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Hemispherical Resonator Gyroscope (HRG) is a classical high precision Coriolis Vibration Gyroscope (CVG), which performs attitude estimation of carrier by detecting the precession of standing wave of resonator, thus, the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope, where the quality factor non-uniformity of resonator is one of main error sources. Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation, which makes the gyroscope have more accurate scale factor, larger measurement range and better dynamic characteristics. In this paper, the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle, then the corresponding equivalent mechanical model is established. According to the “average method”, it can be seen that the ideal resonator excited by the ring electrode works in integral mode, and any position in the circumferential direction of resonator can be a working point, which means that the quality factor non-uniformity has a great effect on the drift of standing wave. Therefore, the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model, and the drift model of standing wave is established by the “average method”, it can be found that both the amplitude of quality factor non-uniformity and angle between the “inherent damping axis” and antinode axis of standing wave can affect the drift rate of standing wave. Moreover, the drift model indicates that if the input angular rate does not reach the threshold, the precession angular rate of standing wave will appear “self-locking” phenomenon, that is, the gyroscope will lose the integral effect.

As a high-precision angular rate sensor, the Frequency-Modulated (FM) gyroscope based on MEMS craft has attracted more and more attention in recent years, owing to its advantages in low power consumption, low temperature sensitivity, very high bandwidth, and excellent scale factor stability. This review summaries the history and latest development of the FM gyroscope research. The theory of the frequency modulation effect of the Coriolis coupling is provided based on the method of rotating wave approximation in a systematic and explicit way. Typical FM gyroscope operation modes, such as QFM, IFM, LFM, and their working principles are introduced minutely. The error sources of FM gyroscopes, and the characters comparison between FM and AM gyroscopes are discussed in detail as well.

We characterised the displacement of a transmission X-ray tube target parallel to the beam axis due to thermal effects using interferometry. Displacements of up to 10 μm with a sensitivity of about 0.4 μm/W deposited power were measured relative to the X-ray tube's mechanical mounting position. They significantly influence the scale factor of dimensional computed tomography measurements by several 10−4 at high geometric magnifications. Finite element simulations revealed that the displacement is due to thermal deformation of the entire target assembly and helped to derive a linearised model that predicted the displacements within a few tenths of a micrometre. Radiographic measurements of a calibrated standard confirmed that the mechanical displacement of the target corresponded with the X-ray focal spot position. The findings help to increase the accuracy of dimensional X-ray computed tomography measurements and to ameliorate the design of transmission X-ray tubes.

The residual intensity modulation (RIM) of the multifunction integrated optic circuit (MIOC) can be classified into the linear term and the nonlinear term, which can impact the performance of the fiber-optic gyroscope (FOG). According to the generation mechanism of the RIM and the demodulation principle of the FOG, a model is established to analyze the influence of RIM on the FOG performance. Simulation shows that both the linear and the nonlinear RIM can lead to a large and sudden change in the FOG output at reset points of the feedback step wave, as well as fluctuations within the reset period. The magnitude of the sudden change at the reset point is proportional to the difference between the linear RIMs of two branches in the MIOC, and the fluctuation within the period of the feedback step wave is more dependent on the nonlinear RIM. The relationship between the FOG output and the linear and nonlinear RIMs are verified by experiments. The RIM-induced output can result in the increase of the bias error and the scale factor error of the FOG, especially at small input angular velocity. Furthermore, the application of FOG for the real-time high-speed position tracking to stabilize the attitude control platform can be limited.

This paper presents an in-run mode-matching method for MEMS gyroscopes based on the power symmetry between the sideband signals in the sense mode. The method takes advantage of the power symmetry of both the noise and the Coriolis response within the upper sideband (USB) and the lower sideband (LSB) of the driving frequency. The power difference is taken as a mismatch detection and is fed to the mode-matching controller, which regulates the tuning electrodes. During the matching control, the history of the estimated mode order is recorded to adaptively tune the controller gain, speeding up the tracking process and reducing the steady ripples. The experiments exhibited that the frequency loop could converge to the steady-state within a reasonable time and with 0.28Hz peak-peak fluctuation. By the mode-matching, the scale factor of the gyroscope under test was boosted by ten times; the angle random walk was enhanced from 8.13deg/h/sqrt(Hz) to 1.99deg/h/sqrt(Hz); the bias instability was improved from 2.09deg/h to 1.12deg/h. The method proposed in this paper can be implemented with a general platform that MEMS gyroscopes usually utilize.

A z-axis decoupled multi-frame vibration MEMS gyroscope (DMFVMG) is presented in this paper. Firstly, the decoupled principle is employed and the sense frame, Coriolis frame and drive frame are arranged through inner fame, intermediate frame and outer frame, and the movement characteristic analysis indicates that the structure is fully decoupled. The structure is simulated through mode analysis, harmonic response and drop shock response. The simulation results show that the resonant frequencies of the Sense Mode and Drive Mode are 10094Hz and 10162Hz, and the maximum deformation and stress with the shock analysis is 7.14 $\mu {\mathrm{ m}}$ and 235.19MPa (among three different directions). Then, the structure is fabricated through MEMS processing, and P-type single-crystalline silicon wafer and 7740 glass wafer are used. After that, the structure is packaged in a ceramic vacuum tube shell and the resonant frequencies and quality values of the sense and drive mode are 10354.21Hz and 5364, 10438.23Hz and 5219, the error between fabrication and simulation is 2.58% and 2.72%. And the monitoring system of DMFVMG prototype is established by analog circuit with drive closed-loop and sense open-loop. Then, the DMFVMG prototype is tested through turntable, and the range, scale factor and intercept are ±300°/s, −19.06mV/°/s and 95.43mV respectively. Finally, five repeated bias tests are arranged and the angular random walking values and bias stability are 0.2408°/ $\surd \text{h}$ , 0.2358°/ $\surd \text{h}$ , 0.2413°/ $\surd \text{h}$ , 0.2397°/ $\surd \text{h}$ and 0.2480°/ $\surd \text{h}$ , 2.858°/h, 3.159°/h, 3.428°/h, 1.891°/h and 3.467°/h respectively.

In the rotational inertial navigation system (RINS), the horizontal gyro drift can be modulated when the IMU rotates around the z axis. At the same time, the scale factor error of the z gyro can be offset by forward and reverse rotation. However, in the forward and backward rotation, the gyro scale factor error will still cause the heading angle output error. Moreover, the change of the scale factor error of the fiber optic gyros(FOG) is sensitive to temperature changes, which makes it difficult to calibrate gyro scale factor error accurately. Therefore, in this paper, a method to calibrate the scale factor errors of two RINSs dynamically is proposed. During the movement of vehicle, the heading angle difference between the RINS1 and RINS2 is calculated real time, the scale factor errors of RINS1 and RINS2 could be estimated at the same time with the least squares filtering algorithm. The simulation experiments show that when RINS1 and RINS2 adopt a reasonable rotation strategy, the gyro scale factor errors were less than 0.5ppm. In the vehicle experiment, the heading angle error caused by the gyro scale factor error is kept below 5”. And the method significantly improves the problem that scale factor error affected by temperature changes during navigation process, and at the same time solves the problem of the calibration coefficient error in the dynamic situation.

This study investigated the variation in electronic portal imager pixel scale at the isocenter plane for Elekta Agility linear accelerators. An in‐house MATLAB script was written to process and calculate the pixel scale based on a metal calibration plate supplied by Elekta. Eight pixel plates were compared and found to have manufacturing tolerances within 0.1 mm of nominal dimensions. The impact of these variations on pixel scale factor was negligible, and plates could be used interchangeably. Uncertainties from other parameters such as source‐to‐surface distance and user variability summed to a combined uncertainty of 0.0003 mm/pixel, compared to a pixel scale range of 0.003 mm/pixel measured across 10 machines. Most of the inter‐machine variation was shown to be attributable to differences in source‐to‐panel distance. Other factors such as focal spot size and shape, electronic portal imager manufacturing consistency, panel sag, and setup errors may account for the residual variation. Individual characterization of machine and imaging panel pixel scale factors is important to ensure accurate geometric information is derived from electronic portal images, which is critical where the portal imager is used for multi‐leaf collimator calibration or other clinical tasks.

The article describes the methods and test results of a solid-wave gyroscope (SVG) — an angular rate sensor (ARS), developed at the Department of Control Devices, Tula State University and manufactured by the serial plant of JSC "Michurinsky Plant" Progress "according to the technology it worked out. The metal resonator SVG-ARS is made of an elinvar alloy and has a cylindrical structure of different thickness, the lower part of which, with a smaller wall thickness, acts as a suspension for the upper cylinder, the resonator itself, which has a conical shape, providing better vibration localization at its end edge. Technological manufacturing defects, different frequencies and variability, are eliminated by balancing " by mass" based on the removal of excess metal at certain points on the end edge of the resonator. The electronic module provides the second mode of primary and secondary oscillations of the resonator edge arising during rotation and creates a signal to compensate for the Coriolis and quadrature components of the output signal at the nodes. The maximum amplitudes of the excitation and compensation signals do not exceed 10 V. Therefore, at large values of mechanical influences, the compensation circuit may not work out the increased signal and the SVG-ARS loses its operability. The total processing time of the compensation signal does not exceed 1 μs. The maximum power consumption of the electronic module is not more than 4 W. When testing for mechanical and temperature effects, the norms were used that are typical for similar devices (angular rate sensors) used on board aircraft. The tests were carried out on the bench equipment of a specialized enterprise. The stability of the zero signal and the scale factor was determined under the simultaneous action of the measured speed and temperature on the SVG-ARS. The values of the random walk and the instability of the zero signal were obtained from the Allan deviation plots. Their values provide a basis for the conclusion about the possibility of using the developed SVG for several hours on board dynamic aircraft in orientation, stabilization and navigation systems. It was found that SVG-ARS possesses impact strength and restores its measuring ability after impact. Tests for vibration resistance revealed resonance frequencies and frequency rangesin which the tested VTG-DUS sample can be used without significant modification. The results of vibration tests can be used to refine the design and control electronics for the operating conditions of a particular aircraft.

The rotational inertial navigation system (RINS) could greatly improve navigation performance by rotating the inertial measurement unit with gimbals. And the self-calibration of error parameters could be achieved conveniently. Among the rate-biased Ring laser gyro (RLG), the input angular velocity can reach tens of degrees per second. Therefore, the attitude errors caused by scale factor is dozens of times that of the other RINS. In this paper, gyro scale factor errors are calibrated through optimal estimation with attitude errors in dual-axis laser RINS. During the movement of vehicle, the dynamic gyro scale factor errors calibration can be performed online by adding parking points. Moreover, the parking points can be accurately determined by the statistical characteristics of accelerometers and gyros output information, without extern sensors. The experiment results indicate that the calibration repeatability scale factor parameters are less than 1ppm, and the attitude errors cause by the scale factor error is reduce from tens of arc seconds to 10 arc seconds, which verifies the effectiveness and accuracy of the method proposed in this paper. Through the compensation of calibration results, the attitude error of RINS is further improved in both the static and dynamic experiment.

For the purpose of realizing the dynamic angle measurement and calibration of the inertial equipment (such as rotary table), a dynamic angle measurement system based on the autocollimator and the fiber optic gyroscope (FOG), which can be used as an angle standard device, is designed in this paper. In this system, the scale factor of the FOG can be calibrated in the field application based on the autocollimator with the precision of $1^{\prime \prime }$ in the range of ±0.05°. Furthermore, the angle measurement deviation between the FOG and the rotary table can be limited in $\pm 3^{\prime \prime }$ when the scale factor of the FOG is calibrated by the autocollimator when necessary. This research can guarantee the long-term accuracy of the scale factor of the FOG in the field application and it will greatly promote the applications of the FOG as an angle standard device in the field of dynamic angle measurement.

The development of wave solid-state gyroscopes (VTG) is one of the promising areas of development of gyroscopic angular velocity sensors. VTG from the standpoint of manufacturing technology, tuning and control systems, as well as accuracy characteristics, has a number of advantages compared to other types of gyroscopes. When developing VTG, they strive to reduce the gyroscope's own care, zero signal bias, and the non-linearity of the scale factor in the operating temperature range However, when creating the device, due attention is often not paid to the existing opportunities to improve the dynamic accuracy of the gyroscope by developing promising structural solutions for building control circuits and information processing. The solution to this problem was the goal of the work.Using the methods of the theory of automatic control, the dynamics of a wave solid-state gyroscope with a metal resonator and piezoelectric elements in the closed-loop mode of Сoriolis acceleration compensation are studied. Piezoelectric elements perform the functions of displacement and force sensors.Two promising structural solutions for constructing VTG control and information processing circuits are proposed and considered. Relations are established for selecting the parameters of the links of these contours, which provide an increase in the dynamic accuracy of the gyroscope. In the first case, the proposed structure for constructing the VTG allows us to significantly reduce the dynamic errors caused by the difference in the scale coefficient of the VTG at different frequencies of the measured angular velocity in the bandwidth. Such a structure for constructing a VTG can be recommended when solving a measurement problem in which it is necessary to accurately measure the angular velocity, and the phase lag of the output signal in relation to the measured angular velocity is of secondary importance. In the second case, the proposed structure of the VTG construction corresponds to the transfer function of the relative measurement error with secondorder astatism, and the absolute measurement error in the frequency band of 10 Hz does not exceed 0.1 %.

A piezoelectric disk gyroscope fabricated with a single-crystal lithium niobate (LN) wafer has been developed for inertial navigation systems for localization during automated driving. LN has a high electromechanical coupling coefficient and a resonator made of a low-cost single-crystal wafer shows a high quality factor, which is suitable for high-performance vibratory gyroscopes. In this study, its crystallographic anisotropies in both in elastic and piezoelectric properties were considered to realize mode matching in the two-wine-glass-mode vibration of a disk resonator. We chose a 155°-Y-cut LN wafer because we found that its elastic compliance is uniform in any in-plane direction. Its anisotropic piezoelectric properties were considered to optimize the electrode design to oscillate the wine-glass modes efficiently. A 25.8-mm-diameter, 330- $\mu \text{m}$ -thick disk resonator with 16 electrodes on each side was designed and fabricated by photolithography and grinding. The as-fabricated LN disk resonator was successfully oscillated in two wine-glass modes with a small frequency split of 0.7% at 95 kHz resonant frequency. Gyroscope operation was successful and the scale factor was $0.35~\mu \text{V}$ /°/s without any preamplifier. [2021-0022]

In order to achieve wideband scaled measurement of low observable object scattering characteristics, the scaling design of the related absorbing material has been within the scope of researchers over recent years. In this work, a tunable material was designed to meet the wideband and high-precision requirements for scaling measurements. The material was produced using magnetorheological (MR) fluid, composed of silicon rubber and flaky carbonyl iron particles (CIPs), and an electric magnet. According to the results, applying the magnetic field made the CIPs in the MR fluid aligned with respect to different parallelism depth. Furthermore, the larger the field strength, the lower the permittivity and the higher the permeability. Based on the Maxwell–Garnett mixing rule, two parameters could be interpolated within a frequency range of 18–40 GHz. Changing the magnetic field resulted in the tunable absorbing property of the composite at frequencies of 2–40 GHz and the adjustable reflection loss in the region of −22 dB to –3 dB. While the thickness of the full-size absorbing coating was 0.7–0.9 mm at 10 GHz and a scale factor of 4, the designed material was as thick as 0.8 mm, and the average radar cross-section (RCS) error of coating plates was less than 0.5 dB. In addition, the scaled frequency band could be tunable within a range of 36–40 GHz as the absorber was as thin as 2 mm, and the mean RCS error was found to be less than 0.6 dB. Therefore, the MR fluid was shown to be a promising candidate for scaled measurements.

Two rolling bearing life models based on the concept of dynamic stress capacity are considered. They are the modified Lundberg–Palmgren model and the Gupta–Zaretsky model. Consistency of these models with patterns of dependences of the bearing life from temperature and scale factor is analyzed. Stability of the model parameters to the conditions of the experiments used to determine them is analyzed as well. A significant dependence of the material’s contact durability on its elastic properties is a negative characteristic of the Gupta–Zaretsky model, since in studies of the temperature dependence of fatigue properties, changes in elastic properties are not explicitly taken into account. The scale factor adopted in the modified Lundberg–Palmgren model is in good agreement with the experimental data for ball bearings with balls up to 25.4 mm, and in the Gupta–Zaretsky model, for bearings with balls larger than 25.4 mm. The results of the stability analysis of the experimental parameters of the considered models to the shear stress life exponent in the life equation without a scale factor, considered in the example of a 32 220 bearing, indicate the preference of the modified Lundberg–Palmgren model. The modified Lundberg–Palmgren model has good validity characteristics. It requires further improvements aimed at taking into account the residual and operating stresses, as well as adequately taking into account the scale factor in calculating ball bearings with a ball diameter over 25.4 mm.

This letter presents a high performance rate-integrating honeycomb disk resonator gyroscope (HDRG). High Q factor resonator and symmetric vibration detection gain are the key to high performance rate-integrating gyroscope. By stiffness-mass decoupling design, HDRG can achieve high Q factor of about 600k and decay time of over 44s. A compensation method is applied to suppress the rate-dependent angular drift caused by the asymmetry circular distribution of detection gains. Finally, the rate-integrating HDRG shows an excellent bias instability of 0.038°/h, 1.05ppm scale factor nonlinearity, wide measurement range of over ±7000°/s and a threshold value of about ±0.0001°/s, which is the best performance in the reported rate-integrating MEMS gyroscopes.

High performance Microelectromechanical system (MEMS) gyroscopes are in great demand in the fields of precise navigation, automatic driving and precise attitude measurement. Honeycomb disk resonator gyroscope(HDRG) which works on wineglass-modes has many advantages including higher immunity to fabrication errors, better resonant mode consistency and better inner electrode arrangement, showing excellent potentials to be the next-generation MEMS gyroscope with high performance and good robustness. In this paper, a new HDRG prototype is designed based on the comprehensive optimizations of resonant structure and electrode configuration. The main structure parameters and the lumped-mass configuration are optimized systematically through the finite element simulation, while the configuration and arrangement of the inner electrodes are optimized based on the vibration amplification effect, offering systematic reference for the optimizations of other MEMS gyroscopes. The new HDRG is fabricated through a SOI fabrication technique and tested with a close-loop digital circuit. Quality factor of the optimized HDRG prototype reaches 650k, proving to be a record in silicon disk resonator gyroscopes. The bias instability of the optimized gyroscope reaches 0.015°/h under room temperature without any compensation, approaching the accuracy of navigation grade. Scale factor nonlinearity reached around 120ppm in the range of ±300°/s without compensation. The comprehensive performance is at the forefront of MEMS resonant gyroscopes.

A maximum likelihood estimator is presented for self-calibrating both accelerometers and gyroscopes in an inertial sensor array, including scale factors, misalignments, biases, and sensor positions. By simultaneous estimation of the calibration parameters and the motion dynamics of the array, external equipment is not required for the method. A computational efficient iterative optimization method is proposed where the calibration problem is divided into smaller subproblems. Further, an identifiability analysis of the calibration problem is presented. The analysis shows that it is sufficient to know the magnitude of the local gravity vector and the average scale factor gain of the gyroscopes, and that the array is exposed to two types of motions for the calibration problem to be well defined. The proposed estimator is evaluated by real-world experiments and by Monte Carlo simulations. The results show that the parameters can be consistently estimated and that the calibration significantly improves the accuracy of the motion estimation. This enables on-the-fly calibration of small inertial sensors arrays by simply twisting them by hand.

This paper presents an in-run scale factor error compensation for the micro-electro-mechanical system (MEMS) gyroscope without system calibration and data fitting. The causes of three scale factor errors (instability, nonlinearity, and asymmetry) are analyzed. Next, the instability and nonlinearity by open-loop detection (Mode I), and closed-loop detection (Mode II) are discussed according to the specific comb capacitance and the front-end detection circuit. The closed-loop detection transfer function is studied, and a series of equivalent conversions are performed to obtain a method (Mode III) for improving the temperature stability of scale factor. The results of the experiment indicated that the nonlinearity and asymmetry of the Mode II and Mode III are increased by 1.8 times and 3.5 times than that of Mode I. Furthermore, the instability of Mode II and Mode III is reduced by 10 times and 19 times over -20°C to 40°C. Besides, the mode III does not affect the static and dynamic performance of gyroscope according to the test results of bias and bandwidth.

This work presents a high reliable hemispherical resonator gyroscope (HRG) with a solution of an oven control system. The dynamics and thermal characteristics are firstly analyzed with a indication that the conventional look-up table (LUT) method can not fully compensate the HRG errors. The temperature cycling experiments show the hysteresis effect of the key parameters of HRG and fit the theoretical analysis. Then an advanced oven control approach is proposed to solve the challenges with optimized mechanical isolation, sensing and actuation electronics. The experimental verification results illustrate a comprehensive improvement for the HRG. Particularly, the bias instability (BI) is one order of magnitude better than uncompensated HRG that reaches a sub 0.001°/hr level. The daily bias and scale factor repeatability is $6\times $ and $3\times $ improved with a 1 week measurement, respectively. It also shows an excellent robustness to the environmental variation by doing a temperature cycling test. The bias level error of the uncompensated system is improved by $40\times $ , and the scale factor stability can be also increased up to $19\times $ . The BI and rate random walk (RRW) are all significantly enhanced to show a good environmental adaptability of the proposed ovenized HRG.

This paper reports a rate integrating gyroscope (RIG) using independently controlled clockwise (CW) and counter clockwise (CCW) modes on a single MEMS resonator. The rotation angle is read out by the phase difference between these modes. A CW/CCW mode separator was used to independently contol these modes superposed on the resonator. The frequency and Q-factor mismatches were compensated by the phases and amplitudes of driving signals. A control system including the mode separator, feedback controllers, signal generators, mismatch compensators were implemented in a field programmable gate array (FPGA). Using the proposed mismatch compensation technique, the equivallent aniso-damping term became 1/100. As a result, the scale factor became constant and the non-linearity became less than 0.2% even when the slow angular rate region around 5°/s. In addition, the temperature coefficient of scale factor as small as −1.84 ± 0.62 ppm/K was achieved without any temperature correction. [2020-0011]

In this work, the drifts of the bias and scale factor induced by the dielectric charging are studied for micro-electro-mechanical system (MEMS) closed-loop accelerometers. At first, the equations of the feedback electrostatic forces, including the built-in voltages resulted from the dielectric charging, are built up for the two capacitors of the accelerometers. Then, the models for the drifts of the bias and scale factor both are established. Based on the models and experimental data, it is found that the drift of the scale factor is always negative because the built-in voltages always decrease the scale factor. However, the drift of the bias can be negative or positive because it is in proportion to the built-in voltages’ difference of the two capacitors, which may be negative or positive. The major output error for the small input acceleration is caused by the drift of the bias. However, for the large acceleration, the error induced by the drift of the scale factor is also vital. Finally, the method of choosing the frequency of the ac reference voltage for suppressing the dielectric charging based on the drift of the scale factor is established. The feasibility is verified by the experimental data.

A review of the methods of obtaining and processing the VOG signal is carried out. A gyroscope with the formation of a phase information signal in an interference loop (at the optical level) is proposed. The analysis of digital phase difference meters is carried out. The advantages of a gyroscope with a phase information signal and digital signal processing are the linearity of the scale factor, an increase in the dynamic range and a reduction in the influence of external factors on the measurement result.

In recent years, navigation technology has rapidly developed. System-level calibration technology for inertial navigation system (INS) has been widely used because it does not rely on high-precision equipment. However, INS introduces a bad coupling error in high-precision ring laser gyroscope (RLG) scale-factor error estimation, accompanied by a large accelerometer-slope bias error. To solve this problem, an improved system-level fitting calibration method is proposed, which changes the 90° rotation increment to 450°, while maintaining the original calibration sequence. Compared with the traditional system-level calibration method, the calibration error of the gyroscope scale-factor error is reduced to 0.2 times, under simulation conditions, without affecting the calibration accuracy of the other parameters. The extreme difference of the gyroscope scale-factor calibration error on multiple experiments reduces from 4.75 to 1.40 ppm under experimental-verification conditions. The mean values of the gyroscope scale factor were closer to the real reference values (no more than 2 ppm). The integral calibration results meet the requirements of a high-precision RLG INS. The proposed method maintains the original calibration sequence and exhibits small changes with high practicability. The proposed method is suitable for applications with high requirements for gyroscope scale factor accuracy, such as highly dynamic aircraft.

The problem of extending the field of effective use of strapdown inertial navigation systems to the class of highly dynamic objects is considered. To ensure effective motion control, high requirements are put forward for the accuracy of determining the orientation angles and coordinates of an object, which can only be satisfied if high-tech precision gyroscopes and accelerometers are used in SINS. Also, the use of SINS is limited by the possible dynamics of the object. The solution to this problem is based on the possibility of taking into account the conditions of the future operation of the SINS due to the rational choice of the placement or configuration of the gyroscopes' sensitivity axes. This choice makes it possible to reduce the requirements for the measuring range of the meter unit while maintaining functionality as part of the strapdown inertial navigation system as a whole. For this purpose, it is proposed to place gyroscopes in a special way relative coordinate system of the instrument. This arrangement allows to use gyroscopes with a relatively small operating range to measure a significant object rotation speed. The choice of such a configuration is realized through the solution of an certain optimization problem with constraints. In the general case, the problem is solved numerically, and in some cases, an analytical solution is possible. An additional advantage of the optimal configuration is the increase in the accuracy of the SINS by reducing the effect of the error of the scale factor of gyroscopes. The resulting solution is applied in practice during the design and creation of a specialized SINS.

We constructed a compact single-beam atomic magnetometer operated in a transverse magnetic-modulation mode or a DC-offset mode. By coupling the laser beam into a polarization maintaining fiber, with a vapor cell of the dimensions 4 mm $\times4$ mm $\times4$ mm, a sensitivity of 30 fT/Hz1/2 has been achieved in the single-beam configuration. In addition to the experimental study of the sensitivity, we perform a theoretical analysis of the single-beam atomic magnetometer in the transverse magnetic-modulation mode and the DC-offset mode. The results indicate both of two modes have almost the same scale factor. We also studied the dynamic working range of the sensor and found, experimentally, that our sensor reaches a dynamic response range of ± 3 nT, with a nonlinear error of 1%. The frequency responses of the transverse magnetic-modulation mode and the DC-offset mode are 125 Hz and 65 Hz, respectively. This sensor will be particularly suitable for applications that require high sensitivity, low cost and compact size, e.g., magnetoencephalography (MEG) and magnetocardiography (MCG).

Through the computational modelling and experimental verification of a stereo-photogrammetry system, the expanded uncertainty on form measurement was estimated and was found to be 32 μ m , 12 μ m and 29 μ m for a 95% confidence interval (coverage factors of k = 3.2, 2.0 and 2.0 respectively) in the x, y and z axis respectively. The contribution of systematic offsets in the system properties was also investigated, demonstrating the complex distortions of the measurement volume that result from these systematic errors. Additionally, a traceable method of applying a scale factor to the reconstruction was demonstrated using a laser interferometer and gauge block. The relative standard uncertainty on the size of the measurements was estimated to be 0.007% corresponding to length measurement uncertainties of around 7 μ m over a 100 mm range. Finally, the residuals from a linear fit of the scale factor were found to exhibit behaviour that would be expected to result from small offsets in the system properties. The outcome of this work is a better understanding of the propagation of uncertainty through the stereo-photogrammetry system as well as highlighting key influence factors that must be addressed in future work.

In order to improve the scale factor stability of interferometric fiber optic gyroscope (IFOG), laser is considered to be an alternative to traditional broadband light source because of its excellent frequency stability. Although the performance of IFOG driven directly by laser is inspiring, it is still necessary for further improvement. The main limiting factor is its narrow linewidth and errors of coherent backscattering, polarization coupling and Kerr effect will be reintroduced in laser-driven IFOG. At present, one of the best methods is using Gaussian white noise (GWN) to drive an external electro-optic phase modulator (EOM) and broaden the optical spectrum of laser which will not cause additional frequency drift to the laser. This review studies the mechanism of phase modulation comprehensively based on theory and simulation. The process of broadening is described by numerical calculation and OptiSystem platform. The spectrum is also broadened as expected in the experiment observed by optical spectrum analyzer (OSA). Furthermore, by broadening the linewidth before laser enters the IFOG system, its angular random walk noise and drift are improved by more than 60% compared with no modulation. The test results also show that the drift has reached the level of broadband light source. Related work enriches the application of laser as light source in IFOG and the research about external phase modulation.

Whole-angle gyroscopes have broad prospects for development with inherent advantages of excellent scale factor, wide bandwidth and measurement range, which are restrictions on rate gyroscopes. Previous studies on the whole-angle mode are based mostly on the linear model of Lynch, and the essential nonlinearity of capacitive displacement detection is always neglected, which has significant negative effects on the performance. In this paper, a novel real-time calibration method of capacitive displacement detection is proposed to eliminate these nonlinear effects. This novel method innovatively takes advantage of the relationship between the first and third harmonic components of detective signals for calibration. Based on this method, the real-time calibration of capacitive displacement detection is achieved and solves the problems of traditional methods, which are usually related to the vibration amplitude, environmental variations and other factors. Furthermore, this novel calibration method is embedded into a whole-angle control system to restore the linear capacitive response in real time and then combined with a microshell resonator for the first time to exploit the enormous potential of an ultrahigh Q factor and symmetric structure. The effectiveness is proven because the angle drift is reduced significantly to improve the scale-factor nonlinearity by 14 times to 0.79 ppm with 0.0673°/h bias instability and a 0.001°/s rate threshold, which is the best reported performance of the MEMS whole-angle gyroscope thus far. More importantly, this novel calibration method can be applied for all kinds of resonators with the requirement of a linear capacitive response even under a large resonant amplitude.

International audience; This paper presents a numerical simulation study of p-i-n photodiodes based on In0.1Ga0.9 N/GaN multiple quantum wells (MQWs) of 2.5-nm-thick In0.1Ga0.9 N QWs and 12-nm-thick GaN barriers embedded into the intrinsic regions. The device performance is evaluated by investigating both the spectral and the frequency responses. The simulated 10-period In0.1Ga0.9 N/GaN MQW photodiode exhibits a peak responsivity of 0.25 A/W at 0.35 μm under a light power density of 0.1 W.cm−2 at -2 V reverse bias voltage and a cutoff frequency of 460 MHz. The effects of the number of quantum wells, reverse bias voltage and polarization on the spectral and frequency responses are then investigated. It is found that the maximum responsivity is 0.29 A/W at 0.35 μm and the cutoff frequency is 8.2 GHz for a 15-period In0.1Ga0.9 N/GaN MQW structure under a reverse bias of -10 V and a polarization scale factor of 0.25. Increasing the polarization scale factor degrades the responsivity performance due to the increased recombination of photocarriers. On the other hand, the cutoff frequency increases significantly with polarization and reaches a high value of 28 GHz for a polarization scale factor of 0.9 due to the increase of the polarization-induced field in the QWs.

A novel cobweb-like disk resonator gyroscope (CDRG) with a very small frequency split between two degenerate modes has been designed and implemented. In comparison with the ring-like DRG (RDRG), the CDRG has fewer fabrication imperfections owing to its all-linear structure. In addition, the CDRG displays a superior nonlinear effect compared with the RDRG, and internal differential electrode excitation and detection were used to further reduce the nonlinear effect. The CDRGs and RDRGs were placed side by side on the same wafer, and the characteristics of these as-fabricated resonators were then tested. The results showed that the resonant frequencies and Q-factors of the CDRGs and RDRGs were approximately 18 kHz and nearly 100k, respectively. The smallest as-fabricated relative frequency split (29.9 ppm) of the CDRGs was about 10.8 times smaller than that (322.5 ppm) of an RDRG built side by side on the same wafer, which had the lowest relative frequency split among all current disk resonator gyros. Finally, the preliminary results for the performance of the CDRG and RDRG in the force-to-rebalance mode and mode matching are given. Under the same conditions, the maximum vibration displacement, scale factor, angular random walk, and bias instability of the CDRG were improved by 62.8%, 112%, 700%, and 314%, respectively, compared with the RDRG.

The results of study of a fiber-optic gyroscope prototype with 0.01–0.001deg/h drift are presented. The gyroscope comprises three feedback loops: one for Sagnac phase difference compensation, the second one for the scale factor stabilization, and the third (fast-response) one for the compensation of constant component of optical signal on the photodetector, affecting the measurement channel. To increase the accuracy of the prototype gyroscope up to the level of 0.001 deg/h, it is proposed to use the fourth and the fifth feedback loops which will suppress the parasitic effects in the integrated optic phase modulators.

Automotive MEMS gyroscopes are used for various purposes, such as rollover prevention and dynamic stability. Although, employment of gyroscopes for automotive applications is reported, what is not discussed is the gyro topology design and optimization for these applications. This article reports parametric topology size optimization of a MEMS gyroscope proper for automotive applications. The structure optimization of a translational dual-mass Coriolis vibratory gyroscope (CVG) with electrostatically sense/excitation mechanism is presented for automotive applications. Fabrication considerations conform to the X-FAB procedures, and application uncertainty is inherent in the vehicle lateral model. The proposed design approach takes into account the inaccessible levels of application uncertainty to optimization, which provides results that are more reliable, compared with the ideal models. More than thirteen thousand virtual cases are studied, in which the gyroscope performance specifications including scale factor, linearity, etc. are calculated. The double-lane-change (DLC) maneuver based on ISO 3888-1 is performed on the optimal candidates in order to apply the vehicle application constrains. The suggested optimal solution is the one with the least yaw rate error with respect to the target yaw rate instructed by the maneuver, which suits best for the automotive application. The results show that the yaw rate error of DLC maneuver improved from about 40% to about 1.4% using the optimization algorithm, which shows the effectiveness of the proposed method.

Предметом вивчення в статті є метод багатомасштабного оброблення зображень з бортових систем оптикоелектронного спостереження для визначення елементів міської інфраструктури. Метою є розробка методу багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження для визначення елементів міської інфраструктури. Завдання: аналіз відомих методів оброблення багатомасштабної послідовності зображень, розробка методу багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження для визначення елементів міської інфраструктури, проведення оброблення зображення з бортової системи оптико-електронного спостереження. Використовуваними методами є: методи теорії імовірності, математичної статистики, методи оптимізації, математичного моделювання та цифрової обробки зображень, методи математичної логіки. Отримані такі результати. Встановлено, що відомі методи оброблення багатомасштабної послідовності зображень не можуть бути напряму застосовані до багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження. Запропоновано метод багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження для визначення елементів міської інфраструктури. В основі методу покладений двоетапний метод виділення об’єктів міської забудови на зображеннях бортових систем оптикоелектронного спостереження з використанням перетворення Хафа. Проведено оброблення зображення з бортової системи оптико-електронного спостереження методом багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження для визначення елементів міської інфраструктури. Висновки. Наукова новизна отриманих результатів полягає в наступному. Запропоновано метод багатомасштабного оброблення зображень з бортових систем оптико-електронного спостереження для визначення елементів міської інфраструктури. На відміну від відомих, передбачається використання двоетапного методу визначення елементів міської інфраструктури на зображеннях з різним значення масштабного коефіцієнта, перемасштабування оброблених зображень з різним значенням масштабного коефіцієнта до вихідного розміру та розрахунок зображення-фільтру, а результуюче оброблене зображення є попіксельним добутком вихідного зображення та зображення-фільтру.

In this paper, we report the effect of geometric parameters by calculating the capacitance scale factor of micromachined vibrating wheel on gimbal gyroscope with various shapes and mass conditions. The behavior of capacitance for vibratory torsional gyroscope with various shapes and mass conditions is investigated using MEMS+™. The structure dimensions of the gyroscope are optimized by matching frequencies in driving and sensing modes. The scale factor and linearity error extracted by calculated capacitance have been changed with various shapes condition unless the area of sensing electrodes and the mass of the gyroscope have been fixed. The mass ratio of gimbal and wheel structure is varied to minimize the linearity error.

Microelectromechanical systems’ (MEMS) inertial measurement unit (IMU) is widely used in many scenarios for its small size, low weight, and low-power consumptions. However, it possesses relatively low positioning accuracy compared with other high-grade IMUs, as errors accumulate quickly over time. This paper mainly focuses on the error characteristics of the gyro part of MEMS IMU by analyzing different kinds of error parameters. As there is no published standard for MEMS gyro error characterization, three dominant error parameters are selected and investigated, namely, scale factor, in-run bias stability, and angular random walk. In addition, Allan variance analysis is deployed as an important part of the scheme with relative results presented in this paper. Not only is theoretical analysis presented, but experimental verification is also carried out correspondingly with an ADIS16490 MEMS IMU. By comparison, we find that the results of in-run bias stability exceed the given features by up to ten times, while the rest of the results agree quite well with the given features. Possible reasons for the exceeding part are given. Calibration testing results not only provide concrete characterization for MEMS gyro errors, but also enhance the importance of overall calibration of MEMS IMU before use.

The objective of this work is to characterize the signals and noises of Geocenter variations time series obtained from different space geodesy techniques as Global Positioning System (GPS), Doppler Orbitography and Radiopositioning Integrated on Satellite (DORIS), and Satellite Laser Ranging (SLR). The proposed methodology is based on the estimation of periodic signals by performing frequency analysis using FAMOUS software (Frequency Analysis Mapping On Unusual Sampling) and evaluation of level and type of noises by Allan variance technique and Three Corned Hat (TCH) method. The available data concern 13 years (from 1993 to 2006) of weekly series of Geocenter residuals components and scale factor variations, according to ITRF2000. The results estimated are more accurate according to GPS and SLR of about 2-8 mm than DORIS of about 8-42 mm, for Geocenter. Better RMS of scale factor was obtained of about 0.1ppb (0.6mm) for GPS technique than SLR and DORIS with 0.6 and 0.9 ppb (3.6 and 5.4mm), respectively. The estimated seasonal signals amplitudes are in the range of few milimeters per technique with centimetre level for Z Geocenter component of DORIS. The Geocenter motion derived from SLR technique is more accurate and close to the geodynamic models. The noise analysis shows a dominant white noise in the SLR and DORIS Geocenter solutions at a level of 0.6-1 mm and 10-40 mm, respectively. However, the GPS solution is characterized by a flicker noise at millimetre level, relating to mismodeling systematic errors.

In high-reliability applications, the health condition of the MEMS gyroscope needs to be known in real time to ensure that the system does not fail due to the wrong output signal. Because the MEMS gyroscope self-test based on the principle of electrostatic force cannot be performed during the working state. We propose that by monitoring the quadrature error signal of the MEMS gyroscope in real time, an online self-test of the MEMS gyroscope can be realized. The correlation between the gyroscope’s quadrature error amplitude signal and the gyroscope scale factor and bias was theoretically analyzed. Based on the sixteen-sided cobweb-like MEMS gyroscope, the real-time built-in self-test (BIST) method of the MEMS gyroscope based on the quadrature error signal was verified. By artificially setting the control signal of the gyroscope to zero, we imitated several scenarios where the gyroscope malfunctioned. Moreover, a mechanical impact table was used to impact the gyroscope. After a 6000 g shock, the gyroscope scale factor, bias, and quadrature error amplitude changed by −1.02%, −5.76%, and −3.74%, respectively, compared to before the impact. The gyroscope failed after a 10,000 g impact, and the quadrature error amplitude changed −99.82% compared to before the impact. The experimental results show that, when the amplitude of the quadrature error signal seriously deviates from the original value, it can be determined that the gyroscope output signal is invalid.

MEMS being the most crucial part in advancement of today's technology plays as the backbone for decrement in size of new electronic devices. They are widely used in pedometry, quad-copters, stabilizing platforms, Inertial Measurement Units (IMUs), Inertial Navigation Systems(INS), robotics and medical field etc. In this research paper we have focused on; bias offset, scale factor error, non-orthogonality, drift due to temperature. Because these errors are the major error sources in MEMS sensors. Different techniques like two position method, six position direct method and six position weighted least square method are used to calibrate MEMS sensors for these errors. Calibration data was collected by the help of CNC machines and a platform made of aluminum to mount the sensors easily. Calibration techniques are implemented on ADXRS649z (single axis gyroscope), MPU-3050 (Three axis digital gyroscope) and ADXL377 (single axis accelerometer) sensors. Temperature compensation is also done to compensate the temperature effects on sensors using controlled temperature chamber and finally, a comparison is made between calibration techniques.

Many applications in our daily life need accurate orientation and motion information. The Inertial Measurement Unit (IMU) is a perfect sensor for that purpose, because of its small size, low power consumption, and affordable price. These low-cost IMUs suffer from several sources of noise, that cause large divergence over time during the absence of an absolute positioning system. In addition to its poor performance, low-cost IMUs do not have reliable noise metrics data information in their vendor specification. Multiple IMUs can be utilized to enhance the overall system performance through fusion. As gyroscope errors have the main contribution in deciding the navigation system performance, this paper proposes two adaptive weighting least square approaches. During fusion, the weights of the LS filter are changed online according to two windowing methodologies, these windowing approaches estimate the bias, noise density, and scale factor level for each sensor measurements inside this window of time, which is then used to estimate the variance accompanied by each sensor that will be used as a weight inside the LS algorithm, these weights are adaptively changing with each period. The second methodology is also based on two different size window techniques, with cascaded LS filter topology. MATLAB navigation toolbox is utilized to generate two gyroscope IMUs row data with different noise configurations like noise density, random walk, and bias instability rates…etc. to imitate real-life raw measurements. These raw measurements are then used to validate and evaluate the two proposed algorithms, by comparing their RMSE to a standard LS method RMSE. The simulation was repeated 100 times and the RMSE of the proposed methodologies showed enhancement in the estimated measurements by more than 20% when compared to the standard LS, under the condition that the noise figures of the sensors are completely random.

In order to investigate the pullout resistance of the Horizontal-Vertical reinforcement, a “denti-geogrid” was assembled by bonding a “denti-strip” with the geogrid and the pullout tests were carried out. Subsequently, the analytical approaches were investigated to calculate the pullout resistance on the basis of the surface sliding model, Perterson and Anderson’s model, Jewell’s model, Chai’s model, and the proposed stress summation model. Moreover, a new index named “scale factor” was suggested to reflect the proportion of bearing resistance provided by transversal members. The research showed that: 1) under the same test conditions, the pullout resistance of denti-geogrid was much higher than that of a common geogrid. All common geogrids showed linear strain softening in the later stage of pullout tests. Given the same normal stresses, due to the expansion of effective areas suffering lateral earth pressure, more denti-strips meant more significant resistance; 2) Among five theoretical approaches, the solutions of the proposed stress summation model made the best agreement with lab test results, with an average relative error of 2.82%. On the other hand, the stress summation model also showed a simplicity in calculation; and 3) Due to higher gradient of the fitting curve of scale factors under lower load, the bearing resistance would be more and more dominant, which means that the lateral resistance of denti-strips could play a decisive role in cases of low stress level.

The paper presents an effective method for scale-factor stabilization and modulation depth control in a low-cost all-fiber interferometric gyroscope utilizing a piezoelectric phase modulator to perform modulation for biasing as well as compensation of the Sagnac phase shift in a closed-loop. The technique uses a virtual-sensor approach consisting in deriving the actual compensation shift from comparison of the real and the modeled gyroscope output intensity signals. The first experimental results are provided, suggesting that the model-base approach can decrease the scale-factor drift by more than one order of magnitude to reduce significantly the effect of the modulator parameter instability.

This paper determines the scale factor for an electromagnetic groundwater flowmeter using an air-cored square pancake coil as the electromagnet. It also proposes the use of an array of electrodes to provide a better estimate of the average water speed between the electrodes.

With the development of the designing and manufacturing level for micro-electromechanical system (MEMS) gyroscopes, the control circuit system has become a key point to determine their internal performance. Nevertheless, the phase delay of electronic components may result in some serious hazards. This study described a real-time circuit phase delay correction system for MEMS vibratory gyroscopes. A detailed theoretical analysis was provided to clarify the influence of circuit phase delay on the in-phase and quadrature (IQ) coupling characteristics and the zero-rate output (ZRO) utilizing a force-to-rebalance (FTR) closed-loop detection and quadrature correction system. By deducing the relationship between the amplitude-frequency, the phase-frequency of the MEMS gyroscope, and the phase relationship of the whole control loop, a real-time correction system was proposed to automatically adjust the phase reference value of the phase-locked loop (PLL) and thus compensate for the real-time circuit phase delay. The experimental results showed that the correction system can accurately measure and compensate the circuit phase delay in real time. Furthermore, the unwanted IQ coupling can be eliminated and the ZRO was decreased by 755% to 0.095°/s. This correction system realized a small angle random walk of 0.978°/√h and a low bias instability of 9.458°/h together with a scale factor nonlinearity of 255 ppm at room temperature. The thermal drift of the ZRO was reduced to 0.0034°/s/°C at a temperature range from −20 to 70 °C.

The paper presents a miniaturized pitch/roll gyroscope with the lowest angle random walk (ARW of 600 $\mu \textbf{dps}/\sqrt{\textbf{Hz}})$ and lowest bias instability (BI of 2.8 dph) ever recorded on planar MEMS sensors for in-plane rate capture. The device is based on NEMS resistive sensing, features a 1.2 mm2footprint, a 100-Hz bandwidth, and can be combined to yaw gyroscopes for ultra-low-noise 3-axis systems. The key advancement over previous implementations is represented by a 10-fold increase in the scale factor, obtained through a novel architecture which, combined with quadrature compensation, optimizes at the same time the energy transfer to the NEMS gauges and the robustness to vibrations.

The precision of the strapdown inertial navigation system (SINS) depended on the work precision of the gyroscope. However, many errors affect the precision of SINS even if the gyroscopes have perfect principles and structures. Before the application of the inertial navigation system (INS), the inertial components must be calibrated to ensure the performance of components, detect whether the precision of the inertial component satisfied the system, and compensate for the error of INS. According to the mathematical model of fiber optic gyroscope (FOG), we propose a multi-position iterative recursive calibration algorithm to compensate for the error of scale factor and installation of FOG. To guarantee the accuracy of the SINS, the error mathematical model of the FOG is established and compensated in the system. Finally, the calibration parameters of FOG are calibrated by the multi-position iterative recursive calibration (MPIRC) and the six-position method. The calibration results show that the accuracy of components calibration parameters of the MPIRC and the six-position is similar, but the accuracy of SINS using MPIRC is higher than that using six-position.

This work reports a novel design for high-frequency piezoelectric gyroscopes using support transducer which enables an efficient energy coupling from a length-extensional mode into a degenerate secondary elliptical mode (n = 3). The gyroscope structure is made by a single crystalline silicon (SCS) disk supported by eight-transducer arms. Large drive mode displacement is excited through piezoelectric AlN thin films on transducer arms. The simulation of the proposed gyroscope shows a high scale factor of 12.24 nA/°/s at resonator Q of 10,000 in a mode-matched condition. The device was fabricated using the PiezoMUMPs process with 10 μm thick silicon structural layer. The fabricated gyroscope shows that the frequency split between drive and sense mode is only 600 Hz at the mean resonant frequency of about 9.976 MHz in air (equivalent to 60 ppm), verifying our design efficacy. The measured scale factor of the proposed gyroscope is around 54.01 μV/°/s before demodulation.

A mode-matching and alignment algorithm for bulk acoustic wave (BAW) resonator gyroscopes via femtosecond laser ablation is presented in this paper and verified on a piezoelectrically-actuated AlN-on-Si disk resonator. Mode-matching is essential to operate piezoelectric BAW resonators as gyros with high sensitivity in air but challenging due to the lack of electrostatic spring-softening effect. In this work, a laser trimming algorithm is implemented to mechanically mode-match and align the two resonant modes of a disk resonator guided by novel numerical maps. After selective laser ablation trimming, the as-born frequency split of 191Hz between 1.4MHz modes of a disk due to fabrication imperfections is reduced to 12Hz, corresponding to 3.8% of its -3dB resonant bandwidth while maintaining a Q-factor of 4600 in air, and 30dB improvement in mode isolation. The laser-trimmed frequencies remain closely matched across the temperature range of -30°C to 90°C, verifying the temperature robustness of laser trimming results. The mode-matched disk resonator is operated as a gyroscope in air and exhibits a large scale factor of 4.12nA/°/s.