A discrete fringe phase unwrapping algorithm (DFPUA) based on Kalman motion estimation is proposed to accurately demodulate the phases of I/Q-interferometers with deeply under-sampled quadrature signals, thus to break through the limitations of the Nyquist frequency for high-speed measurement. The basic concept of DFPUA is to estimate the current displacement according to the former motion state, then confirm the actual phase integer number by comparing the estimated phase decimal with the actual phase decimal; in this way, peak acceleration/jerk instead of peak velocity becomes the factor that determines the sampling rate. Two types of DFPUA including velocity estimation and velocity-acceleration estimation are illustrated in detail. Simulation experiment results indicate that the DFPUA realizes a significant reduction in the sampling rate and the amount of data for low frequency vibration measurement, proposing a practical approach for high-speed and long-time measurement such as ultra-low frequency vibration calibration.
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