The invariant error model in inertial frame is investigated for Strapdown Inertial Navigation System (SINS)/Global Navigation Satellite System (GNSS) integrated navigation, which is no longer limited by small misalignment angle and linear approximation error like traditional SINS/GNSS integrated model, so initial alignment and integrated navigation could be combined into one stage, and the navigation solution is more accurate and faster. At first, the matrix Lie group based navigation state is defined in inertial frame and proved to satisfy group affine without introducing an auxiliary velocity like the Lie group state defined in other frame. Then both the left and right invariant error state models are derived in inertial frame respectively corresponding to the group affine model. On this basis, the left and right invariant measurement models for SINS/GNSS are also derived respectively. Finally, the simulation and a boat-mounted field test are conducted to evaluate the actual performance of the investigated models. The results show that the proposed left invariant error model performs better for SINS/GNSS than right invariant error model and also outperforms other existing SINS/GNSS integration models. Especially compared with the current advanced invariant error model defined in earth frame, the model we investigated is more concise, efficient, and accurate.

Under the strong interference of sky background noise, the reliability of celestial navigation system (CNS) measurement will drop sharply, which leads to performance deterioration for ships’ strapdown inertial navigation system (SINS)/CNS integrated navigation. To solve this problem, a long short-term memory (LSTM) model is trained to forecast a ship’s attitude to detect the attitude provided by the CNS, and the LSTM forecasted attitude can also be used as a backup in case of CNS failure. First, the SINS/CNS integrated model is derived based on an attitude solution of the CNS, which provides more favorable feature data for LSTM learning. Then, the key techniques of LSTM modeling such as dataset construction, LSTM coding method, hyperparameter optimization and training strategy are described in detail. Finally, an experiment is conducted to evaluate the actual performance of the investigated methods. The results show that the LSTM model can accurately forecast a ship’s attitude: the horizon reference error is less than 0.5′ and the yaw error is less than 0.6′, which can provide reliable reference attitude for the SINS when the CNS is invalid.

The traditional Strapdown Inertial Navigation System (SINS)/Global Navigation Satellite System (GNSS) integrated system uses standard Kalman Filter (KF) to estimate the error states, which weakens the correlation between the different error components to directly initialed the Error Covariance Matrix (ECM) into diagonalization. This initialed method is also widely applied in State Transformation Extended Kalman Filter (STEKF) and Invariant Extended Kalman Filter (IEKF), which results in state estimation failing to achieve the optimal performance. To solve this problem, this paper first analyses the transformed relationship from traditional linear error state to the nonlinear error state redefined in STEKF and IEKF, and the strong correlation is found between the redefined error state components, namely the ECM in STEKF or IEKF no longer appears as a diagonal matrix. Then, aiming at the nonlinear error states, the transformed models of ECM in STEKF and IEKF are derived respectively, which establishes the theoretical basis for ECM initialization based on the error states correlation. Finally, the accuracy, feasibility and general applicability of the proposed method are verified by a boat-mounted field trial.

In view of the low accuracy of the motion parameters generated by the typical ship trajectory generator, and the fact that the problem of wind, current and wave interference is not considered, this paper establishes a new ship trajectory generator by analyzing the changes in the ship’s attitude and speed under different motion states. Through simulation, the accuracy of the main motion parameters is significantly improved compared with the typical trajectory generator; the time-varying non-uniform wind, current and wave fields are constructed, and the interference effect of wind, current and waves on ship motion is analyzed by combining the empirical formulas of force and moment; an adaptive neuro fuzzy inference system (ANFIS) based on wind, current and wave interference is designed, and the fuzzy rules of the fuzzy system are determined by training and testing the measured data; the motion parameters of superimposed wind, current and wave interference are compared with the measured data, and the accuracy is further improved after superimposing wind, current and wave interference.

To solve the problem of high-precision and fast initial alignment for the Strapdown Inertial Navigation System (SINS) under both dynamic and static conditions, the high-precision attitude measured by the celestial navigation system (CNS) is used as the reference information for the initial alignment. The alignment algorithm is derived in the Earth-centered inertial (ECI) frame. Compared with the alignment algorithm in the navigation frame, it is independent of position parameters and avoids the influence of the approximate error caused by the dynamic deflection angle. In addition, hull deformation is considered in attitude optimal estimation, which can realize initial the alignment of the SINS installed in various parts of the carrier. On this basis, the velocity measurement information is added to the alignment process, which further improves the accuracy and speed of the initial alignment under static conditions. The experimental results show that the algorithms proposed in this paper have better performance in alignment accuracy, speed, and stability. The attitude and velocity matching algorithm in the ECI frame can achieve alignment accuracy better than 0.6′. The attitude matching algorithm in the ECI frame has better robustness and can be used for both dynamic and static conditions, which can achieve alignment accuracy better than 1.3′.

The initial attitude error is challenging to satisfy the requirements of the linear model due to the complex nature of the ocean environment. This presents a challenge in the transfer alignment of the ship. In order to enhance the precision and velocity of ship transfer alignment, as well as to streamline the alignment processes, this paper proposes a transfer alignment methodology based on the Earth-Centered Earth-Fixed (ECEF) frame special Euclidean group (SE(3)) matrix Lie group. After introducing the two navigation states, velocity and attitude, from the ECEF frame into SE(3), the nonlinear inertial navigation system error state model and its corresponding measurement equations are derived based on the mapping relationship between the Lie groups and Lie algebra. The method effectively solves the error problem due to linear approximation in the traditional transfer alignment method, and applies to misalignment angles of arbitrary scale. The simulation results verify the effectiveness and rapidity of the proposed alignment method in the case of arbitrary misalignment angles.