In this paper, we focus on how gravity anomaly affects height estimation in the high-precision inertial navigation system (INS) and global navigation satellite system (GNSS) integration. The theoretical analysis based on INS error propagation equations shows that the height error is related to gravity anomaly directly. In addition, the height-related elements in the Kalman gain matrix can be used as an indicator to evaluate the extent of the effect to height estimation. Different precision grade INSs integrated with GNSS, and GNSS of different positioning accuracy integrated with high-precision INS are simulated to analyze the effect of gravity anomaly. The simulation results show that the effect can be ignored in low-precision INS cases, while is more significant in high-precision cases, which agrees well with the former theoretical analysis. At last, a shipborne test is conducted and the experimental results show that the maximum height error of high-precision INS/GNSS integration can reach to 0.5m if the gravity anomaly is not compensated, while can fall below than 0.1m after gravity anomaly compensation or modeling. It shows that the existence of gravity anomaly along the track can degrade the vertical positioning accuracy of high-precision INS/GNSS integration, and should be considered in such cases.

A laser Doppler velocimeter (LDV) is usually integrated with an inertial navigation system (INS) to autonomously acquire a vehicle’s position, velocity and attitude. The calibration process is trying to determine the scale factor of the LDV and the installation angles between LDV and INS. As a dead-reckoning system, the calibration accuracy affects the navigation performance of the LDV/INS integrated navigation system. This paper presents how to use time-differenced carrier phase (TDCP) observations instead of differenced GPS (DGPS) or precise point positioning (PPP) techniques to complete the calibration process. Differencing carrier phase observations between two GPS epochs can save the effort in ambiguity fixing and achieve centimeter relative positioning after outlier and cycle slip detection, which is suitable for LDV calibration. In order to finish the calibration within several minutes, an iteration scheme is implemented into the calibration for rapid convergence. The navigation experiment indicates that the horizontal position error of the LDV/INS integrated navigation system can achieve 26.6m/25.5km.

This paper investigates the attitude estimation errors caused by the deflections of vertical (DOV) in the case of a rotational inertial navigation system (INS) integrated with a global satellite navigation system (GNSS). It has been proved theoretically and experimentally that the DOV can introduce a tilt error to the INS/GNSS integration, whereas less attention has been given to its effect to the heading estimation. In fact, due to the intercoupling characteristic of attitude errors, the heading estimation of an INS/GNSS integrated navigation system can also be affected. In this paper, first, the attitude estimation errors caused by DOV were deduced based on the INS’s error propagation functions. Then, the corresponding simulations were conducted and the results were well consistent with the theoretical analysis. Finally, a real shipborne marine test was organized with the aimed to verify the effect of DOV on attitude estimation in the rotational INS/GNSS integration, whereas the global gravity model was used for DOV compensation. The results with DOV compensation were compared with the corresponding results where the compensation was not used and showed that the heading estimation errors caused by DOV could exceed 20 arcsecs, which must be considered in high-precision application cases.

Limited by the detection principle, an electromagnetic log (EML) can only output a velocity measurement relative to the ocean current in marine applications, which thus leads to a negative effect on a strapdown inertial navigation system (SINS)/EML integrated navigation system. The current velocity usually can be modeled as a first-order Gaussian Markov process, while the Markov time correlation constant should be determined in advance and used as a constant during the navigation process. The integrated navigation system will suffer performance degradation if an incorrect time correlation constant is applied. In order to tackle the problem, an ocean current coefficient estimation method is proposed in this manuscript. According to the Markov nature, the current velocity at the present time epoch is determined by that at the previous time epoch. Consequently, the current velocity corrected by the Kalman filter (KF) at the previous time epoch is utilized as the measurement information at the present time epoch, where the current coefficient is introduced into the state vector. The observability analysis shows that the current coefficient is totally observable. Simulation and field test results indicate that the proposed method can accurately estimate the current coefficient. Compared to the SINS/EML integrated navigation system without considering the current effects, the system with an estimated current coefficient minimizes the effect caused by ocean currents.

The hull deformation can be estimated by comparing the angular velocity outputs from two inertial navigation systems (INSs), whose estimation accuracy affects the large ship transfer alignment accuracy greatly. However, due to the existence of the cross-correlation error, which originates from the cross-correlation effect between the ship and dynamic deformation angular velocities, the estimated static hull deformation angle will be biased. Based on the inertial matching equation, an analysis of how the cross-correlation error to the hull deformation angle measurement is provided in this manuscript. It is demonstrated that a linear correlation coefficient between the ship and deformation angular velocities will be coupled into the hull deformation angle estimation as a biased deformation angle error. In order to mitigate the biased error, an error estimation method is further presented to compensate the cross-correlation error, based on the least square estimation and correlation theory. The simulation and experimental results indicate that the proposed method can accurately compensate the cross-correlation error and effectively reduce biased deformation angle error, which is helpful in improving the larger ship transfer alignment accuracy.

This study introduces a challenge faced by CNN in the task of traffic sign detection: how to achieve robustness to distributional shift. At present, all kinds of CNN models rely on strong data augmentation methods to enrich samples and achieve robustness, such as Mosaic and Mixup. In this study, we note that these methods do not have similar effects on combating noise. We explore the performance of augmentation strategies against disturbance in different frequency bands and provide understanding from the Fourier analysis perspective. This understanding can provide a guidance for selecting data augmentation strategies for different detection tasks and benchmark datasets.