As autonomous vehicles become an essential component of modern transportation, they are increasingly vulnerable to threats such as GPS spoofing attacks. This study presents an adaptive detection approach utilizing a dynamically tuned Density Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, designed to adjust the detection threshold (ε) in real-time. The threshold is updated based on the recursive mean and standard deviation of displacement errors between GPS and in-vehicle sensors data, but only at instances classified as non-anomalous. Furthermore, an initial threshold, determined from 120,000 clean data samples, ensures the capability to identify even subtle and gradual GPS spoofing attempts from the beginning. To assess the performance of the proposed method, five different subsets from the real-world Honda Research Institute Driving Dataset (HDD) are selected to simulate both large and small magnitude GPS spoofing attacks. The modified algorithm effectively identifies turn-by-turn, stop, overshoot, and multiple small biased spoofing attacks, achieving detection accuracies of 98.621%, 99.960.1%, 99.880.1%, and 98.380.1%, respectively. This work provides a substantial advancement in enhancing the security and safety of AVs against GPS spoofing threats.