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摘要: 几何滤波是一种利用观测数据对流形上几何状态进行最优估计的方法, 对刚体位姿估计具有重要作用和意义. 针对非高斯条件下几何滤波性能下降的问题, 提出一种基于广义最大相关熵准则(Generalized maximum correntropy criterion, GMCC)的几何滤波方法. 首先, 根据流形上几何状态演化关系, 采用流形无迹变换进行状态预测. 其次, 为抑制非高斯噪声引起的不利影响, 将广义最大相关熵准则推广到流形上, 实现对预测状态的修正来提高滤波的鲁棒性. 然后, 针对由GMCC引出的流形非线性优化问题, 设计了流形上的统计线性化方法, 以及采用黎曼流形优化和定点迭代法求解优化问题. 特别地, 设计了一种广义高斯核参数自适应调整策略, 以在线调整广义相关熵的超参数. 最后, 仿真结果表明, 相较于现有方法, 所提方法具有更高的精度和鲁棒性.Abstract: Geometric filtering is a method that uses observed data to optimally estimate the geometric state on a manifold, and it plays a significant role in rigid body pose estimation. Aiming at the problem of the performance degradation of geometric filtering under non-Gaussian conditions, a geometric filtering method based on the generalized maximum correntropy criterion (GMCC) is proposed. Firstly, according to the evolution relationship of the geometric state on the manifold, the state prediction is performed using the unscented transformation on the manifold. Secondly, in order to suppress the adverse effects of non-Gaussian noise, the GMCC is extended to the manifold to correct the predicted state, thereby improving the robustness of the filtering. Then, for the manifold nonlinear optimization problem induced by GMCC, a statistical linearization method on the manifold is designed, and the optimization problem is solved by Riemannian manifold optimization and fixed-point iteration method. In particular, an adaptive adjustment strategy for the generalized Gaussian kernel parameters is designed to adjust the hyperparameters of the generalized correntropy online. Finally, simulation results demonstrate that, compared to existing methods, the proposed method has higher accuracy and robustness.
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Key words:
- Geometric filtering /
- Kalman filtering /
- generalized correntropy /
- matrix Lie group
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图 4 混合高斯噪声${{n}_{k}^{S}}$下位姿估计的RMSE
Fig. 4 RMSE of pose estimation under noise ${{n}_{k}^{S}}$
图 6 混合高斯噪声$n_{k}^{L}$下位姿估计的RMSE
Fig. 6 RMSE of pose estimation under noise $n_{k}^{L}$
图 7 拉普拉斯分布非高斯噪声下位姿估计的RMSE
Fig. 7 RMSE of pose estimation under Laplace distributed non-Gaussian noise
图 8 伯努利分布非高斯噪声下位姿估计的RMSE
Fig. 8 RMSE of pose estimation under Bernoulli distribution non-Gaussian noise
表 1 混合高斯噪声$ {{n}_{k}^{S}} $下位姿估计的ARMSE
Table 1 ARMSE for pose estimation under noise $ {{n}_{k}^{S}} $
方法 核参数 位置ARMSE(m) 方向ARMSE(deg) EKF N/A 0.3238 1.8220 InEKF N/A 0.3176 1.7876 UKF-M N/A 0.1631 0.4526 MCEKF-LG $ \sigma = 1.0 $ 0.1285 0.4756 $ \sigma = 2.0 $ 0.1478 0.6531 $ \sigma = 2.5 $ 0.2337 0.8422 $ \sigma = 4.0 $ 0.3980 1.2834 GMCGF 自适应 0.1053 0.3667 
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表 2 混合高斯噪声$ n_{k}^{L} $下位姿估计的ARMSE
Table 2 ARMSE for pose estimation under noise $ n_{k}^{L} $
方法 核参数 位置ARMSE(m) 方向ARMSE(deg) EKF N/A 2.0361 3.6154 InEKF N/A 2.0174 3.5294 UKF-M N/A 1.0913 1.7074 MCEKF-LG $ \sigma = 1.0 $ 0.4311 0.9568 $ \sigma = 2.0 $ 0.6099 1.2834 $ \sigma = 2.5 $ 0.8296 1.5069 $ \sigma = 4.0 $ 1.1042 1.7246 GMCGF 自适应 0.2060 0.5214
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表 3 滤波方法的单步执行时间
Table 3 Single step execution time of different methods
方法 执行时间 (ms) EKF 0.1917 InEKF 0.2407 UKF-M 0.5043 MCEKF-LG 0.8994 GMCGF 1.0178
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