Strapdown inertial navigation system (SINS) has been widely used in the field of vehicle navigation because of its excellent properties such as strong autonomy, high concealment and strong anti-interference ability. However, due to the measurement error of inertial measurement unit (IMU) in SINS, the positioning error of pure inertial navigation system will accumulate over time, and it will oscillate and diverge, which can not meet the long-term and high-precision navigation and positioning requirements. It has become the mainstream trend of the development of inertial navigation technology to integrate multiple navigation systems. As a high-precision speed sensor, laser Doppler velocimeter (LDV) has many advantages, such as complete autonomy, wide speed measuring range, non-contact measurement and stable error parameters, and its speed measuring error does not accumulate with time, which is highly complementary to SINS. After reasonably compensating the installation error parameters between the two sensors, the positioning accuracy of integrated navigation can be effectively improved by constructing SINS/LDV vehicle integrated navigation system. At present, researchers have done a lot of in-depth research on the calibration scheme of the main error parameters (scale factor error, installation angle error and lever-arm error) of LDV measurement speed in the process of integrated navigation. However, one-dimensional laser Doppler velocimeter (1D-LDV) is essentially a single-axis sensor, which can only obtain the forward velocity information at the measurement center. Therefore, when the velocity at the 1D-LDV measurement center has vertical or lateral velocity components, the existing lever-arm speed error model will not reflect the real relationship between the measurement velocity output by 1D-LDV and SINS, and then it will affect the navigation and positioning accuracy. In order to improve the positioning accuracy of SINS/LDV integrated navigation system, this paper improves the existing lever-arm speed error model, and proposes a 23-dimensional Kalman filter online calibration algorithm.

Firstly, the existing lever-arm speed error model of the LDV and SINS measurement center is analyzed and introduced. Because of the existence of lever-arm vector, when the carrier has angular motion about a certain coordinate axis, the velocity at the measurement center of LDV and SINS will produce a difference in the plane perpendicular to the coordinate axis, that is the lever-arm speed error, and the difference is related to the angular motion of the carrier and the lever arm value. Subsequently, the existing lever-arm speed error model is improved and a new lever-arm speed error model is proposed. Because 1D-LDV is a single-axis sensor, it can only provide the velocity information of the carrier in the trajectory direction. Therefore, when the carrier moves angularly, the measured velocity output by 1D-LDV will lack the information of the vertical and lateral velocity components at the measurement center and cannot be compensated. Therefore, it is not appropriate to directly describe the relationship between the output velocities of 1D-LDV and SINS by using the traditional lever-arm speed error model. In order to solve this problem, the point where the speed direction always keeps the direction of the carrier during the carrier traveling is introduced, and the lever-arm speed error models of the speed at this point and the the measurement velocity output by 1D-LDV and SINS are constructed respectively, thus isolating the influence of the vertical and lateral speed components at the measurement center of 1D-LDV. After combining the two equations, a new lever-arm speed error model between the measurement velocity output by 1D-LDV and SINS can be obtained. Finally, based on the new lever-arm speed error model, a 23-dimensional Kalman filter online calibration algorithm is proposed, and two groups of vehicle experiments are carried out to verify the effectiveness of this algorithm.

For 1D-LDV, the forward lever-arm between it and the center of the carrier has no contribution to the speed error of the lever-arm, so it can be ignored in calibration and compensation. The results of vehicle experiments show that the error parameters of 1D-LDV can converge quickly by using the proposed algorithm. At the same time, after using the calibration results to compensate the error parameters of the measurement velocity of 1D-LDV, the horizontal positioning accuracy obtained by track calculation has been improved to a certain extent, and the horizontal positioning errors obtained by the two groups of experiments are reduced by 19.66% and 16.97% respectively. The experimental results strongly support the effectiveness of the proposed algorithm.

In this paper, a 23-dimensional Kalman filter online calibration algorithm is proposed. By analyzing the lever-arm speed error between the measured speed of 1D-LDV and the calculated speed of SINS, and introducing the point that the speed direction always keeps the direction of the carrier during the carrier's travel, the existing lever-arm speed error model is improved, thus a new lever-arm speed error model which can accurately reflect the real relationship between the output speed of 1D-LDV and SINS is constructed. The validity of the calibration algorithm is verified by two groups of vehicle experiments. After the lever arm error compensation, the horizontal positioning errors of two experimental trials are reduced from 8.80m and 6.60m to 7.07m and 5.48m respectively, the navigation positioning accuracy is improved to some extent.