Respiratory Motion Estimation With Hybrid Implementation of Extended Kalman Filter

The extended Kalman filter (EKF) can be used for the purpose of training nonlinear neural networks to perform desired input-output mappings. To improve the computational requirements of the EKF, Puskorius proposed the decoupled EKF (DEKF) as a practical remedy for the proper management of computational resources. This approach, however, sacrifices computational accuracy of estimates because it ignores the interactions between the estimates of mutually exclusive weights. To overcome such a limitation, therefore, we proposed hybrid implementation based on EKF (HEKF) for respiratory motion estimation, which uses the channel number for the mutually exclusive groups and the coupling technique to compensate the computational accuracy. Moreover, the authors restricted to a DEKF algorithm in which the weights connecting the inputs to a node are grouped together. If there are multiple input training sequences with respect to the time stamp, the complexity can increase by the power of the input channel number. To improve the computational complexity, we split the complicated neural network into a couple of simple neural networks to adjust separate input channels. The experimental results validated that the prediction overshoot of the proposed HEKF was improved by 62.95% in the average prediction overshoot values. The proposed HEKF showed a better performance of 52.40% improvement in the average of the prediction time horizon. We have evaluated that the proposed HEKF can outperform DEKF by comparing the prediction overshoot values, the performance of the tracking estimation value, and the normalized root-mean-squared error.