121,372 research outputs found
A Box Regularized Particle Filter for state estimation with severely ambiguous and non-linear measurements
International audienceThe first stage in any control system is to be able to accurately estimate the system's state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems. Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error. Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, that of Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), Monte Carlo Markov Chain (MCMC), and the original Box Particle Filter (BPF). The algorithm outperforms existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty. The BRPF reduces the computational load by 73% and 90% for SIR-PF and MCMC, respectively, with similar RMSE values. This work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods.The first stage in any control system is to be able to accurately estimate the system’s state. However, some types of measurements are ambiguous (non-injective) in terms of state. Existing algorithms for such problems, such as Monte Carlo methods, are computationally expensive or not robust to such ambiguity. We propose the Box Regularized Particle Filter (BRPF) to resolve these problems.Based on previous works on box particle filters, we present a more generic and accurate formulation of the algorithm, with two innovations: a generalized box resampling step and a kernel smoothing method, which is shown to be optimal in terms of Mean Integrated Square Error.Monte Carlo simulations demonstrate the efficiency of BRPF on a severely ambiguous and non-linear estimation problem, the Terrain Aided Navigation. BRPF is compared to the Sequential Importance Resampling Particle Filter (SIR-PF), the Markov Chain Monte Carlo approach (MCMC), and the original Box Particle Filter (BPF). The algorithm is demonstrated to outperform existing methods in terms of Root Mean Square Error (e.g., improvement up to 42% in geographical position estimation with respect to the BPF) for a large initial uncertainty.The BRPF yields a computational load reduction of 73% with respect to the SIR-PF and of 90% with respect to MCMC for similar RMSE orders of magnitude. The present work offers an accurate (in terms of RMSE) and robust (in terms of divergence rate) way to tackle state estimation from ambiguous measurements while requiring a significantly lower computational load than classic Monte Carlo and particle filtering methods
An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models
Twisted particle filters are a class of sequential Monte Carlo methods
recently introduced by Whiteley and Lee to improve the efficiency of marginal
likelihood estimation in state-space models. The purpose of this article is to
extend the twisted particle filtering methodology, establish accessible
theoretical results which convey its rationale, and provide a demonstration of
its practical performance within particle Markov chain Monte Carlo for
estimating static model parameters. We derive twisted particle filters that
incorporate systematic or multinomial resampling and information from
historical particle states, and a transparent proof which identifies the
optimal algorithm for marginal likelihood estimation. We demonstrate how to
approximate the optimal algorithm for nonlinear state-space models with
Gaussian noise and we apply such approximations to two examples: a range and
bearing tracking problem and an indoor positioning problem with Bluetooth
signal strength measurements. We demonstrate improvements over standard
algorithms in terms of variance of marginal likelihood estimates and Markov
chain autocorrelation for given CPU time, and improved tracking performance
using estimated parameters.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
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Bandwidth Selection for Multivariate Kernel Density Estimation Using MCMC
Kernel density estimation for multivariate data is an important technique that has a wide range of applications in econometrics and finance. However, it has received significantly less attention than its univariate counterpart. The lower level of interest in multivariate kernel density estimation is mainly due to the increased difficulty in deriving an optimal data-driven bandwidth as the dimension of data increases. We provide Markov chain Monte Carlo (MCMC) algorithms for estimating optimal bandwidth matrices for multivariate kernel density estimation. Our approach is based on treating the elements of the bandwidth matrix as parameters whose posterior density can be obtained through the likelihood cross-validation criterion. Numerical studies for bivariate data show that the MCMC algorithm generally performs better than the plug-in algorithm under the Kullback-Leibler information criterion, and is as good as the plug-in algorithm under the mean integrated squared errors (MISE) criterion. Numerical studies for 5 dimensional data show that our algorithm is superior to the normal reference rule. Our MCMC algorithm is the first data-driven bandwidth selector for kernel density estimation with more than two variables, and the sampling algorithm involves no increased difficulty as the dimension of data increaseBandwidth matrices; Cross-validation; Kullback-Leibler information; mean integrated squared errors; Sampling algorithms.
Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
In this article we develop a new sequential Monte Carlo (SMC) method for
multilevel (ML) Monte Carlo estimation. In particular, the method can be used
to estimate expectations with respect to a target probability distribution over
an infinite-dimensional and non-compact space as given, for example, by a
Bayesian inverse problem with Gaussian random field prior. Under suitable
assumptions the MLSMC method has the optimal bound on the
cost to obtain a mean-square error of . The algorithm is
accelerated by dimension-independent likelihood-informed (DILI) proposals
designed for Gaussian priors, leveraging a novel variation which uses empirical
sample covariance information in lieu of Hessian information, hence eliminating
the requirement for gradient evaluations. The efficiency of the algorithm is
illustrated on two examples: inversion of noisy pressure measurements in a PDE
model of Darcy flow to recover the posterior distribution of the permeability
field, and inversion of noisy measurements of the solution of an SDE to recover
the posterior path measure
An efficient Monte Carlo approach for optimizing decentralized estimation networks constrained by undirected topologies
We consider a decentralized estimation network subject to communication constraints such that nearby platforms can communicate with each other through low capacity links rendering an undirected graph. After transmitting symbols based on its measurement, each node outputs an estimate for the random variable it is associated with as a function of both the measurement and incoming messages from neighbors. We are concerned with the underlying design problem and handle it through a Bayesian risk that penalizes the cost of communications as well as estimation errors, and constraining the feasible set of communication and estimation rules local to each node by the undirected communication graph. We adopt an iterative solution previously proposed for decentralized detection networks which can be carried out in a message passing fashion under certain conditions. For the estimation case, the integral operators involved do not yield closed form solutions in general so we utilize Monte Carlo methods. We achieve an iterative algorithm which yields an approximation to an optimal decentralized estimation strategy in a person by person sense subject to such constraints. In an example, we present a quantification of the trade-off between the estimation accuracy and cost of communications using the proposed algorithm
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