31,303 research outputs found
Interacting Multiple Model-Feedback Particle Filter for Stochastic Hybrid Systems
In this paper, a novel feedback control-based particle filter algorithm for
the continuous-time stochastic hybrid system estimation problem is presented.
This particle filter is referred to as the interacting multiple model-feedback
particle filter (IMM-FPF), and is based on the recently developed feedback
particle filter. The IMM-FPF is comprised of a series of parallel FPFs, one for
each discrete mode, and an exact filter recursion for the mode association
probability. The proposed IMM-FPF represents a generalization of the
Kalmanfilter based IMM algorithm to the general nonlinear filtering problem.
The remarkable conclusion of this paper is that the IMM-FPF algorithm retains
the innovation error-based feedback structure even for the nonlinear problem.
The interaction/merging process is also handled via a control-based approach.
The theoretical results are illustrated with the aid of a numerical example
problem for a maneuvering target tracking application
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains
The number of neurons that can be simultaneously recorded doubles every seven
years. This ever increasing number of recorded neurons opens up the possibility
to address new questions and extract higher dimensional stimuli from the
recordings. Modeling neural spike trains as point processes, this task of
extracting dynamical signals from spike trains is commonly set in the context
of nonlinear filtering theory. Particle filter methods relying on importance
weights are generic algorithms that solve the filtering task numerically, but
exhibit a serious drawback when the problem dimensionality is high: they are
known to suffer from the 'curse of dimensionality' (COD), i.e. the number of
particles required for a certain performance scales exponentially with the
observable dimensions. Here, we first briefly review the theory on filtering
with point process observations in continuous time. Based on this theory, we
investigate both analytically and numerically the reason for the COD of
weighted particle filtering approaches: Similarly to particle filtering with
continuous-time observations, the COD with point-process observations is due to
the decay of effective number of particles, an effect that is stronger when the
number of observable dimensions increases. Given the success of unweighted
particle filtering approaches in overcoming the COD for continuous- time
observations, we introduce an unweighted particle filter for point-process
observations, the spike-based Neural Particle Filter (sNPF), and show that it
exhibits a similar favorable scaling as the number of dimensions grows.
Further, we derive rules for the parameters of the sNPF from a maximum
likelihood approach learning. We finally employ a simple decoding task to
illustrate the capabilities of the sNPF and to highlight one possible future
application of our inference and learning algorithm
The Hitchhiker's Guide to Nonlinear Filtering
Nonlinear filtering is the problem of online estimation of a dynamic hidden
variable from incoming data and has vast applications in different fields,
ranging from engineering, machine learning, economic science and natural
sciences. We start our review of the theory on nonlinear filtering from the
simplest `filtering' task we can think of, namely static Bayesian inference.
From there we continue our journey through discrete-time models, which is
usually encountered in machine learning, and generalize to and further
emphasize continuous-time filtering theory. The idea of changing the
probability measure connects and elucidates several aspects of the theory, such
as the parallels between the discrete- and continuous-time problems and between
different observation models. Furthermore, it gives insight into the
construction of particle filtering algorithms. This tutorial is targeted at
scientists and engineers and should serve as an introduction to the main ideas
of nonlinear filtering, and as a segway to more advanced and specialized
literature.Comment: 64 page
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
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