Learning a Potential Function From a Trajectory

This letter concerns the use of stochastic gradient systems in the modeling of the paths of moving particles and the consequent estimation of a potential function. The work proceeds by setting down a parametric or nonparametric model for the potential function. The method is simple, direct, and flexible, being based on a linear model and the least squares. Explanatories, attractors, and repellors may be included directly. The large sample distribution of the estimated potential function is provided, under specific assumptions. There are direct extensions to updating, sliding window, adaptive, robust, and real-time variants. An example analyzing the path of an elk is presented.