Particle Filters for Infinite (or Large) Dimensional State Spaces-Part 2

Vaswani, Namrata

doi:10.1109/icassp.2006.1660583

Cited by 14 publications

(19 citation statements)

References 17 publications

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“…The effective basis may be fixed or time varying. This is the "large dimensional state spaces (or LDSS)" property, introduced in [17], [19], applied to deforming contours. In other words, the deformation "signal" is approximately bandlimited (spatially), with the approximate cut-off frequency being much smaller than the maximum measurable frequency, 0.5Hz.…”

Section: A Main Ideamentioning

confidence: 99%

“…Using the LDSS property, we proposed to modify the PF method to perform sequential importance sampling [2] only on the effective basis dimensions, while replacing it with deterministic mode tracking (MT) in residual space [17], [19]. In this work, we develop the PF-MT idea for contour tracking using global translation and deformation velocity at subsampled contour locations interpolated using a B-spline basis as the effective basis.…”

Section: A Main Ideamentioning

confidence: 99%

“…But it requires that a part of the state have a linear Gaussian state space model. PFs with time-varying dimension have been used in other contexts cited in [19].…”

Section: A Main Ideamentioning

confidence: 99%

“…When changing K while tracking, one also needs to deal with errors in estimating K, for e.g. using the ideas introduced in [19]. A very important implementation issue is the choice of observation models and the use of efficient resampling techniques [3], for large dimensional problems.…”

Section: Conclusion and Open Issuesmentioning

confidence: 99%

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Time-varying Finite Dimensional Basis for Tracking Contour Deformations

Vaswani

Yezz

Rathi

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-We consider the problem of tracking the boundary contour of a moving and deforming object from a sequence of images. If the motion of the "object" or region of interest is constrained (e.g. rigid or approximately rigid), the contour motion can be efficiently represented by a small number of parameters, e.g. the affine group. But if the "object" is arbitrarily deforming, each contour point can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters for large dimensional problems is impractical, due to the reduction in effective particle size as dimension increases. But in most real problems, at any given time, "most of the contour deformation" occurs in a small number of dimensions ("effective basis") while the residual deformation in the rest of the state space ("residual space") is "small". The effective basis may be fixed or time varying. Based on this assumption, we modify the particle filtering method to perform sequential importance sampling only on the effective basis dimensions, while replacing it with deterministic mode tracking in residual space (PF-MT). We develop the PF-MT idea for contour tracking. Techniques for detecting effective basis dimension change and estimating the new effective basis are presented. Tracking results on simulated and real sequences are shown and compared with past work.

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Section: A Main Ideamentioning

confidence: 99%

Section: A Main Ideamentioning

confidence: 99%

“…But it requires that a part of the state have a linear Gaussian state space model. PFs with time-varying dimension have been used in other contexts cited in [19].…”

Section: A Main Ideamentioning

confidence: 99%

Section: Conclusion and Open Issuesmentioning

confidence: 99%

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Time-varying Finite Dimensional Basis for Tracking Contour Deformations

Vaswani

Yezz

Rathi

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…The main idea of MT was first introduced by us in [29] and first generalized in [2], [35], and [1]. The work of [36] which proposes a "PF using gradient proposal" is related to [29].…”

Section: Relation To Existing Workmentioning

confidence: 99%

Particle Filtering for Large-Dimensional State Spaces With Multimodal Observation Likelihoods

Vaswani

2008

IEEE Trans. Signal Process.

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Abstract-We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavy-tailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector.Sufficient conditions to test for the unimodality of this conditional posterior are derived. Our result is directly extendable to testing for unimodality of any posterior.The number of particles N to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. But in most such problems, most of the state change occurs in only a few dimensions, while the change in the rest of the dimensions is small. Using this property, we propose to replace importance sampling from a large part of the state space (whose conditional posterior is narrow enough) by just tracking the mode of the conditional posterior. This introduces some extra error, but it also greatly reduces the importance sampling dimension. The net effect is much smaller error for a given N, especially when the available N is small. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have nonnegligible failure probabilities. Improved performance of our proposed algorithms over existing PFs is demonstrated for this problem.Index Terms-Importance sampling for multimodal posteriors, large dimensional sequential state estimation, particle filtering, posterior mode tracking, tracking spatially varying physical quantities.

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Parallel Subspace Sampling for Particle Filtering in Dynamic Bayesian Networks

Besada-Portas

Plis

Cruz

et al. 2009

Machine Learning and Knowledge Discovery in Databases

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Abstract. Monitoring the variables of real world dynamic systems is a difficult task due to their inherent complexity and uncertainty. Particle Filters (PF) perform that task, yielding probability distribution over the unobserved variables. However, they suffer from the curse of dimensionality problem: the number of particles grows exponentially with the dimensionality of the hidden state space. The problem is aggravated when the initial distribution of the variables is not well known, as happens in global localization problems. We present a new parallel PF for systems whose variable dependencies can be factored into a Dynamic Bayesian Network. The new algorithms significantly reduce the number of particles, while independently exploring different subspaces of hidden variables to build particles consistent with past history and measurements. We demonstrate this new PF approach on some complex dynamical system estimation problems, showing that our method successfully localizes and tracks hidden states in cases where traditional PFs fail.

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Particle Filters for Infinite (or Large) Dimensional State Spaces-Part 2

Cited by 14 publications

References 17 publications

Time-varying Finite Dimensional Basis for Tracking Contour Deformations

Time-varying Finite Dimensional Basis for Tracking Contour Deformations

Particle Filtering for Large-Dimensional State Spaces With Multimodal Observation Likelihoods

Parallel Subspace Sampling for Particle Filtering in Dynamic Bayesian Networks

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