Scale Factor Stability Research Articles

Influence of the average wavelength on the scale factor stability of interferometric fiber optic gyroscope

The introduction of closed-loop mechanisms has significantly enhanced the performance of interferometric fiber optic gyroscopes (IFOGs). However, the poor scale factor (SF) stability limits its further application due to the use of broadband light sources. This study first reviewed the impact of the average wavelength of a light source on SF stability in a closed-loop IFOG setup. A simulation model is developed according to modulation and demodulation principles, and the SF error is found to be proportional to the wavelength drift in a closed-loop IFOG. Additionally, employing a laser with a more stable average wavelength instead of a super fluorescent fiber source (SFS) for driving the IFOG enhanced the SF stability by an order of magnitude to 0.38 ppm in ambient-air experiments, which is one of the best SF performances achieved thus far. With the significant improvement in stability during the variable temperature tests, the IFOG measures rotation rates more accurately.

Enhancing scale factor stability of IFOGs through an optimized proper frequency measurement method: The even frequency doubled sine wave modulation

Even frequency doubled sine wave modulation is an existing method for measuring the proper frequency of closed-loop interferometric fiber optic gyroscopes (IFOGs). In this paper, we first provide a comprehensive explanation of the underlying principle of this method. Secondly, we refine the existing approach and expand its applicability from IFOGs using square wave modulation to those using four-state modulation. On this foundation, we present both theoretical and experimental evidence demonstrating that this method can enhance the stability of the IFOG’s scale factor. During a linear heating process from −40 °C to 60 °C, the angle random walk (ARW) exhibited a slight decrease of 1.4%, while the stability of the FOG’s scale factor significantly improved by a factor of 6.7 in our evaluation system. Moreover, for the first time, we reveal the interaction between the added sine wave and the original rotation rate demodulation system. This interaction is analyzed theoretically, and the conclusions drawn from this analysis are supported by experimental validation.

Polarization self-compensation in a laser-driven interferometric fiber optic gyroscope with high long-term stability

We present a laser-driven interferometric fiber optic gyroscope (IFOG) with polarization self-compensation to achieve high scale-factor stability, sensitivity, and long-term stability. Coherent light with 200kHz linewidth is employed to keep the scale factor stable. The optical scheme ensures polarization reciprocity as well as the optimal working point for good sensitivity. Furthermore, a hybrid machine learning loop (MLL) method, combining the advantages of PID fast response and artificial neural network (ANN) dynamic search, can control a liquid crystal rotator (LCR) to dynamically compensate for slow drift induced by polarization coupling. In open environment, when the sensitivity is 0.005∘/h, the bias instability (BI) is significantly optimized from 0.6723°/h at 60s (PID) to 0.3869°/h at 200s (MLL), which is close to the Sagnac interferometric limit (SIL). Such IFOG can meet the real-time and robust requirements for inertial navigation systems in long-term measurement.

Combined Temperature Compensation Method for Closed-Loop Microelectromechanical System Capacitive Accelerometer.

This article describes a closed-loop detection MEMS accelerometer for acceleration measurement. This paper analyzes the working principle of MEMS accelerometers in detail and explains the relationship between the accelerometer zero bias, scale factor and voltage reference. Therefore, a combined compensation method is designed via reference voltage source compensation and terminal temperature compensation of the accelerometer, which comprehensively improves the performance over a wide temperature range of the accelerometer. The experiment results show that the initial range is reduced from 3679 ppm to 221 ppm with reference voltage source compensation, zero-bias stability of the accelerometer over temperature is increased by 14.3% on average and the scale factor stability over temperature is increased by 88.2% on average. After combined compensation, one accelerometer zero-bias stability over temperature was reduced to 40 μg and the scale factor stability over temperature was reduced to 16 ppm, the average value of the zero-bias stability over temperature was reduced from 1764 μg to 36 μg, the average value of the scale factor stability over temperature was reduced from 2270 ppm to 25 ppm, the average stability of the zero bias was increased by 97.96% and the average stability of the scale factor was increased by 98.90%.

Temperature compensation of MEMS resonant accelerometers with an on-chip platinum film thermometer

Temperature-dominated drift is generally the main error source for high-performance micromachined resonant accelerometers (MRAs) due to inherent thermal stress effect of resonator structure and die-attach process. This paper describes the design and experimental evaluation of a temperature compensation scheme for MEMS resonant accelerometers that demonstrates excellent bias and scale factor stability against temperature variation. An on-chip temperature sensor fabricated by sputtering platinum film on glass substrate is proposed to accurately sense the temperature-induced frequency change of the resonator. A polynomial fitting-based post-compensation model is firstly used to suppress the temperature sensitivity of the MRA over dynamic temperature environment. The temperature drift test and compensation of four accelerometer prototypes in a range from −40 ∘C to 60 ∘C show that the stability of bias and scale factor has been improved greatly with navigation-grade performance. Temperature compensation results with three improved drift models based on polynomial fitting, convolutional neural network and support vector regression respectively are presented and compared to suppress the temperature drift hysteresis in consecutive temperature-varying tests. These experimental results indicate that this resonant accelerometer exhibits excellent temperature stability after compensation, which offers the promise for high-performance inertial navigation applications.

Improvement and compensation of temperature drift of scale factor of a SOI-based MEMS differential capacitive accelerometer

In recent years, the analysis and improvement of temperature characteristics of Si-based capacitive accelerometers has received considerable research attention in the field of Microelectromechanical system (MEMS) sensors. Generally, the influence of temperature on the accelerometers can be mitigated by optimizing the structural design and compensating the output signal. Herein, the output characteristics of an accelerometer designed with asymmetrically arranged combs were analyzed under various temperatures. The purpose of this paper is to improve the temperature drift of scale factor (TDSF) of MEMS capacitive accelerometer, using the asymmetric layout structure to improve the TDSF fundamentally, and the least square method to achieve temperature compensation efficiently. The variations in the TDSF were compared for the symmetric and asymmetric structures. In addition, we modeled the accelerometer with an asymmetric structure for simulations to analyze the errors resulting from the electrostatic torsion phenomenon induced by the asymmetric structure. Moreover, a temperature compensation model was developed for the scale factor of the accelerometer, which was validated and verified with the data obtained from simulations and experiment. Furthermore, an accelerometer based on silicon on insulator was fabricated and tested to verify the simulation results and the compensation effects. According to the results, the scale factor of the studied accelerometer was 171.83 mV g−1 and the average value of the TDSF was 83.56 ppm °C−1 Overall, the experimental results were almost consistent with the simulation results. Under the asymmetric layout, the scale-factor stability improvement of the accelerometer could reach up to 86.96%, and the error caused by electrostatic torsion was ∼2.93%, which is relatively negligible. After compensation, the range and standard deviation of the scale factor of the accelerometer with respect to temperature were reduced by 94.46% and 95.69%, respectively, and the average value of TDSF was reduced by 95.90%, which verified the effectiveness of the compensation model.

Modulation index detection and stabilization technique of phase modulator in resonant fiber optic gyro base on sampling demodulation

A new modulation index detection and stabilization technique (MIDST) based on sampling demodulation is proposed to reduce the influence of phase modulator (PM) thermal instability on resonant fiber optic gyro (RFOG). Firstly, the factors causing the PM thermal instability and the influence on RFOG are analyzed. Then, a phase modulation index detection technique is proposed to detect the fluctuation of modulation index without complicating the optical path configuration of RFOG. Finally, considering the temperature fluctuation, a modulation index stabilization loop based on auto disturbance rejection controller (ADRC) is designed to stabilize the phase modulation index. In experiments, modulation index can be detected in real time and accurately, and the fluctuation is reduced from 10% to 0.3% over 100 °C temperature range (−40 °C to ＋60 °C) with MIDST. The stability of scale factor and the suppression effect of backscattering noise could be improved effectively.

Optical Inline-Sagnac Current Sensor, Part I: Theory

A study is made of the optical inline-Sagnac interferometer current sensor/transducer with active phase modulation and with spun polarization maintaining fiber. A brief review of the common sensor types is made to give context to the discussion of the optical inline-Sagnac current sensor theory. A new discussion is made of the limitations of the optical inline-Sagnac interferometer current sensor caused by the spun polarization maintaining fiber, the polarizing fiber design, and the temperature effects of each type of fiber. These combined temperature effects limit the sensor to a practical scale factor temperature sensitivity range of about 80 to 200 ppm/°C. The fiber component optical-wavelength effects require a broad-band light source to have a wavelength stability of <0.65 nm to achieve a ±0.1% sensor scale factor stability. The opto-mechanical effects from available spun polarization maintaining fibers limit the measurement head to diameters >30 mm. The transit-time of the light through the sensor is the ultimate bandwidth limit for the device. However, most practical sensors have −3 dB bandwidths >20 kHz. In utility applications the isolation of the sensor to nearby currents is estimated to be −96 dB.

Scale Factor Self-Calibration of MEMS Gyroscopes Based on the High-Order Harmonic Extraction in Nonlinear Detection

This article presents a novel self-calibration method to improve the scale factor (SF) stability by the synchronous control on the first-order and third-order harmonic components of nonlinear detection. On the conventional scheme of a drive loop, the readout amplitude of the first-order harmonic component is controlled at a constant value. However, the actual vibration amplitude of drive-mode motion would drift due to the change of circuit gains between the readout amplitude and actual amplitude, thereby resulting in the deterioration of the SF stability. The third-order harmonic component of nonlinear detection shares the same circuit with the vibration signal, indicating that its readout amplitude can track the change in circuit gains in real time. Therefore, this new approach replaces the original fixed reference with the varying readout amplitude of the third-order harmonic component to eliminate the drive-mode vibration error and eventually calibrate the drift of SF. Experiments performed on a honeycomb disk resonator gyroscope (HDRG) have demonstrated the feasibility of the calibration method. The calibration based on the harmonic extraction yields a short-term SF repeatability of 24.9 ppm and a long-term SF repeatability of 30.8 ppm. Allan deviation analysis of the calibrated SF demonstrates a 3.5-ppm precision upon an average of 200 s. The temperature sensitivity of the SF is reduced from 717.3 ppm/°C to 5.02 ppm/°C and the SF repeatability is improved from 15643 ppm to 94.9 ppm over the temperature range of −30 °C to 30 °C.

Modulator Coefficient Tracking Method of Resonant Integrated Optical Gyroscope Based on Novel Four-State Modulation

A modulator coefficient tracking system (MCTS) with the novel four-state modulation technique is proposed to improve the stability of scale factor for resonant integrated optical gyroscope (RIOG). Firstly, we analyze the influence mechanism of integrated optical phase modulator (IOPM) coefficient on the scale factor stability of RIOG. Then, the novel four-state modulation technique is proposed to synchronously detect angular velocity information and IOPM coefficient without additional optical devices, which consists of the basic triangular modulation signal and the triangular signal for demodulating modulator coefficient. Finally, MCTS based on the novel four-state modulation technique is designed to real-timely track the modulator coefficient and adjust loop-gain to be constant for improving the scale factor stability of RIOG. The experimental results show that the tracking error of MCTS is 0.23% from −40 °C to +60 °C and the scale factor stability of RIOG is optimized to 163.37 ppm. The proposed MCTS with the novel four-state modulation technique can significantly improve the performance of RIOG, which contributes to promoting the applications of RIOGs.

Low-Drift Closed-Loop Fiber Optic Gyroscope of High Scale Factor Stability Driven by Laser With External Phase Modulation

In view of the poor scale factor stability of the interferometric fiber optic gyroscope (IFOG), it is a creative method to use laser to drive the IFOG for its better frequency stabilization characteristics instead of the broadband light source. As the linewidth of laser is narrow, the errors of coherent backscattering, polarization coupling, and Kerr effect are reintroduced which cause more noise and drift. This paper studies laser spectrum broadening based on external phase modulation of Gaussian white noise (GWN). The theoretical analysis and test results indicate that this method has a good effect on spectrum broadening and can be used to improve the performance of the laser-driven IFOG. In the established closed-loop IFOG, a four-state modulation (FSM) is adopted to avoid temperature instability of the multifunction integrated-optic chip (MIOC) and drift caused by the electronic circuit in demodulation. The experimental results show that the IFOG driven by broadened laser has the angular random walk noise of 0.003 8 °/√h and the drift of 0.017 °/h, which are 62% and 66% better than those without modulation respectively, of which the drift has reached the level of the broadband light source. Although the noise still needs further reduction, its scale factor stability is 0.38 ppm, which has an overwhelming advantage compared with the traditional IFOG.

Frequency-Modulated MEMS Gyroscopes: A Review

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.

A temperature compensated biaxial eFM accelerometer in Epi-seal process

This paper reports on the implementation of a vacuum-encapsulated bi-axial resonant accelerometer utilizing the electrostatic frequency modulation (eFM) technique. A novel flexure structure is designed to enable fully-decoupled in-plane displacement of the proof-mass to minimize cross-axis sensitivity. A differential readout scheme leveraging pairs of high quality factor (>12k) free-free beam resonators mitigates the first-order nonlinearities due to temperature effects and unwanted response to proof-mass spurious modes. The fabricated device measures a scale factor of 45.8 Hz/g with negligible cross-axis sensitivity (<2 %). Furthermore, the smooth characteristics of temperature coefficients of frequency (TCf) of the resonators enable an accurate temperature sensor using the common-mode frequency of the resonator pair. Applying a temperature compensation scheme utilizing the common-mode frequency output and pre-characterized TCfs, the accelerometer demonstrates superior performance measuring a VRW of 5.8 μg/√Hz and BI of 5.7 μg with a scale factor stability of 0.38 % and zero-g-output variation of 8.3 mg over temperature range from –20 °C to 80 °C.

Stabilisation of central wavelength of erbium‐doped fibre source as part of high‐accuracy fibre optic gyroscopes

The stability of the central wavelength of the erbium-doped fibre source (EDFS) is one of the most important parameters to ensure the accurate operation of navigation systems based on high-accuracy fibre optic gyroscopes (FOGs). Herein, the method of stabilisation of the EDFS as a part of the FOG is presented. The main advantage of this method is the possibility of quick and simple matching of temperature-compensating spectral filters by changing the pump ratio without modifying the optic scheme. The EDFS optic scheme is based on the double-pass bidirectional pumping configuration. This makes it possible to obtain the world-class stability of the central wavelength of the EDFS as a component of different devices with the spectral selectivity and set the constant value of the optic power of the output light (OL). Also, this is the first study into the dependence of the temperature coefficient of the central wavelength on the pump ratio. The proposed method allows compensating the spectral characteristics of the FOG, achieving the OL central wavelength stability around 0.7 ppm/°C and the FOG scale factor stability around 0.73 ppm/°C.

High Precision Hemispherical Resonator Gyroscopes With Oven Control Systems

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× and 3× 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×, and the scale factor stability can be also increased up to 19×. The BI and rate random walk (RRW) are all significantly enhanced to show a good environmental adaptability of the proposed ovenized HRG.

In-Run Scale Factor Compensation for MEMS Gyroscope Without Calibration and Fitting

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.

Vibration-insensitive optical path length control transducer for ring laser gyroscope

A ring laser gyroscope is an optical sensor based on the Sagnac effect. It has many outstanding advantages, such as a short start-up time, a high precision, a wide dynamic range and a stable scale factor. It is insensitive to accelerations and is in

Enhanced temperature stability of scale factor in MEMS gyroscope based on multi parameters fusion compensation method

Scale factor thermal sensitivity is an essential performance index of microelectromechanical system (MEMS) gyroscopes and is typically used to characterize the temperature stability of inertial sensors. This study demonstrates a novel compensation method to enhance the temperature stability of the scale factor for an amplitude-modulated (AM) MEMS gyroscope operating in split-mode based on multiparameter fusion compensation (MPFC). A mathematical model for the temperature sensitivity of the scale factor is established, which indicates that the resonant frequency of the primary mode, voltage amplitude of the primary mode displacement, frequency split of the two working modes, and demodulation phase error are the decisive factors that affect the thermal sensitivity of the scale factor. The temperature performance of the scale factor can be significantly improved with MPFC by a weighted linear combination of the four factors. The results show that the temperature sensitivity of the scale factor decreases from 370 to 33 ppm/°C over the temperature range of −30 to 70 °C, representing a reduction by an order of magnitude. The thermal sensitivity of the scale factor can be further reduced to approximately 8 ppm/°C by applying the proposed compensation technique after increasing the stability of the demodulation phase error.

Research on the mean-wavelength drift mechanism of SLD light source in FOG

The SLD light source is widely used in fiber optical gyroscope (FOG), and its mean-wavelength stability directly influenced the scale factor stability of FOG. The research on mean-wavelength drift of light source can improve the scale factor of FOG and, consequently, suppress the angle error of inertial navigation system. In this work, the luminous mechanism of semiconductor light source was considered and influence factors of SLD spectrum were analyzed. Based on simulation and experiment, the main causes of SLD mean-wavelength drift has been indicated, including the temperature drift of drive circuit and the temperature control error caused by position of thermistor. This research has made an instructive contribution to the development of FOG light source stability.

Modulation index stabilization technique of integrated optic phase modulator used in resonant integrated optic gyro.

A novel modulation index stabilization technique for tracking the phase modulation index of integrated optic phase modulator (IOPM) is proposed to improve temperature performance of the resonant integrated optic gyro (RIOG). The influence mechanism of IOPM's modulation index fluctuation on the RIOG, especially the angular velocity tracking loop of RIOG, is investigated. A Mach-Zehnder Interferometer (MZI) is ingeniously added into the conventional RIOG structure for detecting the modulation index fluctuation. For synchronously demodulating the output of RIOG and the gain of IOPM in real time, a novel six-state wave modulation scheme is also proposed. Moreover, considering the disturbance and nonlinearity, the system model of IOPM's modulation index controller is established and designed to guarantee high speed and precision tracking. The experimental results demonstrate that the proposed modulation index stabilization technique can in real time demodulate and control the modulation index of IOPM. The gyro scale factor stability of RIOG resulting from the IOPM's modulation index fluctuation is decreased to 189.26 ppm within -40°C to +60°C, which, to the best of our knowledge, is the first time stabilizing the modulation index of IOPM in RIOG at full temperature.