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

Abstract

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.

Online calibration method for SINS/LDV integrated navigation system based on left group error definition

“…According to [33], it is easy to see that the observation in ( 21) and ( 22) is a left-invariant observation for the group state (19). Moreover [34], demonstrates that for SINS/ external velocity sensors integration, the measurement of body velocity is neither left-nor right-invariant observation for the group state (19), but the left-invariant error definition is more suitable when considering IMU bias. Therefore, in the online calibration method based on Lie group SE 2 (3) and GNSS for the SINS/LDV integrated navigation system, the left-invariant group error is used…”

“…Equation (34) shows that the state transition matrix is independent of the global state, even if the errors of the inertial sensor are taken into account. This indicates that the navigation errors will not affect the accuracy of the error differential equations.…”

“…To evaluate the performance of the proposed methods, we compare them with the most widely used calibration method based on a conventional Kalman filter. We denote the calibration method presented in section 2 as SO-KF, the calibration method based on the left error model (34) and the velocity measurement model (38) in section 3 as LSE-V-KF, the calibration method based on the left error model (34) and the displacement increment measurement model (46) in section 3 as LSE-DI-KF, and the calibration method based on the left error model (59) in section 4 as LSE-DR-KF.…”

“…The obtained left and rightinvariant error state models are trajectory-independent, and their log-linearity, an advantage, makes them very suitable for attitude initialization with arbitrary misalignment. Tang et al [34] shows that for SINS/DVL integration using the error state model proposed in [33], the left-invariant error definition is more suitable for SINS/DVL navigation when considering IMU bias. Chang et al [35] incorporates the DR position of the SINS/DVL integration with the attitude, velocity, and position computed by SINS as the elements of the group of triple direct isometries SE 3 (3).…”

A rapid alignment method for high-precision rotational INS within group affine

“…Furthermore, the nonlinear method cannot achieve the accuracy of the conventional two-phases method due to the shortcomings of the nonlinear error state model. Another idea is an alignment method based on Lie group theory [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. It has been noted that some dynamical models satisfy a particular 'group affine' property if their states are defined in Lie group [20].…”