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Title:  Feedback particle filter and its applications 
Author(s):  Yang, Tao 
Director of Research:  Mehta, Prashant G. 
Doctoral Committee Chair(s):  Mehta, Prashant G. 
Doctoral Committee Member(s):  Basar, Tamer; Veeravalli, Venugopal V.; Moulin, Pierre 
Department / Program:  Mechanical Sci & Engineering 
Discipline:  Mechanical Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Nonlinear filtering
estimation particle filtering statistical signal processing optimal transportation target tracking 
Abstract:  The purpose of nonlinear filtering is to extract useful information from noisy sensor data. It finds applications in all disciplines of science and engineering, including tracking and navigation, traffic surveillance, financial engineering, neuroscience, biology, robotics, computer vision, weather forecasting, geophysical survey and oceanology, etc. This thesis is particularly concerned with the nonlinear filtering problem in the continuoustime continuousvalued statespace setting (diffusion). In this setting, the nonlinear filter is described by the KushnerStratonovich (KS) stochastic partial differential equation (SPDE). For the general nonlinear nonGaussian problem, no analytical expression for the solution of the SPDE is available. For certain special cases, finitedimensional solution exists and one such case is the Kalman filter. The Kalman filter admits an innovation errorbased feedback control structure, which is important on account of robustness, cost efficiency and ease of design, testing and operation. The limitations of Kalman filters in applications arise because of nonlinearities, not only in the signal models but also in the observation models. For such cases, Kalman filters are known to perform poorly. This motivates simulationbased methods to approximate the infinitedimensional solution of the KS SPDE. One popular approach is the particle filter, which is a Monte Carlo algorithm based on sequential importance sampling. Although it is potentially applicable to a general class of nonlinear nonGaussian problems, the particle filter is known to suffer from several wellknown drawbacks, such as particle degeneracy, curse of dimensionality, numerical instability and high computational cost. The goal of this dissertation is to propose a new framework for nonlinear filtering, which introduces the innovation errorbased feedback control structure to the particle filter. The proposed filter is called the feedback particle filter (FPF). The first part of this dissertation covers the theory of the feedback particle filter. The filter is defined by an ensemble of controlled, stochastic, dynamic systems (the “particles”). Each particle evolves under feedback control based on its own state, and the empirical distribution of the ensemble. The feedback control law is obtained as the solution to a variational problem, in which the optimization criterion is the KullbackLeibler divergence between the actual posterior, and the common posterior of any particle. The following conclusions are obtained for diffusions with continuous observations: 1) The optimal control solution is exact: The two posteriors match exactly, provided they are initialized with identical priors. 2) The optimal filter admits an innovation errorbased gain feedback structure. 3) The optimal feedback gain is obtained via a solution of an EulerLagrange boundary value problem; the feedback gain equals the Kalman gain in the linear Gaussian case. The feedback particle filter offers significant variance improvements when compared to the bootstrap particle filter; in particular, the algorithm can be applied to systems that are not stable. No importance sampling or resampling is required, and therefore the filter does not suffer samplingrelated issues and incurs low computational burden. The theory of the feedback particle filter is first developed for the continuoustime continuousvalued statespace setting. Its extensions to two other settings are also studied in this dissertation. In particular, we introduce feedback particle filterbased solutions for: i) estimating a continuoustime Markov chain with noisy measurements, and ii) the continuousdiscrete time filtering problem. Both algorithms are shown to admit an innovation errorbased feedback control structure. The second part of this dissertation concerns the extensions of the feedback particle filter algorithms to address additional uncertainties. In particular, we consider the nonlinear filtering problem with i) model uncertainty, and ii) data association uncertainty. The corresponding feedback particle filter algorithms are referred to as the interacting multiple modelfeedback particle filter (IMMFPF) and the probabilistic data associationfeedback particle filter (PDAFPF). The proposed algorithms are shown to be the nonlinear nonGaussian generalization of their classic Kalman filter based counterparts. One remarkable conclusion is that the proposed IMMFPF and PDAFPF algorithm retains the innovation errorbased feedback structure even for the nonlinear nonGaussian case. The results are illustrated with the aid of numerical simulations. 
Issue Date:  20140916 
URI:  http://hdl.handle.net/2142/50708 
Rights Information:  Copyright 2014 Tao Yang 
Date Available in IDEALS:  20140916 
Date Deposited:  201408 
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Dissertations and Theses  Mechanical Science and Engineering

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois