Based on the assumption of continuous fading, a multiple symbol differential approximate automatic sphere decoding (MSDAASD) algorithm was developed by incorporating a recursive form of an approximate maximum-likelihood (ML) metric into automatic sphere decoding. The proposed algorithm is suitable for arbitrary unitary constellations and eliminates the error floor caused by in multiple symbol differential sphere decoding (MSDSD) with quasi-static channel assumption. Compared with decision-feedback detection under the same assumption, MSDAASD achieves similar performance of ML detection with much lower complexity at moderate to high signal-to-noise ratios.