The system's error characteristics is hard to be available when the low cost inertial measurement unit(IMU) is used, because the accuracy of this unit will be changed due to the aircraft manoeuvre. To address this problem, a fuzzy adaptive unscented Kalman filter using Chi-square test(CTFA-UKF) is presented for the integrated navigation system. A rough model of system noise statistics is constructed according to the IMU. Then, the system model can be evaluated through the Chi-square test, and the test value can be obtained. Finally, the estimation of system noise statistics can be calculated by the presupposed fuzzy logic function and test value. The CTFA-UKF can overcome the defect of the low cost IMU. To be concrete, an SINS/GPS integrated navigation system is simulated to verify the effectiveness of the proposed algorithm.