Due to the errors of the accelerometer and gyroscope, the position and the velocity calculated by the inertial navigation system (INS) are divergent with time. We can normally estimate and compensate the errors of the INS using the underwater sensors. However, the underwater sensors such as ultrashort baseline (USBL) acoustic positioning system and Doppler velocity log (DVL) are challenged by the complex environment, which affects the reliability and the accuracy of data processing. From the gravimetry error equation, the horizontal position errors have little influence on the underwater gravimetry. Observability analysis indicates that the velocity error and the position error can be well estimated on the condition of only positional observations in the Kalman filter. Based on these, we proposed a novel method using the INS and depth gauge (DG) based on trajectory constraint without USBL and DVL. In this method, we considered to fit the track of the gravimeter to a straight line because the gravimeter maintains uniform motion in the measuring line and take the fit line and the depth measured by the DG as the observations to correct the errors of the INS. We constructed an underwater experiment in 2019 to test the novel method. The test results showed a repeatability from 1.24 to 2.03 mGal for the space resolution of 200 m. The new method can acquire a good accuracy and can be applied to the gravimetry data processing.

Underwater gravity information plays a major role in deepwater oil and gas exploration. To realize underwater dynamic gravimetry, we have developed a strapdown gravimeter mounted in a pressure capsule for adaption to the underwater environment and we adopted a two-stage towed underwater gravimetry scheme. An improved strapdown gravimeter and other underwater sensors were installed in a towed vessel to form an underwater dynamic gravimetry system. Because the global navigation satellite system cannot be used for underwater dynamic gravimetry, we developed a new method based on underwater multisensor integrated navigation, in which a federal Kalman filter was applied for error estimation. This new method allowed us to obtain the accurate attitude, velocity, and position necessary for gravity estimation. In addition, the gravity data can then be extracted from the noisy data through finite impulse response low-pass filtering. We acquired the underwater gravity data at a depth of 300 m to test the validity of the new method and evaluate the accuracy of the underwater gravity system. The results indicated a repeatability from 0.85 to 0.96 mGal at a half wavelength of approximately 0.2 km and also indicated good consistency with the marine gravity data.

The accuracy of gravity disturbance horizontal components is an obstacle in strapdown airborne vector gravimetry at present. In the strapdown inertial navigation system (SINS) field, the rotation modulation technique has been put into practice to improve the accuracy of navigation for decades, which could suppress the divergence of SINS errors. Since there is a close connection between SINS and strapdown vector gravimetry, we were inspired to research on introducing rotation modulation into strapdown airborne vector gravimetry in this study. In this article, the second section introduced the connections and differences between SINS and vector gravimetry. Then, the third section analyzed three main obstacles in improving the horizontal components accuracy of strapdown airborne vector gravimetry. To solve these problems, the fourth section proposed the mechanism of rotation modulation vector gravimetry from system level which is inspired by rotation modulation inertial navigation system (RMINS). On the basis of the mechanism, the fifth section designed a yaw continuous rotation modulation scheme for vector gravimetry. Simulation and real-world static experiment demonstrated that the designed scheme has a better performance in horizontal components than the classical strapdown gravimetry. Moreover, the experiment with drift showed that rotation modulation could also suppress the effects of the accelerometer long-term drift on gravimetry results. In conclusion, this article introduced the rotation modulation into strapdown airborne vector gravimetry for the first time. It will probably provide a reference for developing the next-generation strapdown airborne vector gravimeter.

In view of the fact that there are dynamic errors in the strapdown dynamic gravimetry, based on the analysis of the error mechanism of the strapdown dynamic gravimetry, a general model to compensate the dynamic error of the strapdown dynamic gravimetry is proposed, and the constraints are established by using the correlation analysis; then, the parameters of the model are estimated. The effectiveness of the proposed method is verified by using the strapdown airborne gravimetry data under the undulated flight conditions. The results show that the repeatability of the repeated gravity measurements under 160-s filtering is improved from 1.41 to 0.70 mGal, while the result under 300-s filtering is 0.62 mGal. It shows that this method can effectively eliminate the dynamic error while maintaining the spatial resolution.

To reduce costs, an unmanned swarm usually consists of nodes with high-accuracy navigation sensors (HAN) and nodes with low-accuracy navigation sensors (LAN). Transmitting and fusing the navigation information obtained by HANs enables LANs to improve their positioning accuracy, which in general is called cooperative navigation (CN). In this method, the accuracy of relative observation between platforms in the swarm have dramatic effects on the positioning results. In the popular research, constructing constraints in three-dimensional (3D) frame could only optimize the position and velocity of LANs but neglected the attitude estimation so LANs cannot maintain a high attitude accuracy when utilizing navigation information obtained by sensors installed during maneuvers over long periods. Considering the performance of the inertial measurement unit (IMU) and other common sensors, this paper advances a new method to estimate the attitude of LANs in a swarm. Because the small unmanned nodes are strictly limited by relevant practical engineering problems such as size, weight and power, the method proposed could compensate for the attitude error caused by strapdown gyroscopic drift, which only use visual vectors built by the targets detected by cameras with the function of range finding. In our method, the coordinates of targets are mainly given by the You Only Look Once (YOLO) algorithm, then the visual vectors are built by connecting the targets in the covisibility graph of the nodes in the swarm. The attitude transformation matrices between each camera frame are calculated using the multivector attitude determination algorithm. Finally, we design an information filter (IF) to determine the attitude of LANs based on the observation of HANs. Considering the problem of positioning reference, the field test was conducted in the open air and we chose to use two-wheeled robots and one UAV to carry out the experiment. The results show that the relative attitude error between nodes is less than 4 degrees using the visual vector. After filtering, the attitude divergence of LANs’ installed low precision IMU can be effectively constrained, and the high-precision attitude estimation in an unmanned CN swarm can be realized.