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The inertial navigation system (INS) and Doppler velocity log (DVL) tightly integrated navigation system is widely used in autonomous underwater vehicles. However, due to the changeable and complex marine environment, the DVL measurement noise may contain a significant amount of outlier interferences, and the system noise also exhibits inherent uncertainty. Although the existing variational-Bayesian-based robust Student’s t Kalman filter (VB-RSTKF) can mitigate the impact of the outliers to a certain extent, the establishment of its state-space model is based on traditional error variable, which makes the estimation consistency poor. In addition, its estimation accuracy is affected by the inaccurate prior prediction error covariance matrix and state noise covariance matrix (SNCM). In this article, in order to improve the estimation consistency, a novel unified Lie group navigation framework is proposed, and the invariant error-based state and the measurement equation are established, respectively. Then, the expectation-maximization (EM)-VB-based RSTKF (EMVB-RSTKF) is proposed to improve the algorithm estimation accuracy within the inaccurate prior SNCM, where the prediction error scale matrix is estimated by using the EM method and the SNCM is indirectly estimated online based on the estimate of prediction error covariance matrix. Finally, the results of simulations and semiphysical filed experiments show that the proposed algorithm has significant advantages in convergence speed and estimation accuracy.

Information fusion is one of the key technologies in airborne multisource navigation, where the federated filter is widely used due to its simple structure. However, the sensor measurement of multisource navigation system will become unreliable in some interferential environment, which leads to the state and measurement noise covariance matrix (MNCM) change over time and estimate difficultly. Inaccurate covariance matrices cause the loss of positioning accuracy in traditional federated filter. To address the problems, this article puts forward an adaptive federal Kalman filtering algorithm based on variational Bayesian and applies it to the inertial navigation system (INS)/global positioning system (GPS)/terrain/geomagnetic multisource navigation system. Simulation and experimental results show that the proposed filter outperforms the traditional federated filter in improving the positioning accuracy under the condition of time-varying or even unknown state and MNCM, which plays a positive role in unmanned aerial vehicle (UAV) multisource navigation.