Covariance matrix analysis in simultaneous localization and mapping

Estimation at a specific time or also known as the filtering technique in estimation and control theory is a method to estimate the desired parameters from indirect and uncertain observations, taking into account the system and measurement errors. One of the applications that implements estimation t...

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Main Author:	Nur Aqilah, Othman
Format:	Thesis
Language:	English
Published:	2016
Subjects:	TA Engineering (General) Civil engineering (General)
Online Access:	http://umpir.ump.edu.my/id/eprint/15776/1/Covariance%20matrix%20analysis%20in%20simultaneous%20localization%20and%20mapping.pdf
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spelling	my-ump-ir.157762023-05-29T07:48:16Z Covariance matrix analysis in simultaneous localization and mapping 2016-04 Nur Aqilah, Othman TA Engineering (General). Civil engineering (General) TK Electrical engineering. Electronics Nuclear engineering Estimation at a specific time or also known as the filtering technique in estimation and control theory is a method to estimate the desired parameters from indirect and uncertain observations, taking into account the system and measurement errors. One of the applications that implements estimation technique is the simultaneous localization and mapping (SLAM) of a mobile robot. SLAM is one of the navigation techniques which enables the mobile robot to move autonomously and observes its surrounding in an unknown environment. SLAM does not require a priori map, but with the aid of sensors on board, the mobile robot incrementally builds a map of the environment and use this map to localize its position. Therefore, an estimation technique is used to provide the approximate location of mobile robot and landmarks at any time based on the measurement data that are recursively recorded by the sensors. In mobile robot SLAM, extended Kalman filter (EKF) has been one of the most preferable estimators due to its relatively simple algorithm and efficiency of the estimation through the representation of the belief by a multivariate Gaussian distribution; unimodal distribution, with a single mean annotated with a corresponding covariance uncertainty. Nonetheless, EKF-based SLAM suffers from high computational cost due to the update process of covariance matrix. One of the objectives of this thesis is to propose an alternative method to simplify the structure of covariance matrix by means of matrix diagonalization method using eigenvalues. The non-diagonal parts of the covariance matrix are cross-correlation elements, which represent the correlation between the position of the robot and the landmarks. In diagonalizing the covariance matrix, these terms would be eliminated. However, this thesis has proven that the cross-correlation elements are important to ensure the accuracy of the estimation; hence it should be integrated in the diagonalization process. In EKF-based SLAM, measurement data are required at each time step to complete the estimation process. Sudden absence of these data might affect the state estimation and the covariance value. Hence, this thesis also investigates the impact of this phenomenon, which is addressed as intermittent measurement condition. The requirement of Gaussian distribution behavior of measurement and system noises has limited the use of extended Kalman filter in all conditions. In mobile robot SLAM, the noise characteristics might be unknown. Therefore, H∞ filter is used instead of EKF under this condition. One of the biggest challenges in implementing H∞ filter-based SLAM is the manual parameter tuning. Thus, this thesis also proposes a sufficient condition for the estimation of H∞ filter-based SLAM by providing a lower boundary of the selection for the parameter gamma under specific assumptions and environmental conditions. All of these issues are examined and investigated from an estimation-theoretic perspective through mathematical analysis. Theorems, lemmas and propositions are proposed to represent the findings of the analysis. The results obtained were validated through simulation analysis. 2016-04 Thesis http://umpir.ump.edu.my/id/eprint/15776/ http://umpir.ump.edu.my/id/eprint/15776/1/Covariance%20matrix%20analysis%20in%20simultaneous%20localization%20and%20mapping.pdf pdf en public masters Universiti Malaysia Pahang Faculty of Electrical and Electronics Engineering Ahmad, Hamzah
institution	Universiti Malaysia Pahang Al-Sultan Abdullah
collection	UMPSA Institutional Repository
language	English
advisor	Ahmad, Hamzah
topic	TA Engineering (General) Civil engineering (General) TA Engineering (General) Civil engineering (General)
spellingShingle	TA Engineering (General) Civil engineering (General) TA Engineering (General) Civil engineering (General) Nur Aqilah, Othman Covariance matrix analysis in simultaneous localization and mapping
description	Estimation at a specific time or also known as the filtering technique in estimation and control theory is a method to estimate the desired parameters from indirect and uncertain observations, taking into account the system and measurement errors. One of the applications that implements estimation technique is the simultaneous localization and mapping (SLAM) of a mobile robot. SLAM is one of the navigation techniques which enables the mobile robot to move autonomously and observes its surrounding in an unknown environment. SLAM does not require a priori map, but with the aid of sensors on board, the mobile robot incrementally builds a map of the environment and use this map to localize its position. Therefore, an estimation technique is used to provide the approximate location of mobile robot and landmarks at any time based on the measurement data that are recursively recorded by the sensors. In mobile robot SLAM, extended Kalman filter (EKF) has been one of the most preferable estimators due to its relatively simple algorithm and efficiency of the estimation through the representation of the belief by a multivariate Gaussian distribution; unimodal distribution, with a single mean annotated with a corresponding covariance uncertainty. Nonetheless, EKF-based SLAM suffers from high computational cost due to the update process of covariance matrix. One of the objectives of this thesis is to propose an alternative method to simplify the structure of covariance matrix by means of matrix diagonalization method using eigenvalues. The non-diagonal parts of the covariance matrix are cross-correlation elements, which represent the correlation between the position of the robot and the landmarks. In diagonalizing the covariance matrix, these terms would be eliminated. However, this thesis has proven that the cross-correlation elements are important to ensure the accuracy of the estimation; hence it should be integrated in the diagonalization process. In EKF-based SLAM, measurement data are required at each time step to complete the estimation process. Sudden absence of these data might affect the state estimation and the covariance value. Hence, this thesis also investigates the impact of this phenomenon, which is addressed as intermittent measurement condition. The requirement of Gaussian distribution behavior of measurement and system noises has limited the use of extended Kalman filter in all conditions. In mobile robot SLAM, the noise characteristics might be unknown. Therefore, H∞ filter is used instead of EKF under this condition. One of the biggest challenges in implementing H∞ filter-based SLAM is the manual parameter tuning. Thus, this thesis also proposes a sufficient condition for the estimation of H∞ filter-based SLAM by providing a lower boundary of the selection for the parameter gamma under specific assumptions and environmental conditions. All of these issues are examined and investigated from an estimation-theoretic perspective through mathematical analysis. Theorems, lemmas and propositions are proposed to represent the findings of the analysis. The results obtained were validated through simulation analysis.
format	Thesis
qualification_level	Master's degree
author	Nur Aqilah, Othman
author_facet	Nur Aqilah, Othman
author_sort	Nur Aqilah, Othman
title	Covariance matrix analysis in simultaneous localization and mapping
title_short	Covariance matrix analysis in simultaneous localization and mapping
title_full	Covariance matrix analysis in simultaneous localization and mapping
title_fullStr	Covariance matrix analysis in simultaneous localization and mapping
title_full_unstemmed	Covariance matrix analysis in simultaneous localization and mapping
title_sort	covariance matrix analysis in simultaneous localization and mapping
granting_institution	Universiti Malaysia Pahang
granting_department	Faculty of Electrical and Electronics Engineering
publishDate	2016
url	http://umpir.ump.edu.my/id/eprint/15776/1/Covariance%20matrix%20analysis%20in%20simultaneous%20localization%20and%20mapping.pdf
_version_	1783731999693864960

Covariance matrix analysis in simultaneous localization and mapping

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