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State estimation for non-linear transmission models of Tuberculosis
Dissertation (MEng(Electronic Engineering))--University of Pretoria, 2021.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613504507215872 |
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| access_status_str | Open Access |
| author2 | Craig, Ian K. |
| author_browse | Craig, Ian K. |
| author_facet | Craig, Ian K. |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MEng(Electronic Engineering))--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/79953 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:12.164Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/79953 State estimation for non-linear transmission models of Tuberculosis Craig, Ian K. duaynestrydom@tuks.co.za le Roux, Johan D. Strydom, Duayne extended Kalman filter hybrid extended Kalman filter Tuberculosis quanta estimation state and parameter estimation non-linear observability Dissertation (MEng(Electronic Engineering))--University of Pretoria, 2021. Given the high prevalence of Tuberculosis (TB) and the mortality rate associated with the disease, numerous models, such as the Gammaitoni and Nucci (GN) model, were developed to model the risk of transmission. These models typically rely on a quanta generation rate as a measurement of infectivity. However this state cannot be measured directly. Since the quanta generation rate cannot be measured directly, the unique contribution of this work is the development of state estimators to estimate the quanta generation rate from available measurements. Towards this end, the GN model is adapted into an augmented single-room GN model, and a simplified two-room GN model. A sensitivity analysis is performed on both models to determine the effects of deviation of parameters and the effect thereof on the uncertainty of the quanta state. An algebraic identifiability analysis is performed on the models to determine whether the parameters are identifiable and distinguishable from one another. An observability analysis shows that both models are observable, i.e. it is theoretically possible to estimate the number of quanta (the quanta state) and the quanta generation rate given available measurements. An additional measurement (rate of change of the measurable variable) is added to increase the observability of the models. Kalman filters are used to estimate the quanta state. First, a continuous-time extended Kalman filter (CEKF) is used for both adapted models using a simulation and measurement time of 60s. Reasonable quanta state estimates are achieved in both cases. A more realistic scenario, with a measurement rate of 1 day, is used next. For these estimates, a hybrid extended Kalman filter (HEKF) is used. Performance of the filter degrades for the quanta state estimates of the HEKFs. The effects of filter tuning and a greater deviation in initial estimates are also investigated and compared. The CEKFs, the adapted models, and real-time measurements could potentially be used in a control system feedback loop to reduce the transmission of TB in confined spaces such as hospitals. Electrical, Electronic and Computer Engineering MEng(Electronic Engineering) Unrestricted 2021-05-18T11:57:29Z 2021-05-18T11:57:29Z 2021-09 2021 Dissertation * S2019 http://hdl.handle.net/2263/79953 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | extended Kalman filter hybrid extended Kalman filter Tuberculosis quanta estimation state and parameter estimation non-linear observability State estimation for non-linear transmission models of Tuberculosis |
| title | State estimation for non-linear transmission models of Tuberculosis |
| title_full | State estimation for non-linear transmission models of Tuberculosis |
| title_fullStr | State estimation for non-linear transmission models of Tuberculosis |
| title_full_unstemmed | State estimation for non-linear transmission models of Tuberculosis |
| title_short | State estimation for non-linear transmission models of Tuberculosis |
| title_sort | state estimation for non linear transmission models of tuberculosis |
| topic | extended Kalman filter hybrid extended Kalman filter Tuberculosis quanta estimation state and parameter estimation non-linear observability |
| url | http://hdl.handle.net/2263/79953 |