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In this paper, we introduce a novel pilot-aided channel estimation method for multicarrier systems operating in doubly-selective fading scenarios. The method makes use of Bernstein basis polynomials (BBP) for capturing the time variation of the channel. By representing the channel in terms of basis functions, we need to track only the slowly varying basis expansion coefficients instead of the actual channel impulse response. These basis expansion coefficients are tracked via Kalman filtering approach by assuming an autoregressive (AR) model for basis expansion model (BEM) coefficients. Simulation studies demonstrate that the BBP with Kalman tracking gives excellent performance even at high mobile velocities.