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This study concerns the strapdown inertial navigation system (SINS) initial alignment under marine mooring condition with large initial error. The ten-dimensional state initial alignment error functions of the SINS with inclusion of non-linear characteristics have been derived. It is pointed out for the first time that the non-linear functions are applied to only a subset of the elements of the state vector, that is, the velocities error and the misalignment angles. Then a computationally efficient refinement of the unscented transformation (UT) called marginalised UT (MUT) is investigated in these special non-linear systems with a linear substructure. A performance comparison between the extended Kalman filter (EKF), the UT-based Kalman filter (UKF) and the MUT-based Kalman filter (MUKF) demonstrates that both the UKF and the MUKF can outperform the EKF and the MUKF and can achieve, if not better, at least a comparable performance to the UKF, at a significantly lower expense.

Underwater vehicles are key carriers for underwater inspection and operation tasks, and the successful implementation of these tasks depends on the positioning and navigation equipment with corresponding accuracy. In practice, multiple positioning and navigation devices are often combined to integrate the advantages of each equipment. Currently, the most common method for integrated navigation is combination of the Strapdown Inertial Navigation System (SINS) and Doppler Velocity Log (DVL). Various errors will occur when SINS and DVL are combined together, such as installation declination. In addition, DVL itself also has errors in the measurement of speed. These errors will affect the final accuracy of the combined positioning and navigation system. Therefore, error correction technology has great significance for underwater inspection and operation tasks. This paper takes the SINS/DVL integrated positioning and navigation system as the research object and deeply studies the DVL error correction technology in the integrated system.

Compared with the strapdown inertial navigation system (SINS), the rotation strapdown inertial navigation system (RSINS) can effectively improve the accuracy of navigation information, but rotational modulation also leads to an increase in the oscillation frequency of attitude errors. In this paper, a dual-inertial navigation scheme that combines the strapdown inertial navigation system and the dual-axis rotation inertial navigation system is proposed, which can effectively improve the attitude error accuracy in the horizontal direction by using the high-position information of the rotation inertial navigation system and the stability characteristics of the attitude error of the strapdown inertial navigation system. Firstly, the error characteristics of the strapdown inertial navigation system and the rotation strapdown inertial navigation system are analyzed, and then the combination scheme and Kalman filter are designed according to the error characteristics, and finally, the simulation experiment shows that the pitch angle error of the dual inertial navigation system is reduced by more than 35% and the roll angle error is reduced by more than 45% compared with the rotation strapdown inertial navigation system. Therefore, the combination scheme of double inertial navigation proposed in this paper can further reduce the attitude error of the rotation strapdown inertial navigation system, and at the same time, the two sets of inertial navigation systems can also enhance the reliability of ship navigation.

This paper proposes an improved adaptive filtering algorithm based on the Sage–Husa adaptive Kalman filtering algorithm to address the issue of measurement noise characteristics impacting the navigation accuracy in strapdown inertial navigation system (SINS)/Doppler Velocity Log (DVL) integrated navigation systems. Addressing the non-positive definite matrix problem prevalent in traditional adaptive filtering algorithms and aiming to enhance measurement noise estimation accuracy, this method incorporates upper and lower thresholds determined by a discrimination factor. In the presence of abnormal measurement data, these thresholds are utilized to adjust the covariance of the innovation, subsequently re-estimating the system’s measurement noise through a decision factor based on the innovation. Simulation and experiment results demonstrate that the proposed improved adaptive filtering algorithm outperforms the classical Kalman filter (KF) in terms of navigation accuracy and stability. Furthermore, the filtering performance surpasses that of the Sage–Husa algorithm. The simulation results in this paper show that the relative position positioning error of the improved method is reduced by 49.44% compared with the Sage–Husa filtering method.

The errors of inertial sensors affect the navigation accuracy of the strapdown inertial navigation system (SINS) and are accumulated over time in nature. In order to continuously maintain the high navigation accuracy of vehicles for a long time period, an initial alignment and self-calibration is necessary after the SINS starts. Additionally, the observability analysis is one of the key techniques during the initial alignment and self-calibration process. For marine systems, the observability of inertial sensor errors is extremely low, as their motion states are always slow. Therefore, studying the rotating SINS is urgent. Since traditional analysis methods have their limitations, the global observation analysis method was used in this paper. On the basis of this method, the relationship between the observability and the kinestate of the rotating SINS has been established. After the discussion about the factors that affect the observability in detail, the design principle of the initial alignment and self-calibration rotating scheme, which is appropriate for marine systems, id proposed. With the proposed principle, a novel initial alignment and self-calibration method, named the eight-position rotating scheme, is designed. Simulations and experiments are carried out to verify its performance. The results have shown that compared with other rotating schemes and the static state, the estimated accuracy of the eight-position scheme rotating about axes x and y was the best, and the position error was significantly reduced with this new rotating scheme. The feasibility and effectiveness of the proposed design principle and the rotating scheme were verified.

The low-cost Strapdown Inertial Navigation System (SINS)/Global Navigation Satellite System (GNSS) is widely used in autonomous vehicles for positioning and navigation. Initial alignment is a critical stage for SINS operations, and the alignment time and accuracy directly affect the SINS navigation performance. To address the issue that low-cost SINS/GNSS cannot effectively achieve rapid and high-accuracy alignment in complex environments that contain noise and external interference, an adaptive multiple backtracking robust alignment method is proposed. The sliding window that constructs observation and reference vectors is established, which effectively avoids the accumulation of sensor errors during the full integration process. A new observation vector based on the magnitude matching is then constructed to effectively reduce the effect of outliers on the alignment process. An adaptive multiple backtracking method is designed in which the window size can be dynamically adjusted based on the innovation gradient; thus, the alignment time can be significantly shortened. Furthermore, the modified variational Bayesian Kalman filter (VBKF) that accurately adjusts the measurement noise covariance matrix is proposed, and the Expectation–Maximization (EM) algorithm is employed to refine the prior parameter of the predicted error covariance matrix. Simulation and experimental results demonstrate that the proposed method significantly reduces alignment time and improves alignment accuracy. Taking heading error as the critical evaluation indicator, the proposed method achieves rapid alignment within 120 s and maintains a stable error below 1.2° after 80 s, yielding an improvement of over 63% compared to the backtracking-based Kalman filter (BKF) method and over 57% compared to the fuzzy adaptive KF (FAKF) method.

The gravity gradient is the second derivative of gravity potential. A gravity gradiometer can measure the small change of gravity at two points, which contains more abundant navigation and positioning information than gravity. In order to solve the problem of passive autonomous, long-voyage, and high-precision navigation and positioning of submarines, an aided navigation method based on strapdown gravity gradiometer is proposed. The unscented Kalman filter framework is used to realize the fusion of inertial navigation and gravity gradient information. The performance of aided navigation is analyzed and evaluated from six aspects: long voyage, measurement update period, measurement noise, database noise, initial error, and inertial navigation system device level. When the parameters are set according to the benchmark parameters and after about 10 h of simulation, the results show that the attitude error, velocity error, and position error of the gravity gradiometer aided navigation system are less than 1 arcmin, 0.1 m/s, and 33 m, respectively.

The quartz flexible accelerometer (QFA) is a critical component in navigation-grade strapdown inertial navigation systems (SINS) due to its bias error, which significantly impacts the overall navigation accuracy of SINS. Temperature variations induce dynamic changes in the bias and scale factor of QFA, leading to a degradation of the navigation accuracy of SINS. To address this issue, this paper proposes a temperature error compensation method based on a non-uniform mutation strategy genetic algorithm (NUMGA) and a polynomial curve model (PCF). Firstly, the temperature bias mechanism of QFA output is analyzed, and a polynomial temperature error model is established. Then, the NUMGA is utilized to identify the model parameters using the −20–40 °C test data, seeking the optimal parameters for the polynomial. Finally, the compensation parameters are used for cold start static test verification. The results demonstrate that the temperature compensation model based on NUMGA-PCF can automatically select the optimal parameters, which enable the model to exhibit a stable decreasing trend on the adaptation curve without multiple fluctuations. Compared to the traditional GA temperature compensation model, the compensation errors in the three axes of QFA in SINS are reduced by 612.24 μg, 60.82 μg, and 875.82 μg, respectively. Before the 20th generation, there are no decrease in convergence speed observed with the in-crease of population diversity. Within the −20–40 °C temperature range, the average values and standard deviations of QFA for the three optimized axes can be maintained below 0.1 μg by using this compensation model.

The operating attitude of a shearer based on a three-dimensional (3D) space scale is the necessary basic information for realizing intelligent mining. Aiming to address the problem of the insufficient perception accuracy of shearers, in this paper, the rotation model of the actual turning mechanism of the strapdown inertial navigation system (SINS) of shearers is established, and the error propagation characteristics of different single-axis rotation modulation schemes are revealed. Through theory and simulation, the optimal rotation modulation scheme is determined to be the improved four-position turn–stop modulation with a rotation of <360°. The experiment shows that the 24 h positioning error of this scheme is 3.7 nmile, and the heading angle changes by 0.06°, which proves that this scheme can effectively improve the attitude perception accuracy of the inertial navigation system (INS). The field application of the shearer operating attitude perception based on this scheme shows that the positioning error after error compensation is 17% of that before compensation, and the heading angle error is 75% of that before compensation, which verifies that this scheme can significantly improve the accuracy of shearer operating attitude perception in field applications. This scheme can achieve higher precision perception accuracy based on SINS and has broad application prospects in the field of high-precision pose perception of coal mining machines, roadheaders, and other equipment.

To improve the reliability of strapdown inertial navigation system (SINS)/Doppler radar/odometer integrated navigation system, the federated Kalman filter with two-stage fault detection structure is designed, and a fault-tolerant SINS/Doppler radar/odometer integrated navigation method is proposed. Firstly, the pre-fault detection module sets before the local filter, and the residual chi-square test in the carrier coordinate system is selected to detect the abrupt faults of Doppler radar and odometer. Then, the secondary-fault detection module emplaces between the local filter and the main filter, and the sequential probability ratio test (SPRT) is selected to further detect the ramp faults that are difficult to detect by the residual chi-square test. To address the limitation of the SPRT in accurately determining the end time of faults, an improved SPRT is proposed. The improved SPRT reduces the influence of historical fault on the fault statistics by introducing forgetting factors to improve its sensitivity to the fault end. The simulation experiment indicates that the proposed method can quickly detect and isolate abrupt and ramp faults, and promptly restore normal operation of the integrated navigation system after the fault ends, effectively improving the fault tolerance and reliability of the integrated navigation system.