This work concerns wireless cellular networks applying time division duplexing (TDD) massive multiple-input multiple-output (MIMO) technology. Such systems suffer from pilot contamination during channel estimation, due to the shortage of orthogonal pilot sequences. This paper presents a solution based on pilot sequence hopping, which provides a randomization of the pilot contamination. It is shown that such randomized contamination can be significantly suppressed through appropriate filtering. The resulting channel estimation scheme requires no inter-cell coordination, which is a strong advantage for practical implementations. Comparisons with conventional estimation methods show that the MSE can be lowered as much as an order of magnitude at low mobility. Achievable uplink and downlink rates are increased by 42 and 46%, respectively, in a system with 128 antennas at the base station.