Real-time FPGA-based Kalman filter for constant and non-constant velocity periodic error correction

Displacement measuring interferometry has high resolution and high dynamic range, which is widely used in displacement metrology and sensor calibration. Due to beam leakage in the interferometer, imperfect polarization components, and ghost reflections, the displacement measurement suffers from periodic error, whose pitch is multiple harmonics of the Doppler frequency. In dynamic measurements, periodic error is usually on the order of nanometers, which impacts the dynamic measurement accuracy. This paper presents an approach to estimate and correct periodic error in real time based on an extended Kalman filter, which has the capability to deal with both constant and non-constant velocity motions. This algorithm is implemented on an application-specific hardware architecture in an FPGA, which has advantages in throughput and resource usage compared with conventional implementations. The measurement validation shows that this approach can effectively eliminate the periodic error for both constant and non-constant velocity motion, and the residual error reaches to the level of the background noise of the interferometer.