  In parallel with advances in microscale imaging techniques, the fields of
biology and materials science have focused on precisely extracting particle
properties based on their diffusion behavior. Although the majority of
real-world particles exhibit anisotropy, their behavior has been studied less
than that of isotropic particles. In this study, we introduce a new method for
estimating the diffusion coefficients of individual anisotropic particles using
short-trajectory data on the basis of a maximum likelihood framework.
Traditional estimation techniques often use mean-squared displacement (MSD)
values or other statistical measures that inherently remove angular
information. Instead, we treated the angle as a latent variable and used belief
propagation to estimate it while maximizing the likelihood using the
expectation-maximization algorithm. Compared to conventional methods, this
approach facilitates better estimation of shorter trajectories and faster
rotations, as confirmed by numerical simulations and experimental data
involving bacteria and quantum rods. Additionally, we performed an analytical
investigation of the limits of detectability of anisotropy and provided
guidelines for the experimental design. In addition to serving as a powerful
tool for analyzing complex systems, the proposed method will pave the way for
applying maximum likelihood methods to more complex diffusion phenomena.
