Invariant Error-Based Integrated Solution for SINS/DVL in Earth Frame: Extension and Comparison.

The error propagation of traditional strapdown inertial navigation system (SINS)/Doppler velocity log (DVL) is not autonomous because its error state model is trajectory-dependence. Recently, the invariant error defined on the Lie group has raised much attention due to its trajectory-independent and autonomous error propagation. In this article, the invariant error-based Kalman filter for the SINS/DVL integration solution is investigated with a main focus on its extension and comparison. The contributions of this study are threefold. First, the invariant error defined on the matrix Lie group (group of double direct isometrics) is extended to model the nongroup 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, a theoretical analysis is performed, and a comprehensive evaluation is conducted under different maneuvering conditions by lake field trial. Finally, the variational Bayesian approach is introduced into the invariant error-based Kalman filter to infer the inaccurate process noise covariance matrix (PNCM) and time-varying measurement noise covariance 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 applications.