Expectation propagation for state estimation with discrete-valued hidden random variables

Download

Elif Sarıtaş - PhD Thesis.pdf

Date

2023-2-21

Author

Sarıtaş, Elif

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

228
views

193
downloads

In this thesis, the expectation propagation (EP) approach of Minka is considered for the estimation problems in dynamical systems with discrete hidden random variables where optimal posteriors are usually intractable. The concept of context adjustment is introduced to avoid/alleviate indefinite covariance problems encountered in standard EP implementations in a systematic way. Additionally, the moment projection (Mprojection) problem involving pseudo-Gaussian likelihoods as factors is solved to be used in the backward pass of the proposed smoothers. The first type of estimation problem of interest investigates the so-called jump Markov linear systems (JMLS), where the state dynamics and/or measurement relation jumps between different alternatives based on the state of a Markov chain. This type of system model is extensively used in applications such as target tracking, fault detection and isolation, and machine learning. In the thesis, filtering and smoothing algorithms are derived using EP with context adjustment for JMLSs, and their relation to the existing methods in the literature is discussed. The simulation results on several scenarios show that the proposed algorithms have similar or better performance compared with the alternative methods. The second type of problem considered in the thesis is the state estimation under measurement origin uncertainty. This problem, also known as data association or correspondence problem, frequently appears in applications such as sensor fusion and target tracking with imperfect sensors. A fixed-interval smoother based on EP with context adjustment is presented for the data association in multi-target tracking problem. Moreover, the suggested smoother is adapted to the filtering problem through a sliding-window mechanism. The proposed methods are compared to their alternatives with a discussion of their benefits and shortcomings.

Subject Keywords

Expectation propagation, Jump Markov linear systems, Switching dynamical systems, State estimation, Data association, Multi-target tracking, Smoothing, Filtering

URI

https://hdl.handle.net/11511/102582

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Recent results on Bayesian Cramér-Rao bounds for jump Markov systems Fritsche, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2016-07-08) In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightnes...
Online state estimation for discrete nonlinear dynamic systems with nonlinear noise and interference Demirbaş, Kerim (2015-01-01) This paper presents a real-time recursive state filtering and prediction scheme (PR) for discrete nonlinear dynamic systems with nonlinear noise and random interference, such as undesired random jamming or clutter. The PR is based upon discrete noise approximation, state quantization, and a suboptimal implementation of multiple composite hypothesis testing. The PR outperforms both the sampling importance resampling (SIR) particle filter and auxiliary sampling importance resampling (ASIR) particle filter; wh...
Effective optimization with weighted automata on decomposable trees Ravve, E. V.; Volkovich, Z.; Weber, Gerhard Wilhelm (Informa UK Limited, 2014-01-02) In this paper, we consider quantitative optimization problems on decomposable discrete systems. We restrict ourselves to labeled trees as the description of the systems and we use weighted automata on them as our computational model. We introduce a new kind of labeled decomposable trees, sum-like weighted labeled trees, and propose a method, which allows us to reduce the solution of an optimization problem, defined in a fragment of Weighted Monadic Second Order Logic, on such a tree to the solution of effec...
Vester's Sensitivity Model for Genetic Networks with Time-Discrete Dynamics Moreno, Liana Amaya; DEFTERLİ, ÖZLEM; Fuegenschuh, Armin; Weber, Gerhard Wilhelm (2014-07-03) We propose a new method to explore the characteristics of genetic networks whose dynamics are described by a linear discrete dynamical model x(t+1) = Ax(t). The gene expression data x(t) is given for various time points and the matrix A of interactions among the genes is unknown. First we formulate and solve a parameter estimation problem by linear programming in order to obtain the entries of the matrix A. We then use ideas from Vester's Sensitivity Model, more precisely, the Impact Matrix, and the determi...
Estimation and hypothesis testing in multivariate linear regression models under non normality İslam, Muhammed Qamarul (Informa UK Limited, 2017-01-01) This paper discusses the problem of statistical inference in multivariate linear regression models when the errors involved are non normally distributed. We consider multivariate t-distribution, a fat-tailed distribution, for the errors as alternative to normal distribution. Such non normality is commonly observed in working with many data sets, e.g., financial data that are usually having excess kurtosis. This distribution has a number of applications in many other areas of research as well. We use modifie...

Citation Formats

E. Sarıtaş, “Expectation propagation for state estimation with discrete-valued hidden random variables,” Ph.D. - Doctoral Program, Middle East Technical University, 2023.