Soft-Magnet-Based Position Estimation Using an Approximate Extended Kalman Filter With a Hybrid Analytical-Neural Network Model

Soft-magnet (SM)-based position tracking is a new wireless magnetic tracking method that can reject ferromagnetic disturbances. Conventionally, position estimation is implemented either by a standard extended Kalman filter (EKF) using a dipole-based analytical measurement model or by an EKF or particle filter (PF) using a neural network model. The former method, however, fails to achieve satisfactory estimation accuracy due to the large modeling error, while the latter is time-consuming and fails to achieve real-time tracking. In this article, a hybrid analytical-neural network measurement model is built to improve the modeling accuracy and generalization, which uses a neural network to compensate for the analytical modeling error. An approximate EKF (AEKF) framework is, furthermore, developed to use the hybrid model and improve position estimation accuracy and computational efficiency simultaneously. In the AEKF, only the analytical part is linearized to compute the measurement Jacobian efficiently while the compensated hybrid model is used to compute the innovation (measurement residual) to ensure accuracy. Experimental results show that the root-mean-square (rms) position error ranges from 2.64 to 5.62 mm across the workspace, which rivals the standard EKF and the PF with an accurate pure neural network model. The average update time of the proposed algorithm is, however, only 13.82 ms (update rate: 73 Hz), which is three times faster than the standard EKF using a pure neural network model. In conclusion, the proposed AEKF algorithm with a hybrid model can achieve accurate and real-time position estimation simultaneously with good generalization for the SM-based tracking system.