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The strapdown inertial navigation systems (SINS) have been widely used for many vehicles, such as commercial airplanes, Unmanned Aerial Vehicles (UAVs), and other types of aircrafts. In order to evaluate the navigation errors precisely and efficiently, a prediction method based on support vector machine (SVM) is proposed for positioning error assessment. Firstly, SINS error models that are used for error calculation are established considering several error resources with respect to inertial units. Secondly, flight paths for simulation are designed. Thirdly, the $\epsilon $ -SVR based prediction method is proposed to predict the positioning errors of navigation systems, and particle swarm optimization (PSO) is used for the SVM parameters optimization. Finally, 600 sets of error parameters of SINS are utilized to train the SVM model, which is used for the performance prediction of new navigation systems. By comparing the predicting results with the real errors, the latitudinal predicting accuracy is 92.73%, while the longitudinal predicting accuracy is 91.64%, and PSO is effective to increase the prediction accuracy compared with traditional SVM with fixed parameters. This method is also demonstrated to be effective for error prediction for an entire flight process. Moreover, the prediction method can save 75% of calculation time compared with analyses based on error models.