Millimeter wave (mmWave) is an attractive option for high data rate applications. Enabling mmWave communications requires appropriate beamforming, which is conventionally realized by a lengthy beam training process. Such beam training will be a challenge for applying mmWave to mobile environments. As a solution, a beam tracking method requiring to train only one beam pair to track a path in the analog beamforming architecture is developed. Considering its low complexity which is suitable for mobile settings, the extended Kalman filter is chosen as the tracking filter. Several effects impacting the performance of the proposed tracking algorithm, such as the signal-to-noise ratio (SNR) and array size, are investigated. It is found that at the same SNR, narrower beams, which are more sensitive to angular changes, can provide more accurate estimates. Too narrow beams, however, degrade tracking performance because beam misalignment could happen during the measurement. Finally, a comparison to prior work is given where it is shown that our approach is more suitable for fast-changing environments thanks to the low measurement overhead.