Research on Operating Error of Fiber Optic Gyro across Stripes

 After nearly 20 years of development, the domestic interferometric fiber optic gyro is becoming mature, and has completely replaced the mechanical gyroscope in many fields, and has become a key component in modern navigation instruments. With the development of the modulation mode of fiber optic gyro from analog triangle wave to digital square wave, the precision of fiber optic gyroscope is gradually improved.

1 Fiber optic gyro modulation mode

The modulation modes of fiber optic gyro mainly include two state modulation, four state modulation and random modulation

1.1 Two-state modulation scheme

The two-state modulation scheme adopts the modulated mode of +π-θ, square wave of 0 plus step wave (θ is the biased phase), and the typical two-state modulation waveform is shown in Figure 1. The high and low level of the phase square wave and the interference of the previous state form two interference phases of +π-θ and -π+θ, respectively. Rate step waves are generated to offset the phase shift caused by the input angular rate, and the height of each step should be equal to the phase shift caused by the input angular rate, so that the operating point can be stabilized at +π-θ and -π+θ. When the step wave accumulates out of the range 0 ~ 2π, only 2π reset of the rate step wave is needed to realize the modulation of the fiber optic gyro.
Since the responses of +π-θ and -π+θ to the diagonal acceleration of the two operating points are opposite, the angular acceleration can be demodulated by the light intensity difference between the two points.

1.2 Four-state modulation scheme

Because the two operating points of the two-state modulation are symmetric about the Y-axis, the demodulation half-wave voltage gain cannot be stabilized. To solve this problem, A set of fixed +π+θ, 0 square waves can be added on the basis of two-state modulation to generate stable +π+θ, +π-θ, -π+θ and -π-θ operating points (denoted as A, B, C, D). This modulation scheme is called four-state modulation.

1.3 Random modulation scheme

In order to solve the problem of dead zone and zero deviation caused by crosstalk, a random modulation scheme is adopted in this paper. The errors introduced by electron crosstalk can be cancelled out by using the randomly generated four-state modulated signal instead of the modulated square wave of the original fixed sequence, so the dead zone and zero deviation problems can be effectively suppressed. Since the phase waveform of random modulation ranges from -2π to +2π and the rate step wave ranges from 0 to 2π, the final shape of the modulated wave ranges from -2π to 4π. At a half-wave voltage of 4V, a modulation amplitude of 6π requires a voltage range of 6V. Therefore, in this paper, the step wave and the modulation phase are superimposed and then 2π reset. The reset mode is fundamentally different from the step wave reset mode and is called "group reset mode".

3 Cross-stripe work effects

3.1 Nonlinear deterioration at high speed

Since the modulation mode reconfiguration of two-state modulation and four-state modulation occurs only when the rate step wave is out of the range 0 ~ 2π, it is highly correlated with the step wave, but not with the modulation phase. Therefore, the probabilities of the four states A, B, C, and D working across the fringes are exactly equal.
According to the angular acceleration demodulation formula (1) and (2), it can be seen that the angular rate errors caused by the cross-fringes of A and B are of opposite polarity (the same is true for C and D). Therefore, in demodulation of angular acceleration, most of the errors caused by cross-fringe operation are statistically offset (A and B offset, C and D offset). The nonlinear errors of two-state modulation and four-state modulation with frequent cross-fringes at high speed can be suppressed to a lower degree. In the random modulation scheme using the "combined reset mode", the modulation signal is A, B, C, D four states of the modulation phase and angular rate step wave superimposed together, and then determine whether to reset. Therefore, the cross-fringe probabilities of the four modulated states are closely related to their own phases, resulting in huge differences in the cross-fringe probabilities of the four states A, B, C and D, and the cross-fringe errors are difficult to offset each other. Since the relationship between the probability and the input Angle rate is nonlinear, the error cannot be synthesized linearly by the input Angle rate, so a 500×10-6 nonlinear error is generated.

3.2 Zero bias stability decreases

In a single demodulation cycle, using the step wave 2π reset or the combination reset formula, the light intensity error of the cross-stripe work will be mistakenly demodulated. The error appears in the form of noise in the Angle addition rate demodulation and half-wave voltage gain demodulation of the optical fiber Dorrata, which worsens the zero-bias stability.

3.3 Total temperature zero drift increases

The half-wave voltage gain closed-loop cannot keep the light intensity of each operating point consistent in the cross-fringe operation because of the cross-fringe error.
If only A, B, C, D4 operating points in the zero-order fringe are considered to demodulated the half-wave voltage gain, then there is an error between the obtained half-wave voltage gain and the physical parameters of the Y-waveguide, and the error changes with the change of half-wave voltage gain, resulting in a whole-temperature zero-bias drift.

4 cross-stripe working error solution

Using narrow-spectrum light source can greatly improve the interference spectrum and reduce the cross-fringe error. But the narrow spectrum light source will reduce the coherence coefficient, resulting in the host interference, resulting in the decline of the precision of fiber optic gyro. Because of this, it is not feasible to use narrow spectrum light source to solve the cross-fringe error.
Another solution is to set the bias phase θ to 0.5π, which has the smallest difference in cross-fringe light intensity and can reduce the cross-fringe error. However, the bias phase has a larger impact on the noise of the gyroscope, and when θ is set to 0.5π, the fiber optic gyro cannot work in the optimal noise bias phase, thus reducing the precision of the gyroscope.

5 Summary

By analyzing the mechanism of cross-stripe operation, we find out the error source that causes the non-linear malformation of fiber optic gyro in cross-stripe operation. An effective modulation and demodulation scheme for the error source is established, and the error induced by the error source is suppressed to a very low range. However, the modulation scheme based on step-wave resetting is always inferior to the random modulation scheme based on combinatorial resetting in terms of suppressing dead zone and crosstalk, which can be predicted if the pair modulation scheme and random based on combinatorial resetting mode are combined
When the modulation scheme is combined, the cross-fringe error can be solved on the basis of effectively suppressing dead zone and crosstalk.

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