The inertial measurement unit (IMU), integrating sensors such as accelerometers and gyroscopes, serves as a pivotal device in fields like navigation, attitude control, and motion analysis. However, traditional IMU calibration algorithms fail to meet the high precision requirements of unmanned aerial vehicles (UAVs) due to their significant errors. Recognizing the cumbersome and low-precision nature of traditional calibration methods, this paper proposes a calibration approach for onboard strapdown inertial navigation systems (SINS) based on the combination of Particle Swarm Optimization (PSO) and Long Short-Term Memory (LSTM) neural networks. Beginning with mechanics of SINS, an error model is established for inertial navigation. Subsequently, by training and employing the PSO-LSTM network, efficient prediction of the inertial navigation error model is achieved. Experimental results demonstrate significant advantages in prediction efficiency for the PSO-LSTM model compared to methods such as least squares, BP neural networks, and pure LSTM neural networks, with its root mean square error consistently lower than other models. The proposed approach not only enhances the accuracy and efficiency of inertial navigation error calibration but also provides robust technical support for the safe and stable flight of UAVs.