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Abstract
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$^{\circ }/\sqrt{\mathrm{h}}$, 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.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical rotational sensing has applications in navigation as an optical gyroscope and is usually done with a Sagnac interferometer through phase measurement. At present, interferometric fiber optic gyroscopes (IFOGs) are widely utilized owing to their high sensitivity and portability [1–5]. In general, the performance of IFOGs can be evaluated in terms of short-term sensitivity and long-term drift [6,7]. Short-term noise directly limits the detection sensitivity. Long-term drift leads to instability. Therefore, high-sensitivity IFOGs with low bias instability (BI) and angular random walk (ARW) have always drawn lots of interest and attention around the world [8–19], and becoming a goal of many researchers.
Commonly, IFOGs based on the minimal scheme consist of a broadband source, two couplers, a polarizer, and a polarization-maintaining (PM) fiber. It can effectively mitigate the main error sources, namely Kerr-induced drift, Rayleigh backscattering, and polarization error [20–23], which significantly promotes short-term sensitivity. However, the broadband source and PM fiber bring some negative effects in long-term drift [24,25]. For one thing, the mean wavelength of the broadband source is difficult to stabilize which yields a worse stable scale factor for the IFOGs [26]. For another thing, the PM fiber can hardly maintain a single polarization in practice due to external environmental factors, such as temperature, magnetic field, and vibration [23,27–32], which induces random coupling between two orthogonally polarized light (we refer to it as "polarization coupling"). As a result, there exists an obvious slow drift in the output of IFOGs. Therefore, compared with short-term sensitivity, long-term stability is the core bottleneck of the current engineering application.
In order to reduce slow drift and improve the environmental adaptability of IFOGs, software compensation methods have been widely used. The existing software compensation methods can be classified into two types: Traditional compensation [33–35] and artificial intelligence (AI) algorithms [30,36–42]. PID control is the most commonly used traditional fitting method in gyroscopes due to its quick response. However, it is difficult for a PID controller [43], whose structure and parameters are fixed in the whole control process, to achieve good performance in a time-varying system. By comparison, AI methods, such as artificial neural networks (ANN) [43–45], can fully learn the nonlinear characteristics of the data via using different construction ways, complex network structure, and appropriate training methods, to adaptively search for optimal parameters but usually have to take a lot of time to obtain training samples and construct the model, limiting its application in continuous measurement situations [46,47]. Hence, combining PID control with ANN can dynamically compensate for polarization error and achieve great long-term stability in IFOG.
In this paper, we devote to developing a laser-driven IFOG with polarization self-compensation to achieve high scale-factor stability, sensitivity, and long-term stability. Coherent light with 200$\mathrm {kHz}$ linewidth is employed to keep the scale-factor stability. The combination of a polarization beam splitter (PBS), Faraday rotator (FR), and half-wave plate (HWP) can ensure polarization reciprocity. Benefiting from the combination, the bias phase of an electro-optic modulator (EOM) can be fixed at optimal working point for good sensitivity. Furthermore, a liquid crystal rotator (LCR) is controlled by a hybrid machine learning loop (MLL) method based on an artificial neural network (ANN) and a PID to dynamically compensate for the slow drift induced by external environment fluctuations. The experimental results show that, in the open environment, when the sensitivity is achieved to 0.005$\mathrm {^{\circ }/\sqrt {h}}$, the BI is improved from 0.6723$\mathrm {^{\circ }/h}$ at 60$\mathrm {s}$ using traditional PID method to 0.3869$\mathrm {^{\circ }/h}$ at 200$\mathrm {s}$ via MLL. Moreover, under the same light intensity, the ARW and BI of the current IFOG is nearly equal to the Sagnac interferometric limit (SIL). Such IFOG can meet the real-time and robust requirements for inertial navigation systems in long-term measurement.
2. Principle and theory
2.1 Theoretical model with noise and drift analysis
The schematic diagram is shown in Fig. 1(a). The light is emitted from a distributed feedback laser with 200 $\rm {kHz}$ linewidth and passes a Glan polarizer to generate a vertically polarized light ($y$). Different from these IFOGs based on the conventional minimal scheme, a polarization beam splitter (PBS1), Faraday rotators (FR1 and FR2), and half-wave plates (HWP1 and HWP2) are the key components to keep polarization reciprocity in the current IFOG.
Fig. 1. (a) Experiment setup of the polarization self-compensation IFOG. Laser: distributed feedback laser with 200kHz linewidth, and the central wavelength is 795nm; GL: Glan prism with extinction ratio $\epsilon \thickapprox −50 \mathrm {dB}$; HWP: half-wave plate; PBS: polarization beam splitter with extinction ratio $\epsilon \leq -30 \mathrm {dB}$; FR: Faraday rotator; EOM: electro-optic modulator for shifting phase with half-wave voltage 230V; LCR: liquid crystal rotator for adjusting polarization; PMF: 300m polarization-maintaining fiber, radius 10.1 cm, intrinsic frequency 333kHz; M: mirror; PD1: a photoelectric detector for signal measurement; DAQ: digital acquisition card with $50 \rm {kps}$ sample rate; PID: proportion integration differentiation controller; AWG: arbitrary waveform generator; VC: voltage controller, used to generate high voltage. SUM: addition operator. The red arrow shows the polarization direction of the incident light, while the blue arrow shows the polarization direction of the returned light. (b) Machine learning loop (MLL) schematic diagram. It’s a loop between the fiber optic gyroscope hardware system and the hybrid machine learning algorithm. PD1: Photoelectric detection. The ANN and PID parts are socked together and run separately depending on the cost value. ANN: contains an input layer, an output layer, and five hidden layers with 64 neurons in a single layer. Each hidden layer contains a linear layer and a dropout layer. The dropout layer is a regularization method [48] that prevents the ANN from falling into a local minimum or overfitting during the prediction process. The dropout rate is set to $\eta =0.2$.
With the help of a half-wave plate (HWP0), the vertical ($y$) light and the horizontal ($x$) light go through PBS1 with the same powers to ignore the Kerr-induced drift. Then, the vertical ($y$) light and the horizontal ($x$) light propagate in CW and CCW direction respectively. After passing through an electro-optic modulator (EOM), there is a phase difference $\phi _{0}$ between the vertical ($y$) light and the horizontal ($x$) light. Here it can be fixed at an optimal working point to obtain great measurement sensitivity and a linear scale factor for IFOG. In CW direction, after passing through FR1 and HWP1, the direction of the polarization remains unchanged. In CCW direction, with the help of FR2 and HWP2, the direction of polarization rotates counterclockwise by 90$^{\circ }$. In this way, the polarization of CW and CCW directions are both vertical($y$) when coupling into the fiber coil. Benefiting from the optical scheme, the light coupled into orthogonal (unwanted) polarization cannot enter the photodetector (PD1), which partially reduces the noise of the proposed IFOG.
Subsequently, the lights in CW and CCW direction pass through a 300$\rm {m}$ PM fiber coil. However, in practice, the temperature variation makes the PM fiber can hardly maintain the single polarization. As a result, there is a rotation angle $\theta _{n}$ caused by polarization changes. In this case, a liquid crystal rotation (LCR) modulator with the rotation angle $\theta _{c}$ is employed to compensate for $\theta _{n}$. Hence, the lights returning to PBS1 are
Here $A_{0}$ and $\omega _{0}$ are the amplitude and the central frequency of the light source. $\phi _{cw}$ and $\phi _{ccw}$ are the induced phase by the Sagnac effect in CW and CCW, respectively. Finally, the horizontal ($x$) light goes through PBS2 and is detected by PD1, which is
Here $\phi =\phi _{cw}-\phi _{ccw}$ is the phase difference related to the rotational angular velocity $\Omega =\frac {c\lambda }{4\pi Lr}\phi$. $c$ is the speed of light in vacuum. $\lambda$ is the laser wavelength. $L$ is the length of the Sagnac loop. $r$ is the radius of the optical fiber loop. Under static conditions $\phi \approx 0$, the interference signal $I_{1}(t)$ is stabilized at $I_{0}=|A_{0}|^2$ , which is defined as the target value. When the phase difference induced by EOM is $\phi _{0}=-\frac {\pi }{2}$ nearby, the bias phase of the IFOG can be fixed at the optimal working point to obtain great measurement sensitivity and a linear scale factor. According to Eq. (3), when $\theta _{c} =\theta _{n}$, the polarization coupling angle $\theta _{n}$ caused by environmental fluctuations can be compensated via the rotation angle $\theta _{c}$ of LCR. The relationship between polarization rotation angle $\theta _{c}$ and LCR modulation amplitude is given in Fig. 2(f). So in the case of small angles, the gyroscope output and the LCR modulation voltage approximately satisfy the cosine function squared relation. Below we briefly introduce how to control LCR via a hybrid machine learning loop (MLL) method to realize polarization self-compensation.
Fig. 2. MLL training and predicted results. (a) Cost versus run numbers. The purple dots are generated by the differential evolution algorithm during iterations, and the red dots are iterated and generated by the neural network. (b) Parameters versus run numbers. The modulation frequency of the LCR [10kHz- 50kHz], which is normalized. The voltage of the LCR [3.75V- 4V], which is normalized, too. It is positively correlated with the polarization rotation angle $\theta _{n}$, but not completely proportional to it. (c) The relationship between the cost and voltage predicted by MLL when the modulation frequency is kept at the optimum (26kHz). (d) The predicted relationship between the cost and modulation frequency when the voltage of LCR is 3.915V. The dashed lines indicate the maximum and minimum boundaries of the ANN prediction. (e) ANN predicted parameters and PID total output vs time. The sampling average interval is 1s. (f) LCR modulation amplitude vs polarization rotation angle $\theta _{c}$.
2.2 Hybrid machine learning loop method for polarization self-compensation
Based on the machine-learning package [49], the working principle of the hybrid machine learning loop (MLL) method is shown in Fig. 1(b). The output $I_{1}(t)$ detected by PD1 is sent to the computer via the digital acquisition (DAQ) card. The MLL algorithm program in a computer can actively search the optimal voltage amplitude and modulation frequency for LCR to compensate for the polarization coupling angle $\theta _{n}$ caused by environmental fluctuations. In order to avoid the accumulation of charge drift in the LCR, square-wave modulation with variable parameters is adopted. The whole MLL is divided into 4 processes as follows.
•Initialization. The differential evolution algorithm [50] built-in ANN stochastically generates two sets of parameters, the voltage amplitude and modulation frequency, within the range we set to initialize the IFOG. These parameters are passed through LCR to the IFOG, then the corresponding outputs are fed back to the MLL to optimize the parameters which eventually approach the target value. After the beginning twenty loops, the ANN obtains the initial training data set and constructs the error model between the output values and the target value, also called the $cost$ function, given as
where $I_{0}$ is the target value discussed in Eq. (3).•ANN search. We set $k$ as a threshold for $cost(t)$. When $cost(t)$ is larger than the threshold $k$, the ANN starts working. The voltage amplitude and modulation frequency of LCR are continuously iterated by the built-in gradient descent and backpropagation algorithms [51] in ANN. In this process, the ANN can update the voltage amplitude and modulation frequency parameters for the next loop and predict whether the cost reaches the optimal minimum. The cost function updates in the direction of minimizing until it is smaller than the threshold $k$. Meanwhile, in order to find the minimum of the cost function, the mean-square error loss function [52] is adapted in ANN to determine the "distance" between the predicted value $cost_{pre}(t_{i})$ and the measured value $cost(t_{i})$ of the $i$ loop.
where $N$ is the number of training samples. Besides, to prevent overfitting, the differential evolution iteration is added to the loop every three times shown by the purple dots in Fig. 2(a).•Fast feedback. As shown in Fig. 1(b), the ANN pauses until it has found the global minimum $cost(t) \rightarrow 0$. The corresponding parameters are the final control values for LCR. To ensure the compensation effect of LCR, the optimal $cost$ is fed to the PID controller (model SIM960) as its locking setpoint via the communication line for a small range of fast feedback. Finally, the outputs of ANN together with PID are fed back to LCR for dynamic adjustment.
•Real-time monitoring. When the ANN completes the prediction in the previous loop, it doesn’t stop working. On the contrary, it continuously monitors the output of our IFOG. When a sudden external event causes the PID to unlock and the condition $cost>k$ is satisfied, a fast search is carried out by ANN to pull back to the optimal parameters. But if PID locks ($cost<k$ is always satisfied at any time ), ANN will identify and receive this PID total output into the training dataset. So the prediction optimal parameters are adaptively updated over time.
Figure 2 shows the training process and prediction results of the MLL. The target value $I_{0}$ is $40.0 {\mathrm{\mu} \mathrm{W}}$. Here, the maximum running number is 80. The threshold $k$ we set is 0.02$\rm {\mu {W}}$, which is usually set as 3 times intensity fluctuations. In Fig. 2(a)(b), the cost function and the parameters, including voltage and frequency, gradually converge to stable values after about 30 iterations. This indicates that ANN has found the best cost and the corresponding optimal parameters. In Fig. 2(c) and (d), the optimal frequency and voltage predicted by ANN are about 26kHz and 3.915V. The corresponding optimal cost is 0.016$\rm {\mu {W}}$. It can be fed to PID as the locking setpoint. The small feedback output of PID is added to the output of the ANN through the adder shown in Fig. 1(a). This is the PID total output in Fig. 2(e). Finally, the voltage of LCR is locked at about 3.915V nearby and the optimal voltage varies with time as shown in Fig. 2(e), which is equivalent to the optimal polarization rotation angle $\theta _{c}=0.40^{\circ }$ nearby. Hence, the optimal voltage and frequency for LCR are adaptively locked by MLL to improve long-term stability.
3. Experimental setup and results
Based on the experimental setup shown in Fig. 1(a), the short-term sensitivity and long-term drift are analyzed. The performance of the current IFOG is analyzed under static conditions and without intrinsic frequency modulation. At a room temperature of $21.0\rm {^{\circ }{C}}$, the average intensity before entering PBS1 is locked at 120$\rm {\mu {W}}$. Intensity stability root meam square $\mathrm {{(RMS)\approx 10^{-4}}}$. The final light intensity at the PD1 is 40.0$\mathrm {\mu {W}}$. With the help of HWP0, the lights go through PBS1 with the same powers. The combination of FR and HWP remains the polarization in CW and CCW direction the same in the PM fiber coil while perpendicularity at PBS1. The output is detected by PD1 and transmitted to the hybrid machine learning algorithm program by DAQ. The updated voltage amplitude and modulation frequency obtained by the ANN are transmitted to AWG. The resultant output light intensity of the proposed IFOG goes back to the software algorithm to predict whether the result is within the given boundary. The optimal minimum cost is passed to PID as a setpoint. The output of PID together with the optimal modulated signal predicted by ANN are added and then fed back to LCR. Finally, LCR compensates for the polarization drift without destroying the reciprocity of the path. The response time of the LCR for $\mathrm {{90^{\circ }}}$ rotation is about 0.15 ms, which can also be replaced by a Lithium niobate electro-optical polarization modulator. In addition, when the proposed IFOG without fiber coil, it is a typical Sagnac interferometer and provides a good benchmark for demonstrating the effect of polarization compensation, called the Sagnac interferometric limit (SIL). Below we analyze the performance of the polarization self-compensation IFOG in detail and compare it with SIL.
3.1 Scale factor
In IFOG, the relation between the angular velocity $\Omega$ and the interference signal $I_1(t)$ can be calibrated via scale factor. Therefore, $\Omega$ can be obtained from $I_1(t)$ via scale factor.
In this experiment, the interference signal $I_{1}(t)$ detected by PD1 is shown in Fig. 3(a). When the EOM is working at $\phi _{0} =-\frac {\pi }{2}$, the interference signal slope is the largest. Under this situation, the IFOG can be fixed at the optimal working point to obtain great measurement sensitivity. When a tiny phase bias is applied to this IFOG, the intensity of the interference signal is shown in Fig. 3(b). Hereby, the relation between the phase shift $\phi$ and the change of output light intensity $\Delta I=I-I_{0}$ satisfies $\phi =K_{1}\Delta I$ with $K_{1}={0.025204\pm 0.000085}\mathrm { \ (rad/\mu W)}$. As $\Omega =\frac {c\lambda }{4\pi Lr}\phi$, the scaling factor between $\Omega$ and $\Delta I$ is $K=K_{1}K_{2}=3.245\times 10^{4} \mathrm {^{\circ }/(h\cdot \mu W)}$. Here $K_{2}=\frac {c\lambda }{4\pi Lr} =1.292\times 10^{6}\mathrm {{^{\circ }{/(h\cdot rad)}}}$ is the conversion factor between $\Omega$ and $\phi$.
Fig. 3. Scale factor calibration of the IFOG. (a) The interference signal of the gyroscope when the triangular wave scanning signal with an amplitude of $460\mathrm {{V_{pp}}}$ and frequency of $0.4\mathrm {Hz}$ drives the EOM. The visibility reaches 99.3%. (b) The calibration factor between the gyroscope output light intensity and phase, where the black dots are the experimental data and the red line is the fitting line.
3.2 Short-term measurement sensitivity
To obtain the sensitivity of the proposed IFOG, we employ the relation between signal-to-noise ratio (SNR) and sensitivity as follow [53–55]:
where $\delta \Omega$ is the short-term angular velocity sensitivity. $\phi$ is the small phase shift we introduce. The unit of SNR is dB. $B$ is the detection bandwidth. $K_{2}$ is the conversion factor between $\Omega$ and $\phi$ above.In Fig. 4, the tiny phase shift $\rm {\phi =4.8\times 10^{-4}rad}$ is applied by a sinusoidal voltage ($\mathrm {900Hz, 0.05V_{pp}}$) on EOM. It shows under the same output light intensity of 40.0 $\mathrm { \mu W}$, the noise power spectrum of SIL is 8.9dB lower than the IFOG with a 300m fiber coil, which indicates that the fiber coil indeed introduces extra noise. Besides, the SNRs of IFOG with software compensation are respectively 61.97dB (PID) and 63.04dB (MLL), which are better than the IFOG without feedback (56.49dB). Meanwhile, the MLL algorithm (red line) is about 1dB better than the single PID control (blue line). Based on Eq. (6), the equivalent angular velocity sensitivity is achieved at 0.00582$\mathrm {{^{\circ }/\sqrt {h}}}$ (PID), 0.00513$\mathrm {{^{\circ }/\sqrt {h}}}$ (MLL), and 0.01093$\mathrm {{^{\circ }/\sqrt {h}}}$ (without feedback). Hence, although the utilization of the fiber coil induces extra noise compared with SIL, the sensitivity of our polarization self-compensation IFOG is still maintained at 0.005$\rm {^{\circ }\sqrt {h}}$ level.
Fig. 4. The power spectra obtained by different methods. A tiny phase shift $\mathrm {{\phi =4.8\times 10^{-4}rad}}$ $\mathrm {(900Hz,0.05V_{pp})}$ is introduced through EOM. The four lines are the signal-to-noise ratio(SNR) corresponding to the case PID, MLL, Without feedback, and SIL, respectively, with a resolution bandwidth of 2Hz and output light intensity $40 {\mathrm{\mu} \mathrm{W}}$.
3.3 Long-term drift and robustness
In addition to the short-term sensitivity, long-term drift plays a crucial role in inertial navigation systems. At the optimal bias point $\phi _{0} =- \frac {\pi }{2}$, the static output for 2 hours is shown in Fig. 5. The angular velocity drift without software feedback can reach $58.633\mathrm {^{\circ }/h}$. By comparison, the one-hour drifts with PID and MLL can be lower than $5.062\rm {^{\circ }/h}$ and $2.980\rm {^{\circ }/h}$, respectively. Under the same conversion factor $K_{2}=1.292\times 10^{6}\mathrm {{^{\circ }{/(h\cdot rad)}}}$, the equivalent one-hour drift of the angular velocity in Sagnac interferometer is $7.197\rm {^{\circ }/h}$. Here we define the suppression ratio:
where $Z_{1}$ is the drift with a software algorithm optimization (PID and MLL). $Z_{0}$ is the initial drift without software feedback. The suppression ratio of MLL and PID algorithms reach 91.3% and 94.9%, respectively. The results show that the software algorithms, including PID and MLL, can effectively compensate for the polarization change.Fig. 5. The long-time output of gyroscope corresponding to different methods. The output interval is 0.25s, and the sample rate is $50\rm {kps}.$
Figure 6 shows the Allan variance calculated from the data sampled in Fig. 5. The angular random walk (ARW) and bias instability (BI) obtained by Allan variance are shown in Table 1. Compared with the IFOG without feedback, the utilization of the MLL method optimizes the BI from $11.4256\rm {^{\circ }/h}$ at 120s to $0.3869\rm {^{\circ }/h}$ at 200s and optimizes ARW from $0.2098\rm {^{\circ }/\sqrt {h}}$ to $0.0502 \rm {^{\circ }/\sqrt {h}}$. The corresponding BI suppression rate reaches 96.61%. Besides, both the ARW and BI of the proposed IFOG exceed the performance of a single PID (ARW $0.0540\rm {^{\circ }/\sqrt {h}}$, BI $0.6723\rm {^{\circ }/h}$) and approaches Sagnac interferometric limit (SIL, ARW $0.0454\rm {^{\circ }/\sqrt {h}}$, BI $0.3883\rm {^{\circ }/h}$), which is measured by the proposed IFOG without fiber coil but with the same conversion factor $K_{2}=1.292\times 10^{6}\mathrm {{^{\circ }{/(h\cdot rad)}}}$. Hence, the MLL method effectively decreases the long-term slow drift. It is important to point out that the optimization results are based on the current experimental setup. If the $K_{2}$ factor is increased or the laser linewidth is larger in the future, the optimization limit of the MLL method will be further raised [23,24].
Table 1. Allan variance results when the IFOG is in static sensing.
Furthermore, the robustness is also a very important indicator for IFOG. In this experiment, we artificially apply a $0.13 \rm {rad}$ phase bias to EOM at about $130\rm {s}$ to simulate a sudden vibration. The experimental results are shown in Fig. 7. The recovery time of MLL is only about 22s. In contrast, the oscillation duration of PID is much longer than 180s and is difficult to reset. Hence, the MLL method, combining the advantages of PID fast response and ANN dynamic search, can control the LCR to dynamically compensate for slow drift induced by polarization coupling. In actual testing, the recovery time could be further shortened by reducing the number of iterations or narrowing the range of parameters.
Fig. 7. Robustness comparison under the sudden external fluctuation. The red line represents the MLL method, and the blue line corresponds to the single PID method. Sample rate 25 points per second. The red part of the oscillation is caused by the parameter search and iteration of the ANN. The blue part of the oscillation is PID oscillation caused by a sudden external interference.
Therefore, although the PM fiber coil introduces extra drift, the proposed polarization Self-compensation IFOG can effectively compensate for slow drift while ensuing short-term sensitivity at the same time.
4. Conclusion
In conclusion, we propose a polarization self-compensation IFOG 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 together with the software algorithm decreases the intensity fluctuation induced by polarization coupling. Here the combination of polarization beam splitter (PBS), Faraday rotator (FR), and half-wave plate (HWP) allow the polarizations to maintain consistency in the PM fiber coil, which ensures the polarization reciprocity. Furthermore, an LCR modulator is controlled via the hybrid machine learning loop (MLL) method based on the ANN and PID to compensate for the polarization coupling drift dynamically. Experiment results show that the proposed IFOG can effectively improve the long-term stability with good short-term sensitivity ($\mathrm {0.005^{\circ }/\sqrt {h}}$). Compared with the single PID method, the BI of our IFOG is reduced from $\rm {0.6723^{\circ }/h}$ at 60s to $\rm {0.3869^{\circ }/h}$ at 200s. More importantly, the ARW and BI of the current IFOG are close to the Sagnac interferometric limit (SIL). The good long-term stability and robustness of this IFOG are extremely useful in complex and volatile environments, as well as suitable for inertial navigation systems and fiber-optic systems.
Funding
National Natural Science Foundation of China (12104161, U23A2075, 12274132, 12174409); E-Institutes of Shanghai Municipal Education Commission (202101070008E00099); Science and Technology Commission of Shanghai Municipality (19YF1414300); China Postdoctoral Science Foundation (2023M741187); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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