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

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Elif Sarıtaş - PhD Thesis.pdf

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2023-2-21

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Sarıtaş, Elif

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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

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

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