Aiming at problem that extend Kalman filter（ EKF） suffers from noise covariance matrix has great influence on estimated accuracy and difficulty in selecting noise covariance matrix

propose a method to optimize the EKF based on particle swarm optimization（ PSO）. State augmented EKF

in which the noise covariance matrix is optimized and selected by PSO

is used to estimate speed and sensorless control of permanent magnet synchronous motor（ PMSM） is realized

use STM32F407ZET6 as the core controller to build the control system

the experimental results show that the EKF observer optimized by PSO can estimate the speed with high precision and achieve precise control.