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Kalman filter (KF) is the most commonly used estimation technique for integrating signals from short-term high performance systems, like inertial navigation systems (INSs), with reference systems exhibiting long-term stability, like the global positioning system (GPS). However, KF only works well under appropriately predefined linear dynamic error models and input data that fit this model. The latter condition is rather difficult to be fulfilled by a low-cost inertial measurement unit (IMU) utilizing microelectromechanical system (MEMS) sensors due to the significance of their long- and short-term errors that are mixed with the motion dynamics. As a result, if the reference GPS signals are absent or the Kalman filter is working for a long time in prediction mode, the corresponding state estimate will quickly drift with time causing a dramatic degradation in the overall accuracy of the integrated system. An auxiliary fuzzy-based model for predicting the KF positioning error states during GPS signal outages is presented in this paper. The initial parameters of this model is developed through an offline fuzzy orthogonal-least-squares (OLS) training while the adaptive neuro-fuzzy inference system (ANFIS) is implemented for online adaptation of these initial parameters. Performance of the proposed model has been experimentally verified using low-cost inertial data collected in a land vehicle navigation test and by simulating a number of GPS signal outages. The test results indicate that the proposed fuzzy-based model can efficiently provide corrections to the standalone IMU predicted navigation states particularly position.