The error propagation of traditional strapdown inertial navigation system (SINS)/Doppler velocity log (DVL) is not autonomous because its error state model is trajectorydependence. Recently, the invariant error defined on Lie group has raised much attention due to its trajectory-independent and autonomous error propagation. In this paper, the invariant errorbased Kalman filter for SINS/DVL integration solution is investigated with main focus on its extension and comparison. The contributions of this study are threefold. First, the invariant error defined on matrix Lie group (group of double direct isometrics) are extended to model the non-group-affine traditional SINS mechanism and the group-affine transformed SINS mechanism, both of them are derived in Earth frame and augmented with the drift and bias of the inertial measurement units (IMUs). Then, the observation equations for different invariant error-based state models are derived for SINS/DVL application, theoretical analysis is performed and comprehensive evaluation are conducted under different maneuvering condition by lake field trial. Finally, the variational Bayesian approach is introduced into invariant errorbased Kalman filter to inferring the inaccurate process noise covariance matrix (PNCM) and time-varying measurement noise covariant matrix (MNCM) from a practical perspective, experimental results demonstrate that it can improve the navigation accuracy significantly. This study is expected to facilitate the selection of appropriate invariant error to SINS/DVL application.

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