Integrated navigation systems for various applications, generally employs the centralized Kalman filter (CKF) wherein all measured sensor data are communicated to a single central Kalman filter. The advantage of CKF is that there is a minimal loss of information and high precision under benign conditions. But CKF may suffer computational overloading, and poor fault tolerance. The alternative is the federated Kalman filter (FKF) wherein the local estimates can deliver optimal or suboptimal state estimate as per certain information fusion criterion. FKF has enhanced throughput and multiple level fault detection capability. The Standard CKF or FKF require that the system noise and the measurement noise are zero-mean and Gaussian. Moreover it is assumed that covariance of system and measurement noises remain constant. But if the theoretical and actual statistical features employed in Kalman filter are not compatible, the Kalman filter does not render satisfactory solutions and divergence problems also occur. To resolve such problems, in this paper, an adaptive Kalman filter scheme strengthened with fuzzy inference system (FIS) is employed to adapt the statistical features of contributing sensors, online, in the light of real system dynamics and varying measurement noises. The excessive faults are detected and isolated by employing Chi Square test method. As a case study, the presented scheme has been implemented on Strapdown Inertial Navigation System (SINS) integrated with the Celestial Navigation System (CNS), GPS and Doppler radar using FKF. Collectively the overall system can be termed as SINS/CNS/GPS/Doppler integrated navigation system. The simulation results have validated the effectiveness of the presented scheme with significantly enhanced precision, reliability and fault tolerance. Effectiveness of the scheme has been tested against simulated abnormal errors/noises during different time segments of flight. It is believed that the presented scheme can be applied to the navigation system of aircraft or unmanned aerial vehicle (UAV).