No abstract

Accurate vehicle localization is important for autonomous driving and advanced driver assistance systems. Existing precise localization systems based on the global navigation satellite system cannot always provide lane-level accuracy even in open-sky environments. Map-based localization using high-definition (HD) maps is an interesting method for achieving greater accuracy. We propose a map-based localization method using a single camera. Our method relies on road link information in the HD map to achieve lane-level accuracy. Initially, we process the image—acquired using the camera of a mobile device—via inverse perspective mapping, which shows the entire road at a glance in the driving image. Subsequently, we use the Hough transform to detect the vehicle lines and acquire driving link information regarding the lane on which the vehicle is moving. The vehicle position is estimated by matching the global positioning system (GPS) and reference HD map. We employ iterative closest point-based map-matching to determine and eliminate the disparity between the GPS trajectories and reference map. Finally, we perform experiments by considering the data of a sophisticated GPS/inertial navigation system as the ground truth and demonstrate that the proposed method provides lane-level position accuracy for vehicle localization.

Unlike the study of the fixed point property (FPP, for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for Khalimsky (K-, for short) topological spaces, the present paper studies the product property of the FPP for K-topological spaces. Furthermore, the paper investigates the FPP of various types of connected K-topological spaces such as non-K-retractable spaces and some points deleted K-topological (finite) planes, and so on. To be specific, after proving that not every one point deleted subspace of a finite K-topological plane X is a K-retract of X, we study the FPP of a non-retractable topological space Y, such as one point deleted space Y ∖ { p } .

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

This paper proposes a real-time position accuracy improvement method for a low-cost global positioning system (GPS), which uses geographic data for forming a digital road database in the digital map information. We link the vehicle’s location to the position on the digital map using the map-matching algorithm to improve the position accuracy. In the proposed method, we can distinguish the vehicle direction on the road and enhance the horizontal accuracy using the geographic data composed of the vector point set of the digital map. We use the iterative closest point (ICP) algorithm that calculates the rotation matrix and the translation vector to compensate for the disparity between the GPS and the digital map information. We also use the least squares method to correct the error caused by the rotation of the ICP algorithm and link on the digital map to eliminate the residual disparity. Finally, we implement the proposed method in real time with a low-cost embedded system and demonstrate the effectiveness of the proposed method through various experiments.