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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.
A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
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Cited by 10 (1 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Multirate signal processing
 Real and Silicon Ears,” Johns Hopkins APL Tech. Dig
, 1993
"... delaytolerant particle filtering through selective ..."
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Cited by 5 (0 self)
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delaytolerant particle filtering through selective
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.
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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[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.
ADAPTIVE STOPPING FOR FAST PARTICLE SMOOTHING
"... Particle smoothing is useful for offline state inference and parameter learning in nonlinear/nonGaussian statespace models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles ..."
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Cited by 1 (1 self)
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Particle smoothing is useful for offline state inference and parameter learning in nonlinear/nonGaussian statespace models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejectionsamplingbased FFBS (RSFFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RSFFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RSFFBS. Index Terms — Sequential Monte Carlo, particle smoothing, backward simulation. 1.
Keywords Sequential Monte Carlo · Twofilter smoothing · State–space models ·
"... Abstract Twofilter smoothing is a principled approach for performing optimal smoothing in nonlinear nonGaussian state–space models where the smoothing distributions are computed through the combination of ‘forward ’ and ‘backward ’ time filters. The ‘forward ’ filter is the standard Bayesian filt ..."
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Abstract Twofilter smoothing is a principled approach for performing optimal smoothing in nonlinear nonGaussian state–space models where the smoothing distributions are computed through the combination of ‘forward ’ and ‘backward ’ time filters. The ‘forward ’ filter is the standard Bayesian filter but the ‘backward ’ filter, generally referred to as the backward information filter, is not a probability measure on the space of the hidden Markov process. In cases where the backward information filter can be computed in closed form, this technical point is not important. However, for general state–space models where there is no closed form expression, this prohibits the use of flexible numerical techniques such as Sequential Monte Carlo (SMC) to approximate the twofilter smoothing formula. We propose here a generalised twofilter smoothing formula which only requires approximating probability distributions and applies to any state–space model, removing the need to make restrictive assumptions used in previous approaches to this problem. SMC algorithms are developed to implement this generalised recursion and we illustrate their performance on various problems.
AUTOMATIC CONTROL
, 2011
"... Technical reports from the Automatic Control group in Linköping are available from ..."
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Technical reports from the Automatic Control group in Linköping are available from
Smoothing Algorithms for the Probability Hypothesis Density Filter
, 2010
"... The probability hypothesis density (PHD) filter is a recursive algorithm for solving multitarget tracking problems. The method consists of replacing the expectation of a random variable used in the traditional Bayesian filtering equations, by taking generalized expectations using the random sets fo ..."
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The probability hypothesis density (PHD) filter is a recursive algorithm for solving multitarget tracking problems. The method consists of replacing the expectation of a random variable used in the traditional Bayesian filtering equations, by taking generalized expectations using the random sets formalism. In this approach, a set of observations is used to estimate the state of multiple and unknown number of targets. However, since the observations does not contains all information required to infer the multitarget state, the PHD filter is constructed upon several approximations that diminishes the underlying combinatorial problem. More specifically, the PHD filter is a firstorder moment approximation to a full posterior density, so there is an inherent loss of information. In dynamic estimation problems, smoothing is used gather more information about the system state in order to improve the error of