7,499 research outputs found
Joint Probabilistic Data Association-Feedback Particle Filter for Multiple Target Tracking Applications
This paper introduces a novel feedback-control based particle filter for the
solution of the filtering problem with data association uncertainty. The
particle filter is referred to as the joint probabilistic data
association-feedback particle filter (JPDA-FPF). The JPDA-FPF is based on the
feedback particle filter introduced in our earlier papers. The remarkable
conclusion of our paper is that the JPDA-FPF algorithm retains the innovation
error-based feedback structure of the feedback particle filter, even with data
association uncertainty in the general nonlinear case. The theoretical results
are illustrated with the aid of two numerical example problems drawn from
multiple target tracking applications.Comment: In Proc. of the 2012 American Control Conferenc
Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality
Approximating adequate number of clusters in multidimensional data is an open
area of research, given a level of compromise made on the quality of acceptable
results. The manuscript addresses the issue by formulating a transductive
inductive learning algorithm which uses multivariate Chebyshev inequality.
Considering clustering problem in imaging, theoretical proofs for a particular
level of compromise are derived to show the convergence of the reconstruction
error to a finite value with increasing (a) number of unseen examples and (b)
the number of clusters, respectively. Upper bounds for these error rates are
also proved. Non-parametric estimates of these error from a random sample of
sequences empirically point to a stable number of clusters. Lastly, the
generalization of algorithm can be applied to multidimensional data sets from
different fields.Comment: 16 pages, 5 figure
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