In orthogonal frequency-division multiplexing (OFDM) systems, parametric channel estimation-based algorithms are known to improve performance when the multipath is sparse in nature. Likewise, subspace-based techniques, that exploit the slowly-varying delay-subspace, are also known to improve the channel estimation performance. However, these methods assumed that the channel is constant over one or many OFDM symbols. In this letter, we present the parametric- and delay-subspace-based algorithms for channel estimation in scenarios where the channel is varying within an OFDM symbol duration. It is also shown that performance considerably improves, when these methods are used in conjunction with a Kalman-based channel-tracking algorithm.