Handwritten signature authentication, a biometric authentication technology based on gesture behavior characteristics, is widely used for identity verification in fields like e-commerce, electronic contracts, finance, and legal sectors. However, it faces challenges such as high error rates, security vulnerabilities, and privacy concerns. To address these, this study designs a digital trajectory authentication method that leverages behavioral feature recognition. Utilizing the MediaPipe hand detection model, the method captures the airwriting trajectory through video analysis. Then, the model generates joint temporal feature descriptors from both time and frequency domains. Furthermore, a weighted probability matching strategy is adopted to construct a digital trajectory authentication model. Experiment results show that our method has an average authentication error rate (EER) of 3.04% on edge devices, which fully meets the accuracy of authentication recognition and is of great significance for the development of identity verification technology.