(Georgia Institute of Technology, 2008)
Oh, Sang Min; Rehg, James M.; Balch, Tucker; Dellaert, Frank
Switching Linear Dynamic System (SLDS) models are a popular technique for modeling complex nonlinear dynamic
systems. An SLDS provides the possibility to describe complex temporal patterns more concisely and accurately than an
HMM by using continuous hidden states. However, the use of SLDS models in practical applications is challenging for
several reasons. First, exact inference in SLDS models is computationally intractable. Second, the geometric duration model
induced in standard SLDSs limits their representational power. Third, standard SLDSs do not provide a systematic way to
robustly interpret systematic variations governed by higher order parameters.
The contributions in this paper address all three challenges above. First, we present a data-driven MCMC sampling
method for SLDSs as a robust and efficient approximate inference method. Second, we present segmental switching linear
dynamic systems (S-SLDS), where the geometric distributions are replaced with arbitrary duration models. Third, we extend
the standard model with a parametric model that can capture systematic temporal and spatial variations. The resulting
parametric SLDS model (P-SLDS) uses EM to robustly interpret parametrized motions by incorporating additional global
parameters that underly systematic variations of the overall motion.
The overall development of the proposed inference methods and extensions for SLDSs provide a robust framework to
interpret complex motions. The framework is applied to the honey bee dance interpretation task in the context of the on-going
BioTracking project at Georgia Institute of Technology. The experimental results suggest that the enhanced models provide
an effective framework for a wide range of motion analysis applications.
(Georgia Institute of Technology, 2006-12)
Khan, Zia; Balch, Tucker; Dellaert, Frank
In several multitarget tracking applications, a target may return more than one measurement per target and interacting
targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially
applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for
interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in
this model using a Markov chain Monte Carlo (MCMC)-based auxiliary variable particle filter. We Rao-Blackwellize the Markov chain to
eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares
updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when
combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include
experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video,
and laser range data. We also show the algorithm exhibits real time performance on a conventional PC.