The Influence of Nonlinear High-Intensity Dynamic Processes on the Standing Wave Precession of a Non-Ideal Hemispherical Resonator.

The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange's second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

Standing Wave Binding of Hemispherical Resonator Containing First-Third Harmonics of Mass Imperfection under Linear Vibration Excitation.

Due to complicated processing technology, the mass distribution of a hemispherical resonator made of fused silica is not uniform, which can affect the azimuth of the standing wave of a resonator under the linear vibration excitation. Therefore, the analysis of standing wave evolution of a resonator with mass imperfection under linear vibration excitation is of significance for the improvement of the output accuracy of a gyroscope. In this paper, it is assumed that the resonator containing the first-third harmonics of mass imperfection is excited by horizontal and vertical linear vibration, respectively; then, the equations of motion of an imperfect resonator under the second-order vibration mode are established by the elastic thin shell theory and Lagrange mechanics principle. Through error mechanism analysis, it is found that, when the frequency of linear vibration is equal to the natural frequency of resonator, the standing wave is bound in the azimuth of different harmonics of mass imperfection with the change in vibration excitation direction. In other words, there are parasitic components in the azimuth of the standing wave of a resonator under linear vibration excitation, which can cause distortion of the output signal of a gyroscope. On the other hand, according to the standing wave binding phenomenon, the azimuths of the first-third harmonics of mass imperfection of a resonator can also be identified under linear vibration excitation, which can provide a theoretical method for the mass balance of an imperfect resonator.

Revised error calibration model of linear accelerometer on precision centrifuge.

The common error calibration model of a linear accelerometer usually cannot meet the accuracy requirement without considering the influence of misalignments in the precision centrifuge test. In order to improve the calibration accuracy, a series of coordinate systems is established and precise accelerations along the input axes of the accelerometers are deduced first. Then, by analyzing the mechanisms of the main error sources, the revised error calibration model is established which includes the misalignments, the radius errors, and the nonlinearity error terms. Then, the measurement methods are proposed to estimate the initial angular misalignments, the installation angular misalignments, and the installation radius misalignments by a theodolite and the accelerometer themselves in the different modes of the centrifuge, respectively. Finally, the experimental measurement results show that the initial angular misalignments are estimated accurately and less than 0.5' after adjustment. Further investigation shows that the adequacy of the common error calibration model decline obviously and the calibration accuracies are lower than 6 × 10-3g/g without considering the misalignments. After compensating for the misalignments in the revised model, the error coefficients are identified precisely, and the calibration accuracies are higher than 1.5 × 10-3g/g.

An Improved ACKF/KF Initial Alignment Method for Odometer-Aided Strapdown Inertial Navigation System.

For a land-vehicle strapdown inertial navigation system (SINS), the problem of initial alignment with large misalignment angle in-motion needs to be solved urgently. This paper proposes an improved ACKF/KF initial alignment method for SINS aided by odometer. The SINS error equation with large misalignment angle is established first in the form of an Euler angle. The odometer/gyroscope dead reckoning (DR) error equation is deduced, which makes the observation equation linear when the position is taken as the observation of the Kalman filter. Then, based on the cubature Kalman filter, the Sage-Husa adaptive filter and the characteristics of the observation equation, an improved ACKF/KF method is proposed, which can accomplish initial alignment well in the case of unknown measurement noise. Computer simulation results show that the performance of the proposed ACKF/KF algorithm is superior to EKF, CKF and AEKF method in accuracy and stability, and the vehicle test validates its advantages.

A Separated Calibration Method for Inertial Measurement Units Mounted on Three-Axis Turntables.

Inertial Measurement Unit (IMU) calibration accuracy is easily affected by turntable errors, so the primary aim of this study is to reduce the dependence on the turntable's precision during the calibration process. Firstly, the indicated-output of the IMU considering turntable errors is constructed and with the introduction of turntable errors, the functional relationship between turntable errors and the indicated-output was derived. Then, based on a D-suboptimal design, a calibration method for simultaneously identifying the IMU error model parameters and the turntable errors was proposed. Simulation results showed that some turntable errors could thus be effectively calibrated and automatically compensated. Finally, the theoretical validity was verified through experiments. Compared with the traditional method, the method proposed in this paper can significantly reduce the influence of the turntable errors on the IMU calibration accuracy.

An Optimization-Based Initial Alignment and Calibration Algorithm of Land-Vehicle SINS In-Motion.

For a running freely land-vehicle strapdown inertial navigation system (SINS), the problems of self-calibration and attitude alignment need to be solved simultaneously. This paper proposes a complete alignment algorithm for the land vehicle navigation using Inertial Measurement Units (IMUs) and an odometer. A self-calibration algorithm is proposed based on the global observability analysis to calibrate the odometer scale factor and IMU misalignment angle, and the initial alignment and calibration method based on optimal algorithm is established to estimate the attitude and other system parameters. This new algorithm has the capability of self-initialization and calibration without any prior attitude and sensor noise information. Computer simulation results show that the performance of the proposed algorithm is superior to the extended Kalman filter (EKF) method during the oscillating attitude motions, and the vehicle test validates its advantages.