Navigation accuracy of the inertial navigation system (INS) could be greatly improved by rotating the inertial measurement unit around gimbals. However, the attitude output accuracy of rotational INS (RINS) would be affected by the non-orthogonal angles of gimbals, which should be accurately calibrated and compensated. In this paper, a novel self-calibration method for non-orthogonal angles of gimbals is proposed in tri-axis RINS. The three non-orthogonal angles could be calibrated using attitude errors and velocity errors as measurements without external equipment. The self-calibration scheme in this method could reduce the coupling of non-orthogonal angles with other errors, and the observability is clear to demonstrate during calibration. The proposed method is verified by both simulations and experiments. The experimental results show that the calibration accuracy of non-orthogonal angles could be less than 2”, and after compensation, the attitude output accuracy is improved from 200” to less than 10”. Therefore, the proposed calibration method could greatly improve the attitude output accuracy and make RINS more effective in some task systems where high attitude output accuracy is urgently required.

A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System

The attitude accuracy of the rotational inertial navigation system (RINS) is affected by the oscillatory attitude error caused by the installation error of the rotation axes. Data on the specific force, gyro measurement, attitude, or velocity errors are necessary to estimate the installation error. However, these errors are difficult to obtain and even unavailable in autonomous navigation. As the configuration consisting of two RINSs has been installed in the same vessel, we propose a self-calibration method to address the installation error solely using the attitude difference of two RINSs. We then constructed the Kalman filter based on the attitude difference model of two RINSs. The asynchronous time of the rotation sequence of two RINSs is optimized to improve the observability degree of the Kalman model. The proposed algorithm is examined by undertaking a test using two RINSs. Results indicate that the estimation accuracy of the installation error is at 6 arcsec level. The oscillatory attitude errors of RINS 1 are reduced from 305 to 6 arcsec, and those of RINS 2 are decreased from 131 to 6 arcsec after 350 s. The test results prove the effectiveness of the proposed installation error calibration method.

A Self-Calibration Method for the Installation Errors of Rotation Axes Based on the Asynchronous Rotation of Rotational Inertial Navigation Systems

Navigation errors of inertial navigation system can be effectively restrained by rotating inertial measurement units (IMU), enhancing accuracy in long-endurance navigation. However, nonorthogonal angles between rotating axes are inevitable during manufacturing. Coupled into the navigation error, nonorthogonal angles can lead to navigation accuracy, especially attitude accuracy decline during rotation. Therefore, the calibration and compensation of nonorthogonal angles will enhance the systemic reliability. In this study, we first established nonorthogonal angles model, then estimated the effect on sensitive errors of IMU using the proposed model. Based on the relationship between nonorthogonal angles and IMU attitude, an improved calibration algorithm of estimating nonorthogonal angles is presented. The results of theoretical analysis demonstrated that this method can effectively calibrate nonorthogonal angles in a simple and fast way, which is desirable for practical requirements. Simulation and comparison analysis indicated that the calibration of nonorthogonal angles is effective and practical. Finally, the feasibility of calibration and compensation is also verified by the improvement of navigation accuracy in the experiment.

Analysis and Calibration of the Nonorthogonal Angle in Dual-Axis Rotational INS

Rotation modulation is an effective method to enhance the accuracy of an inertial navigation system (INS) by modulating the gyroscope drifts and accelerometer bias errors into periodically varying components. The typical RINS drives the inertial measurement unit (IMU) rotation along the vertical axis and the horizontal sensors’ errors are modulated, however, the azimuth angle error is closely related to vertical gyro drift, and the vertical gyro drift also should be modulated effectively. In this paper, a new rotation strategy in a dual-axis rotational INS (RINS) is proposed and the drifts of three gyros could be modulated, respectively. Experimental results from a real dual-axis RINS demonstrate that the maximum azimuth angle error is decreased from 0.04° to less than 0.01° during 1 h. Most importantly, the changing of rotation strategy leads to some additional errors in the velocity which is unacceptable in a high-precision INS. Then the paper studies the basic reason underlying horizontal velocity errors in detail and a relevant new calibration method is designed. Experimental results show that after calibration and compensation, the fluctuation and stages in the velocity curve disappear and velocity precision is improved.

https://www.mdpi.com/1424-8220/15/8/18443/pdf

An Accurate Calibration Method Based on Velocity in a Rotational Inertial Navigation System.

Rotation modulation (RM) technology can effectively improve the navigation accuracy of strapdown inertial navigation system (SINS) by the periodic rotation of the rotation mechanism. But the original error characteristics of SINS will be changed after introducing the rotation modulation technology. Aiming at the practical micro-electro-mechanical system RMSINS, the error characteristics are comprehensively analyzed, and then a complete error model is established. At the same time, a reasonable parameter calibration scheme and the compensation method are designed to compensate the error in this paper. On this basis, static and dynamic experiments are carried out. The position accuracies of the rotation modulation state in the static and dynamic experiments are about ten times and about three times than that of the non-rotation state. The experimental results show that the proposed error analysis and compensation method are feasible which have been applied to the practical engineering.

Error Analysis and Compensation of MEMS Rotation Modulation Inertial Navigation System

By rotating a strapdown inertial navigation system (INS) over one or more axes, a number of error sources originating from the employed sensors cancel out during the integration process. Rotary angle accuracy has an effect on the performance of rotational INS (RINS). The application of existing calibration methods based on gyroscope measurements is restricted by the structure of the inertial measurement unit (IMU) and scale factor stability of the gyroscope. The multireadhead method has problems in miniaturization and cost. Hence, optical angle encoder calibration methods using accelerometers are proposed, on the basis of navigation error and accuracy requirement analyses for a single-axis RINS. The test results show that the accuracy of calibration methods proposed is higher than 4 arcsec (1σ).

Lei Wang

Papers

Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems