Learning a potential function from a trajectory

December, 2006
Report Number: 
David R. Brillinger

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 model for the potential function which leads to a stochastic differential equation. The method is simple, direct and flexible being based on a linear model and least squares. The estimated potential function may be used for: simple description, summary, comparison, seeking patterns, simulation, prediction, and model appraisal. Explanatories, attractors and repellors, may be included in the potential function directly. The large sample distribution of the estimated potential function is provided. There is an example analyzing the path of an elk. There are direct extensions to: updating, sliding window, adaptive, robust and real time variants. equation, stochastic gradient system, surveillance, tracking, waypoint data.

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