自适应SVD–UKF算法及在穿刺状态估计中的应用

Adaptive SVD–UKF algorithm and application to puncture state estimation

中文关键词  自适应滤波  奇异值分解  无迹卡尔曼滤波  Sage-Husa估计器  柔性针

英文关键词  adaptive filter  singular value decomposition  unscented Kalman filter  Sage-Husa estimator  flexible needle

中文摘要

      柔性针在实际穿刺过程中会产生不规则形变, 导致柔性针模型存在参数不确定性问题, 影响穿刺精度. 本文针对柔性针穿刺过程存在的不确定性问题以及超声成像等设备存在的量测噪声统计特征不准确性问题, 提出了一种带有噪声估计器的自适应奇异值分解无迹卡尔曼滤波算法. 该算法采用自适应因子实时修正动力学模型误差, 通过奇异值分解抑制系统状态协方差矩阵的负定性, 利用Sage-Husa估计器在线估计噪声的统计特性, 减小了系统状态估计误差. 将新算法应用于带有曲率不定性的柔性针穿刺模型进行计算仿真, 仿真结果显示, 新的算法较现有的UKF算法相比, 估计误差减小了0.28 mm(82.7%), 与AUKF算法相比, 估计误差减小0.06 mm(52%). 因此, 新算法可有效改善滤波性能, 提高穿刺状态的估计精度.

英文摘要

      The flexible needle may produce irregular deformation during the actual puncture process, which leads to the problem of parameter uncertainty in the flexible needle model and affects the puncture accuracy. Aiming at the uncertainty of the flexible needle puncture process and the inaccurate statistical characteristics of measurement noise of equipments such as ultrasound imaging systems, an adaptive singular value decomposition unscented Kalman filter algorithm with a noise estimator is proposed. The algorithm corrects the dynamics model errors in real time by using an adaptive factor, improve the numerical stability of the covariance matrix by taking singular value decomposition, using the Sage-Husa estimator to estimate the statistical characteristics of the noise online, and reducing the system state estimation error. Finally, the new algorithm is applied to the flexible needle puncture model with curvature uncertainty for calculation and simulation. Simulation results show that the estimation error of the new algorithm is reduced by 0.28 mm (82.7%) compared with the existing UKF algorithm. Compared with AUKF algorithm, the estimation error is reduced by 0.06 mm (52%). Thus, the new algorithm can effectively improve the filtering performance and the accuracy of needle state estimation.