A new technique is proposed to improve the performance of differential detection (DD) of M-ary differential phase-shift keying (MDPSK) significantly, applying sequence estimation. In order to obtain an appropriate representation of the received signal, a nonlinear time-variant finite impulse response or infinite impulse response prediction-error filter is used. For both filter structures the optimum coefficients are derived, assuming transmission over an additive white Gaussian noise (AWGN) channel. Delayed decision-feedback sequence estimation (DDFSE) is employed to estimate the transmitted symbol sequence. It is shown by simulations that even for decision-feedback equalization, which is a simple special case of DDFSE, a significant performance improvement of conventional DD under AWGN conditions results. In contrast to other noncoherent low-complexity receivers proposed in literature, this receiver is very robust under flat fading (Rayleigh and Ricean) conditions.