Recent advancements in connected vehicle (CV) technology have spurred research into CV-based realtime traffic signal control. However, existing studies still face challenges related to low penetration rates and low positioning accuracy in the current CV data environment. To address these challenges, we propose a CV-based adaptive traffic signal control framework for urban intersections, enhanced by leveraging the continuity of CV trajectories. The framework comprises an arrival-prediction component and a signal optimization component. By leveraging trajectory continuity to trace the travel information of CVs at upstream intersections, the arrival-prediction component restores the vehicle departure distributions, calibrates the platoon dispersion process, and predicts vehicle arrivals at the studied intersection over an extended period. The signal optimization component employs a rolling-horizon scheme for real-time signal timing optimization with the objective of minimizing the total delay, which is efficiently solved using dynamic programming (DP). Evaluation results demonstrate that our proposed framework outperforms actuated control even with a modest 5% penetration rate, particularly in medium- and high-volume scenarios. Under medium-volume scenarios with penetration rates of 0.05 and 0.2, the average vehicle delays are improved by 18.8% and 35.2%, respectively, compared to actuated control. This underscores the effectiveness of the framework in situations with limited CV data, i.e., low penetration rates and low positioning accuracy.