The position-time trajectory of a biological subject moving in a complex environment contains rich information about how it interacts with the local setting. Whether the subject be an animal or an intracellular endosomal vesicle, the two primary modes of biological locomotion are directional movement and random walk, respectively characterized by velocity and diffusion coefficient. This contribution introduces a method to quantitatively divide a single-particle trajectory into segments that exhibit changes in the diffusion coefficient, velocity, or both. With the determination of these two physical parameters given by the maximum likelihood estimators, the relative precisions are given as explicit functions of the number of data points and total trajectory time. The method is based on rigorous statistical tests and does not require any presumed kinetics scheme. Results of extensive characterizations, extensions to 2D and 3D trajectories, and applications to common scenarios are also discussed.
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