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摘要:
全球导航卫星系统/惯性导航系统(GNSS/INS)组合导航可以提供连续、高精度的位置、速度、姿态信息,被广泛应用于无人机的状态估计。其中滤波算法的构建是其组合关键。不同组合导航的模式会对导航定位结果产生相应的影响。针对直接法和间接法这2种常见的组合模式,分别构建了基于扩展卡尔曼滤波(EKF)的全球定位系统/惯性导航系统(GPS/INS)松组合模式,并将其运用于不同飞行场景下无人机(UAV)的实时动态状态估计。仿真场景以及实际数据验证结果表明,间接法在精度和稳定性方面优于直接法,直接法在滤波计算速率方面优于间接法。因此,当系统具有较高的计算性能,且面向高精度的应用情况下可选择间接法作为无人机导航的技术方案;对于快速求解但精度要求不高的应用情况下,选择直接法作为无人机导航的技术方案可以在一定程度上降低系统的成本。
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关键词:
- 组合导航 /
- 扩展卡尔曼滤波(EKF) /
- 直接法 /
- 间接法 /
- 惯性导航系统(INS) /
- 全球定位系统(GPS)
Abstract:Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integrated navigation that could provide continuous and high-accuracy position, velocity and attitude are widely used in UAV state estimation. Particularly, the design of filtering algorithm is the key to the integration. Besides, different modes of integrated navigation influence the navigation and positioning results. In this paper, the direct and indirect modes based Extended Kalman Filter (EKF) algorithms are designed for the loosely-coupled Glolal Positioning System/Inertial Navigation System (GPS/INS) integration in Unmanned Aerial Vehicle (UAV) state estimation and tested in different scenarios. The results of simulation and field test indicate that the integration algorithm with the indirect mode can provide higher accuracy and stability state estimation results than the direct mode but with an increased computational cost. It is recommended to choose the indirect mode based integration for the applications with higher accuracy and reliability, while for the applications with the requirements of lower accuracy and fast computation, the direct mode based integration is recommended to reduce the system cost.
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表 1 惯性导航系统参数设置
Table 1. Parameter setting of INS
传感器 参数 数值 陀螺仪 随机常数/((°)·h-1) 0.05 随机漂移均方差/((°)·h-1) 0.05 一阶马尔可夫驱动白噪声方差/((°)·h-1) 1×10-9 相关时间/s 10000 加速度计 一阶马尔可夫驱动白噪声
方差/(m·s-2)
相关时间/s0.3×9.81×10-6
10000表 2 仿真环境下丢星场景1设置
Table 2. Setting of lost star in Scenario 1 under simulation environment
飞行阶段 丢星时间/s 间隔/s 上升段 60~75 15 平飞段 220~235 15 下降段 400~415 15 表 3 仿真环境下丢星场景2设置
Table 3. Setting of lost star in Scenario 2 undersimulation environment
飞行阶段 丢星时间/s 间隔/s 上升段 60~65 5 平飞段 220~225 5 下降段 400~405 5 表 4 场景1最大位置误差
Table 4. Maximum position error in Scenario 1
方向 最大位置误差/m 直接法 间接法 东向 102.8 9.5 北向 81.3 9.1 天向 271.1 1.9 表 5 场景2下直接法、间接法和GPS的位置RMSE
Table 5. Position RMSE of direct mode, indirect mode and GPS in Scenario 2
组合模式 位置RMSE/m 东向 北向 天向 2D 3D 直接法 0.89 0.86 2.08 1.24 2.42 间接法 0.49 0.53 0.87 0.71 1.12 直接法(不计丢星部分) 0.24 0.49 0.85 0.55 1.01 间接法(不计丢星部分) 0.22 0.46 0.89 0.51 1.02 GPS(不计丢星部分) 0.68 1.20 1.81 1.38 2.27 表 6 场景2下直接法和间接法的速度RMSE
Table 6. Velocity RMSE of direct mode and indirect mode in Scenario 2
组合模式 速度RMSE/(m·s-1) 东向 北向 天向 2D 3D 直接法 0.34 0.66 0.26 0.74 0.78 间接法 0.04 0.04 0.04 0.05 0.06 表 7 场景2下直接法和间接法的姿态RMSE
Table 7. Attitude RMSE of direct mode and indirect mode in Scenario 2
组合模式 姿态RMSE/rad 横滚角 俯仰角 偏航角 直接法 0.7685 1.1931 1.0991 间接法 0.0380 0.0378 0.0407 表 8 场景2下直接法和间接法运行时间
Table 8. Runtime of direct mode and indirect mode in Scenario 2
组合模式 运行时间/s 直接法 10.38 间接法 24.30 表 9 组合导航系统测量精度
Table 9. Measurement accuracy of integrated navigation system
传感器 参数 数值 IMU 采样率/Hz 100 陀螺仪零偏/((°)·h-1) 2 陀螺角速率随机游走/((°)· ) 0.12 加速度计零偏/μ g 300 加速度随机游走/(m·s-1· ) 0.12 GPS 采样率/Hz 10 位置测量噪声/m 0.04 表 10 直接法、间接法和GPS的位置RMSE(与Inertial Explorer相比)
Table 10. Position RMSE of direct mode, indirect mode and GPS (compared to Inertial Explorer)
组合模式 位置RMSE/m 东向 北向 天向 2D 3D 直接法 0.67 1.14 2.59 1.33 2.90 间接法 0.52 1.69 1.86 1.77 2.56 GPS(不计丢星) 0.68 1.75 2.81 1.88 3.38 表 11 直接法和间接法的速度RMSE
Table 11. Velocity RMSE of direct mode and indirect mode
组合模式 速度RMSE/(m·s-1) 东向 北向 天向 2D 3D 直接法 0.68 0.70 1.03 0.98 1.42 间接法 0.16 0.16 0.18 0.22 0.28 表 12 直接法和间接法的姿态RMSE
Table 12. Attitude RMSE of direct mode and indirect mode
组合模式 姿态RMSE/rad 横滚角 俯仰角 偏航角 直接法 0.9085 0.3232 1.2498 间接法 0.0067 0.0124 0.3835 表 13 直接法和间接法运行时间
Table 13. Runtime of direct mode and indirect mode
组合模式 运行时间/s 直接法 18.47 间接法 33.22 表 14 各丢星部分最大位置误差
Table 14. Maximum position error in lost-star parts
飞行阶段 丢星时间/s 间隔/s 最大位置误差/m 直接法 间接法 上升段 189~193.8 4.8 10.0 3.0 平飞段 769.2~771.5 2.3 4.2 1.5 下降段 822.2~824.8 2.6 6.1 1.7 -
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