A method for estimating the state of a system, as well as an extended Kalman filter (EKF), allows nonlinear mathematical models to be used for describing the system. Accurate precision is provided since the method is based on an EKF technique while using a filter that implements a first degree Stirling approximation formula. The method may be used for estimating position and speed of a brushless motor, and may be implemented in a relative device. Such a device may be introduced in a control loop of a brushless motor of a power steering system for a vehicle to provide a countering torque on the steering wheel based on speed of the vehicle and a steering angle of the vehicle.