Per-survivor processing (PSP) is now seen as an attractive approach to performing maximum-likelihood sequence estimation (MLSE) over mobile radio channels that are rapidly time varying. An optimal PSP strategy incorporates statistical channel modeling and Kalman filtering. For severely time-dispersive channels, this approach becomes prohibitively complex. A novel filtering algorithm is presented to approximate Kalman PSP. MLSE with the new scheme offers a large reduction in computational complexity, and achieves performance close to the optimal Kalman approach and superior to existing PSP schemes in rapidly fading channels. The exact expressions presented for the pairwise error probability of MLSE with Kalman PSP may be used to predict the detector performance without resorting to lengthly simulations.