In this paper we present a technique for obtaining Vocal Tract (VT) time functions from the acoustic speech signal. Knowledge-based Acoustic Parameters (APs) are extracted from the speech signal and a pertinent subset is used to obtain the mapping between them and the VT time functions. Eight different vocal tract constriction variables consisting of live constriction degree variables,. lip aperture (LA), tongue body (TBCD), tongue tip (TTCD), velum (VEL), and glottis (GLO); and three constriction location variables, lip protrusion (LP), tongue tip (TTCL), tongue body (TBCL) were considered in this study. The TAsk Dynamics Application model (TADA ) is used to create a synthetic speech dataset along with its corresponding VT time functions. We explore Support Vector Regression (SVR) followed by Kalman smoothing to achieve mapping between the APs and the VT time functions.