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43
ON THE USE OF BACKWARD SIMULATION IN THE PARTICLE GIBBS SAMPLER
"... The particle Gibbs (PG) sampler was introduced in [1] as a way to incorporate a particle filter (PF) in a Markov chain Monte Carlo (MCMC) sampler. The resulting method was shown to be an efficient tool for joint Bayesian parameter and state inference in nonlinear, nonGaussian statespace models. Ho ..."
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Cited by 11 (7 self)
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The particle Gibbs (PG) sampler was introduced in [1] as a way to incorporate a particle filter (PF) in a Markov chain Monte Carlo (MCMC) sampler. The resulting method was shown to be an efficient tool for joint Bayesian parameter and state inference in nonlinear, nonGaussian statespace models. However, the mixing of the PG kernel can be very poor when there is severe degeneracy in the PF. Hence, the success of the PG sampler heavily relies on the, often unrealistic, assumption that we can implement a PF without suffering from any considerate degeneracy. However, as pointed out by Whiteley [2] in the discussion following [1], the mixing can be improved by adding a backward simulation step to the PG sampler. Here, we investigate this further, derive an explicit PG sampler with backward simulation (denoted PGBSi) and show that this indeed is a valid MCMC method. Furthermore, we show in a numerical example that backward simulation can lead to a considerable increase in performance over the standard PG sampler. Index Terms — Particle Markov chain Monte Carlo, particle filter, particle Gibbs, backward simulation, Gibbs sampling.
Bayesian semiparametric Wiener system identification
, 2013
"... We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a statespace model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We av ..."
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Cited by 10 (7 self)
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We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a statespace model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problemspecific parameterizations. We also consider sparsitypromoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.
A Novel Sequential Monte Carlo Approach for Extended Object Tracking Based on Border
"... Abstract—Extended objects are characterised with multiple measurements originated from different locations of the object surface. This paper presents a novel Sequential Monte Carlo (SMC) approach for extended object tracking based on border parametrisation. The problem is formulated for general nonl ..."
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Cited by 7 (3 self)
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Abstract—Extended objects are characterised with multiple measurements originated from different locations of the object surface. This paper presents a novel Sequential Monte Carlo (SMC) approach for extended object tracking based on border parametrisation. The problem is formulated for general nonlinear problems. The main contribution of this work is in the derivation of the likelihood function for nonlinear measurement functions, with sets of measurements belonging to a bounded region. Simulation results are presented when the object is surrounded by a circular region. Accurate estimation results are presented both for the object kinematic state and object extent. Index Terms—sequential Monte Carlo methods, measurement uncertainty, nonlinear estimation
Bayesian inference and learning in Gaussian process statespace models with particle MCMC
 In Advances in Neural Information Processing Systems (NIPS
, 2013
"... Statespace models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric statespace models. We ..."
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Cited by 7 (3 self)
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Statespace models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric statespace models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity. 1
RaoBlackwellized particle smoothers for mixed linear/nonlinear statespace models
, 2011
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A bimodal sound source model for vehicle tracking in traffic monitoring
 in Proceedings of the 19 th European Signal Processing Conference (EUSIPCO
, 2011
"... The paper addresses road traffic monitoring using a compact microphone array. More precisely, estimation of both speed and wheelbase distance of detected vehicles is performed. The detection algorithm is based on the comparison between theoretical and measured correlation time series using the two d ..."
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Cited by 4 (4 self)
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The paper addresses road traffic monitoring using a compact microphone array. More precisely, estimation of both speed and wheelbase distance of detected vehicles is performed. The detection algorithm is based on the comparison between theoretical and measured correlation time series using the two dimensional BravaisPearson correlation coefficient. The tracking step is conducted with a particle filter specifically designed to model the positionvariant bimodal sound source nature of the vehicles, i.e. taking into account the sound emitted by both vehicle axles. Sensitivity and performance studies using simulations and real measurements show that the bimodal approach reduces the tracking failure risk in harsh conditions when vehicles are tracked, at the same time, in opposite directions. 1.
Article Road Target Search and Tracking with Gimballed Vision Sensor on an Unmanned Aerial Vehicle
, 2012
"... Abstract: This article considers a sensor management problem where a number of road bounded vehicles are monitored by an unmanned aerial vehicle (UAV) with a gimballed vision sensor. The problem is to keep track of all discovered targets and simultaneously search for new targets by controlling the p ..."
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Abstract: This article considers a sensor management problem where a number of road bounded vehicles are monitored by an unmanned aerial vehicle (UAV) with a gimballed vision sensor. The problem is to keep track of all discovered targets and simultaneously search for new targets by controlling the pointing direction of the vision sensor and the motion of the UAV. A planner based on a statemachine is proposed with three different modes; target tracking, known target search, and new target search. A highlevel decision maker chooses among these subtasks to obtain an overall situational awareness. A utility measure for evaluating the combined search and target tracking performance is also proposed. By using this measure it is possible to evaluate and compare the rewards of updating known targets versus searching for new targets in the same framework. The targets are assumed to be road bounded and the road network information is used both to improve the tracking and sensor management performance. The tracking and search are based on flexible target density representations provided by particle mixtures and deterministic grids.
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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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.
Identification of Gaussian Process StateSpace Models with Particle Stochastic Approximation EM
"... Abstract: Gaussian process statespace models (GPSSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper)parameters governing the properties of this nonparametric representa ..."
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Cited by 3 (1 self)
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Abstract: Gaussian process statespace models (GPSSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper)parameters governing the properties of this nonparametric representation. The Bayesian formalism enables systematic reasoning about the uncertainty in the system dynamics. We present an approach to maximum likelihood identification of the parameters in GPSSMs, while retaining the full nonparametric description of the dynamics. The method is based on a stochastic approximation version of the EM algorithm that employs recent developments in particle Markov chain Monte Carlo for efficient identification.
PARTICLE METROPOLIS HASTINGS USING LANGEVIN DYNAMICS
"... Particle Markov Chain Monte Carlo (PMCMC) samplers allow for routine inference of parameters and states in challenging nonlinear problems. A common choice for the parameter proposal is a simple random walk sampler, which can scale poorly with the number of parameters. In this paper, we propose to us ..."
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Particle Markov Chain Monte Carlo (PMCMC) samplers allow for routine inference of parameters and states in challenging nonlinear problems. A common choice for the parameter proposal is a simple random walk sampler, which can scale poorly with the number of parameters. In this paper, we propose to use loglikelihood gradients, i.e. the score, in the construction of the proposal, akin to the Langevin Monte Carlo method, but adapted to the PMCMC framework. This can be thought of as a way to guide a random walk proposal by using drift terms that are proportional to the score function. The method is successfully applied to a stochastic volatility model and the drift term exhibits intuitive behaviour.