AbstractSuperior tracking performance for fast fading mobile radio channels is obtained by extending channel models used in the adaptive recursive least squares maximum likelihood sequence estimation (RLS‐MLSE) derived from the theory of maximum likelihood signal estimation. Conventional adaptive maximum likelihood sequence estimators used the simple Markov model or random walk model to describe fluctuations of the impulse response of a frequency‐selective fading channel.In this paper, a second‐order Markov model that incorporates the first‐order time derivative of the impulse response is used. This higher‐order state variable approach improves the adaptability of the channel estimation algorithm and gives a significant improvement in signal transmission performance. Computer simulations show that the RLS‐MLSE based on this higher‐order state variable model yields good performance of 40 kbit/s QPSK with the maximum Doppler frequency up to 160 Hz.