Orthogonal time frequency space (OTFS) has shown to be a promising modulation technology that achieves the robust wireless transmission in high-mobility environments. The high mobility incurred Doppler effect in OTFS system, is represented as a continuous and relatively large band in the Doppler frequency. It yields the equivalent channel responses (ECRs) in the system change significantly within one symbol block, posing a challenge to channel estimation (CE) or tracking. In order to tackle this issue, in this paper, a set of transform-domain basis functions is designed to span a low-dimensional subspace for modeling the OTFS channel. Then, the CE can be performed by estimating a few projection coefficients of ECRs in the developed subspace, with training pilots. According to the individual transmission characteristic of OTFS signal, we propose a corner-inserted pilot pattern, which targets the low pilot overhead and satisfactory CE performance. Moreover, an OTFS signal detector, leveraging the time-domain channel equalization, linear-complexity interference cancellation and delay-Doppler domain maximal ratio combining detection, is developed to retrieve the transmitted data symbols. The simulations show the precisely estimated ECRs enable the detector to ideally demodulate 256-ary quadrature amplitude modulation signaling, under a velocity of 550 km/h at 5.9 GHz carrier frequency.