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It is well-known that the performance of acoustic-to-articulatory inversion improves by smoothing the articulatory trajectories estimated using Gaussian mixture model (GMM) mapping (denoted by GMM + Smoothing). GMM + Smoothing also provides similar performance with GMM mapping using dynamic features, which integrates smoothing directly in the mapping criterion. Due to the separation between smoothing and mapping, what objective criterion GMM + Smoothing optimizes remains unclear. In this work a new integrated smoothness criterion, the smoothed-GMM (SGMM), is proposed. GMM + Smoothing is shown, both analytically and experimentally, to be identical to the asymptotic solution of SGMM suggesting GMM + Smoothing to be a near optimal solution of SGMM.


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