This article proposes to use a newly derived transformed inertial navigation system (INS) mechanization to fuse INS with other complementary navigation systems. Through formulating the attitude, velocity, and position as one group state of a group of double direct spatial isometries $\mathbb{S}{\mathbb{E}_2}(3)$ , the transformed INS mechanization has proven to be group affine, which means that the corresponding vector error state model will be trajectory-independent. In order to make use of the transformed INS mechanization in inertial-based integration, both the right and left vector error state models are derived. The INS/GPS and INS/Odometer integration are investigated as two representatives of inertial-based integration. Some application aspects of the derived error state models in the two applications are presented, which include how to select the error state model, initialization of the $\mathbb{S}{\mathbb{E}_2}(3)$ based error state covariance, and feedback correction corresponding to the error state definitions. Extensive Monte Carlo simulations and land vehicle experiments are conducted to evaluate the performance of the derived error state models. It is shown that the most striking superiority of using the derived error state models is their ability to handle the large initial attitude misalignments, which is just the result of log-linearity property of the derived error state models. Therefore, the derived error state models can be used in the so-called attitude alignment for the two applications. Moreover, the derived right error state-space model is also very preferred for long-endurance INS/Odometer integration due to the filtering consistency caused by its less dependence on the global state estimate.

The task of strapdown inertial navigation system (SINS) initial alignment is to calculate the attitude transformation matrix from body frame to navigation frame. In this paper, such attitude transformation matrix is divided into two parts through introducing the initial inertially fixed navigation frame as inertial frame. The attitude changes of the navigation frame corresponding to the defined inertial frame can be exactly calculated with known velocity and position provided by GNSS. The attitude from body frame to the defined inertial frame is estimated based on the SINS mechanization in inertial frame. The attitude, velocity and position in inertial frame are formulated together as element of the group of double direct spatial isometries (). It is proven that the group state model in inertial frame satisfies a particular “group affine” property and the corresponding error model satisfies a “log-linear” autonomous differential equation on the Lie algebra. Based on such striking property, the attitude from body frame to the defined inertial frame can be estimated based on the linear error model with even extreme large misalignments. Two different error state vectors are extracted based on right and left matrix multiplications and the detailed linear state-space models are derived based on the right and left errors for SINS mechanization in inertial frame. With the derived linear state-space models, the explicit initial alignment procedures have been presented. Extensive simulation and field tests indicate that the initial alignment based on the left error model can perform quite well within a wide range of initial attitude errors, although the used filter is still a type of linear Kalman filter. This method is promising in practical products abandoning the traditional coarse alignment stage.

In this paper, the nonlinear initial alignment method for Strapdown inertial navigation system is investigated. As an important part of the nonlinear initial alignment method, the dynamic model based on nonlinear error equations is re-derived with the consideration of the mismatch between the calculated navigation frame and the actual navigation frame. Then, the recursive nonlinear initial alignment procedure based on the modified model under the marine mooring condition is elaborated. The superiority of the proposed method over traditional method in terms of rapidness, accuracy, and consistency is validated through simulated and experimental tests.

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.

The atomic gravimeter is an innovative quantum sensor featuring high precision, great sensitivity, and lasting stability. Currently, one research focus is on the combination of the atomic gravimeter with an accelerometer to implement dynamic measurements and gather gravity information in a real-time and highly precise manner. The Kalman filter framework was utilized with gravity and accelerometer drift as its states to observe the outputs of the atomic gravimeter and accelerometer, and the fusion of their data is realized. It can restrain the influence of dynamic vibration noise and obtain high precision gravity information in real time. Moreover, the accelerometer drift was estimated and compensated for, so as to enhance the lasting stability of the system. Laboratory static, swing platform and lake navigation tests were carried out to verify the effectiveness and feasibility of the proposed method. As revealed in the static test, the proposed method could effectively inhibit the effect of noise, and enhance the precision of gravity measurement. After making a compensation for drift, the noise coefficients of the accelerometer, including the bias stability (B), acceleration random walk (K), and rate ramp (R) decreased noticeably. The swing platform test further verified the applicability of the proposed method in dynamic conditions. As proved in the lake test, better results were obtained at a maximum velocity of 8.5 km h⁻¹. The gravity from the high-precision strap-down gravimeter on the same boat was taken as the reference, and processed to obtain the residual error of 2.03 ± 7.12 mGal, so that the proposed method was superior to the offline 300 s smooth filter. The proposed method offers a new approach for the study of atomic gravimeter dynamic measurement.

An atomic interference gravimeter (AIG) is of great value in underwater aided navigation, but one of the constraints on its accuracy is vibration noise. For this reason, technology must be developed for its vibration isolation. Up to now, three methods have mainly been employed to suppress the vibration noise of an AIG, including passive vibration isolation, active vibration isolation and vibration compensation. This paper presents a study on how vibration noise affects the measurement of an AIG, a review of the research findings regarding the reduction of its vibration, and the prospective development of vibration isolation technology for an AIG. Along with the development of small and movable AIGs, vibration isolation technology will be better adapted to the challenging environment and be strongly resistant to disturbance in the future.