29,665 research outputs found
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost
Poyiadjis et al. (2011) show how particle methods can be used to estimate
both the score and the observed information matrix for state space models.
These methods either suffer from a computational cost that is quadratic in the
number of particles, or produce estimates whose variance increases
quadratically with the amount of data. This paper introduces an alternative
approach for estimating these terms at a computational cost that is linear in
the number of particles. The method is derived using a combination of kernel
density estimation, to avoid the particle degeneracy that causes the
quadratically increasing variance, and Rao-Blackwellisation. Crucially, we show
the method is robust to the choice of bandwidth within the kernel density
estimation, as it has good asymptotic properties regardless of this choice. Our
estimates of the score and observed information matrix can be used within both
online and batch procedures for estimating parameters for state space models.
Empirical results show improved parameter estimates compared to existing
methods at a significantly reduced computational cost. Supplementary materials
including code are available.Comment: Accepted to Journal of Computational and Graphical Statistic
ILAPF: Incremental Learning Assisted Particle Filtering
This paper is concerned with dynamic system state estimation based on a
series of noisy measurement with the presence of outliers. An incremental
learning assisted particle filtering (ILAPF) method is presented, which can
learn the value range of outliers incrementally during the process of particle
filtering. The learned range of outliers is then used to improve subsequent
filtering of the future state. Convergence of the outlier range estimation
procedure is indicated by extensive empirical simulations using a set of
differing outlier distribution models. The validity of the ILAPF algorithm is
evaluated by illustrative simulations, and the result shows that ILAPF is more
accurate and faster than a recently published state-ofthe-art robust particle
filter. It also shows that the incremental learning property of the ILAPF
algorithm provides an efficient way to implement transfer learning among
related state filtering tasks.Comment: 5 pages, 4 figures, conferenc
Robustness of System-Filter Separation for the Feedback Control of a Quantum Harmonic Oscillator Undergoing Continuous Position Measurement
We consider the effects of experimental imperfections on the problem of
estimation-based feedback control of a trapped particle under continuous
position measurement. These limitations violate the assumption that the
estimator (i.e. filter) accurately models the underlying system, thus requiring
a separate analysis of the system and filter dynamics. We quantify the
parameter regimes for stable cooling, and show that the control scheme is
robust to detector inefficiency, time delay, technical noise, and miscalibrated
parameters. We apply these results to the specific context of a weakly
interacting Bose-Einstein condensate (BEC). Given that this system has
previously been shown to be less stable than a feedback-cooled BEC with strong
interatomic interactions, this result shows that reasonable experimental
imperfections do not limit the feasibility of cooling a BEC by continuous
measurement and feedback.Comment: 14 pages, 8 figure
Bibliographic Review on Distributed Kalman Filtering
In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud
The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area
State-Observation Sampling and the Econometrics of Learning Models
In nonlinear state-space models, sequential learning about the hidden state
can proceed by particle filtering when the density of the observation
conditional on the state is available analytically (e.g. Gordon et al., 1993).
This condition need not hold in complex environments, such as the
incomplete-information equilibrium models considered in financial economics. In
this paper, we make two contributions to the learning literature. First, we
introduce a new filtering method, the state-observation sampling (SOS) filter,
for general state-space models with intractable observation densities. Second,
we develop an indirect inference-based estimator for a large class of
incomplete-information economies. We demonstrate the good performance of these
techniques on an asset pricing model with investor learning applied to over 80
years of daily equity returns
Fast Monte-Carlo Localization on Aerial Vehicles using Approximate Continuous Belief Representations
Size, weight, and power constrained platforms impose constraints on
computational resources that introduce unique challenges in implementing
localization algorithms. We present a framework to perform fast localization on
such platforms enabled by the compressive capabilities of Gaussian Mixture
Model representations of point cloud data. Given raw structural data from a
depth sensor and pitch and roll estimates from an on-board attitude reference
system, a multi-hypothesis particle filter localizes the vehicle by exploiting
the likelihood of the data originating from the mixture model. We demonstrate
analysis of this likelihood in the vicinity of the ground truth pose and detail
its utilization in a particle filter-based vehicle localization strategy, and
later present results of real-time implementations on a desktop system and an
off-the-shelf embedded platform that outperform localization results from
running a state-of-the-art algorithm on the same environment
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