Orthogonal frequency division multiplexing (OFDM) technique, when used in wireless environments, is known to be robust against frequency selective fading. However, when the channel shows time selective fading, rapid variations destroy the subcarrier orthogonality and introduce inter-carrier interference (ICI). The use of ICI mitigation schemes requires the availability of channel state information (CSI) at the receiver, which is a non-trivial task in fast fading systems. In our work, we have addressed the problem of estimation of rapidly varying channels for OFDM systems. The channel is modeled using complex exponentials as basis functions and the estimation process makes use of the cyclic prefix (CP) part available in OFDM symbols as training. The system is viewed as a state space model and Kalman filter is employed to estimate the channel. Following this, a time domain ICI mitigation filter that maximizes the received SINR (signal to interference plus noise ratio) is employed for equalization. This method performs considerably well in terms of MSE as well as BER at very high Doppler spreads.