Aerobics is an internationally famous fitness and sports competition program. This paper aims to design an aerobics arm movement trajectory recognition method with the assistance of a sports computer to detect aerobics movements in real-time. The study first introduces the Gaussian kernel function based on the Kalman filter pose solution method to construct the aerobics arm GP-SUKF pose solution model. The acceleration data are then coordinate transformed to remove the gravity component of each axis, and the features of the aerobics action trajectory are extracted by combining the time-frequency domain integration method and eliminating the cumulative error. Finally, a support vector machine algorithm based on particle swarm optimization is constructed to classify and identify the features extracted from the trajectory of the extracted aerobics arm. In the simulation experiments, the algorithm in this paper provides more motion trajectory points for the aerobics arm movements. It is closer to the actual value of the wrist movements offered by the OptiTrack system, with the error ranging from 0.02m to 0.04m, and a better tracking effect can be obtained in the case of fast movements. This study can accurately track the trajectory of aerobics arm movements and provide more accurate posture and movement assistance for professional athletes and bodybuilders.