Aiming at the situation that the underwater integrated navigation system is easy to be disturbed and the output is unavailable during the task of underwater vehicle, a RVBAKF/ LSTM hybrid method is proposed in this paper. Considering the actual underwater working environment of autonomous underwater vehicles (AUV), the measured value of Doppler velocity log (DVL) is prone to outliers or even interruption, so it is very important to improve the fault tolerance of integrated navigation system. For the processing of outliers, a robust adaptive filter based on VB theory is proposed. Its advantage is to realize the adaptation of time-varying noise and reduce the interference of outliers to the integrated navigation system. Firstly, selecting the SINS output related to AUV velocity, such as velocity, attitude, angular velocity and specific force as the training input when the DVL output is normal. When DVL output is interrupted, the long short-term memory (LSTM) model is used to provide pseudo measurement values for integrated navigation system. The effectiveness of the method is verified by the on-board experimental data. When the DVL output is interrupted, the method can effectively improve the accuracy of the integrated navigation system. The method in this paper is compared with four different hybrid methods, and the results are obviously better than the four methods.

In this paper, a new Euler angle model without approximation based on SE(3) is proposed to solve the problem that the low common frame performance of conventional Euler angle error model based on SE(3) for inertial navigation system (INS) when the misalignment angle error is large. Firstly, the Euler angle error is represented by the relationship between Euler angle and the attitude matrix. Then, the left/right error model based on SE(3) without approximation is rederived, extending the conventional Euler angle error model based on SE(3) to the application of large misalignment angle error. Finally, the validity of the proposed model is verified by theoretical analysis and field experiments. The results show that the proposed model is more applicable to INS/GPS and INS/DVL, respectively. Especially in the case of large misalignment angle, the convergence and accuracy of the proposed model are higher than the conventional model.

In response to the lack of specific demonstration and analysis of the research on the necessity of the Lie group strapdown inertial integrated navigation error model based on the Euler angle, two common integrated navigation systems, strapdown inertial navigation system/global navigation satellite system (SINS/GNSS) and strapdown inertial navigation system/doppler velocity log (SINS/DVL), are used as subjects, and the piecewise constant system (PWCS) matrix, based on the Lie group error model, is established. From three aspects of variance estimation, the observability and performance of the system with large misalignment angles for low, medium, and high accuracy levels, traditional error model, Lie group left error model, and right error model are compared. The necessity of research on Lie group error model is analyzed quantitatively and qualitatively. The experimental results show that Lie group error model has better stability of variance estimation, estimation accuracy, and observability than traditional error model, as well as higher practical value.

Vertical information (vertical velocity and altitude) is important in three-dimensional navigation. In order to improve the vertical accuracy of strapdown inertial navigation system/global navigation satellite system integrated navigation (SINS/GNSS) while reducing costs, firstly, the propagation laws of vertical error sources in two types of SINS/GNSS (vertical velocity set to 0 and not set to 0) are systematically analyzed. Furthermore, a vertical accuracy improvement method considering the gravitational anomaly is proposed. In this method, the gravitational anomaly is considered as one of the vertical error sources. Then, the processing method of error sources in integrated navigation is referenced, and two processing modes of gravitational anomaly are designed. The first method is to represent the gravitational anomaly as one of the system states of SINS/GNSS. The number of dimensions for the system is expanded from 15 to 16. The corresponding mathematical model is derived to ‘absorb’ the vertical errors caused by the gravitational anomaly. The second is to represent the gravitational anomaly as one of the vertical system noises. Thereby, the Kalman filter is adjusted in real time using the above adaptive method to improve the accuracy of the estimated state. The corresponding errors are then suppressed. Field experiments show that both modes of the proposed method can effectively improve the vertical accuracy.

Gravity matching is a key technology in gravity-aided inertial navigation. The traditional Sandia inertial matching algorithm introduces linearization errors using the linear error model, which can diminish navigation accuracy. To address this issue, we propose a novel gravity-matching algorithm based on modified adaptive transformed cubature quaternion estimation (MA-TCQUE), designed for a nonlinear error model to enhance accuracy in gravity-aided navigation. Additionally, the proposed algorithm can estimate the measurement noise matrix demonstrating improved filtering stability in complex and dynamic environments. Finally, simulation and experimental results validate the advantages of the proposed matching algorithm compared to existing state-of-the-art methods.

The virtual spherical vector position model (VSVPM) is widely used in global navigation. Strapdown inertial navigation system/ doppler velocity log (SINS/DVL) is a commonly used underwater navigation method. In order to improve the performance of SINS/DVL under this framework, this paper proposes the Euler error model based on the attitude error of body frame. Firstly, the rotational difference between the calculated frame and the ideal frame is defined as the attitude error. Then, based on matrix operation rules, the corresponding differential equations of attitude, velocity, and position errors are derived. And according to the rules of linear approximation, a linear state-space model based on attitude error of body frame is obtained, and the corresponding measurement equations and feedback corrections of SINS/DVL are provided. Finally, the effectiveness of the proposed model is validated through simulation and field test. The results show that, in case of large misalignment angles, the proposed model exhibits superior attitude convergence velocity and accuracy compared to traditional error models, with a reduction of at least 92.79%. This work also provides a reasonable explanation for which attitude error representation is more accurate.