Gravity geologic method is one of the important to derive seafloor topography by using altimetry-gravity, and its committed step is gridding of regional gravity anomaly. Hence, we proposed a topography constraint factor weight optimization (TCFWO) method based on ordinary kriging method. This method fully considers the influence of topography factors on the construction of regional gravity grid besides horizontal distance. The results of regional gravity anomaly models constructed in the Markus-Wake seamount area show that the TCFWO method is better than ordinary kriging method. Then, the above two regional gravity models were applied to invert the seafloor topography. The accuracy of derived topographic models was evaluated by using the shipborne depth data and existing seafloor topography models, including ETOPO1 and V19.1 model. The experimental results show that the accuracy of ST_TCFWO (seafloor topography model inverted by TCFWO method) is better than ST_KR (seafloor topography model inverted by kriging method) and ETOPO1 model. Compared with the ST_KR, the accuracy of the ST_TCFWO has improved about 26%. In addition, the accuracy of seafloor topography is affected by the variation of depth, the distribution of control points and the type of terrain. In different depth layers, the ST_TCFWO has better advantages than ST_KR. In the sparse shipborne measurements area, the accuracy of ST_TCFWO is better than that of V19.1, ETOPO1 and ST_KR. Moreover, compared to other models, ST_TCFWO performs better in flat submarine plain or rugged seamount area.

Gravity matching navigation is one of key technologies for underwater navigation. Terrain contour matching (TERCOM), as a sequence matching method, is insensitive to the error of the initial position and has high robustness. However, it suffers from the matching low-efficiency and out-of-domain mismatches due to the grid traversal search and the domain boundary limitation, which affects TERCOM underwater navigation ability. To address these problems, a novel domain-center adaptive-transfer matching method (DAMM) is proposed. It first uses the optimal positioning of horizontal-and-vertical pre-matching lines to realize the adaptive transfer of the domain center from the INS-indicated ending point to the on-line optimal matching position. Then, a new re-matching grid domain based on this on-line transferred domain-center index value is adaptively generated, and the repositioning and update for the optimal matching position are performed by following the optimization principle of the matching indexes, which contributes to improving the matching efficiency and out-of-domain positioning reliability of underwater gravity matching navigation. Experimental results verify the outstanding underwater navigation performance of DAMM on the matching efficiency and out-of-domain positioning reliability. For three different gravity tracks, the DAMM matching efficiency, compared with TERCOM, is improved by 71%, while the number of out-of-domain mismatches and positioning accuracy are improved by more than 92% and 84%, respectively, on average.

In this study, we improved the matching efficiency of underwater terrain matching navigation. Firstly, a new geodesic-based method was developed by combining the law of the shortest arc in spherical geometry with the theory of the attitude control in space and maritime environments. Secondly, along a design track, the geodesic-based method helped reduce the radius of the search matching area, and improved the matching efficiency. Finally, for parameter setting, the search matching time of underwater terrain matching navigation was reduced from 9.84 s to 1.29 s (about 7.6 times), with the matching accuracy being invariable using the new geodesic-based method.

This paper focuses on the selection of matching areas in the gravity-aided inertial navigation system. Firstly, the Sobel operator was used in convolution of the gravity anomaly map to obtain the feature map. The convolution slope parameters were constructed by combining the feature map and the gravity anomaly map. The characteristic parameters, such as the difference between convolution rows and columns, convolution variance of the feature map, the pooling difference, and range of the gravity anomaly map, were combined. Based on the support vector machine algorithm, the convolution slope parameter-support vector machine combined method is proposed. Second, we selected the appropriate training sample set and set parameters to verify. The results show that compared with the pre-calibration results, the classification accuracy of the test set is more than 92%, which proves that the convolution slope parameter-support vector machine combined method can effectively distinguish between the suitable and the unsuitable area. Thirdly, we applied this method to another region. The navigation experiment was performed in the split-matching area. The average positioning error was better than 100 m, and the correct rate was more than 90%. The results show that sailing in the selected area can accurately match the trajectory and reduce the positioning error.

Global Navigation Satellite System Reflectometry (GNSS-R) is of great significance for the extraction and research of precise information of sea surface topography. Improving measurement accuracy is necessary for realizing spaceborne GNSS-R sea surface altimetry application. The main error source of GNSS-R distance measurement is the error of the specular reflection point positioning, which directly affects the sea surface altimetry accuracy on the reference datum. There is an elevation error of several tens of meters between the reflection reference surface used by the existing specular reflection point geometric positioning methods and the sea surface elevation, which is importantly influenced by the earth’s gravity field. Therefore, the gravity field reflection reference surface correction is the key to improving the specular reflection point positioning accuracy. In this study, based on the correction of the GNSS-R reflection reference surface, research on improving the positioning accuracy of the specular reflection point is carried out. Firstly, in order to reduce the positioning error caused by the elevation difference between the reflection reference surface and the sea surface, the gravity field reflection reference surface correction method (GFRRSCM) which corrects the reflection reference surface from the WGS-84 ellipsoid to geoid is proposed, and the positioning accuracy is improved by 25.15 m. Secondly, the normal projection reflection reference surface correction method (NPRRSCM) is proposed to correct the specular reflection point determined by the GFRRSCM from the reflection reference plane of the radial to that of the normal. Additionally, in the process of solving the spatial geometric relationship of the reflection path, the approximate substitution error is reduced by directly solving the normal projection on the plane, and the positioning accuracy is further improved by 13.05 m towards the normal. Thirdly, based on the gravity field normal projection reflection reference surface combination correction method (GF-NPRRSCCM), the specular reflection point positioning accuracy is synthetically improved by 28.66 m.

This paper mainly studies the improvement of the efficiency and out-of-domain reliability of gravity matching navigation for underwater vehicles. To overcome the traversal low-efficiency problem of the traditional terrain contour matching (TERCOM) algorithm and improve the positioning reliability of its out-of-domain mismatches, a novel soft-margin local semicircular-domain re-searching model (SLSR) is proposed by integrating the soft-margin circular grid matching (SCGM) mechanism and the local semicircular grid re-matching (LSGR) mechanism. SCGM uses three times the inertial navigation cumulative error and adds the unit grid resolution as the soft margin boundary to generate the soft-margin circular domain, which contributes to reducing in-domain matching grid points and enhancing the matching efficiency of algorithms. Then the optimal matching position in this soft-margin circular domain is obtained by using the optimization principle of matching indices. LSGR is triggered when the optimal matching position of SCGM is located near the soft-margin circular-domain boundary. It employs this optimal matching point as the center and the unit inertial navigation error as the radius to recreate the semicircular local re-searching matched grid domain (termed as semicircular domain). Moreover, the optimal matching point in this semicircular domain is obtained by the matching index optimization principle, and then it is compared and updated to obtain the final best matching position of SLSR. The simulation results show that SCGM and LSGR of the proposed SLSR method can effectively improve the matching efficiency and out-of-domain matching reliability of underwater navigation, respectively. Under the same testing conditions for the tracking starting points from three gravity regions, the number of out-of-domain mismatches of SLSR, compared with TERCOM, are lower up to 92.68%, 90.24% and 98.62%, while the average matching accuracies are relatively improved by 88.37%, 85.48% and 83.66%, which verifies the validity and feasibility of the proposed SLSR model on improving the efficiency and out-of-domain reliability of underwater gravity matching navigation.