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Modeling a Hidden Dynamical System Using Energy Minimization and Kernel Density Estimates
In this paper we develop a kernel density estimation (KDE) approach to
modeling and forecasting recurrent trajectories on a compact manifold. For the
purposes of this paper, a trajectory is a sequence of coordinates in a phase
space defined by an underlying hidden dynamical system. Our work is inspired by
earlier work on the use of KDE to detect shipping anomalies using high-density,
high-quality automated information system (AIS) data as well as our own earlier
work in trajectory modeling. We focus specifically on the sparse, noisy
trajectory reconstruction problem in which the data are (i) sparsely sampled
and (ii) subject to an imperfect observer that introduces noise. Under certain
regularity assumptions, we show that the constructed estimator minimizes a
specific energy function defined over the trajectory as the number of samples
obtained grows.Comment: 16 pages, 8 figures, 3 tables Added additional experiments and
corrected notatio