22,745 research outputs found
Use of Bridging Strategy between the Ensemble Kalman Filter and Particle Filter for the Measurements with Various Quasi-Gaussian Noise
Filtering and estimation are two important tools of engineering. Whenever the state of the system needs to be estimated from the noisy sensor measurements, some kind of state estimator is used. If the dynamics of the system and observation model are linear under Gaussian conditions, the root mean squared error can be computed using the Kalman Filter. But practically, noise frequently enters the system as not strictly Gaussian. Therefore, the Kalman Filter does not necessarily provide the better estimate. Hence the estimation of the nonlinear system under non-Gaussian or quasi-Gaussian noise is of an acute interest. There are many versions of the Kalman filter such as the Extended Kalman filter, the Unscented Kalman filter, the Ensemble Kalman filter, the Particle filter, etc., each having their own disadvantages. In this thesis work I used a bridging strategy between the Ensemble Kalman filter and Particle filter called an Ensemble Kalman Particle filter. This filter works well in nonlinear system and non-Gaussian measurements as well. I analyzed this filter using MATLAB simulation and also applied Gaussian Noise, non-zero mean Gaussian Noise, quasi-Gaussian noise (with drift), random walk and Laplacian Noise. I applied these noises and compared the performances of the Particle filter and the Ensemble Kalman Particle filter in the presence of linear and nonlinear observations which leads to the conclusion that the Ensemble Kalman Particle filter yields the minimum error estimate. I also found the optimum value for the tuning parameter which is used to bridge the two filters using Monte Carlo Simulation
Phase Space Formulation of Filtering. Insight into the Wave-Particle Duality
A phase space formulation of the filtering process upon an incident quantum
state is developed. This formulation can explain the results of both quantum
interference and delayed-choice experiments without making use of the
controversial wave-particle duality. Quantum particles are seen as localized
and indivisible concentrations of energy and/or mass, their probability
amplitude in phase space being described by the Wigner distribution function.
The wave or particle nature appears in experiments in which the interference
term of the Wigner distribution function is present or absent, respectively,
the filtering devices that modify the quantum wavefunction throughout the
set-up, from its generation to its final detection, being responsible for the
modification of the Wigner distribution function.Comment: 32 pages, 12 figure
Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering
Recently, the Frank-Wolfe optimization algorithm was suggested as a procedure
to obtain adaptive quadrature rules for integrals of functions in a reproducing
kernel Hilbert space (RKHS) with a potentially faster rate of convergence than
Monte Carlo integration (and "kernel herding" was shown to be a special case of
this procedure). In this paper, we propose to replace the random sampling step
in a particle filter by Frank-Wolfe optimization. By optimizing the position of
the particles, we can obtain better accuracy than random or quasi-Monte Carlo
sampling. In applications where the evaluation of the emission probabilities is
expensive (such as in robot localization), the additional computational cost to
generate the particles through optimization can be justified. Experiments on
standard synthetic examples as well as on a robot localization task indicate
indeed an improvement of accuracy over random and quasi-Monte Carlo sampling.Comment: in 18th International Conference on Artificial Intelligence and
Statistics (AISTATS), May 2015, San Diego, United States. 38, JMLR Workshop
and Conference Proceeding
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem
A phase space mathematical formulation of quantum mechanical processes
accompanied by and ontological interpretation is presented in an axiomatic
form. The problem of quantum measurement, including that of quantum state
filtering, is treated in detail. Unlike standard quantum theory both quantum
and classical measuring device can be accommodated by the present approach to
solve the quantum measurement problemComment: 29 pages, 4 figure
Application of Sequential Quasi-Monte Carlo to Autonomous Positioning
Sequential Monte Carlo algorithms (also known as particle filters) are
popular methods to approximate filtering (and related) distributions of
state-space models. However, they converge at the slow rate, which
may be an issue in real-time data-intensive scenarios. We give a brief outline
of SQMC (Sequential Quasi-Monte Carlo), a variant of SMC based on
low-discrepancy point sets proposed by Gerber and Chopin (2015), which
converges at a faster rate, and we illustrate the greater performance of SQMC
on autonomous positioning problems.Comment: 5 pages, 4 figure
Statistical Inference for Partially Observed Markov Processes via the R Package pomp
Partially observed Markov process (POMP) models, also known as hidden Markov
models or state space models, are ubiquitous tools for time series analysis.
The R package pomp provides a very flexible framework for Monte Carlo
statistical investigations using nonlinear, non-Gaussian POMP models. A range
of modern statistical methods for POMP models have been implemented in this
framework including sequential Monte Carlo, iterated filtering, particle Markov
chain Monte Carlo, approximate Bayesian computation, maximum synthetic
likelihood estimation, nonlinear forecasting, and trajectory matching. In this
paper, we demonstrate the application of these methodologies using some simple
toy problems. We also illustrate the specification of more complex POMP models,
using a nonlinear epidemiological model with a discrete population,
seasonality, and extra-demographic stochasticity. We discuss the specification
of user-defined models and the development of additional methods within the
programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this
paper is provided at the pomp package website: http://kingaa.github.io/pom
Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes
SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for
filtering and related sequential problems. Gerber and Chopin (2015) introduced
SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two
objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose
members are usually less familiar with state-space models and particle
filtering; (b) to extend SQMC to the filtering of continuous-time state-space
models, where the latent process is a diffusion. A recurring point in the paper
will be the notion of dimension reduction, that is how to implement SQMC in
such a way that it provides good performance despite the high dimension of the
problem.Comment: To be published in the proceedings of MCMQMC 201
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