Comparison of R-Adaptive Unscented Kalman Filters for Sensorless PMSM Estimation

Abstract

This paper compares three unscented Kalman filters that adapt the measurement covariance R for sensorless permanent magnet synchronous motor (PMSM) estimation: an exponentially weighted UKF (UKF-QR), a master–slave UKF (UKF-MSQ), and a bounded Sage–Husa UKF (UKF-SH). The main contribution is a controlled comparison using the same initial conditions, voltage inputs, and noisy current measurements along a common PMSM trajectory generated by linear quadratic integral (LQI) speed control. Each adaptation coefficient is selected independently using Bayesian optimization and development tests, then fixed before evaluation. Two 50-trial Monte Carlo tests examine measurement-noise changes alone and in combination with parameter mismatch, speed changes, and load disturbances. Fixed-R and oracle-R UKFs provide reference results. In the noise-only test, the adaptive filters reduce settled-window mean squared error (MSE) by about 80% for d-axis current, 86% for q-axis current, and 70–71% for speed relative to the fixed UKF. UKF-QR gives the lowest MSE among the adaptive filters. Under combined stress, UKF-MSQ gives the lowest adaptive d-axis current and speed MSE, 2.809 × 10⁻³ A² and 7.265 × 10⁻³ (rad/s)², and the best average covariance tracking. UKF-QR gives the lowest adaptive q-axis current MSE. UKF-MSQ also has the lowest 95th-percentile speed MSE among the adaptive filters, although the fixed and oracle-R references give lower values. These results favor UKF-MSQ when average speed accuracy and covariance tracking are the main priorities under the tested disturbances.