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This paper proposes to analyze a real-time signal processing algorithm for on-line velocity measurement of a moving target, with a laser sensor using optical feedback interferometry. This velocity is based on an accurate estimation of the Doppler frequency from a spectral analysis of the laser diode output signal. This study takes into account both main causes of disrupting noises: additive noise and multiplicative noise caused by the speckle effect. A very simple expression is given for the Doppler frequency estimation bias based on an autoregressive spectral analysis method intensive Monte Carlo simulations, which are compared with experimental results, show that relative bias and standard deviations of about 0.1% and 0.5% respectively can be obtained for a wide range of velocities.