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摘要:
针对无法保证各子阵天线附近均安装高精度子惯性测量单元（IMU）的问题，提出了一种基于最小二乘拟合的分布式位置姿态测量系统（POS）全局估计方法。首先，建立了考虑一维柔性变形角的主/子传递对准误差模型；然后，采用卡尔曼滤波（KF）估计已安装子IMU的子阵天线运动参数；最后，在已获取运动参数的基础上，采用最小二乘拟合估计未安装子IMU的子阵天线运动参数。半物理仿真实验结果表明，所提方法精确实现了阵列天线运动参数的全局估计，且未安装子IMU的子阵天线运动参数估计精度与相邻的子阵天线运动参数估计精度相当。
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关键词:
- 惯性测量单元(IMU) /
- 传递对准 /
- 卡尔曼滤波(KF) /
- 最小二乘拟合 /
- 分布式位置姿态测量系统(POS)
Abstract:Aimed at the problem that it is impossible to install high-precision sub-Inertial Measurement Unit (IMU) on every sub-array in engineering practice, a global estimation method based on the least square fitting for distributed Position and Orientation System (POS) is proposed. Firstly, a transfer alignment error model from master system to slave system considering one-dimensional flexibility deformation is built. Secondly, Kalman Filter (KF) is used to estimate motion parameters of array antenna of the sub-arrays with sub-IMUs. Finally, the least square fitting is used to estimate the motion parameters of the sub-arrays without sub-IMU. The semi-physical simulation results show that the proposed method can realize the global estimation of the motion parameters of array antenna, and the estimation precision of the motion parameters of sub-arrays without sub-IMU is almost the same as that of its neighboring sub-arrays.
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图 1 分布式POS与InSAR联合飞行实验的设备
Figure 1. Flight experiment equipment with distributed POS and InSAR
图 2 阵列天线与IMU在一侧机翼的分布示意图
Figure 2. Distribution schematic diagram of array antennas and IMUs on one wing
表 1 阵列天线与IMU在载体坐标系下的坐标
Table 1. Coordinates of array antennas and IMUs in body coordinate
子阵天线 x轴坐标/m No.1 1 No.2 2 No.3 3 No.4 4 No.5 5 No.6 6 No.7 7 No.8 8 No.9 9 No.10 10 No.11 11 No.12 12 
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表 2 传递对准估计的子阵天线运动参数误差统计结果
Table 2. Statistical results of sub-antenna motion parameter errors using transfer alignment estimation
运动参数 RMSE No.1 No.3 No.5 No.7 No.9 No.11 纬度/m 0.004 6 0.009 8 0.030 4 0.043 5 0.053 0 0.076 6 经度/m 0.016 0 0.025 0 0.041 8 0.056 6 0.064 7 0.075 7 高度/m 0.015 2 0.029 6 0.032 4 0.040 3 0.051 7 0.069 1 东向速度/(m·s-1) 0.005 0.006 0.008 0.016 2 0.017 5 0.022 0 北向速度/(m·s-1) 0.004 0.006 0.009 0.019 1 0.022 0 0.025 2 天向速度/(m·s-1) 0.003 9 0.006 9 0.012 1 0.018 0 0.023 5 0.026 2 航向角/(°) 0.008 0 0.011 0 0.013 8 0.014 3 0.014 7 0.025 2 俯仰角/(°) 0.001 5 0.002 2 0.002 8 0.003 5 0.004 2 0.004 8 横滚角/(°) 0.001 3 0.002 6 0.002 8 0.003 1 0.004 4 0.004 7
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表 3 最小二乘拟合估计的子阵天线运动参数误差统计结果
Table 3. Statistical results of sub-antenna motion parameter errors using least square fitting estimation
参数 RMSE No.2 No.4 No.6 No.8 No.10 No.12 纬度/m 0.055 1 0.023 4 0.038 2 0.050 1 0.065 1 0.081 6 经度/m 0.018 8 0.038 5 0.049 6 0.060 8 0.071 8 0.085 6 高度/m 0.019 9 0.030 7 0.038 5 0.047 9 0.063 7 0.089 5 东向速度/(m·s-1) 0.004 6 0.007 2 0.011 9 0.017 4 0.021 7 0.026 9 北向速度/(m·s-1) 0.005 6 0.007 7 0.001 8 0.020 4 0.023 7 0.027 8 天向速度/(m·s-1) 0.005 1 0.010 4 0.017 2 0.020 6 0.024 4 0.028 2 航向角/(°) 0.009 0 0.013 3 0.014 0 0.016 0 0.023 3 0.028 6 俯仰角/(°) 0.001 9 0.002 4 0.003 3 0.004 0 0.004 4 0.004 8 横滚角/(°) 0.002 1 0.002 5 0.003 1 0.004 3 0.004 6 0.004 9
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