Nonlinear Parameter Estimators in Dynamic Environments
A Bayesian Approach
Sasan Vakili (TU Delft - Mechanical Engineering)
Bart De Schutter – Promotor (TU Delft - Mechanical Engineering)
Peyman Mohajerin Esfahani – Promotor (University of Toronto, TU Delft - Mechanical Engineering)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
This thesis develops a hierarchy of Bayesian estimation methods for Wiener-type state-space models, motivated by autonomous underwater vehicle (AUV) bathymetric mapping and related robotic perception problems. The focus is on a class of models in which a known linear dynamical process is observed through an unknown, possibly nonlinear output map whose parameters must be inferred from noisy input-output data. In this setting, the observation model is driven by latent, stochastic system states. The central objective is to design parameter estimators that are both statistically accurate and computationally tractable, enabling their embedding within navigation and mapping pipelines.
The work begins with a maximum a posteriori (MAP) estimator for identifying an unknown output map, formulated as a linear time-varying (LTV) observation-model identification problem. In this setting, the MAP estimation problem is posed over the entire state-parameter trajectory and shown to be non-convex. A semidefinite-programming (SDP) relaxation based on linear matrix inequalities (LMIs) is then derived to obtain a conservative but tractable approximation, whose solution serves as a warm start for quasi-Newton re!nement. Numerical experiments validate the efficacy of the proposed method in terms of estimation accuracy and computational efficiency....