Analyzing the accuracy of lines´ covariances in the EKF-based localization of a mobile robot

This paper deals with the problem of estimating the line parameters´ covariances, which must be estimated in the process of Kalman-filtering-based localization of a mobile robot. The mobile robot is equipped with a laser range finder (LRF) sensor. In each environment scan the line-segments´ parameters and their covariances must be extracted out of the LRF´s reflection points in order to perform the correction step of the Extended Kalman Filter (EKF). The LRF´s points, which correspond to an environment line segment, are simulated in Matlab. The line parameters´ covariances, which arise from the LRF´s noise, are estimated with the method resulting from the classic least-squares (LSQ). The accuracy of the estimated covariances is analyzed by comparing them to the statistically obtained reference covariances. A special case when the mobile robot is far away from the environment line segment is considered. This cause that the variance of the observed environment line is very large, which has great effect to the correction equation of the EKF. The accuracy of the method resulting from the classic LSQ is analyzed in dependence to the number of line segment points.