Computational time analysis in extended kalman filter based simultaneous localization and mapping

The simultaneous localization and mapping (SLAM) of a mobile robot is one of the applications that use estimation techniques. SLAM is a navigation technique that allows a mobile robot to navigate around autonomously while observing its surroundings in an unfamiliar environment. SLAM does not require a priori map, instead the mobile robot creates a map of the area incrementally with the help of sensors on board and uses this map to localize its location Due to its relatively easy algorithm and efficiency of estimation via the representation of the belief by a multivariate Gaussian distribution and a unimodal distribution, with a single mean annotated and corresponding covariance uncertainty, the extended Kalman filter (EKF) has become one of the most preferred estimators in mobile robot SLAM. However, due to the update process of the covariance matrix, EKF-based SLAM has high computational time. In SLAM, if more observation is being made by mobile robot, the state covariance size will be increasing. This eventually requires more memory and processing time due to excessive computation needs to be calculated over time. Therefore there is a need of enhancing the estimation performance by reducing the computational time in SLAM. Three phases involve in this research methodology which the first is theoretical formulation of the mobile robot model. This is followed by the environment and estimation method used to solve the SLAM of mobile robot. Simulation analysis was used to verify the findings. This research attempts to introduce a new approach to simplify the structure of the covariance matrix using the eigenvalues matrix diagonalization method. Through simulation result it is proved that time taken to complete the SLAM process using diagonalized covariance was reduced as compared to the normal covariance. However, there is one limitation encountered from this method in which the covariance values become too small, that indicates an optimistic estimation. For this reason, second objective is motivated to improve the optimistic problem. Addition of new element into the diagonal matrix, which is known as a pseudo element, is also investigated in this study. Via mathematical approach, these problems are discussed and explored from estimation-theoretic point of view. Through adding the pseudo noise element into diagonalized covariance, the optimistic condition of covariance matrix can be improved. This was shown through the increased size of covariance ellipses at the end of simulation process. Based on the findings it can be concluded that the addition of pseudo matrix in the updated state covariance can further improved the computational time for mobile robot estimation