The calibration of an inertial measurement unit (IMU) is a key technique to improve the accuracy of an inertial navigation system. Adding more parameters into the model and reducing the estimation errors is essential for improving the calibration methods. Given its advantage of not requiring high-precision equipment, the multi-position calibration method has been widely discussed and has shown great potential in recent years. In this paper, the multi-position calibration method is improved by introducing the accelerometer nonlinear scale factor. The observation equations for the improved multi-position calibration method are established based on a nonlinear accelerometer model. The particle swarm optimization algorithm is adopted to solve the complicated nonlinear equations. In addition, Allan variance is used to determine the optimal data collection time. The accuracy and the robustness of the proposed calibration method are verified by the simulation test. The laboratory and field experiment results for a navigation-grade IMU prove that the proposed method can successfully identify the accelerometer nonlinear scale factor and improve the multi-position calibration accuracy. The comparison of several other calibration methods highlights the superior performance of the proposed method without precise orientation control.

An inertial navigation system (INS) has been widely used in challenging GPS environments. With the rapid development of modern physics, an atomic gyroscope will come into use in the near future with a predicted accuracy of 5 × 10⁻⁶°/h or better. However, existing calibration methods and devices can not satisfy the accuracy requirements of future ultra-high accuracy inertial sensors. In this paper, an improved calibration model is established by introducing gyro g-sensitivity errors, accelerometer cross-coupling errors and lever arm errors. A systematic calibration method is proposed based on a 51-state Kalman filter and smoother. Simulation results show that the proposed calibration method can realize the estimation of all the parameters using a common dual-axis turntable. Laboratory and sailing tests prove that the position accuracy in a five-day inertial navigation can be improved about 8% by the proposed calibration method. The accuracy can be improved at least 20% when the position accuracy of the atomic gyro INS can reach a level of 0.1 nautical miles/5 d. Compared with the existing calibration methods, the proposed method, with more error sources and high order small error parameters calibrated for ultra-high accuracy inertial measurement units (IMUs) using common turntables, has a great application potential in future atomic gyro INSs.

A rotational inertial navigation system (RINS) has been wildly used in long term marine navigation. In a dual-axis RINS, with all constant biases averaged out, the errors which can not be averaged out become the main error source. In this paper, the gyro geomagnetic biases of a dual-axis RINS are modelled, analysed and calibrated. The gyro geomagnetic biases are proved unable to be averaged out, but can be modulated to be a constant value in the navigation frame. A slope error term of longitude error is found to be caused by gyro geomagnetic biases in north and upward directions, which increases linearly with time and is remarkable in long term navigation. Thus, a calibration method based on least square regression is proposed to compensate the slope error term. Laboratory and sailing experimental results show that the divergence speed of longitude error can be effectively slowed down by the compensation of gyro geomagnetic biases. In long term independent navigation, the position accuracy of dual-axis RINS is improved about 50% by the calibration method proposed in this paper.