Bayesian Optimization-based EKF Covariance Auto-tuning and Robustness Evaluation for Sensorless PMSM Drives

This study proposes a speed-dependent Bayesian optimization (BO) method for tuning the noise covariance matrices of an extended Kalman filter (EKF) used in sensorless speed estimation of permanent magnet synchronous motor (PMSM) drives. The estimation accuracy of the EKF is strongly affected by the process and measurement noise covariance matrices Q and R. In practice, these matrices are typically selected empirically (on a trial-and-error basis), which is time-consuming and does not guarantee optimal performance over a broad speed range. In the proposed method, the root-mean-square error of the estimated speed was formulated as a black-box objective function of the log-scaled covariance parameters. A Gaussian process surrogate model and the expected improvement acquisition function were utilized to search the parameter space efficiently. The covariance matrices were optimized independently at three representative operating speeds. All evaluations were performed via Monte Carlo simulations over 10 independent realizations of the current-measurement noise on a PMSM drive with 20% parameter mismatches in the stator resistance, inductance, and flux linkage. The results show that the proposed BO-tuned EKF successfully improves speed estimation performance compared with a fixed covariance setting (optimized at 600 revolutions per minute), especially in the low-speed region where the fixed setting has difficulty tracking the actual speed. Furthermore, a comparison with particle swarm optimization under the same evaluation budget further confirmed the superior sample efficiency of the proposed BO-based tuning approach. Finally, closed-loop sensorless control simulations with estimated-state feedback validate the practical applicability and reveal the distinct coupling characteristics between the estimator and closed loops, further supporting the necessity of speed-dependent covariance scheduling. These findings imply that automated, speed-dependent covariance tuning can shorten drive commissioning and extend the reliable operating range of sensorless drives toward low speeds.