An adaptive per-survivor processing maximum likelihood sequence estimation (PSP-MLSE) using state-space based recursive least-squares (RLS) is proposed for rapidly time varying multi-path fading channels. Unlike PSP-MLSE using Kalman filtering, it does not require the knowledge of model statistics, and with an aid of state-space modeling, it has a robust performance to the fade rate, compared to PSP-MLSE using conventional RLS.