- Title
- State and parameter estimation for nonlinear state-space models using variational inference
- Creator
- Courts, Jarrad
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2021
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- In modern society, autonomous and computer-controlled systems surround us. These systems range from comparatively simple examples, such as air-conditioners, to more complex examples, such as self-driving cars, unmanned marine vehicles, and industrial processes. It is beneficial to have mathematical models of such systems as they can be employed as a surrogate of the actual system for prediction, control, decision-making, and analysis. These mathematical models can come in many different forms. A widely used and flexible class of mathematical models employed for these purposes are probabilistic nonlinear state-space models. These models often rely on parameters such as masses, damping coefficients, and motor constants. Typically, these parameters are unknown and are estimated. The process of estimating these parameters is known as system identification and is generally intractable to perform exactly. Closely related to the problem of system identification is the similarly intractable problem of state estimation. In this thesis, approximate solutions based on variational inference are developed to address the state estimation problem, the maximum likelihood system identification problem, and the Bayesian system identification problem, all using assumed Gaussian posterior densities. The use of variational inference allows for a principled approach that implicitly accounts for the assumptions required to approximate the intractable probability densities and frames the estimation problems as optimisation problems. These optimisation problems are deterministic and efficiently solved using readily obtained, exact first- and second-order derivatives. While the developed approach applies directly to general probabilistic state-space models, it is common to assume additive Gaussian noise models. This assumption results in a more structured system identification problem. Specialisations of the developed system identification approaches are made to take advantage of this additional structure. These specialisations increase robustness and reduce the computational cost. The results obtained, across a range of examples, demonstrate that the developed method outperforms alternative assumed Gaussian methods. This outperformance is partially a result of introducing fewer assumptions. Furthermore, the results obtained closely match state-of-the-art particle methods, with increased robustness and, at times, a significant reduction in runtime. Overall, this thesis develops efficient assumed density approaches to system identification and state estimation. The developed approaches are intended for nonlinear systems and use a minimal number of assumptions, addressing a gap in the range of available methods.
- Subject
- Bayesian inference; system identification; variational inference; nonlinear models
- Identifier
- http://hdl.handle.net/1959.13/1501701
- Identifier
- uon:55165
- Rights
- Copyright 2021 Jarrad Courts
- Language
- eng
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| View Details Download | ATTACHMENT01 | Thesis | 10 MB | Adobe Acrobat PDF | View Details Download | ||
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