Covariance matrix analysis in simultaneous localization and mapping - Nur Aqilah, Othman (2016)
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.