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A resilient positioning, navigation, and timing (PNT) system is a necessity for the robust navigation of autonomous vehicles (AVs). A global navigation satellite system (GNSS) provides satellite-based PNT services. However, a spoofer can tamper the authentic GNSS signal and could transmit wrong position information to an AV. Therefore, an AV must have the capability of real-time detection of spoofing attacks related to PNT receivers, whereby it will help the end-user (the AV in this case) to navigate safely even if the GNSS is compromised. This paper aims to develop a deep reinforcement learning (RL)-based turn-by-turn spoofing attack detection method using low-cost in-vehicle sensor data. We have utilized the Honda Research Institute Driving Dataset to create attack and non-attack datasets to develop a deep RL model and have evaluated the performance of the deep RL-based attack detection model. We find that the accuracy of the deep RL model ranges from 99.99% to 100%, and the recall value is 100%. Furthermore, the precision ranges from 93.44% to 100%, and the f1 score ranges from 96.61% to 100%. Overall, the analyses reveal that the RL model is effective in turn-by-turn spoofing attack detection.