A new nonlinear algorithm is proposed for strapdown inertial navigation system (SINS)/celestial navigation system (CNS)/global positioning system (GPS) integrated navigation systems. The algorithm employs a nonlinear system error model which can be modified by unscented Kalman filter (UKF) to give predictions of local filters. And these predictions can be fused by the federated Kalman filter. In the system error model, the rotation vector is introduced to denote vehicle’s attitude and has less variables than the quaternion. Also, the UKF method is simplified to estimate the system error model, which can both lead to less calculation and reduce algorithm implement time. In the information fusion section, a modified federated Kalman filter is proposed to solve the singular covariance problem. Specifically, the new algorithm is applied to maneuvering vehicles, and simulation results show that this algorithm is more accurate than the linear integrated navigation algorithm. A new nonlinear algorithm is proposed for strapdown inertial navigation system (SINS) / celestial navigation system (CNS) / global positioning system (GPS) integrated navigation systems. The algorithm employs a nonlinear system error model which can be modified by unscented Kalman filter (UKF And the predictions can be fused by the federated Kalman filter. In the system error model, the rotation vector is introduced to denote vehicle’s attitude and has less variables than the quaternion. Also, the UKF method is fused to estimate the system error model, which can both lead to less calculation and reduce algorithm implement time. In the information fusion section, a modified federated Kalman filter is proposed to solve the singular covariance problem. Specifically, the new algorithm is applied to maneuvering vehicles , and simulation results show that this algorithm is more accurate than the linear integrated navigation algorithm.