Objective  In the rotational ring laser gyro inertial navigation system, the rotary mechanism propels the inertial measurement unit (IMU) to rotate periodically concerning the vehicle. It takes work to get the attitude information directly. High-accuracy attitude information is essential for long-endurance high-accuracy autonomous navigation. High-accuracy vehicle attitude decoupling techniques for dual-axis rotational inertial navigation systems are of great practical importance. To extract the vehicle attitude information in the rotational laser inertial navigation system, decoupling the IMU attitude from the dual-axis attitude is necessary. However, there are inevitable nonorthogonal angles in the dual-axis rotational inertial navigation system. Installing the inner and outer axis frames cannot guarantee the inner axis zero frames, and the outer axis frame cannot be completely orthogonal. Similarly, when mounting the IMU on an inner axis frame, there is no guarantee that the IMU frame is entirely orthogonal to the inner axis frame. By calibrating the nonorthogonal errors, an accurate attitude transfer model can be established, and the accurate attitude information of the vehicle can be obtained.

  Methods  An optimal calibration method for nonorthogonal errors in dual-axis rotational RLG INS is proposed. The proposed calibration method allows accurate calibration of nonorthogonal angles between the rotational axes of the dual-axis rotational inertial navigation system. Based on the mechanical structure of the dual-axis rotational inertial navigation system and the definition of the coordinate frame, the spatial relative position model between the coordinate frame was established, including the spatial position relationship between the outer and inner axis frame and the spatial position relationship between the IMU and the inner axis frame. The IMU's attitude to the vehicle's attitude transfer model is constructed, which includes the nonorthogonal angles. Furthermore, the calibration problem is converted into an optimization problem based on the attitude transfer model. A fitness function is constructed using the vehicle attitude error as the fitness. The particle swarm optimization algorithm finds the optimal global solution to the created fitness function. The nonorthogonal angles calibration of the dual-axis rotary mechanism is achieved.

  Results and Discussions  Calibration tests and navigation tests were conducted to verify the effectiveness of the proposed nonorthogonal angles calibration method. The test equipment consisted of a dual-axis rotational modulated laser inertial navigation system self-developed by the National Defense University of Science and Technology (Fig.4) and a set of GNSS equipment to obtain the reference position of the test site. The specifications of the inertial measurement unit are shown (Tab.1). The parameters of the particle swarm optimization algorithm are set (Tab.2). The 30 Monte Carlo tests were conducted to verify that the PSO algorithm did not fall into a local optimum or fail to converge completely. The result shows the convergence of the fitness values for the 30 Monte Carlo tests (Fig.5). As the number of iterations increases, the fitness values converge well and do not fall into a local optimum. The results from a randomly selected set of 30 Monte Carlo tests are shown (Tab.3). The dual-axis rotational modulated laser inertial navigation system is placed on a static base platform. An initial alignment is performed for 600 s to obtain the initial attitude, followed by a 16-order navigation rotational modulated phase. The calibration results from Tab.3 are then substituted into the attitude solution process to get the vehicle's attitude information. The vehicle's attitude error is shown (Fig.6-8), where the red curve is the attitude without nonorthogonal angles calibration, and the blue curve is the vehicle attitude after calibration compensation using the conventional method. The green curve is the vehicle attitude obtained after compensating for the proposed calibration method. The solved vehicles attitude is shown (Fig.9). In the case of a static base, the actual vehicle attitude remains unchanged. If the nonorthogonal angles are not compensated, the vehicle's attitude calculated by IMU has a significant fluctuation due to the oscillating attitude error generated by the nonorthogonal angles. The statistical values of the vehicle attitude error are show (Tab.4). Compared with the conventional method, the pitch error is reduced by 89.29% with the proposed method, the roll error is reduced by 73%, and the yaw error is reduced by 81.39%. The repeatability of the proposed method was verified with the Monte Carlo tests (Fig.10).

  Conclusions  An optimal calibration method for nonorthogonal errors in dual-axis rotational RLG INS is proposed. The experimental results show that the nonorthogonal angles can be effectively achieved with the proposed nonorthogonal angles calibration method, which can significantly reduce the vehicle attitude error and decouple the attitude information of the IMU from the rotating mechanism to obtain the vehicle attitude information with high accuracy. The proposed calibration method is more accurate than conventional methods and does not require a specific rotation path. The technique is simple to operate. The inertial navigation system can calibrate the nonorthogonal angles in situ by executing 16-position navigation paths during the standby phase. With the proposed calibration method, the dual-axis rotational inertial navigation system can output high-accuracy attitudes, guaranteeing high-accuracy autonomous navigation.