High-precision vehicle trajectory data is crucial for the realization of intelligent transportation systems. However, existing vehicle trajectory sensing technologies are limited by the range of data collection, making it challenging to obtain full-period and full-area vehicle trajectory data, which cannot meet the demands for trajectory tracking accuracy and real-time performance in practical applications. Considering the characteristics of vehicle trajectory data across radar scenarios, a cross-device vehicle trajectory tracking method was proposed based on radar data. Firstly, trajectory data was filtered based on the lower bound of the confidence interval, and the position and velocity of vehicle trajectories were smoothed and denoised using Kalman filtering. Next, the trajectory timestamp, position coordinates, speed, direction, and lane number from the radar detection area were used as model inputs, while the position information of non-overlapping areas was used as output to construct a non-overlapping area trajectory prediction model based on long short-term memory (LSTM). Subsequently, a fast dynamic time warping (DTW) algorithm based on trajectory condition constraints and search area limitations was proposed to compute trajectory similarity, enabling cross-radar device vehicle trajectory tracking. Finally, verification was conducted using overlapping and non-overlapping scenario data from radar detection on highways. Experimental results show that the trajectory tracking accuracy in overlapping scenarios reaches 92.2%, and the trajectory matching accuracy in non-overlapping areas reaches 90.3%.