We present an analysis of the publicly available HARPS radial velocity (RV) measurements for Alpha Cen B, a star hosting an Earth-mass planet candidate in a 3.24 day orbit. The goal is to devise robust ways of extracting low-amplitude RV signals of low mass planets in the presence of activity noise. Two approaches were used to remove the stellar activity signal which dominates the RV variations: 1) Fourier component analysis (pre-whitening), and 2) local trend filtering (LTF) of the activity using short time windows of the data. The Fourier procedure results in a signal at P = 3.236 days and K = 0.42 m/s which is consistent with the presence of an Earth-mass planet, but the false alarm probability for this signal is rather high at a few percent. The LTF results in no significant detection of the planet signal, although it is possible to detect a marginal planet signal with this method using a different choice of time windows and fitting functions. However, even in this case the significance of the 3.24-d signal depends on the details of how a time window containing only 10% of the data is filtered. Both methods should have detected the presence of Alpha Cen Bb at a higher significance than is actually seen. We also investigated the influence of random noise with a standard deviation comparable to the HARPS data and sampled in the same way. The distribution of the noise peaks in the period range 2.8 - 3.3 days have a maximum of approximately 3.2 days and amplitudes approximately one-half of the K-amplitude for the planet. The presence of the activity signal may boost the velocity amplitude of these signals to values comparable to the planet. It may be premature to attribute the 3.24 day RV variations to an Earth-mass planet. A better understanding of the noise characteristics in the RV data as well as more measurements with better sampling will be needed to confirm this exoplanet.
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