LAUSR

A phase demodulation strategy based on the Kalman filter for sinusoidal encoders is proposed in this article. For the state equation and observation equation in the constructed phase demodulation model, phase angle, phase angular speed, and speed fluctuation are system states, and the sine and cosine signals output by the encoder are the system observations. In addition, due to the nonlinear relationship between observations and system states, the observation function is linearized by the extended Kalman approach. In order to implement the Kalman filter on the hardware platform with a field programmable gate array (FPGA), the matrix model of the Kalman filter is further derived into an algebraic model, which only contains sine, cosine, and basic algebraic operations. Compared to the arctangent method, the proposed method has noise suppression capability, and compared to the conventional phase-locked loop (PLL) method, the proposed method has better dynamic performance without the acceleration-associated phase error. Both simulation and experimental results can prove the effectiveness of the proposed method.