Ring Laser Gyro G-Sensitive Misalignment Calibration in Linear Vibration Environments.

In modern aerospace technology, strapdown inertial navigation systems (SINS) are widely used, using fiber-optic (FOG) or ring laser (CLG) gyroscopes. During the operation of such systems, the sensitivity axes are rotated relative to the basic coordinate system. The resulting angles between the axes of the base coordinate system and the axes of sensitivity of the navigation system (non-orthogonality) are one of the factors leading to an increase in the measurement errors of the device, which affects the measurement accuracy. During operation, the system is affected by vibrations of various nature, the impact of which can contribute to the appearance of non-orthogonality. The purpose of this work is to determine the maximum permissible vibration amplitudes affecting the SINS body according to the permissible values ​​of the deviation of the FOG sensitivity axes for two variants of the SINS layout. An approach to determining the permissible amplitudes of an external harmonic impact on the unit of a strapdown inertial navigation system based on fiber-optic or ring laser gyroscopes is considered. A design scheme, mathematical and finite element models for calculating natural frequencies and forced oscillations of a strapdown inertial navigation system unit have been developed. In various frequency ranges, numerical calculations have determined the boundary values ​​of the amplitudes of the external harmonic impact on the base of specific configurations of the SINS assembly. It has been established that dangerous states take place in the region of the 1st natural frequency of the system, as well as near higher frequencies. Comparison of the results for design options 1 and 2 allows us to conclude that in order to weaken the effect of vibrations on the accuracy of the SINS unit, it is advisable that the lowest natural vibration frequencies for the SINS assembly be as high as possible (more than 1000 Hz).
 Key words: vibration; fiber optic gyroscope; strapdown inertial navigation system; finite element method; natural frequencies and modes of vibration.

A correcting digital filter for a mechanically dithered single-axis ring laser gyro (RLG) is proposed. The filter is intended to determine the angular position of a strapdown inertial navigation system (SINS) in the RLG sensitivity axis using the known value of the RLG angular position with respect to inertial space, taking into account the models of the suspension elastic forces nonlinearity, the hysteresis model of vibration energy dissipation, and the model of the suspension piezoceramic vibratory drive. Parameterized models of nonlinearity, dissipation, and the output characteristic of the suspension piezoceramic drive have been developed. A method for finding nonlinearity parameters of elastic forces using a set of experimental amplitudefrequency characteristics (AFC) is proposed. Numerical simulations of the AFCs of an elliptic eliminator and a correcting filter under sinusoidal rotation of the SINS with the amplitude of 1 arcmin in the frequency band of 80–3600 Hz have been performed. The efficiency of the proposed filter has been verified experimentally under pulse action on the SINS; the test results are discussed. Comparison of the experimental and calculated data shows the adequacy of the proposed models and satisfactory operation of the correcting digital filter.

Several static tests indicate that the Ring Laser Gyro (RLG) bias inside of the Strap-down Inertial Navigation System (SINS) varies remarkably as long time working. Further experiments and analyzing results show that the SINS external metal shell could insure the inside temperature rising gently and evenly, and the RLG drifts could be viewed mainly affected by RLG inside temperature field. In order to ac hieve better RLG stability character istic within full temperature range, investigated the BP and RBF Artificial Neural Networks (ANN) nonlinear modeling and compensation technology. Firstly, introduced two typical structures for BP an d RBF neural networks, and then, take a set of static tests data from 25 $ C to 55 $ C as training samples, separately built up four-l ayer BP and two-layer RBF neural networks for RLG drifts. In order to compare the compensation effects, first-order and second-order piecewise Least Square (LS) fitting technologies are also implemented here. Four new expe rimental data were adopted to check the modeling validity. The compensation results show that the RLG drifts stability could be improved by 20%-40%; the precision of BP network modeling method is better than th at of first-order linear piecewise LS f itting, and the precision of RBF is better than that of second-order piecewise LS fitting. Keywords: Strap-down Inertial Navigation System (SINS), Ring Laser Gyro (RLG), drifts, Artificial Neural Network (ANN), Least Square (LS)

Strap-down inertial navigation system (SINS) is widely used in military field, to facilitate the study of SINS algorithms and various coupled navigation algorithms, a simulation system of SINS is designed. Based on modular design, with good portability and expansibility, the system consists of four independent modules: analysis module of motion state, trajectory simulator, IMU simulation module and SINS calculation module. With graphical interface, the system can control every motion state of the trajectory, which is convenient to generate various trajectories efficiently. Using rotation vector attitude algorithm to process simulation data, experiment results show that the attitude, velocity and position error is consistent with the theoretical value, which verifies the rationality of the simulation model and the availability of the simulation system.

Extended Kalman filter (EKF) is a widely used estimator for integrated navigation systems, and it works well in general situations. However, in adverse conditions such as partially observable environments and highly dynamic maneuvers, the performance of the traditional EKF-based strap-down inertial navigation system (SINS)/GPS integrated navigation system is easily to be affected by the dynamic changes of the specific force, thus leading to the problem of error covariance inconsistency. Though the inconsistency problem can be overcome to some extent if the system matrix, the states and the error covariance matrix are propagated as fast as possible in the SINS calculation rate, the problem cannot be fully solved. State transformation extended Kalman filter (ST-EKF) mechanization, with a new converted velocity error model for the SINS, is proposed, which can also be used to solve the inconsistency problem. In the ST-EKF, the specific force vector in the system error model is replaced by the nearly constant gravity vector for local navigation. Since the propagation and the updating of the ST-EKF can be executed simultaneously in the updating interval, the computation cost is greatly reduced compared with the traditional EKF. Experiments for the GPS/SINS tightly coupled navigation, including linear vibration Monte Carlo test and an unmanned aerial vehicle flight test, are implemented to evaluate the performance of the proposed ST-EKF. The results show that the proposed ST-EKF has superior performance to the traditional EKF, especially in partially observable situations.

Noncommutativity error of a strapdown inertial navigation system (SINS) in an unmanned aerial vehicle's (UAV) vibration environment is analysed. The traditional analysis of noncommutativity errors is based on a coning motion model, which is inconsistent with a UAV's vibration environment. In this paper the UAV's vibration form is discussed and is modelled as a sinusoidal angular vibration and a random angular vibration. Then, SINS motion models under these two forms of vibration are built up and the formulas for the noncommutativity errors are derived separately. In addition, the effect of a multi-sample algorithm is explored, which is an effective method for compensating for noncommutativity errors in cases of coning motion. Finally, the UAV's vibration environment is simulated and it is indicated that the simulation results of the SINS's noncommutativity errors are consistent with theoretical analysis.

The strapdown inertial navigation system can provide the navigation information for the boom-type roadheader in the unmanned roadway tunneling working face of the coal mine. However, the complex vibration caused by the cutting process of the boom-type roadheader may result in significant errors of its attitude and position measured by the strapdown inertial navigation system. Thus, an error compensation method based on the vibration characteristics of the roadheader is proposed in this paper. In order to further analyze the angular and linear vibration of the fuselage, as the main vibration sources of the roadheader, the dynamic model of the roadheader is formulated based on the cutting load. Following that, multiple sub-samples compensation algorithms for the coning and sculling errors are constructed. Simulation experiments were carried out under different subsample compensation algorithms, different coal and rock characteristics, and different types of roadheader. The experimental results show that the proposed error compensation algorithm can eliminate the effect of the angular and linear vibration on the measurement accuracy. The coning and sculling error of the strapdown inertial navigation system can reduce at least 52.21% and 42.89%, respectively. Finally, a strapdown inertial navigation error compensation accuracy experiment system is built, and the validity and superiority of the method proposed in this paper are verified through calculation and analysis of the data collected on the actual tunneling work face.

Self-alignment of full skewed RSINS: Observability analysis and full-observable Kalman filter

The strap-down inertial navigation system (SINS), especially the SINS composed by dithered ring laser gyroscope (DRLG) is a kind of equipment, which providing high reliability and performance for moving vehicles. However, the mechanical dither which is used to eliminate the “Lock-In” effect can cause vibration disturbance to the INS and lead to dithering coupling problem in the inertial measurement unit (IMU) gyroscope triad, so its further application is limited. Among DRLG errors between the true gyro rotation rate and the measured rotation rate, the frequently considered one is the input axis misalignment between input reference axis which is perpendicular to the mounting surface and gyro angular rate input axis. But the misalignment angle between DRLG dither axis and gyro angular rate input axis is often ignored by researchers, which is amplified by dither coupling problem and that would lead to negative effects especially in high accuracy SINS. In order to study the problem more clearly, the concept of misalignment between DRLG dither axis and gyro angle rate input axis is researched. Considering the error of misalignment is of the order of 10 -3 rad. or even smaller, the best way to measure it is using DRLG itself by means of an angle exciter as an auxiliary. In this paper, the concept of dither axis misalignment is explained explicitly firstly, based on this, the frequency of angle exciter is induced as reference parameter, when DRLG is mounted on the angle exciter in a certain angle, the projections of angle exciter rotation rate and mechanical oscillation rate on the gyro input axis are both sensed by DRLG. If the dither axis has misalignment error with the gyro input axis, there will be four major frequencies detected: the frequency of angle exciter, the dither mechanical frequency, sum and difference frequencies of the former two frequencies. Then the amplitude spectrum of DRLG output signal obtained by the using LabVIEW program. if there are only angle exciter and the dither mechanical frequencies, the misalignment may be too small to be detected, otherwise, the amplitude of the sum and difference frequencies will show the misalignment angle between the gyro angle rate input axis and the dither axis. Finally, some related parameters such as frequency and amplitude of the angle exciter and sample rate are calculated and the results are analyzed. The simulation and experiment result prove the effectiveness of the proposed method..

Navigation of Hypersonic vehicles in the radio frequency (RF) blackout area during atmospheric reentry is challenging as the vehicles can only use the inertial navigation system (INS) as autonomous navigation method in this area. In this paper, strapdown inertial navigation system (SINS) based on the Fiber Optic Gyroscope (FOG) is used for navigation in blackout area. However, without external navigation measurement, the errors of SINS caused by the FOG drift and accelerometer bias would cumulate with time and degrade navigation accuracy. To solve this problem, single axis rotation modulation along with the azimuth axis of the body frame is adopted. The Generic Hypersonic Vehicle (GHV) model designed by NASA Langley Research Center is used to build the reentry fight model which can generate navigation information for simulation. Through derivation the error equations of FOG SINS in the North-East-Down (NED) navigation frame, the principle of error compensation by rotation modulation can be well understood. The simulation results show that rotation modulation can effectively decrease the impact of inertial sensor drift and improve the navigation accuracy in blackout area.

Initial alignment is of vital importance to inertial navigation systems (INS). The two main methods of self-alignment, the traditional gyro-compassing alignment method and the Kalman filter method, are discussed. We apply and compare the two methods via simulation and test in use of a strapdown inertial navigation system (SINS) based fiber optic gyroscope (FOG), respectively. The simulation and test show that Kalman filter method is better in convergent time and accuracy of attitude and azimuth, however, gyro-compassing alignment method is better in robustness. This provides a useful reference for designing alignment algorithm for FOG SINS.

Flight trials began this month on the Ferranti FIN3000 “Laser Gyro” Strapdown Inertial Navigation System (INS). Initial trials of the prototype system, designed and developed by the Edinburgh‐based Navigation Systems Department, are being carried out in the Company's HS125 aircraft.

This paper develops an improved hybrid calibration scheme for the strapdown inertial navigation system (SINS) that combines the advantages of an optimal rotational norm calibration method and an improved system-level calibration method. To accurately determine the scale factors and misalignment error of gyros triad, the optimal rotation norm calibration method is applied. Similarly, the improved system-level calibration method based on the 24-dimensional error state Kalman filter (ESKF) plays an important role in accelerometer calibration and gyro biases calibration. The clockwise and counterclockwise multi-cycles rotation scheme is designed to eliminate the effects of the Earth's rate and gyros biases, and then provide accurate rotational norm to completely determine the gyros triad scale factors and misalignment. In addition, the improved ESKF system-level calibration method is employed to estimate accelerometer parameters and gyros biases. Simulation test verify the validity of the proposed method, and the calibration experiences and the verification tests of the two high-precision optical gyros inertial measurement units (IMU) are carried out. For comparison, the traditional 30-dimensional system-level calibration is also performed. The attitude error of high maneuvering swing test indicate that the gyros calibration accuracy of hybrid calibration scheme is better than that of traditional system-level calibration scheme. Furthermore, the positioning error of pure inertial navigation solution in static and dynamic condition for two calibration methods indicate that the hybrid calibration scheme significantly improves the positioning accuracy, especially in the dynamic experiment, that is, the proposed scheme provides a more accurate calibration of the IMU.

A novel nonlinear attitude error model based on square root cubature information filter (SR-CIF) is proposed aiming to speed up the convergence rate of DVL-aided strapdown inertial navigation system (SINS) in-motion initial alignment for autonomous underwater vehicle (AUV) when both large initial heading error and large initial level attitude errors exist The new nonlinear attitude error model and measurement model are applicable for initial alignment after a short-time coarse alignment with large attitude errors exist. The SR-CIF embeds the whole iterative process into the data structure framework of the information filtering, replacing the covariance matrix in the square root cubature Kalman filter (SR-CKF) with an information matrix which simplifies the filter initialization. The square root technology ensures the symmetry and positive definiteness of the information matrix with enhanced stability of the filter. The simulation and experimental results indicate that the proposed DVL-aided alignment filter is effective with large initial attitude errors. The rate of convergence and estimation accuracy of the SR-CIF is higher than that of the conventional SR-CKF with large attitude misalignments.

In this paper, A laser gyroscope strap-down inertial navigation system (SDINS) error model with 12 system state parameters is derived, and the observability of SDINS is discussed by observability analysis of piece-wise constant system (PWCS) and observable degree analysis method based on the singular value decomposition (SVD). It is demonstrated that four-position alignment can make the system completely observable, and all the system state parameters can be estimated by Kalman filter. The simulation indicates the efficiency of the analysis results.