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The statistics of the diffusive motion of particles often serve as anexperimental proxy for their interaction with the environment. However,inferring the physical properties from the observed trajectories ischallenging. Inspired by a recent experiment, here we analyze the problem ofparticles undergoing two-dimensional Brownian motion with transient tetheringto the surface. We model the problem as a Hidden Markov Model where thephysical position is observed, and the tethering state is hidden. We develop analternating maximization algorithm to infer the hidden state of the particleand estimate the physical parameters of the system. The crux of our method is asaddle-point-like approximation, which involves finding the most likelysequence of hidden states and estimating the physical parameters from it.Extensive numerical tests demonstrate that our algorithm reliably finds themodel parameters, and is insensitive to the initial guess. We discuss thedifferent regimes of physical parameters and the algorithm's performance inthese regimes. We also provide a ready-to-use open source implementation of ouralgorithm.

Hidden Markov modeling of single particle diffusion with stochastic tethering