8,232 research outputs found
Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning
The problem of state estimation for unobservable distribution systems is
considered. A deep learning approach to Bayesian state estimation is proposed
for real-time applications. The proposed technique consists of distribution
learning of stochastic power injection, a Monte Carlo technique for the
training of a deep neural network for state estimation, and a Bayesian bad-data
detection and filtering algorithm. Structural characteristics of the deep
neural networks are investigated. Simulations illustrate the accuracy of
Bayesian state estimation for unobservable systems and demonstrate the benefit
of employing a deep neural network. Numerical results show the robustness of
Bayesian state estimation against modeling and estimation errors and the
presence of bad and missing data. Comparing with pseudo-measurement techniques,
direct Bayesian state estimation via deep learning neural network outperforms
existing benchmarks
A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems
This paper presents a review of the literature on State Estimation (SE) in
power systems. While covering some works related to SE in transmission systems,
the main focus of this paper is Distribution System State Estimation (DSSE).
The paper discusses a few critical topics of DSSE, including mathematical
problem formulation, application of pseudo-measurements, metering instrument
placement, network topology issues, impacts of renewable penetration, and
cyber-security. Both conventional and modern data-driven and probabilistic
techniques have been reviewed. This paper can provide researchers and utility
engineers with insights into the technical achievements, barriers, and future
research directions of DSSE
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
On-line Bayesian parameter estimation in general non-linear state-space models: A tutorial and new results
On-line estimation plays an important role in process control and monitoring.
Obtaining a theoretical solution to the simultaneous state-parameter estimation
problem for non-linear stochastic systems involves solving complex
multi-dimensional integrals that are not amenable to analytical solution. While
basic sequential Monte-Carlo (SMC) or particle filtering (PF) algorithms for
simultaneous estimation exist, it is well recognized that there is a need for
making these on-line algorithms non-degenerate, fast and applicable to
processes with missing measurements. To overcome the deficiencies in
traditional algorithms, this work proposes a Bayesian approach to on-line state
and parameter estimation. Its extension to handle missing data in real-time is
also provided. The simultaneous estimation is performed by filtering an
extended vector of states and parameters using an adaptive
sequential-importance-resampling (SIR) filter with a kernel density estimation
method. The approach uses an on-line optimization algorithm based on
Kullback-Leibler (KL) divergence to allow adaptation of the SIR filter for
combined state-parameter estimation. An optimal tuning rule to control the
width of the kernel and the variance of the artificial noise added to the
parameters is also proposed. The approach is illustrated through numerical
examples.Comment: A condensed version of this article has been published in: Tulsyan,
A., Huang, B., Gopaluni, R.B., Forbes, J.F. "On simultaneous on-line state
and parameter estimation in non-linear state-space models". Journal of
Process Control, vol 23, no. 4, 201
Robust Particle Filtering via Bayesian Nonparametric Outlier Modeling
This paper is concerned with the online estimation of a nonlinear dynamic
system from a series of noisy measurements. The focus is on cases wherein
outliers are present in-between normal noises. We assume that the outliers
follow an unknown generating mechanism which deviates from that of normal
noises, and then model the outliers using a Bayesian nonparametric model called
Dirichlet process mixture (DPM). A sequential particle-based algorithm is
derived for posterior inference for the outlier model as well as the state of
the system to be estimated. The resulting algorithm is termed DPM based robust
PF (DPM-RPF). The nonparametric feature makes this algorithm allow the data to
"speak for itself" to determine the complexity and structure of the outlier
model. Simulation results show that it performs remarkably better than two
state-of-the-art methods especially when outliers appear frequently along time.Comment: 5 pages, 3 figure
Enhancement of Low-cost GNSS Localization in Connected Vehicle Networks Using Rao-Blackwellized Particle Filters
An essential function for automated vehicle technologies is accurate
localization. It is difficult, however, to achieve lane-level accuracy with
low-cost Global Navigation Satellite System (GNSS) receivers due to the biased
noisy pseudo-range measurements. Approaches such as Differential GNSS can
improve the accuracy, but usually require an enormous amount of investment in
base stations. The emerging connected vehicle technologies provide an
alternative approach to improving the localization accuracy. It has been shown
in this paper that localization accuracy can be enhanced by fusing GNSS
information within a group of connected vehicles and matching the configuration
of the group to a digital map to eliminate the common bias in localization. A
Rao-Blackwellized particle filter (RBPF) was used to jointly estimate the
common biases of the pseudo-ranges and the vehicles positions. Multipath
biases, which are non-common to vehicles, were mitigated by a multi-hypothesis
detection-rejection approach. The temporal correlation was exploited through
the prediction-update process. The proposed approach was compared to the
existing static and smoothed static methods in the intersection scenario.
Simulation results show that the proposed algorithm reduced the estimation
error by fifty percent and reduced the estimation variance by two orders of
magnitude.Comment: 7 pages, 7 figures, IEEE ITS
Bayesian Model for Multiple Change-points Detection in Multivariate Time Series
This paper addresses the issue of detecting change-points in multivariate
time series. The proposed approach differs from existing counterparts by making
only weak assumptions on both the change-points structure across series, and
the statistical signal distributions. Specifically change-points are not
assumed to occur at simultaneous time instants across series, and no specific
distribution is assumed on the individual signals. It relies on the combination
of a local robust statistical test acting on individual time segments, with a
global Bayesian framework able to optimize configurations from multiple local
statistics (from segments of a unique time series or multiple time series).
Using an extensive experimental set-up, our algorithm is shown to perform well
on Gaussian data, with the same results in term of recall and precision as
classical approaches, such as the fused lasso and the Bernoulli Gaussian model.
Furthermore, it outperforms the reference models in the case of non normal data
with outliers. The control of the False Discovery Rate by an acceptance level
is confirmed. In the case of multivariate data, the probabilities that
simultaneous change-points are shared by some specific time series are learned.
We finally illustrate our algorithm with real datasets from energy monitoring
and genomic. Segmentations are compared to state-of-the-art approaches based on
fused lasso and group fused lasso.Comment: 29 pages, 27 figure
Bayesian peak-bagging of solar-like oscillators using MCMC: A comprehensive guide
Context: Asteroseismology has entered a new era with the advent of the NASA
Kepler mission. Long and continuous photometric observations of unprecedented
quality are now available which have stimulated the development of a number of
suites of innovative analysis tools.
Aims: The power spectra of solar-like oscillations are an inexhaustible
source of information on stellar structure and evolution. Robust methods are
hence needed in order to infer both individual oscillation mode parameters and
parameters describing non-resonant features, thus making a seismic
interpretation possible.
Methods: We present a comprehensive guide to the implementation of a Bayesian
peak-bagging tool that employs a Markov chain Monte Carlo (MCMC). Besides
making it possible to incorporate relevant prior information through Bayes'
theorem, this tool also allows one to obtain the marginal probability density
function for each of the fitted parameters. We apply this tool to a couple of
recent asteroseismic data sets, namely, to CoRoT observations of HD 49933 and
to ground-based observations made during a campaign devoted to Procyon.
Results: The developed method performs remarkably well at constraining not
only in the traditional case of extracting oscillation frequencies, but also
when pushing the limit where traditional methods have difficulties. Moreover it
provides an rigorous way of comparing competing models, such as the ridge
identifications, against the asteroseismic data.Comment: Accepted for publication in A&
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
Bayesian Structured Sparsity Priors for EEG Source Localization Technical Report
This report introduces a new hierarchical Bayesian model for the EEG source
localization problem. This model promotes structured sparsity to search for
focal brain activity. This sparsity is obtained via a multivariate Bernoulli
Laplacian prior assigned to the brain activity approximating an
pseudo norm regularization in a Bayesian framework. A partially collapsed Gibbs
sampler is used to draw samples asymptotically distributed according to the
posterior associated with the proposed Bayesian model. The generated samples
are used to estimate the brain activity and the model hyperparameters jointly
in an unsupervised framework. Two different kinds of Metropolis-Hastings moves
are introduced to accelerate the convergence of the Gibbs sampler. The first
move is based on multiple dipole shifts within each MCMC chain whereas the
second one exploits proposals associated with different MCMC chains. We use
both synthetic and real data to compare the performance of the proposed method
with the weighted mixed norm regularization and a method based on a
multiple sparse prior, showing that our algorithm presents advantages in
several scenarios.Comment: 38 pages, extended version of a paper that will be submitted for
publicatio
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