karst surface area, the IHHO-LSSVM method outperforms the conventional HHO-LSSVM and standard LSSVM methods in terms of external conformity accuracy, stability, and adaptability. Specifically, the IHHO-LSSVM method achieves remarkable accuracy levels of 0.0101 meters in the bridge strip area and 0.0125 meters in the karst surface area, representing significant improvements over traditional methods. Furthermore, the proposed method exhibits superior stability across different terrain types, with reduced variance in prediction errors. These findings not only highlight the superior performance of the proposed method but also provide valuable insights and a reliable reference for the establishment of GNSS elevation anomaly fitting models in various complex terrains. The study contributes to the field of geodetic surveying by offering a more precise and robust solution for elevation anomaly fitting, particularly in challenging geographical conditions.
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图 1 初始(a)与改进(b) 的能量变化曲线
Figure 1. Change diagrams of the original energy (a) and optimized energy (b)
图 2 初始(a)与改进(b)逃逸距离变化
Figure 2. Change diagrams of the initial escape distance (a) and the improved escape distance (b)
表 1 组合模型参数
Table 1. Parameters of the combined model
参数名 含义 数值 sizepop 种群规模 50 T 最大迭代次数 50 bu 模型参数上界 10000 bl 模型参数下界 0.01 dim 优化参数个数 2 
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表 2 三种方法的外符合精度统计
Table 2. Statistics of external coincidence accuracy for three methods
Comp.
orderIHHO-LSSVM HHO-LSSVM LSSVM c σ Acc/m c σ Acc/m c σ Acc/m 1 9.4563 0.0627 0.0101 48.3160 0.3132 0.0120 242.7275 0.3364 0.0159 2 9.2120 0.0467 0.0101 46.3075 0.4095 0.0126 902.8057 1.0192 0.0153 3 8.6297 0.0454 0.0101 6.3957 0.2001 0.0125 667.4809 0.8753 0.0157 4 6.5542 0.0673 0.0099 5.3087 0.2064 0.0126 834.2785 0.9877 0.0160 5 5.0345 0.0939 0.0103 3.1908 0.1504 0.0125 518.1796 0.7436 0.0157 6 4.7826 0.0836 0.0103 4.1458 0.1677 0.0122 641.3714 0.8620 0.0155 7 6.3225 0.0759 0.0100 19.8899 0.3015 0.0125 746.0421 0.3305 0.0154 8 9.9653 0.0475 0.0102 99.9546 0.5915 0.0129 254.1818 0.3484 0.0155 9 10.9717 0.0592 0.0103 25.6355 0.3020 0.0123 571.8598 0.8055 0.0162 10 7.3621 0.0492 0.0099 46.7021 0.3757 0.0124 946.7136 1.0382 0.0161 $\bar A_{\mathrm{cc}} $ ― ― 0.0101 ― ― 0.0125 ― ― 0.0157 注: Acc为精度.
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表 3 检查点的预测结果及精度分析
Table 3. Prediction results and accuracy analysis of checkpoints
Checkpoints Given height
anomaly/mResidual error/m IHHO HHO LSSVM 1 –20.7172 –0.0140 –0.0240 –0.0320 2 –20.6537 0.0338 0.039 1 0.0423 3 –20.5230 0.00 6 –0.0078 –0.0116 4 –20.0759 0.0120 0.0030 0.0016 5 –20.0170 –0.0011 0.0015 0.0020 6 –19.9065 –0.0002 –0.0003 –0.0003 7 –20.4448 0.0031 –0.0036 –0.0060 8 –19.8739 –0.0005 0.0025 0.0039 9 –19.9360 0.0063 0.0095 0.0100 10 –20.1365 0.0152 0.0075 0.0038 11 –20.4328 0.0046 0.0124 0.0139 12 –20.4832 –0.0013 –0.0400 –0.0523 13 –19.9431 –0.0067 –0.0007 0.0004 14 –19.9499 0.0123 0.0027 –0.0004 15 –20.0201 0.0105 0.0065 0.0039 16 –20.0453 –0.010 5 –0.0026 –0.0003 17 –19.8213 –0.0154 –0.0067 –0.0043 18 –19.7091 0.0123 0.0092 0.0092 19 –20.0251 –0.0206 –0.0191 –0.0174 20 –19.6036 0.0096 0.0078 0.0043
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