Data Analysis and Modeling of Fiber Optic Gyroscope Drift

A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan variance method and each error coefficient is identified. Furthermore, a random drift error model for IFOG is built by the method of time series analysis. The conclusion provides supports for improving IFOG design and compensating for errors of IFOG in practice.

Effect of radiation-induced mean wavelength shift in optical fibers on the scale factor of an interferometric fiber optic gyroscope at a wavelength of 1300 nm

In order to analyze the effect of wavelength-dependent radiation-induced attenuation （RIA） on the mean trans- mission wavelength in optical fiber and the scale factor of interferometric fiber optic gyroscopes （IFOGs）, three types of polarization-maintaining （PM） fibers are tested by using a 60Co γ-radiation source. The observed different mean wave- length shift （MWS） behaviors for different fibers are interpreted by color-center theory involving dose rate-dependent absorption bands in ultraviolet and visible ranges and total dose-dependent near-infrared absorption bands. To evaluate the mean wavelength variation in a fiber coil and the induced scale factor change for space-borne IFOGs under low radiation doses in a space environment, the influence of dose rate on the mean wavelength is investigated by testing four germanium （Ge） doped fibers and two germanium-phosphorus （Ge-P） codoped fibers irradiated at different dose rates. Experimental results indicate that the Ge-doped fibers show the least mean wavelength shift during irradiation and their mean wavelength of optical signal transmission in fibers will shift to a shorter wavelength in a low-dose-rate radiation environment. Finally, the change in the scale factor of IFOG resulting from the mean wavelength shift is estimated and tested, and it is found that the significant radiation-induced scale factor variation must be considered during the design of space-borne IFOGs.

Filtering of long-term dependent fractal noise in fiber optic gyroscope

Stochastic noises of fiber optic gyroscope （FOG） mainly contain white noise and fractal noise whose long-term dependent component causes FOG a rather slow drift. In order to eliminate this component, a two-step filtering methodology is proposed. Firstly, fractional differencing （FD） method is introduced to trans-form fractal noise into fractional white noise based on the estima-tion of Hurst exponent for long-term dependent fractal process, which together with the existing white noise make up of a gener-alized white noise. Further, an improved denoising algorithm of wavelet maxima is developed to suppress the generalized white noise. Experimental results show that the basic noise terms of FOG greatly decrease, and especially the slow drift is restrained effectively. The proposed methodology provides a promising ap-proach for filtering long-term dependent fractal noise.

Effect of radiation-induced color centers absorption in optical fibers on fiber optic gyroscope for space application

The effects of color centers＇ absorption on fibers and interferometric fiber optical gyroscopes（IFOGs） are studied in the paper. The irradiation induced attenuation（RIA） spectra of three types of polarization-maintaining fibers（PMFs）, i.e.,P-doped, Ge-doped, and pure silica, irradiated at 100 Gy and 1000 Gy are measured in a wavelength range from 1100 nm to1600 nm and decomposed according to the Gaussian model. The relationship of the color centers absorption intensity with radiation dose is investigated based on a power model. Furthermore, the effects of all color centers＇ absorption on RIA and mean wavelength shifts（MWS） at 1300 nm and 1550 nm are discussed respectively. Finally, the random walk coefficient（RWC） degradation induced from RIA and the scale factor error induced by MWS of the IFOG are simulated and tested at a wavelength of 1300 nm. This research will contribute to the applications of the fibers in radiation environments.

Suppression of modulation-induced polarization error in spliceless open-loop fiber optic gyroscope [Invited]

The suppression of polarization cross talk in lead zirconate titanate phase modulators as a key error source has been challenging for open-loop fiber optic gyroscopes(FOGs).We developed a polarization-diversity optical frequency domain reflectometry(OFDR)to measure the distributed modulation polarization error in the modulator.The error contributes 8×10^(−6) rad to FOG’s bias instability.Using a UV-fabricated in-fiberλ/4 wave plate and polarization-mode converter with fiber taper technology,the modulation error has been suppressed by 15 dB in assembled FOGs.This approach reduced error with temperature from 25°/h to 0.7°/h,meeting the requirements of control-level gyroscopes with bias errors less than 1°/h.

Effect of ^(60)Co-gamma radiation on the random walk error of interferometric fiber optic gyroscopes

Two 60Co-gamma radiation experiments were launched to explore the radiation effect on optical components and interferometric fiber optic gyroscope (IFOG). In optical components radiation experiment, the result showed that polarization-maintaining (PM) fiber coil loss was the most affected parameter in all the RWC (random walk coefficient) related parameters, compared with the weak sensitivity of other components parameters. In the IFOG radiation experiment, the RWC performance degradation was found to be almost due to an increase of the PM fiber attenuation. Based on the experiment result, a RWC prediction model in radiation, which is obtained by embedding PM fiber loss expression into the RWC model, was built following a power law of dose and dose rate. An IFOG RWC in space radiation environment was predicted from radiation dose and dose rate by the RWC prediction model. This RWC value calculated from test data is fully accorded to the RWC value predicted from radiation dose.

Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths

Fiber optical gyroscope(FOG)is a highly reliable navigation element,and the degradation trajectories of its two accuracy indexes are monotonic and non-monotonic respectively.In this paper,a flexible accelerated degradation testing(ADT)model is used for analyzing the bivariate dependent degradation process of FOG.The time-varying copulas are employed to consider the dynamic dependency structure between two marginal degradation processes as the Wiener process and the inverse Gaussian process.The statistical inference is implemented by utilizing an inference function for the margins(IFM)approach.It is demonstrated that the proposed method is powerful in modeling the joint distribution with various margins.

Experimental optimization of an erbium-doped super-fluorescent fiber source for fiber optic gyroscopes

Double-pass forward and double-pass backward erbium-doped super-fluorescent fiber sources（EDSFSs） were combined in one configuration.A 980 nm laser diode pumped the same erbium-doped fiber from both directions using a coupler as a power splitter.The double-pass configuration was achieved by coating the fiber end face.Firstly,an optimal fiber length was found to obtain a high stability of output light wavelength with pump power, and then 1530/1550 nm wavelength division multiplexing was used for spectrum planarization,which expanded the bandwidth to more than 22 nm.The final step was a test of temperature stability.The results show that the rate of the central wavelength change kept to below 3.5 ppm/℃in the range of -40 to 60℃and 1-2 ppm/℃in the range of 20-30℃.Considering all the three factors of the fiber optic gyro applications,we selected 80 mA as the pump current,in which case the central wavelength temperature instability was calculated as 2.70 ppm/℃, 3 dB bandwidth 22.85 nm,spectral flatness 0.2 dB,output power 5.17 mW and power efficiency up to 9.92%.This experimental result has a significant reference value to the selection of devices and proper design of ED-SFSs for the application of high-precision fiber optic gyroscopes.

Research of Optical Fiber Coil Winding Model Based on Large-deformation Theory of Elasticity and Its Application

Optical fiber coil winding model is used to guide proper and high precision coil winding for fiber optic gyroscope （FOG） application. Based on the large-deformation theory of elasticity, stress analysis of optical fiber free end has been made and balance equation of infinitesimal fiber is deduced, then deformation equation is derived by substituting terminal conditions. On condition that only axial tensile force exists, approximate curve equation has been built in small angle deformation scope. The comparison of tangent point longitudinal coordinate result between theory and approximation gives constant of integration, and expression with tangent point as origin of coordinate is readjusted. Analyzing the winding parameters of an example, it is clear that the horizontal distance from the highest point of wheel to fiber tangent point has millimeter order of magnitude and significant difference with fiber tension variation, and maintains invariant when wheel radius changes. The height of tension and accurate position of tangent point are defined for proper fiber guide. For application to fiber optic gyroscope, spiral-disc winding method and nonideal deformation of straddle section are analyzed, and then spiral-disc quadrupole pattern winding method has been introduced and realized by winding system. The winding results approve that the winding model is applicable.

Fiber Optic Gyroscope Dynamic North-Finder Algorithm Modeling and Analysis Based on Simulink

In view of the problems such as the lower automation level and the insufficient precision of the traditional fiber optic gyroscope （FOG） static north-finder, this paper focuses on the in-depth analysis of the FOG dynamic north-finder principle and algorithm. The simulation model of the FOG dynamic north found algorithm with the least square method by points is established using Simulink toolbox, and then the platform rotation speed and sampling frequency, which affect FOG dynamic north found precision obviously, are simulated and calculated, and the optimization analysis is carried out as a key consideration. The simulation results show that, when the platform rotation speed is between 4.5°/s and 8.5°/s and the sampling frequency is at about 50Hz in the case of using the parameters of this paper, the FOG dynamic north finding system can reach the higher precision. And the conclusions can provide the reference and validation for the engineering and practical of FOG dynamic north-finder.

Suppression of backscattering induced noise by the sideband locking technique in a resonant fiber optic gyroscope

Polarization fluctuation induced noise and backscattering-induced noise are the dominant noises in resonant fiber optic gyroscopes. This Letter proposes a new method to suppress the carrier and backscattering induced noise by the sideband locking technique. Besides choosing an optimized modulation depth and different clockwise and counterclockwise modulation frequencies, the sideband is locked to the cavity resonance. With the proper modulation frequency, the carrier frequency component locates at a position far away from the resonant frequency, and then it is suppressed by the cavity itself, which can be taken as a bandpass filter. The amplitude of the carrier frequency can be suppressed by 20–25 d B additionally by the cavity and the total intensity suppression ratio can reach 115.74 d B. The backscattering induced noise can be eliminated for the adoption of different frequencies. The method can realize a stable and high suppression ratio without high requirements for parameter accuracy or device performance.

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 0.0038°/√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.

Noise decomposition and parameter optimization method for high sensitivity fiber optic gyroscope

A novel random walk coefficient(RWC) model of the interferometric fiber optic gyroscope(IFOG) to decompose fundamental noise sources, namely the shot noise, the excess noise, the thermal noise, and the detection circuit noise, from the overall noise was developed. The coefficients of the model were extracted from the measured RWC instead of by calculating the accurate IFOG parameters, which is simpler and more accurate. The correctness and the accuracy of the model were verified by experiments. Using this model, the RWC of the experimental IFOG was predicted and the quantitative contributions of the noise sources were determined. According to the predicted results, the parameters of the IFOG were optimized. Finally, based on the model, a noise decomposition and parameter optimization method was proposed for high sensitivity IFOG design.

Reduction of nonreciprocal errors in a differential interferometric fiber optical gyroscope using optically differential processing

The bias stability of differential interferometric fiber optical gyroscope is analyzed.Thermal error causing long-term bias drift are reduced by putting the 90°splice in the middle of the fiber coil and applying a wide spectrum light source.Also,a kind of novel optical differential processing,which is much more precise than the electronic differential processing,is proposed for reducing the residual nonreciprocal error in the final differential output.An experimental setup based on optical differential processing was built.An^100 fold reduction in the long-term bias drift is demonstrated experimentally compared with the primary differential interferometric fiber optical gyroscope.

An investigation of numerical aperture of air-core photonic bandgap fiber

Air-core photonic bandgap fiber(PBF)is the perfect choice of the next-generation fiber optical gyroscope(FOG),with excellent temperature,electromagnetism and radiation adaptability.Numerical aperture is an important optical parameter of PBF for application in FOG.The PBF’s maximum theoretical numerical aperture(NAmax)is calculated and compared with the far-field numerical aperture(NAeff)through experiments.The result indicates that the relationship between NAmax and NAeff has much stronger dependence on wavelength than that of the conventional fiber,and they get close at wavelengths near the middle of the photonic bandgap with the error less than 5%.Furthermore,photonic bandgap fiber optical gyroscope(PBFOG)with no fusion splicing points is proposed,and the optimization method and results of the PBF’s structure parameters for application in PBFOG are given from the aspect of numerical aperture.

De-Noising Stochastic Noise in FOG Based on Second-Generation DB4 Wavelet and SURE-Threshold

An effective de-noising method for fiber optic gyroscopes （FOGs） is proposed. This method is based on second-generation Daubechies D4 （DB4） wavelet transform （WT） and level-dependent threshold estimator called Stein＇s unbiased risk estimator （SURE）. The whole approach consists of three critical parts： wavelet decomposition module, parameters estimation module and SURE de-noising module. First, DB4 wavelet is selected as lifting base of the second-generation wavelet in the decomposition module. Second, in the parameters estimation module, maximum likelihood estimation （MLE） is used for stochastic noise parameters estimation. Third, combined with soft threshold de-noising technique, the SURE de-noising module is designed. For comparison, both the traditional universal threshold wavelet and the second-generation Harr wavelet method are also investigated. The experiment results show that the computation cost is 40% less than that of the traditional wavelet method. The standard deviation of de-noised FOG signal is 0.012 and the three noise terms such as angle random walk, bias instability and quantization noise are reduced to 0.007 2°/√h, 0.004 1° / h, and 0.008 1°, respectively.

Adaptive Dual Wavelet Threshold Denoising Function Combined with Allan Variance for Tuning FOG-SINS Filter

Allan variance(AV)stochastic process identification method for inertial sensors has successfully combined the wavelet transform denoising scheme.However,the latter usually employs a traditional hard threshold or soft threshold that presents some mathematical problems.An adaptive dual threshold for discrete wavelet transform(DWT)denoising function overcomes the disadvantages of traditional approaches.Assume that two thresholds for noise and signal and special fuzzy evaluation function for the signal with range between the two thresholds assure continuity and overcome previous difficulties.On the basis of AV,an application for strap-down inertial navigation system(SINS)stochastic model extraction assures more efficient tuning of the augmented 21-state improved exact modeling Kalman filter(IEMKF)states.The experimental results show that the proposed algorithm is superior in denoising performance.Furthermore,the improved filter estimation of navigation solution is better than that of conventional Kalman filter(CKF).