This paper has been accepted for presentation at the 2021 IEEE International Symposium on Biomedical Imaging (ISBI) (ISBI 2021) to be held virtually on April 13-16, 2021. In this paper, we present a novel algorithm for needle tracking in ultrasound-guided needle insertion. We utilize a novel weighted RANSAC curve fitting method combined with probabilistic Hough transform to track the curved needle robustly, and the algorithm can additionally utilize external tracking information, such as robotic kinematics, to further improve the tracking accuracy. We compared against classical tracking algorithms and a U-Net model, testing over different needle curvature and tissues. Our proposed algorithm achieves higher accuracy in tip location, shaft fitting, and tip angle. In-vivo porcine experiments with naturally bending short needles also show our method better tracked the tip location.