In life-critical applications, the real-time detection of faults is very important in Global Positioning System/Inertial Navigation System (GPS/INS) integrated navigation systems. A new fault detection method for soft fault detection is developed in this paper with the purpose of improving real-time performance. In general, the innovation information obtained from a Kalman filter is used for test statistic calculations in Autonomous Integrity Monitored Extrapolation (AIME). However, the innovation of the Kalman filter is degraded by error tracking and closed-loop correction effects, leading to time delays in soft fault detection. Therefore, the key issue of improving real-time performance is providing accurate innovation to AIME. In this paper, the proposed algorithm incorporates Least Squares-Support Vector Machine (LS-SVM) regression theory into AIME. Because the LS-SVM has a good regression and prediction performance, the proposed method provides replaced innovation obtained from the LS-SVM driven by real-time observation data. Based on the replaced innovation, the test statistics can follow fault amplitudes more accurately; finally, the real-time performance of soft fault detection can be improved. Theoretical analysis and physical simulations demonstrate that the proposed method can effectively improve the detection instantaneity.