Gyroscope Unit Research Articles

CALIBRATION OF THE INERTIAL MEASUREMENT UNIT IN CRITICAL CONDITIONS

Calibration of the inertial measuring unit (IMU) is an independent task and is the most important stage in preparing for operation both platform and strapdown inertial navigation systems (INS). The traditional calibration of IMU, containing at least three gyroscopes and three accelerometers, carried out in specialized testing laboratories, has been studied in sufficient detail. However, the widespread use of IMUs using MEMS sensors with characteristic instability of parameters leads to the need for additional calibration of IMUs IMUediately before INS operation in critical or field conditions. Under such conditions, firstly, there is no testing equipment necessary for the full implementation of traditional calibration, and secondly, the recalibration process itself is limited in time.In the article, studies were carried out on the possibility of using the method of successive rotations for the recalibration of IMU in the field. With this approach, in contrast to the test rotation method, there is no need to rotate the IMU by 180 degrees, but it is enough to rotate the IMU by small angles. Calculation ratios are obtained for determining the scale factors and zero signals of the accelerometer unit for two positions of the IMU. The experiment carried out confirmed the validity of the calculated ratios obtained. In addition, a recalibration method is described, which makes it possible to estimate, in addition to scale factors and zero signals of the accelerometer unit, also the tilt angles of the base on which the IMU is installed. To do this, you must have at least five different IMU positions.In addition, the calibration of the gyroscope unit when tactical and navigational accuracy class gyroscopes are used is considered. For gyroscopes of the tactical accuracy class and which are manufactured using MEMS technology, biases are determined in the critical conditions, which are not stable from start to start. Algorithms for determining biases and scale factors were obtained for the calibration of the gyroscope unit of the navigation accuracy class, for which the same two positions in which the accelerometer unit was calibrated were used. That is, during the calibration of the IMU in critical conditions, it is possible to simultaneously calibrate the gyroscope unit and the accelerometer unit, which saves the overall calibration time.

An anti‐vibration‐shock inertial matching measurement method for hull deformation

In order to establish a unified spatial reference for the whole ship, inertial matching measurement of hull deformation is widely used because of its continuity and concealment. However, the vibration-shock signal of shipborne equipment often brings short-time output disturbance to the user-side fibre gyroscope unit (FGU), and the disturbance will bring great challenges to the accuracy and convergence of inertial matching measurement. To solve these problems, the authors put forward a new algorithm named as attitude quaternion matching method-improved double factor adaptive Kalman filter-parameter adaptive Kalman filter (AQM-IDFAKF-PAKF). (1) The AQM established the FGU attitude as observation to build the basic model for hull deformation inertial matching method. (2) The authors introduced IDFAKF to track the trend of dynamic hull deformation in vibration interference by using historical data. (3) After judging the anti-vibration-shock calculation stop node, PAKF was utilised to adaptively adjust the parameters of hull deformation matching after vibration-shock, so as to quickly calculate the static hull deformation angle after shock interference. Numerical simulation results illustrated that the AQM-IDFAKF-PAKF can quickly converge the calculation of hull deformation angle with a small steady-state error under the condition of vibration-shock signal interference.

Model-based fault detection filter for Markovian jump linear systems applied to a control moment gyroscope

We study a fault detection problem in the context of Markovian Jump Linear Systems (MJLS). The major contribution of this paper is the design of a mode-dependent mixed H∞/H− Fault Detection Filter (FDF) under the MJLS formulation, which is obtained by solving a Linear and Bilinear Matrices Inequalities (LMI / BMI) optimization problem. As a secondary contribution, we present a simulation of the theoretical results using a Control Moment Gyroscope unit, which is extensively used as an actuator for attitude control of spacecraft and satellites. The attitude control of satellites is a class of problem that is within the framework of MJLS, since it allows us to model the loss of communication between the various components of the network system. Therefore, designing Fault Detection Filters under this framework provides reliable solutions. From the simulations results, it is possible to observe that the proposed mixed H∞/H− fault detection solution outperformed the approach using only the H∞ norm, showing that it could be a valuable alternative for the fault detection problem.

A real-time calibration method for the systematic errors of a star sensor and gyroscope units based on the payload multiplexed

With the star sensor and gyroscope units integrated for attitude determination, it will provide continuous and accurate attitude information for satellites with a high update rate. This integration could take full advantage of each other. In order to guarantee the accuracy of satellite attitude determination, the calibration of its systematic errors is of critical importance. In this paper, a calibration method for the star tracker and GUs integrated system is proposed based on the satellite payload multiplexed. Firstly, the satellite attitude kinematics model is introduced. Then the measurement model with respect to the systematic errors including the installation errors and GUs drift errors is built for the star sensor, the payload and the GUs. Finally, the state model and observation model are established, according to which the systematic errors are calibrated by a Kalman filter. Simulation results indicate that the proposed method is effective at estimating the systematic errors of the star sensor and GUs integrated system.

Attitude-correlated frames adding approach to improve signal-to-noise ratio of star image for star tracker.

When applied inside Earth's atmosphere, the star tracker is sensitive to sky background produced by atmospheric scattering and stray light. The shot noise induced by the strong background reduces star detection capability and even makes it completely out of operation. To improve the star detection capability, an attitude-correlated frames adding (ACFA) approach is proposed in this paper. Firstly, the attitude changes of the star tracker are measured by three gyroscope units (GUs). Then the mathematical relationship between the image coordinates at different time and the attitude changes of the star tracker is constructed (namely attitude-correlated transformation, ACT). Using the ACT, the image regions in different frames that correspond to the same star can be extracted and added to the current frame. After attitude-correlated frames adding, the intensity of the star signal increases by n times, while the shot noise increases by n~n/2 times due to its stochastic characteristic. Consequently, the signal-to-noise ratio (SNR) of the star image enhances by a factor of n~2n. Simulations and experimental results indicate that the proposed method can effectively improve the star detection ability. Hence, there are more dim stars detected and used for attitude determination. In addition, the star centroiding error induced by the background noise can also be reduced.

A Comprehensive Calibration Method for a Star Tracker and Gyroscope Units Integrated System.

The integration of a star tracker and gyroscope units (GUs) can take full advantage of the benefits of each, and provide continuous and accurate attitude information with a high update rate. The systematic error calibration of the integrated system is a crucial step to guarantee its attitude accuracy. In this paper, a comprehensive calibration method for the star tracker and GUs integrated system is proposed from a global perspective. Firstly, the observation model of the predicted star centroid error (PSCE) with respect to the systematic errors including the star tracker intrinsic parameter errors, GUs errors and fixed angle errors is accurately established. Then, the systematic errors are modeled by a series of differential equations, based on which the state-space model is established. Finally, the systematic errors are decoupled and estimated by a Kalman filter according to the established state-space model and observation model. The coupling between the errors of the principal point and subcomponents of the fixed angles (i.e., and ) is analysed. Both simulations and experiments indicate that the proposed method is effective at estimating the systematic errors of the star tracker and GUs integrated system with high accuracy and robustness with respect to different star centroid accuracies and gyroscope noise levels.

Band gap characteristics of periodic gyroscopic systems

The stop and pass bands (i.e. the band gaps) characteristics are determined for gyroscopic systems by developing an approach which is compatible with such class of systems which is based on the concept of Bloch wave propagation in periodic structures. In this approach, the dispersion curves of the periodic gyroscopic systems are determined for different rotational speeds. The obtained characteristics are compared with non-rotating systems in an attempt to quantify the effect of the gyroscopic forces on the “band gap” characteristics. The developed approach is illustrated by a new class of drill strings with passive periodic inserts. These inserts are utilized to filter out the vibration transmission along the drill string. Such mechanical filtering capabilities allow the vibrations to propagate along the periodic drill string only within specific frequency bands called the ‘pass bands’ and completely block it within other frequency bands called the ‘stop bands’. The inserts introduce impedance mismatch zones along the vibration transmission path to impede the propagation of vibration along the drill string. The design and the location of the inserts are selected to confine the dominant modes of vibration of the drill string within the stop bands generated by the periodic arrangement of the inserts in order to completely block the propagation of the vibrations.A finite element model (FEM) that simulates the operation of this new class of drill strings is developed to describe the complex nature of the vibration encountered during drilling operations. The FEM is used to extract the dispersion characteristics of the gyroscopic unit cell of the drill string in order to determine its stop and pass band characteristics. Experimental prototype of the passive periodic drill string is built and tested to demonstrate the feasibility and effectiveness of the concept of periodic drill string in mitigating undesirable vibrations. The experimental results are used to validate the developed theoretical model in order to develop a scalable design tool that can be used to predict the dynamical behavior of this new class of drill strings.

Mathematical Modeling and Scaling of the Friction Losses of a Mechanical Gyroscope

Friction is a complicated phenomenon that plays a central role in a wide variety of physical systems. An accurate modeling of the friction forces is required in the model-based design approach, especially when the efficiency optimization and system controllability are the core of the design. In this work, a gyroscopic unit is considered as case study: the flywheel rotation is affected by different friction sources that needs to be compensated by the flywheel motor. An accurate modeling of the dissipations can be useful for the system efficiency optimization. According to the inertial sea wave energy converter (ISWEC) gyroscope layout, friction forces are modeled and their dependency with respect to the various physical quantities involved is examined. The mathematical model of friction forces is validated against the experimental data acquired during the laboratory testing of the ISWEC gyroscope. Moreover, in the wave energy field, it is common to work with scale prototypes during the full-scale device development. For this reason, the scale effect on dissipations has been correlated based on the Froude scaling law, which is commonly used for wave energy converter scaling. Moreover, a mixed Froude–Reynolds scaling law is taken into account, in order to maintain the scale of the fluid-dynamic losses due to flywheel rotation. The analytical study is accompanied by a series of simulations based on the properties of the ISWEC full-scale gyroscope.

Centroid error compensation method for a star tracker under complex dynamic conditions

The traditional approach of a star tracker for reducing the dynamic error concentrates on a single frame of star images. Through correlating adjacent star images together with their angular relations sensed by a gyroscope unit (GU), the attitude-correlated frames (ACF) approach expands the view from one single frame to frame sequences. However, the star centroid is shifted from the star true position at the center time of the exposure period under complex dynamic conditions, which is called the complex motion induced error (CMIE) in this paper. The CMIE has a large effect on the performance of the ACF approach. This paper presents a method to compensate the CMIE through reconstructing the star trajectory with the angular velocity of the star tracker sensed by a GU, which achieves effective compensation of the CMIE crossing the boresight direction. Since the observation sensitivity to the CMIE along the boresight direction is low, the attitudes from two different fields of view (FOVs) are combined to improve its compensation accuracy. Then the ACF approach is applied to the obtained results where the CMIE has already been compensated completely. Simulations under shipboard dynamic conditions and experiments under oscillating conditions indicate that the proposed method is effective in improving the performance of the ACF approach and reducing the dynamic error of a star tracker under complex dynamic conditions.

Coupling Mechanism Analysis and Fabrication of Triaxial Gyroscopes in Monolithic MIMU.

A novel fully decoupled micro inertial measurement unit (MIMU) is presented in this paper. The proposed MIMU structure, mostly focusing on the gyroscope unit, is highly symmetrical and can be limited to an area of 10,000 μm × 10,000 μm. Both the tri-axis gyroscope and tri-axis accelerometer structures are fabricated on the same single silicon chip, which can differentially detect three axes’ angular velocities and linear accelerated velocities at the same time. By elaborately arranging different decoupling beams, anchors and sensing frames, the drive and sense modes of the tri-axis gyroscope are fully decoupled from each other. Several dynamic models, including decoupling beams with fabrication imperfections, are established for theoretical analysis. The numerical simulation made by MATLAB shows the structural decoupling of three sense modes, and indicates that the key decoupling beams, which affect the quadrature error, can be improved in design. The whole fabrication process, including silicon on glass (SOG) process, dry/wet etching as well as the methods for improving the fabrication quality, is then shown. Experiments for mode frequency and quality factors of four modes (drive, yaw, pitch and roll) have been performed, and are found to be 455 (6950.2 Hz), 66 (7054.4 Hz), 109 (7034.2 Hz) and 107 (7040.5 Hz) respectively. The analysis and experiment both prove that this novel MIMU has the potential value of further intensive investigation.

An interval Kalman filter–based fuzzy multi-sensor fusion approach for fault-tolerant heading estimation of an autonomous surface vehicle

This article presents a novel fuzzy–logic based multi-sensor data fusion algorithm for combining heading estimates from three separate weighted interval Kalman filters to construct a robust, fault-tolerant heading estimator for the navigation of the Springer autonomous surface vehicle. A single, low-cost gyroscopic unit and three independent compasses are used to acquire data onboard the vehicle. The gyroscope data, prone to sporadic bias drifts, are fused individually with readings from each of the compasses via a weighted interval Kalman filter. Unlike the standard Kalman filter, the weighted interval Kalman filter is able to provide a robust heading estimate even when subject to such gyroscope bias drifts. The three ensuing weighted interval Kalman filter estimates of the vehicle’s heading are then fused via a fuzzy logic algorithm designed to provide an accurate heading estimate even when two of the three compasses develop a fault at any time. Simulations and real-time trials demonstrate the effectiveness of the proposed method.

An improved method for dynamic measurement of deflections of the vertical based on the maintenance of attitude reference.

A new method for dynamic measurement of deflections of the vertical (DOV) is proposed in this paper. The integration of an inertial navigation system (INS) and global navigation satellite system (GNSS) is constructed to measure the body's attitude with respect to the astronomical coordinates. Simultaneously, the attitude with respect to the geodetic coordinates is initially measured by a star sensor under quasi-static condition and then maintained by the laser gyroscope unit (LGU), which is composed of three gyroscopes in the INS, when the vehicle travels along survey lines. Deflections of the vertical are calculated by using the difference between the attitudes with respect to the geodetic coordinates and astronomical coordinates. Moreover, an algorithm for removing the trend error of the vertical deflections is developed with the aid of Earth Gravitational Model 2008 (EGM2008). In comparison with traditional methods, the new method required less accurate GNSS, because the dynamic acceleration calculation is avoided. The errors of inertial sensors are well resolved in the INS/GNSS integration, which is implemented by a Rauch–Tung–Striebel (RTS) smoother. In addition, a single-axis indexed INS is adopted to improve the observability of the system errors and to restrain the inertial sensor errors. The proposed method is validated by Monte Carlo simulations. The results show that deflections of the vertical can achieve a precision of better than 1″ for a single survey line. The proposed method can be applied to a gravimetry system based on a ground vehicle or ship with a speed lower than 25 m/s.

Design of a Novel MEMS Gyroscope Array

This paper reports a novel four degree-of-freedom (DOF) MEMS vibratory gyroscope. A MEMS gyroscope array is then presented using the novel gyroscope unit. In the design of the proposed 4-DOF MEMS vibratory gyroscope, the elements of the drive-mode are set inside the whole gyroscope architecture, and the elements of sense-mode are set around the drive-mode, which thus makes it possible to combine several gyroscope units into a gyroscope array through sense-modes of all the units. The complete 2-DOFvibratory structure is utilized in both the drive-mode and sense-mode of the gyroscope unit, thereby providing the desired bandwidth and inherent robustness. The gyroscope array combines several gyroscope units by using the unique detection mass, which will increase the gain of sense-mode and improve the sensitivity of the system. The simulation results demonstrate that, compared to a single gyroscope unit, the gain of gyroscope array (n = 6)is increased by about 8 dB; a 3 dB bandwidth of 100 Hz in sense-mode and 190 Hz in drive-mode are also provided. The bandwidths of both modes are highly matched with each other, providing a bandwidth of 100 Hz for the entire system, thus illustrating that it could satisfy the requirements in practical applications.

A Ship Deformation Measurement Method Based on Quasi-Static Model

Angular matching method was used to measure ship’s deformation, three-axis fiber optic gyroscope units(FGU) are installed on various point of the ship, based on the model advanced by Mochalov, considering the character of ship’s static deforming angle varies, a quasi-static model was established, Kalman filter was introduced to estimate the ship’s quasi-static and dynamic deforming angles. To make the estimation more precise, gyro drifts was taking into account. Besides the theory simulation, practical experiment in sea area is also carried out, which lays the firm foundation for actual application of ship deformation measurement based on three-axis fiber optic gyroscope.

A “telescopic” system in the calibration problem for strapdown inertial navigation systems

An algorithm for the bench calibration of strapdown inertial navigation systems is studied. This algorithm was developed at the Moscow Institute of Electromechanics and Automatics. A mathematical model for the calibration process is constructed. A method for representing the original calibration problem in the form of a standard estimation problem is proposed with the aid of a so-called “telescopic” system. On the basis of the original algorithm, a new calibration algorithm is constructed; this new algorithm allows one to improve the estimation accuracy for the parameters of accelerometer and gyroscope units. The maximum attainable estimation accuracy for these parameters is determined.

Stellar sensor based nonlinear model error filter for gyroscope drift extraction

The conventional gyroscope based spacecraft attitude determination approaches are afflicted by the integration drift of gyroscope. To ameliorate the performance of gyroscope, many compensation algorithms have been developed. A novel spacecraft attitude determination algorithm, which is based on the stellar sensor and nonlinear model error filter algorithm, is discussed in this paper. This algorithm uses the attitude quaternion obtained from stellar sensor to generate the attitude information of spacecraft, which could compensate the drift error of the gyroscope unit. This approach could be utilized both as the gyroscope error compensation in high precision integrate navigation system and as an attitude determination unit individually in low precision mini-satellite task. Two verifications of different satellite orbits have been launched and the performance of our approach was proved.

The use of holographic interferometry in adjustment of gyroscope units

The possibility of employing holographic interferometry to regulate and adjust precision instruments is examined using certain gyroscope components as an example. The results of experimental investigation are presented.

The use of holographic interferometry in adjustment of gyroscope units

The use of holographic interferometry in adjustment of gyroscope units

On a Method of Measuring a Ship's Oscillations

There are many sorts of apparatus for measuring the oscillations of ships around and in the direction of the three axes. The ordinary type of apparatus measures directly the displacement itself, but it is very difficult to get any sort of pendulum that has a period sufficiently long enough to measure the displacement of a body that is oscillating slowly, such as a ship at the period of 45 seconds to about 20 seconds. Moreover here are some cases in studying the motion of ships, when knowledge of the velocity or acceleration of oscillations is necessary.So, utilizing the operating circuit of electronic analogue computers, we succeeded in setting up a system of measuring capable of getting displacement, velocities and accelerations at once. By integrating or differentiating once or twice the easiest of these three measurements to obtain, the remaining two measurements will automatically be obtained.We made a set of integrators, differentiatars and multipliers by the circuit of ana-com., and by using an angular velocity meter of a rate gyroscope unit as a pick up, we established a measuring system of angular oscillations of ships.We used this set on the voyage of a certain ship, and because we received excellent results, we want to report our method and conclusions in the following paper.