A robust adaptive filtering algorithm based on predicted residuals in integrated navigation
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摘要:
全球卫星导航系统（GNSS）和惯性导航系统（INS）进行融合可以有效提高导航系统的精度及可靠性，现已被广泛使用。卡尔曼滤波是常用的融合导航算法，但由于载体运动状态变化及观测粗差的影响，滤波的性能会严重降低。为了解决以上问题，构建抗差自适应卡尔曼滤波（RAKF）提高组合导航的状态估计的性能至关重要。设计了一种基于预测残差的抗差自适应滤波组合导航算法，通过构建基于预测残差的自适应因子，结合抗差估计算法，有效解决GNSS/INS组合导航中观测异常和动力学模型的异常扰动，提高滤波的稳定性、可靠性及精度。实验结果表明：与基于标准卡尔曼滤波GNSS/INS组合导航相比，所设计算法在有观测异常和动力学模型异常扰动的情况下可以有效提高组合导航的定位精度；在松组合和紧组合2种模式中，3D定位精度分别提升了45.9%和46.8%。
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关键词:
- 预测误差 /
- 卡尔曼滤波 /
- 自适应滤波 /
- 抗差估计 /
- GNSS/INS组合导航
Abstract:Integration of the global navigation satellite system (GNSS) and the inertial navigation system (INS) can effectively improve the accuracy and reliability of the navigation system, and therefore has been widely used in many applications. In particular, the Kalman filter is commonly used in the fusion algorithm, but its performance will be severely degraded due to the vehicle motion and the low quality GNSS measurements. To deal with the above issues, a robust adaptive Kalman filter (RAKF) based algorithm has been proposed for the GNSS/INS fusion. By the construction of adaptive factor based on predicted residuals in the robust estimation process, the proposed algorithm can effectively improve the stability, reliability and accuracy of the system in the conditions of abnormal disturbance in the GNSS measurements and vehicle dynamic model. The simulation results show that the 3D positioning results obtained by the proposed algorithm is superior to the standard Kalman filter in both loosely and tightly coupled integrated navigation, with an improvement of 45.9% and 46.8%, respectively.
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图 1 基于预测残差的抗差自适应滤波组合导航算法结构
Figure 1. Framework of robust adaptive filtering integrated navigation algorithm based on predictive residuals
图 5 松组合导航场景1中自适应因子
Figure 5. Adaptive factors of loosely coupled integrated navigation in Scenario 1
图 6 松组合导航场景1中位置误差
Figure 6. Position errors of loosely coupled integrated navigation in Scenario 1
图 7 松组合导航场景2中位置误差
Figure 7. Position errors of loosely coupled integrated navigation in Scenario 2
图 8 紧组合导航场景1中自适应因子
Figure 8. Adaptive factors of tightly coupled integrated navigation in Scenario 1
图 9 紧组合导航场景1位置误差
Figure 9. Position errors of tightly coupled integrated navigation in Scenario 1
图 10 紧组合导航场景2位置误差
Figure 10. Position errors of tightly coupled integrated navigation in Scenario 2
表 1 惯性导航系统参数设置
Table 1. Parameters settings of INS
传感器 参数 设置值 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/h 104 加速度计 相关时间/h 104 一阶马尔可夫驱动白噪声方差/(m·s−2) 0.3×9.81×10−6 
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表 2 滤波参数初值
Table 2. Initial value of filtering parameters
参数 组合
模式初值 ${\boldsymbol{\varPhi }}$ 松/紧 ${{\boldsymbol{I}}_{18 \times 18}}$ ${\boldsymbol{Q}}$ 松/紧 ${\text{diag} }\left( \underbrace {0,\cdots,0}_{\rm{9} }, \underbrace {4.3\times10^{-14},\cdots}_{ {3} },\underbrace {5\times10^{-21},\cdots}_{\rm{3} },0,0,0\right)$ $ {\boldsymbol{R}} $ 松组合 ${\text{diag} }\left(2.25,2.25,2.25 \right)$ 紧组合 ${\text{diag} }\left(\underbrace {2.25,\cdots,2.25}_{\rm{9}}\right)$ ${\boldsymbol{H}}$ 松组合 $[{ {\boldsymbol{I} }_{6 \times 6} }\quad{ {{\boldsymbol{0}}}_{6 \times 12} }]$ 紧组合 $[{ {\boldsymbol{I} }_{9 \times 9} }\quad{ {{\boldsymbol{0}}}_{9 \times 9} }]$ ${{\boldsymbol{\bar P}}_{\boldsymbol{0}}}$ 松/紧 ${\text{diag} }\left( 2.25,2.25,2.25,\;4,4,4,\;{ 1 } \times {\text{1} }{ {\text{0} }^{ - 8} }{\text{, 9} }{\text{.6} } \times {\text{1} }{ {\text{0} }^{ - 7} }\right.$, $\left.{\text{5} }{\text{.9} } \times {\text{1} }{ {\text{0} }^{ - 4} },{ { {2.25,2.25,2.25 } } } \right)$
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表 3 松组合导航场景1中的位置RMSE
Table 3. Position RMSE of loosely coupled integrated navigation in Scenario 1
m 算法 东向 北向 天向 3D位置 算法1 0.80 1.36 1.68 2.30 算法2 0.68 1.25 1.60 2.13 本文算法 0.68 1.25 1.60 2.13
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表 4 松组合导航场景2中位置RMSE
Table 4. Position RMSE of loosely coupled integrated navigation in Scenario 2
m 算法类型 东向 北向 天向 3D位置 算法1 1.96 2.32 2.43 3.90 算法2 1.93 2.00 2.47 3.72 本文算法 0.67 1.22 1.60 2.11
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表 5 紧组合导航场景1中位置RMSE
Table 5. Position RMSE of tightly coupled integrated navigation in Scenario 1
m 算法 东向 北向 天向 3D位置 算法1 0.74 1.28 0.78 1.66 算法2 0.64 1.29 0.68 1.59 本文算法 0.64 1.29 0.68 1.59
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表 6 紧组合导航场景2位置RMSE
Table 6. Position RMSE of tightly coupled integrated navigation in Scenario 2
m 算法 东向 北向 天向 3D位置 算法1 1.54 2.47 1.09 3.10 算法2 1.44 2.28 1.03 2.89 本文算法 0.68 1.34 0.68 1.65
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表 7 松组合和紧组合导航中算法的性能
Table 7. Performance of algorithm in loosely and tightly coupled integrated navigation
% 组合模式 3D定位精度提升 场景1 场景2 松组合 7.5 45.9 紧组合 4.2 46.8
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