This paper proposes a new approach for the joint processing of signal detection and channel estimation based on the expectation-maximization (EM) algorithm in orthogonal frequency division multiplexing (OFDM) mobile communications. Conventional schemes based on the EM algorithm estimate a channel impulse response using Kalman filter, and employ the random walk model or the first-order autoregressive (AR) model to derive the process equation for the filter. Since these models assume that the time-variation of the impulse response is white noise without considering any autocorrelation property, the accuracy of the channel estimation deteriorates under fast-fading conditions, resulting in an increased packet error rate (PER). To improve the accuracy of the estimation of fast-fading channels, the proposed scheme employs a differential model that allows the correlated time-variation to be considered by introducing the first- and higher-order time differentials of the channel impulse response. In addition, this paper derives a forward recursive form of the channel estimation along both the frequency and time axes in order to reduce the computational complexity. Computer simulations of channels under fast multipath fading conditions demonstrate that the proposed method is superior in PER to the conventional schemes that employ the random walk model.