56,427 research outputs found
A Box Particle Filter for Stochastic and Set-theoretic Measurements with Association Uncertainty
This work develops a novel estimation approach for nonlinear dynamic stochastic systems by combining the sequential Monte Carlo method with interval analysis. Unlike the common pointwise measurements, the proposed solution is for problems with interval measurements with association uncertainty. The optimal theoretical solution can be formulated in the framework of random set theory as the Bernoulli filter for interval measurements. The straightforward particle filter implementation of the Bernoulli filter typically requires a huge number of particles since the posterior probability density function occupies a significant portion of the state space. In order to reduce the number of particles, without necessarily sacrificing estimation accuracy, the paper investigates an implementation based on box particles. A box particle occupies a small and controllable rectangular region of non-zero volume in the target state space. The numerical results demonstrate that the filter performs remarkably well: both target state and target presence are estimated reliably using a very small number of box particles
Bayesian Model Search for Nonstationary Periodic Time Series
We propose a novel Bayesian methodology for analyzing nonstationary time
series that exhibit oscillatory behaviour. We approximate the time series using
a piecewise oscillatory model with unknown periodicities, where our goal is to
estimate the change-points while simultaneously identifying the potentially
changing periodicities in the data. Our proposed methodology is based on a
trans-dimensional Markov chain Monte Carlo (MCMC) algorithm that simultaneously
updates the change-points and the periodicities relevant to any segment between
them. We show that the proposed methodology successfully identifies time
changing oscillatory behaviour in two applications which are relevant to
e-Health and sleep research, namely the occurrence of ultradian oscillations in
human skin temperature during the time of night rest, and the detection of
instances of sleep apnea in plethysmographic respiratory traces.Comment: Received 23 Oct 2018, Accepted 12 May 201
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
Neural network based approximations to posterior densities: a class of flexible sampling methods with applications to reduced rank models
Likelihoods and posteriors of econometric models with strong endogeneity and weakinstruments may exhibit rather non-elliptical contours in the parameter space.This feature also holds for cointegration models when near non-stationarity occursand determining the number of cointegrating relations is a nontrivial issue, and in mixture processes where the modes are relatively far apart. The performance ofMonte Carlo integration methods like importance sampling or Markov ChainMonte Carlo procedures greatly depends in all these cases on the choice of the importance or candidate density. Such a density has to be `close' to the targetdensity in order to yield numerically accurate results with efficient sampling. Neural networks seem to be natural importance or candidate densities, as they havea universal approximation property and are easy to sample from. That is, conditionallyupon the specification of the neural network, sampling can be done either directly orusing a Gibbs sampling technique, possibly using auxiliary variables. A key step in the proposed class of methods is the construction of a neural network that approximatesthe target density accurately. The methods are tested on a set of illustrative modelswhich include a mixture of normal distributions, a Bayesian instrumental variable regression problem with weak instruments and near non-identification, a cointegrationmodel with near non-stationarity and a two-regime growth model for US recessionsand expansions. These examples involve experiments with non-standard, non-ellipticalposterior distributions. The results indicate the feasibility of theneural network approach.Markov chain Monte Carlo;Bayesian inference;neural networks;importance sample
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