For rotational inertial navigation system(RINS), the system error can be compensated by rotating the inertial measurement unit (IMU) with one or more axis regularly, and the error compensation effect is determined by the rotation scheme of IMU.A reasonable rotation scheme should remove the system errors caused by inertial sensors errors and meanwhile, should not introduce other additional errors by the rotation. The error compensation demerits of two common rotation schemes are discussed. In these two schemes, the attitude errors caused by installation error are not modulated completely in a whole rotation period, which will cause accumulative velocity errors by integration. The accumulative velocity errors will sequentially increase the amplitude of position oscillation error. Based on the aforementioned analysis, a comprehensive error compensation scheme for dual-axis RINS is proposed. The proposed scheme can not only modulate the constant bias of inertial sensors, but also compensate the scale factor errors and installation errors coupled with IMU rotation. Moreover, the coupling errors are modulated into a zero-mean form with half amplitude of those two traditional schemes. As a result, the system errors of RINS with this rotation scheme can be modulated to a maximum extent. The superiority of the proposed scheme is verified through simulations with 4 different error conditions. Under the same synthesized error condition, the position error of the proposed scheme decreases to 0.37nmile/72hours from 0.98nmile/72hours in the other two schemes.

Traditional rotational inertial navigation systems are based on rotation around one or two sensitive axes of inertial sensors. However, as the rotation and sensitive axes of inertial sensors lie along the same direction, it is difficult to modulate the relative error of the inertial sensor in the axial direction. This paper proposes a dual-axis rotation scheme based on the diagonal rotation of the inertial measurement unit (IMU) body. The scheme selects the body diagonal of the three orthogonal inertial sensors of the IMU as the horizontal rotation axis, and sets the vertical rotation axis orthogonal to this axis. As the rotation axis and the inertial sensor are oriented in different directions, at any moment of rotation, the errors of the inertial sensor in the three axial directions can all be modulated, especially the installation error. First, a mathematical model based on the diagonal rotation of the IMU body is established. On this basis, the coordinate transformation relationship and the error equations are derived, and the error propagation characteristics are obtained. Finally, the comprehensive error of the system is tested. Under the same error conditions, the system latitude error is reduced from 0.1089 nautical miles/72 h in the traditional scheme to 0.0368 nautical miles/72 h, and the longitude error is reduced from 0.3587 nautical miles/72 h to 0.1332 nautical miles/72 h. These results verify the effectiveness of the proposed scheme. This method of rotating around the body diagonal of the IMU also exhibits certain advantages when applied to other rotational inertial navigation schemes.

The system-level calibration technology of rotational inertial navigation is one of the main methods to improve the accuracy of inertial navigation, and the design of the calibration scheme is the key to calibration technology. By the establishment of the error model of inertial navigation system, a 30-position calibration scheme is designed in this study. Based on the 30-dimensional Kalman filter, the constant errors, scale factor errors and installation error of gyroscope and accelerometer are identified. Comparing the traditional schemes and the 30-position scheme with the simulation experiment, the observability of the 30-position scheme is higher, the residual error of the estimated sensor is smaller and the navigation positioning accuracy after the estimated inertial sensor error parameter compensation is higher, which verifies the feasibility of the 30-position scheme. Finally, the measured experiment uses the 30-position scheme to estimate the error of a certain type of IMU sensor, and the calibration curve of the error parameter is well converged before the end of the calibration experiment, so it has certain practical value.

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.

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.

When magnetic matching aided navigation is applied to an underwater vehicle, the magnetometer must be installed inside the vehicle, considering the navigation safety and concealment of the underwater vehicle. Then, the interference magnetic field will seriously affect the accuracy of geomagnetic field measurement, which directly affects the accuracy of geomagnetic matching aided navigation. Therefore, improving the accuracy of geomagnetic measurements inside the vehicle through error compensation has become one of the most difficult problems that requires an urgent solution in geomagnetic matching aided navigation. In order to solve this problem, this paper establishes the calculation model of the internal magnetic field of the underwater vehicle and the geomagnetic measurement error model of the ship-borne magnetometer. Then, a compensation method for the geomagnetic measurement error of the ship-borne magnetometer, based on the constrained total least square method, is proposed. To verify the effectiveness of the method proposed in this paper, a simulation experiment of geomagnetic measurement and compensation of a ship-borne three-axis magnetometer was constructed. Among them, to be closer to the real situation, a combination of the geomagnetism model, the elliptic shell model and the magnetic dipole model was used to simulate the internal magnetic field of the underwater vehicle. The experimental results indicated that the root mean square error of geomagnetic measurement in an underwater vehicle was less than 5 nT after compensation, and the accuracy of geomagnetic measurement met the requirements of geomagnetic matching aided navigation.