30,803 research outputs found
Nonlinear State Estimation Using Optimal Gaussian Sampling with Applications to Tracking
This thesis is concerned with the ubiquitous problem of estimating the hidden state of a discrete-time stochastic nonlinear dynamic system. The focus is on the derivation of new Gaussian state estimators and the improvement of existing approaches. Also the challenging task of distributed state estimation is addressed by proposing a sample-based fusion of local state estimates. The proposed estimation techniques are applied to extended object tracking
Distributed Target Tracking and Synchronization in Wireless Sensor Networks
Wireless sensor networks provide useful information for various applications but pose challenges in scalable information processing and network maintenance. This dissertation focuses on statistical methods for distributed information fusion and sensor synchronization for target tracking in wireless sensor networks.
We perform target tracking using particle filtering. For scalability, we extend centralized particle filtering to distributed particle filtering via distributed fusion of local estimates provided by individual sensors. We derive a distributed fusion rule from Bayes\u27 theorem and implement it via average consensus. We approximate each local estimate as a Gaussian mixture and develop a sampling-based approach to the nonlinear fusion of Gaussian mixtures. By using the sampling-based approach in the fusion of Gaussian mixtures, we do not require each Gaussian mixture to have a uniform number of mixture components, and thus give each sensor the flexibility to adaptively learn a Gaussian mixture model with the optimal number of mixture components, based on its local information. Given such flexibility, we develop an adaptive method for Gaussian mixture fitting through a combination of hierarchical clustering and the expectation-maximization algorithm. Using numerical examples, we show that the proposed distributed particle filtering algorithm improves the accuracy and communication efficiency of distributed target tracking, and that the proposed adaptive Gaussian mixture learning method improves the accuracy and computational efficiency of distributed target tracking.
We also consider the synchronization problem of a wireless sensor network. When sensors in a network are not synchronized, we model their relative clock offsets as unknown parameters in a state-space model that connects sensor observations to target state transition. We formulate the synchronization problem as a joint state and parameter estimation problem and solve it via the expectation-maximization algorithm to find the maximum likelihood solution for the unknown parameters, without knowledge of the target states. We also study the performance of the expectation-maximization algorithm under the Monte Carlo approximations used by particle filtering in target tracking. Numerical examples show that the proposed synchronization method converges to the ground truth, and that sensor synchronization significantly improves the accuracy of target tracking
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.
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Numerical Fitting-based Likelihood Calculation to Speed up the Particle Filter
The likelihood calculation of a vast number of particles is the computational
bottleneck for the particle filter in applications where the observation
information is rich. For fast computing the likelihood of particles, a
numerical fitting approach is proposed to construct the Likelihood Probability
Density Function (Li-PDF) by using a comparably small number of so-called
fulcrums. The likelihood of particles is thereby analytically inferred,
explicitly or implicitly, based on the Li-PDF instead of directly computed by
utilizing the observation, which can significantly reduce the computation and
enables real time filtering. The proposed approach guarantees the estimation
quality when an appropriate fitting function and properly distributed fulcrums
are used. The details for construction of the fitting function and fulcrums are
addressed respectively in detail. In particular, to deal with multivariate
fitting, the nonparametric kernel density estimator is presented which is
flexible and convenient for implicit Li-PDF implementation. Simulation
comparison with a variety of existing approaches on a benchmark 1-dimensional
model and multi-dimensional robot localization and visual tracking demonstrate
the validity of our approach.Comment: 42 pages, 17 figures, 4 tables and 1 appendix. This paper is a
draft/preprint of one paper submitted to the IEEE Transaction
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