Strapdown inertial navigation system has been the main navigation and positioning method for long voyage and long-endurance underwater navigation. In order to solve the problem that velocity information provided by Doppler velocity log and position information provided by acoustic single transponder are easily contaminated by non-Gaussian noise, a federated robust Kalman filter algorithm was proposed. In the proposed method, the Mahalanobis distance algorithm was used to introduce a inflated factor to inflate the measurement noise covariance, which can improve the robustness of integrated navigation system. At the same time, the information distribution coefficient was adaptively tuned based on the performance of the sub-filter, which can guarantee the accuracy of integrated navigation system. The semi-physical simulation test for underwater integrated navigation was carried out by the federated robust Kalman filter algorithm and traditional federated Kalman filter algorithm based on measured data of the river test. The experiment results demonstrate that the federated robust Kalman filter algorithm has better performance in underwater integrated navigation compared with the traditional federated Kalman filter algorithm under the non-Gaussian condition and it can meet the requirements of fault tolerance and robustness for underwater integrated navigation system.