  Maintaining reliable millimeter wave (mmWave) connections to many fast-moving
mobiles is a key challenge in the theory and practice of 5G systems. In this
paper, we develop a new algorithm that can jointly track the beam direction and
channel coefficient of mmWave propagation paths using phased antenna arrays.
Despite the significant difficulty in this problem, our algorithm can
simultaneously achieve fast tracking speed, high tracking accuracy, and low
pilot overhead. In static scenarios, this algorithm can converge to the minimum
Cram\'er-Rao lower bound of beam direction with high probability. Simulations
reveal that this algorithm greatly outperforms several existing algorithms.
Even at SNRs as low as 5dB, our algorithm is capable of tracking a mobile
moving at an angular velocity of 5.45 degrees per second and achieving over
95\% of channel capacity with a 32-antenna phased array, by inserting only 10
pilots per second.
