Dynamical model parameters from ultrasound tongue kinematics

A common approach is to cast this problem in terms of a dynamical system with point attractor dynamics, where a small number of parameters drive the vocal tract to a stable equilibrium position (Browman and Goldstein, 1986; Fowler, 1980; Gafos, 2006; Saltzman and Munhall, 1989; Tilsen, 2016). A standard model in this framework is the linear harmonic oscillator, m x + b x + kx = 0 (1) where m is mass (typically m = 1), k is a stiffness coefficient, and b is a damping coefficient, usually set to critically damped b = 2 mk. Gestural activation can be governed by step activation, with gestural parameters changing instantaneously at the point of activation and remaining constant over the activation interval. In this study we focus on whether the parameters of a linear harmonic oscillator can be estimated from ultrasound tongue imaging data, which we compare with the more common method of fitting to electromagnetic articulography (EMA) data. A major barrier to this goal is that the linear harmonic oscillator is known to be a poor fit to empirical articulatory trajectories, as it predicts overly short time-to-peak velocity, meaning that it is inappropriate for evaluating how the model can fit different data modalities. There are three common solutions to this issue. The first allows gestural activation to vary over time (Byrd and Saltzman, 1998), which adds extrinsic complexity to the model. The second is a nonlinear model, such as adding a cubic term to the linear model (Kirkham, 2025b; 2 Sorensen and Gafos, 2016), or novel nonlinear models (Stern and Shaw, 2025). The third is to abandon oscillatory models and develop new time-dependent (i.e.