Range-based positioning by estimating the time of arrival (ToA) of the line-of-sight (LoS) path using orthogonal frequency-division multiplexing (OFDM) signals has gained remarkable attention. Multipath propagation significantly influences the ToA estimate, resulting in position errors. To mitigate these errors, the multipath channel needs to be accurately estimated, usually with a large number of known pilot symbols. A tradeoff between the data rate and the multipath channel estimation performance must be made for joint communication and positioning applications. This paper proposes a semiblind range tracking algorithm, which allows the reduction of the required number of pilot symbols significantly. For moving receivers, the algorithm needs, only in the beginning, an OFDM symbol with known pilot symbols, which increases the data rate dramatically. Instead of tracking the complex amplitude of individual subcarriers, the proposed algorithm directly tracks the multipath channel parameters, including the complex amplitude, delay, and angle of arrival (AoA) of individual multipath components. The estimated delay of the first arrived path, i.e., its ToA, is used to calculate the range between the transmitter and receiver antennas. Evaluations of the algorithm are provided by simulations in an artificial scenario and using channel sounder measurement data. The results show that the proposed tracking algorithm can effectively track the range between transmitter and receiver and detect the data.