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Reliable curb detection is critical for safe autonomous driving in urban contexts. Curb detection and tracking are also useful in vehicle localization and path planning. Past work utilized a 3D LiDAR sensor to determine accurate distance information and the geometric attributes of curbs. However, such an approach requires dense point cloud data and is also vulnerable to false positives from obstacles present on both road and off-road areas. In this paper, we propose an approach to detect and track curbs by fusing together data from multiple sensors: sparse LiDAR data, a mono camera and low-cost ultrasonic sensors. The detection algorithm is based on a single 3D LiDAR and a mono camera sensor used to detect candidate curb features and it effectively removes false positives arising from surrounding static and moving obstacles. The detection accuracy of the tracking algorithm is boosted by using Kalman filter-based prediction and fusion with lateral distance information from low-cost ultrasonic sensors. We next propose a line-fitting algorithm that yields robust results for curb locations. Finally, we demonstrate the practical feasibility of our solution by testing in different road environments and evaluating our implementation in a real vehicle\footnote{Demo video clips demonstrating our algorithm have been uploaded to Youtube: https://www.youtube.com/watch?v=w5MwsdWhcy4, https://www.youtube.com/watch?v=Gd506RklfG8.}. Our algorithm maintains over 90\% accuracy within 4.5-22 meters and 0-14 meters for the KITTI dataset and our dataset respectively, and its average processing time per frame is approximately 10 ms on Intel i7 x86 and 100ms on NVIDIA Xavier board.