SA-LM Optimization-based Fusion Positioning Method Using GNSS/Cellular Signals of Opportunity
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摘要: 在全球导航卫星系统(GNSS)可见卫星数量不足或观测几何构型退化的受限环境下, 针对GNSS/蜂窝机会信号融合定位中观测质量差异大、非线性优化易陷入不利局部极值甚至发散的问题, 提出一种基于模拟退火Levenberg-Marquardt优化的融合定位方法. 首先, 在迭代扩展卡尔曼滤波状态估计框架下, 将模拟退火机制引入Levenberg-Marquardt优化过程, 对未满足确定性接受条件的候选步采用概率接受准则, 以提高退化观测条件下的迭代收敛可靠性, 并给出算法的收敛性分析. 其次, 构建由定位精度因子与伪距残差驱动的双因子动态加权机制, 增强位置估计的鲁棒性. 进一步设计指数加权状态平滑方法, 抑制状态估计的瞬时波动, 提高定位轨迹的连续性与稳定性. 仿真与实测结果表明, 所提方法的三维和高程均方根误差分别为7.59 m和6.06 m, 与对比方法中性能最优的双dog-leg增量估计方法相比分别降低约35.40% 和45.55%.Abstract: In constrained environments, global navigation satellite system (GNSS) may be limited by an insufficient number of visible satellites or degraded observation geometry. To address large disparities in observation quality and the tendency of nonlinear optimization to converge to undesirable local minima or even diverge in GNSS/cellular signals of opportunity fusion positioning, a fusion positioning method based on simulated annealing Levenberg-Marquardt (SA-LM) optimization is proposed. First, within a state estimation framework based on the iterated extended Kalman filter, a simulated annealing mechanism is incorporated into the Levenberg-Marquardt optimization process. Candidate steps that fail to satisfy the deterministic acceptance condition are accepted according to a probabilistic acceptance criterion to improve the reliability of iterative convergence under degraded observation conditions. A convergence analysis of the algorithm is also provided. Second, a dual-factor dynamic weighting mechanism driven by position dilution of precision and pseudorange residuals is developed to enhance the robustness of position estimation. Furthermore, an exponentially weighted state smoothing method is designed to suppress instantaneous fluctuations in the state estimate and improve the continuity and stability of the positioning trajectory. Simulation and field test results show that the proposed method achieves 3D and vertical RMSEs of 7.59 m and 6.06 m, respectively, representing reductions of approximately 35.40% and 45.55% compared with the double dog-leg incremental estimation method, which performs best among the comparison methods.
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图 3 GNSS与蜂窝机会信号融合定位实验平台
Fig. 3 GNSS and cellular signals of opportunity fusion positioning experimental platform
图 5 两种典型北斗卫星构型的天空图
Fig. 5 Skyplots of two representative BeiDou satellite configurations
图 6 开阔环境下SA-LM与DDIE的定位轨迹对比
Fig. 6 Positioning trajectory comparison between SA-LM and DDIE in the open-sky environment
图 7 林荫道环境下不同蜂窝测距噪声条件的定位轨迹对比(北斗实测数据/蜂窝半仿真数据)
Fig. 7 Positioning trajectory comparison under different cellular ranging noise conditions in the tree-lined road environment (field test BeiDou data/semi-simulated cellular data)
图 8 加权融合模块消融实验定位误差对比
Fig. 8 Positioning error comparison of ablation experiments on the weighted fusion module
图 9 核心模块耦合消融实验定位误差对比
Fig. 9 Positioning error comparison of ablation experiments on core-module coupling
表 1 蜂窝基站信息
Table 1 Cellular base station information
小区标识 频段(MHz) 双工模式 坐标(纬度, 经度, 高度) 位置 135 1 835.6 FDD (112.854 8, 27.889 2, 116.3) 法学院 33 2 140.0 FDD (112.856 1, 27.891 1, 134.6) 第三教学楼 447 1 835.6 FDD (112.860 6, 27.884 8, 85.1) 琴湖宿舍 236 2 140.0 FDD (112.857 0, 27.885 8, 84.0) 南山阶梯教室 
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表 2 测试场景与观测配置
Table 2 Test scenarios and observation configurations
场景 数据来源 配置项 参数取值 场景1
开阔环境北斗/蜂窝实测 PCI 135, 33, 477 E1卫星集合 C3, C35, C40 E2卫星集合 C1, C7, C26, C40, C59 场景2
林荫道环境北斗实测/
蜂窝半仿真可用卫星数 2 ~ 3颗 E3蜂窝测距噪声 $[\mu,\;\sigma]$=[5, 5] m E4蜂窝测距噪声 $[\mu,\;\sigma]$=[10, 8] m E5蜂窝测距噪声 $[\mu,\;\sigma]$=[20, 10] m 重复次数 100次
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表 3 两种北斗卫星/蜂窝基站退化构型下融合定位RMSE比较(m)
Table 3 RMSE comparison of fusion positioning under two degraded configurations of BeiDou satellites and cellular base stations (m)
卫星基站组合 方法 RMSE3D RMSEH RMSEV E1 LM[27] 74.79 12.35 73.76 WLS[17] 150670417.40 14149889.48 140901624.70 SDHA[15] 55.75 9.72 54.90 MOPSO[20] 75.04 12.53 73.98 DDIE[30] 11.75 3.77 11.13 SA-LM 7.59 4.57 6.06 E2 LM[27] 37.54 17.73 33.11 WLS[17] 34.80 16.23 30.81 SDHA[15] 23.85 10.44 21.46 MOPSO[20] 37.54 17.72 33.12 DDIE[30] 17.17 9.12 14.57 SA-LM 10.32 7.40 7.21
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表 4 不同蜂窝测距噪声条件下融合定位RMSE比较(北斗实测数据/蜂窝半仿真数据) (m)
Table 4 RMSE comparison of fusion positioning under different cellular ranging noise conditions (field test BeiDou data/semi-simulated cellular data) (m)
方法 E3 E4 E5 RMSE3D RMSEH RMSEV RMSE3D RMSEH RMSEV RMSE3D RMSEH RMSEV LM[27] 43.74 10.96 42.34 53.56 15.73 51.20 71.04 21.52 67.71 WLS[17] — — — — — — — — — SDHA[15] 24.40 4.64 23.96 29.97 7.86 28.92 43.71 12.37 41.93 MOPSO[20] 3350.98 1055.43 3179.98 4538.81 1474.40 4292.84 4643.85 1513.76 4390.03 DDIE[30] 8.82 6.25 6.21 20.34 10.60 17.36 39.38 16.26 35.86 SA-LM 15.04 3.44 14.64 15.14 4.45 14.47 15.21 5.18 14.29
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表 5 开阔环境下不同迭代优化算法的定位精度对比(m)
Table 5 Positioning accuracy comparison of different iterative optimization algorithms in the open-sky environment (m)
算法 E1 E2 RMSE3D RMSEH RMSEV RMSE3D RMSEH RMSEV LM-IEKF 8.32 4.57 6.97 10.49 7.42 7.45 BFGS-IEKF 41.72 8.60 40.82 70.76 23.38 68.93 DDIE-IEKF 7.90 4.59 6.43 10.50 7.40 7.48 SA-LM 7.59 4.57 6.06 10.32 7.40 7.21
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表 6 林荫道环境下不同迭代优化算法的定位精度对比(北斗实测数据/蜂窝半仿真数据) (m)
Table 6 Positioning accuracy comparison of different iterative optimization algorithms in the tree-lined environment (field test BeiDou data/semi-simulated cellular data) (m)
算法 E3 E4 E5 RMSE3D RMSEH RMSEV RMSE3D RMSEH RMSEV RMSE3D RMSEH RMSEV LM-IEKF 15.49 3.47 15.09 15.61 4.58 14.91 15.67 5.37 14.71 BFGS-IEKF 33.75 7.15 32.83 39.98 9.26 38.78 38.61 9.21 37.35 DDIE-IEKF 15.50 3.47 15.10 15.61 4.58 14.92 15.68 5.38 14.71 SA-LM 15.04 3.46 14.64 15.14 4.45 14.47 15.21 5.18 14.29
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表 7 不同迭代优化算法的计算效率比较
Table 7 Computational efficiency comparison of different iterative optimization algorithms
算法 单次迭代复杂度 平均迭代次数 平均单历元耗时(s) LM ${\rm{O}}(D_rD_x^2+D_x^3)$ 4.98 0.0164 BFGS ${\rm{O}}(D_rD_x+D_x^2)$ 18.27 0.0183 DDIE ${\rm{O}}(D_rD_x^2+D_x^3)$ 3.73 0.0021 SA-LM ${\rm{O}}(D_rD_x^2+D_x^3)$ 3.53 0.0018 注: Dx和Dr分别表示状态向量维数和残差向量维数.
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表 8 加权融合模块消融实验配置
Table 8 Settings for ablation experiments on the weighted fusion module
配置 PDOP加权 伪距残差加权 状态平滑 基线 × × × PDOP加权 √ × × 双因子加权 √ √ × 双因子加权 + 平滑 √ √ √
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表 9 所提方法优于各子组合的历元比例(%)
Table 9 Epoch ratio of the proposed method outperforming sub-combinations (%)
实验 < 1 Sub < 2 Subs < 3 Subs E1 100.00 93.89 20.56 E2 100.00 85.56 14.44 E5 100.00 88.30 29.82
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表 10 核心模块耦合消融实验配置
Table 10 Settings for ablation experiments on core-module coupling
配置 SA-LM优化 双因子加权 状态平滑 基线 × × × 仅SA-LM √ × × 仅双因子加权 × √ × SA-LM + 双因子加权 √ √ × 完整方法 √ √ √
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