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29
A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 72 (9 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Fast Particle Smoothing: If I Had a Million Particles
 In International Conference on Machine Learning (ICML
, 2006
"... We propose e#cient particle smoothing methods for generalized statespaces models. ..."
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Cited by 37 (5 self)
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We propose e#cient particle smoothing methods for generalized statespaces models.
A sequential smoothing algorithm with linear computational cost
, 2008
"... In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method ..."
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Cited by 16 (1 self)
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In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles). 1
System Identification of Nonlinear StateSpace Models
, 2009
"... This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient i ..."
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Cited by 13 (6 self)
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This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of socalled “particle smoothing” methods to compute required conditional expectations via a sequential Monte Carlo approach. Simulation examples demonstrate the efficacy of these techniques.
M.: Expectation propagation for inference in nonlinear dynamical models with Poisson observations
 In: Proc IEEE Nonlinear Statistical Signal Processing Workshop. (2006
"... Neural activity unfolding over time can be modeled using nonlinear dynamical systems [1]. As neurons communicate via discrete action potentials, their activity can be characterized by the numbers of events occurring within short predefined timebins (spike counts). Because the observed data are hig ..."
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Cited by 5 (2 self)
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Neural activity unfolding over time can be modeled using nonlinear dynamical systems [1]. As neurons communicate via discrete action potentials, their activity can be characterized by the numbers of events occurring within short predefined timebins (spike counts). Because the observed data are highdimensional vectors of nonnegative integers, nonlinear state estimation from spike counts presents a unique set of challenges. In this paper, we describe why the expectation propagation (EP) framework is particularly wellsuited to this problem. We then demonstrate ways to improve the robustness and accuracy of Gaussian quadraturebased EP. Compared to the unscented Kalman smoother, we find that EPbased state estimators provide more accurate state estimates. 1.
A BackwardSimulation Based RaoBlackwellized Particle Smoother for Conditionally Linear Gaussian Models
"... Abstract: In this article, we develop a new RaoBlackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forwardfiltering backwardsimulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space ..."
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Cited by 3 (2 self)
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Abstract: In this article, we develop a new RaoBlackwellized Monte Carlo smoothing algorithm for conditionally linear Gaussian models. The algorithm is based on the forwardfiltering backwardsimulation Monte Carlo smoother concept and performs the backward simulation directly in the marginal space of the nonGaussian state component while treating the linear part analytically. Unlike the previously proposed backwardsimulation based RaoBlackwellized smoothing approaches, it does not require sampling of the Gaussian state component and is also able to overcome certain normalization problems of twofilter smoother based approaches. The performance of the algorithm is illustrated in a simulated application.
Identification of Mixed Linear/Nonlinear StateSpace Models
"... Abstract — The primary contribution of this paper is an algorithm capable of identifying parameters in certain mixed linear/nonlinear statespace models, containing conditionally linear Gaussian substructures. More specifically, we employ the standard maximum likelihood framework and derive an expec ..."
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Cited by 2 (2 self)
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Abstract — The primary contribution of this paper is an algorithm capable of identifying parameters in certain mixed linear/nonlinear statespace models, containing conditionally linear Gaussian substructures. More specifically, we employ the standard maximum likelihood framework and derive an expectation maximization type algorithm. This involves a nonlinear smoothing problem for the state variables, which for the conditionally linear Gaussian system can be efficiently solved using a so called RaoBlackwellized particle smoother (RBPS). As a secondary contribution of this paper we extend an existing RBPS to be able to handle the fully interconnected model under study. I.
A NEW APPROACH TO PARTICLE BASED SMOOTHED MARGINAL MAP
"... We present here a new method of finding the MAP state estimator from the weighted particles representation of marginal smoother distribution. This is in contrast to the usual practice, where the particle with the highest weight is selected as the MAP, although the latter is not necessarily the most ..."
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Cited by 2 (2 self)
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We present here a new method of finding the MAP state estimator from the weighted particles representation of marginal smoother distribution. This is in contrast to the usual practice, where the particle with the highest weight is selected as the MAP, although the latter is not necessarily the most probable state estimate. The method developed here uses only particles with corresponding filtering and smoothing weights. We apply this estimator for finding the unknown initial state of a dynamical system and addressing the parameter estimation problem. 1.
Bayesian Learning in Nonlinear StateSpace Models
"... We describe Bayesian learning in nonlinear statespace models (NSSMs). NSSMs are a general method for the probabilistic modelling of sequences and timeseries. They take the form of iterated maps on continuous statespaces, and can have either discrete or continuous valued output functions. Th ..."
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Cited by 1 (0 self)
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We describe Bayesian learning in nonlinear statespace models (NSSMs). NSSMs are a general method for the probabilistic modelling of sequences and timeseries. They take the form of iterated maps on continuous statespaces, and can have either discrete or continuous valued output functions. They are generalizations of the more well known statespace models such as Hidden Markov models (HMMs), and LinearGaussian statespace models (LSSMs). In this paper, we describe the problems of Bayesian learning and inference and in NSSMs. We present an MCMC methods of sampling from the posterior of the parameters given observed data.
2012, Sequential Bayesian techniques applied to nonvolcanic tremor
 Journal of Geophysical Research
"... [1] This paper uses sequential Bayesian techniques such as particle filters and smoothers to track in time both the nonvolcanic tremor (NVT) source location on the plate interface and the angle of arrival via horizontal phase slowness. Sequential Bayesian techniques enable tracking of evolving geop ..."
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Cited by 1 (0 self)
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[1] This paper uses sequential Bayesian techniques such as particle filters and smoothers to track in time both the nonvolcanic tremor (NVT) source location on the plate interface and the angle of arrival via horizontal phase slowness. Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential tremor observations. These techniques provide a formulation where the geophysical parameters that characterize dynamic, nonstationary processes are continuously estimated as new data become available. In addition to the optimal solution, particle filters and smoothers can calculate the underlying probability densities for the desired parameters, providing the uncertainties in the estimates. The tremor tracking has been performed using array beamforming. Here it is demonstrated that the uncertainties both in the NVT source location estimates and phase slowness estimates are reduced using a particle filter compared to just using a beamformer based inversion. Particle smoothers further reduces the uncertainty, giving the best performance out of the three methods used here.