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.

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The rotational inertial navigation system (INS) has received wide attention in recent years because it can achieve high precision without using costly inertial sensors. However, the introduction of the turntable causes additional errors, including mounting errors between the inertial measurement unit (IMU) axes and the turntable axes. Analysis, calibration and compensation of the mounting errors are necessary in rotational INS. In this paper, the mounting errors are introduced into the sensor model of a dual-axis rotational INS. Analysing the improved model indicated that the mounting errors’ effect on the IMU errors is inconspicuous, but the effect on the output attitude is significant. If the output attitude is not required, the mounting errors can be ignored; conversely, it is important to calibrate and compensate for such errors. A calibration method for the mounting errors is designed using the thin-shell (TS) algorithm, and the method's precision has the same order of magnitude as the residuals of gyro misalignment in the simulation test. Laboratory experimental results validate the theory and proved that the calibration and compensation method for mounting errors proposed in this paper helps improve the output attitude's precision without a precise installation.

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.

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