Nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signal

Abstract

The invention provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on an Xe atom frequency harmonic signal, which comprises the following steps: firstly, measuring an Xe atom magnetic moment precession signal in a nuclear magnetic resonance gyroscope through a phase-locked loop, and feeding back a measurement result to a magnetic field transverse coil so as to maintain Xe atom transverse magnetic moment stable precession; the frequency component of the measured Xe atom magnetic moment precession signal is subjected to harmonic analysis, the harmonic signal amplitude of Xe atom resonance frequency oscillation contained in the frequency component is obtained, the harmonic signal amplitude is directly caused by transverse residual magnetism, whether the harmonic signal amplitude exists or not and the magnitude of the harmonic signal amplitude can represent the transverse residual magnetism state, and the harmonic signal amplitude is used as a reference quantity to determine whether the transverse residual magnetism exists or not. And adjusting the output of the magnetic field transverse coil of the nuclear magnetic resonance gyroscope to minimize the amplitude of the harmonic signal, thereby realizing the online monitoring and closed-loop compensation of the transverse residual magnetism. The influence of the transverse residual magnetism on the precision of the nuclear magnetic resonance gyroscope can be effectively inhibited, and the long-term stability and the measurement accuracy of the nuclear magnetic resonance gyroscope are improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of inertial sensing and quantum precision measurement, and particularly relates to a nuclear magnetic resonance gyro magnetic field compensation method based on an Xe atomic frequency harmonic signal. BACKGROUND

[0002] As a core measurement component of an inertial navigation system, a high-precision gyroscope directly determines the positioning accuracy and long-term stability of the inertial navigation system. With the continuous upgrading of the requirements of equipment intelligentization and miniaturization, traditional mechanical gyroscopes and optical gyroscopes are limited by the bottlenecks of large volume and power consumption, strong environmental sensitivity, and the like, and have been difficult to meet the application requirements of long-time navigation and high-precision navigation scenes.

[0003] A nuclear magnetic resonance gyro (NMRG) based on the principle of quantum precision measurement, with the natural anti-interference of the nuclear spin system, low angular random walk and miniaturization potential, has become a key direction to break through the technical blockade of foreign countries and realize the self-controlling of high-end inertial navigation equipment. Compared with other atomic spin gyroscopes, the nuclear magnetic resonance gyro not only has the advantages of long nuclear spin relaxation time and high measurement precision, but also has the characteristics of small size, low power consumption and easy integration, and is recognized as one of the most promising micro high-precision gyro technologies for engineering application.

[0004] However, in the process of transforming the nuclear magnetic resonance gyro from laboratory research to engineering application, the transverse residual magnetic interference is always one of the main bottleneck problems restricting the improvement of the precision. The core working principle of the nuclear magnetic resonance gyro is to detect the closed-loop precession frequency of Xe atoms (or other inert gas atoms) nuclear spin to inverse the carrier rotation information, and the inevitable transverse residual magnetism (such as the additional magnetic field introduced by the z-axis coil tilt, the residual magnetic field of the magnetic shield, etc.) in the system will directly disturb the precession state of the Xe atom magnetic moment, cause the deflection of the precession axis and the fluctuation of the closed-loop resonance frequency, thereby introducing the gyro measurement error and reducing the navigation precision.

[0005] To solve the problem of transverse remanence interference, the prior art generally adopts the compensation scheme of "embedding alkali metal magnetometer": the size of the transverse remanence is evaluated by detecting the transverse bias of the spin signal of alkali metal atoms (such as Rb and Cs), and the magnetic field coil current is regulated based on the evaluation result to compensate the transverse remanence. However, there are still some specific problems in the actual application of this scheme: first, the magnetic field information measured by the alkali metal atoms may be different from the magnetic field experienced by the Xe atoms, thereby affecting the accuracy of magnetic compensation; second, the scheme measures the amplitude information of the spin signal of alkali metal atoms, which is easily affected by the state of the embedded alkali metal magnetometer, such as temperature, light intensity, demodulation phase, carrier frequency, etc.; in addition, the scheme needs to extract the bias information of the alkali metal magnetometer, which may also increase the complexity of signal processing. These problems ultimately restrict the engineering application of nuclear magnetic resonance gyroscopes in high-precision navigation scenarios. SUMMARY

[0006] In view of the above problems existing in the prior art, the present application provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals.

[0007] To achieve the above technical purpose, the technical scheme adopted by the present application is as follows: On the one hand, the present application provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals, comprising the following steps: S1, measuring the Xe atomic magnetic moment precession signal in the nuclear magnetic resonance gyroscope and feeding back the measurement result to the magnetic field transverse coil to maintain stable precession of the Xe atomic transverse magnetic moment, forming a first closed loop; S2, performing harmonic analysis on the frequency component of the Xe atomic magnetic moment precession signal measured in S1 to obtain the harmonic signal amplitude contained in the frequency component oscillating at the Xe atomic resonance frequency; S3, taking the harmonic signal amplitude as a reference quantity, adjusting the output of the magnetic field transverse coil of the nuclear magnetic resonance gyroscope to minimize the harmonic signal amplitude, forming a second closed loop for compensating the transverse remanence.

[0008] Further, in S2, based on the harmonic analysis result, it is judged whether there is transverse remanence in the nuclear magnetic resonance gyroscope, and when it is determined that there is transverse remanence, S3 is executed.

[0009] On the other hand, a nuclear magnetic resonance gyroscope magnetic field compensation system based on Xe atomic frequency harmonic signals is provided, comprising: A first closed loop control module for measuring the Xe atomic magnetic moment precession signal in the nuclear magnetic resonance gyroscope and feeding back the measurement result to the magnetic field transverse coil to maintain stable precession of the Xe atomic transverse magnetic moment; The harmonic analysis module is connected with the first closed-loop control module, and is used for performing harmonic analysis on a frequency component of the Xe atomic magnetic moment precession signal measured by the first closed-loop control module, and obtaining a harmonic signal amplitude oscillating at the Xe atomic resonance frequency contained in the frequency component. The second closed-loop compensation module is connected with the harmonic analysis module and the transverse magnetic field coil, and is used for taking the harmonic signal amplitude as a reference quantity to adjust the magnetic field transverse coil output of the nuclear magnetic resonance gyroscope, so as to minimize the harmonic signal amplitude and realize compensation for the transverse residual magnetism.

[0010] Further, the harmonic analysis module further includes a judgment unit, which is used for judging whether the transverse residual magnetism exists in the nuclear magnetic resonance gyroscope according to the harmonic analysis result, and triggering the second closed-loop compensation module to work only when it is judged that the transverse residual magnetism exists.

[0011] The present application provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals. First, the Xe atomic magnetic moment precession signal in the nuclear magnetic resonance gyroscope is measured by a phase-locked loop, and the measurement result is fed back to the magnetic field transverse coil to maintain the stable precession of the Xe atomic transverse magnetic moment. Then, the frequency component of the measured Xe atomic magnetic moment precession signal is subjected to harmonic analysis, and the harmonic signal amplitude oscillating at the Xe atomic resonance frequency contained in the frequency component is obtained. The harmonic signal amplitude is directly caused by the transverse residual magnetism, and the existence and size of the harmonic signal amplitude can represent the transverse residual magnetism state. Taking the harmonic signal amplitude as a reference quantity, the magnetic field transverse coil output of the nuclear magnetic resonance gyroscope is adjusted to minimize the harmonic signal amplitude, and online monitoring and closed-loop compensation of the transverse residual magnetism are realized. The present application can effectively suppress the influence of the transverse residual magnetism on the accuracy of the nuclear magnetic resonance gyroscope, and improve the long-term stability and measurement accuracy of the nuclear magnetic resonance gyroscope. Compared with the prior art, the beneficial effects of the present application are as follows: The nuclear magnetic resonance gyroscope magnetic field compensation scheme proposed in the present application is directly based on Xe atomic frequency harmonic signals, reflects the transverse magnetic field change sensed by the Xe atoms, and is less affected by the alkali metal atomic state and the non-ideal characteristics of the alkali metal magnetometer, which is of great significance to improving the magnetic compensation accuracy in the nuclear magnetic gyroscope.

[0012] The magnetic field compensation method based on Xe atomic frequency harmonic signals proposed in the present application measures the residual magnetism size through the frequency signal, and has stronger anti-interference ability compared with the traditional embedded alkali metal magnetometer measurement signal amplitude.

[0013] The magnetic field compensation method based on Xe atomic frequency harmonic signals proposed in the present application directly extracts residual magnetism information from the Xe atomic closed-loop frequency signal of the nuclear magnetic gyroscope, without the need for additional hardware structures and control algorithms, which is of positive significance to simplifying the gyro signal processing and improving the integration. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from the structures shown in the drawings without creative labor.

[0015] Figure 1 Flow chart of the Xe atomic frequency harmonic signal based nuclear magnetic resonance gyroscope magnetic field compensation method in an embodiment; Figure 2 Simulation curve diagram of the influence of transverse residual magnetism on Xe atomic frequency time domain signal in an embodiment; Figure 3 Fourier spectrum analysis diagram of Xe atomic frequency signal in an embodiment; Figure 4 Schematic diagram of transverse residual magnetism compensation process using Xe atomic frequency harmonic signal in an embodiment. DETAILED DESCRIPTION

[0016] The technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments only constitute some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0017] In a nuclear magnetic resonance gyroscope, the precession of Xe atomic transverse magnetic moment satisfies the following Bloch equation: (1) wherein, represents the amplitude of the transverse component of Xe atomic magnetic moment, represents the phase of the transverse component of Xe atomic magnetic moment, represents the longitudinal component of Xe atomic magnetic moment, , respectively represent the longitudinal relaxation rate and the transverse relaxation rate of Xe atomic magnetic moment, represents the steady-state magnetic moment of Xe atom, , , respectively represent the equivalent angular frequencies in x, y, z directions caused by magnetic field and rotation, , is the vector form of , includes three components, , , ​gyromagnetic ratio, B is the vector form of the main magnetic field, Ω is the vector form of the gyroscopic rotation angular frequency .

[0018] Consider a NMR gyroscope with transverse remanence, the magnetic field components in x, y, z directions are: (2) where Bx is the transverse feedback excitation magnetic field to maintain the precession of Xe atomic transverse magnetic moment, Bx is the feedback excitation magnetic field amplitude, φx is the phase of Xe atomic transverse magnetic moment precession, φx is the phase difference between the feedback excitation magnetic field and Xe atomic magnetic moment precession, Bz is the main magnetic field along z direction, , Bx and By represent the x, y direction components of the transverse remanence respectively.

[0019] Substitute the three-axis magnetic field in formula (2) into formula (1), and consider the transverse remanence as a small quantity, use the first-order perturbation: (3) where Bx and By represent the x, y direction components of the transverse remanence respectively. Bx and By represent the x, y direction components of the transverse remanence respectively. Bx and By represent the x, y direction components of the transverse remanence respectively. Bx and By represent the x, y direction components of the transverse remanence respectively.

[0020] Substitute formula (3) into formula (1) to obtain the equation satisfied by the zero-order perturbation, i.e. formula (4), and the equation satisfied by the first-order perturbation, i.e. formula (5): (4) (5) where , , , , and the second harmonic term is ignored.

[0021] For the equation satisfied by the zero-order perturbation, i.e. formula (4), its steady-state result can be directly obtained: (6) Substitute formula (6) into formula (5) to obtain the first-order perturbation result.​​​

[0022] Substitute the first-order perturbation result into formula (3) to obtain an analytical formula considering the influence of the transverse residual magnetism on the closed-loop precession of Xe atoms.

[0023] It is found from formula (5) that the first-order perturbation of the precession frequency of Xe atoms contains where , The physical meaning of this term is that when there is non-zero transverse residual magnetism, the precession frequency of Xe atoms contains a harmonic signal oscillating at the frequency Conversely, the presence of transverse residual magnetism in the NMRG can be determined through this signal.

[0024] Based on the above analysis, in an embodiment, a nuclear magnetic resonance gyro magnetic field compensation method based on a Xe atom frequency harmonic signal is provided to accurately extract transverse residual magnetism information and realize closed-loop compensation, including the following steps: S1, measuring a Xe atom magnetic moment precession signal in a nuclear magnetic resonance gyro, and feeding back the measurement result to a magnetic field transverse coil to maintain Xe atom transverse magnetic moment precession, forming a first closed loop; S2, performing harmonic analysis on the frequency component of the Xe atom magnetic moment precession signal measured in S1, and obtaining the amplitude of the harmonic signal containing the Xe atom resonance frequency oscillation in the frequency component; S3, taking the harmonic signal amplitude as a reference quantity, adjusting the output of the magnetic field transverse coil of the nuclear magnetic resonance gyro to minimize the harmonic signal amplitude, forming a second closed loop for compensating the transverse residual magnetism.

[0025] Specifically, in S1 of the above embodiment, the Xe atom magnetic moment precession signal in the nuclear magnetic resonance gyro is measured, including measuring the phase, frequency and amplitude of the Xe atom magnetic moment precession signal in the nuclear magnetic resonance gyro through a phase-locked loop (PLL), and feeding back the phase, frequency and amplitude of the Xe atom magnetic moment precession signal in the measurement result to the magnetic field transverse coil to maintain the stable precession of the Xe atom transverse magnetic moment.

[0026] In another embodiment, a nuclear magnetic resonance gyro magnetic field compensation method based on a Xe atom frequency harmonic signal is provided, including the following steps: S1, measuring a Xe atom magnetic moment precession signal in a nuclear magnetic resonance gyro, and feeding back the measurement result to a magnetic field transverse coil to maintain Xe atom transverse magnetic moment stable precession, forming a first closed loop; S2, performing harmonic analysis on the frequency component of the Xe atom magnetic moment precession signal measured in S1, and based on the harmonic analysis result, determining whether there is transverse residual magnetism in the nuclear magnetic resonance gyro, when it is determined that there is transverse residual magnetism, obtaining the amplitude of the harmonic signal containing the Xe atom resonance frequency oscillation in the frequency component, and performing S3; S3, taking the harmonic signal amplitude as a reference quantity, adjusting the magnetic field transverse coil output of the nuclear magnetic resonance gyroscope to minimize the harmonic signal amplitude, and forming a second closed loop for compensating the transverse residual magnetism.

[0027] The above embodiments combine the correlation mechanism of transverse residual magnetism and Xe atomic frequency harmonic signal amplitude. The transverse magnetic field coil current of the nuclear magnetic resonance gyroscope can be closed-loop regulated by a PID control algorithm, and the harmonic signal amplitude can be locked to the lowest level to offset the transverse magnetic field interference. This method can solve the problems of the traditional nuclear magnetic resonance gyroscope magnetic field compensation, such as being affected by the alkali metal atom state, weak anti-interference ability, and complex hardware structure.

[0028] In S2 of an embodiment, the frequency component of the Xe atomic magnetic moment precession signal measured in S1 is analyzed by harmonic analysis to determine whether the frequency component of the Xe atomic magnetic moment precession signal contains a harmonic signal oscillating at a frequency of If yes, it is determined that there is transverse residual magnetism, and if not, it is determined that there is no transverse residual magnetism. According to the foregoing analysis, the harmonic signal amplitude is related to the first-order perturbation of the Xe atomic precession frequency caused by the transverse residual magnetism, and the first-order perturbation of the Xe atomic precession frequency contains wherein , , 、 respectively represent the equivalent angular frequencies corresponding to the x and y direction transverse residual magnetism multiplied by the gyromagnetic ratio, 、 respectively represent the x and y direction components of the transverse residual magnetism, represents the gyromagnetic ratio, is the zero-order solution of the phase of the transverse component of the Xe atomic magnetic moment; when there is transverse residual magnetism in the nuclear magnetic resonance gyroscope, the frequency component of the Xe atomic magnetic moment precession signal contains a harmonic signal oscillating at a frequency of Therefore, by analyzing the frequency component of the Xe atomic magnetic moment precession signal measured in S1, it can be determined whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope.

[0029] In S3 of any of the above embodiments, a closed-loop feedback control method such as PID is used to adjust the transverse magnetic field coil output of the nuclear magnetic resonance gyroscope. According to the deviation of the harmonic signal amplitude from the preset target value, a compensation control signal for adjusting the transverse magnetic field coil output of the nuclear magnetic resonance gyroscope is generated.

[0030] The above embodiment utilizes the relationship between the transverse residual magnetism and the harmonic of the Xe atom closed loop resonance frequency derived by the Xe atom magnetic moment Bloch equation and the perturbation iteration method, extracts the frequency signal harmonic oscillation amplitude as the criterion of the transverse residual magnetism, and combines the PID control algorithm to regulate the transverse coil current to realize the closed loop compensation. The method avoids the interference of the alkali metal non-ideal characteristics to improve the magnetic compensation accuracy; utilizes the frequency signal characteristics to enhance the anti-interference ability; and simplifies the system integration without additional hardware. The problem of Xe atom frequency fluctuation caused by the transverse residual magnetism is effectively solved, and key technical support is provided for high-precision measurement and engineering application of the nuclear magnetic resonance gyroscope.

[0031] As shown in Figure 2 , a simulation curve diagram of the influence of the transverse residual magnetism on the Xe atom frequency time domain signal is given. In the simulation experiment, the parameters are set as follows: , , , , . The dotted line in the figure is the Xe atom resonance frequency curve changing with time when the transverse residual magnetism is 10 nT, and the solid line is the Xe atom resonance frequency curve changing with time when there is no transverse residual magnetism. It can be seen that the transverse residual magnetism will increase the fluctuation of the Xe atom resonance frequency. This verifies the correctness of the theoretical analysis result of formula (5), and gives the basic principle of measuring the transverse residual magnetism by using the Xe atom frequency harmonic signal. By measuring the Xe atom frequency harmonic signal amplitude, the transverse residual magnetism of the system can be characterized.

[0032] Figure 3 A Fourier spectrum analysis diagram of the Xe atom frequency signal under the influence of the transverse residual magnetism is given. The simulation parameters are the same as those in Figure 2 , the dotted line is the spectrum analysis result of the Xe atom resonance frequency changing with time when the transverse residual magnetism is 10 nT, and the solid line is the spectrum analysis result of the Xe atom resonance frequency changing with time when there is no transverse residual magnetism. It can be found from the dotted line that when there is 10 nT transverse residual magnetism, the Xe atom resonance frequency indeed contains a harmonic signal fluctuating at the resonance frequency (118.6 Hz), while the solid line representing the result without transverse residual magnetism does not have this harmonic signal. These results are consistent with the prediction results of formula (5), and the correctness of the theoretical analysis is verified again.

[0033] Figure 4 The results of compensating the transverse residual magnetism by controlling the transverse magnetic field coil current under similar conditions are given. It can be seen from the figure that during the process of continuously offsetting the transverse residual magnetism by adjusting the coil magnetic field, the Xe atom frequency harmonic signal amplitude continuously decreases, and when the transverse residual magnetism is almost completely offset, the harmonic signal amplitude also decreases to zero, thereby verifying the feasibility of the magnetic field compensation method of the nuclear magnetic resonance gyroscope based on the Xe atom frequency harmonic signal proposed in the present application.

[0034] Another embodiment provides a nuclear magnetic resonance gyroscope magnetic field compensation system based on Xe atomic frequency harmonic signals, comprising: A first closed-loop control module for measuring Xe atomic magnetic moment precession signals in the nuclear magnetic resonance gyroscope and feeding back the measurement results to the magnetic field transverse coil to maintain stable precession of the Xe atomic transverse magnetic moment; A harmonic analysis module connected to the first closed-loop control module for performing harmonic analysis on the frequency components of the Xe atomic magnetic moment precession signals measured by the first closed-loop control module and obtaining the harmonic signal amplitude contained in the frequency components oscillating at the Xe atomic resonance frequency; A second closed-loop compensation module connected to the harmonic analysis module and the transverse magnetic field coil for adjusting the output of the magnetic field transverse coil of the nuclear magnetic resonance gyroscope with the harmonic signal amplitude as a reference quantity to minimize the harmonic signal amplitude and achieve compensation for the transverse residual magnetism.

[0035] Further, the harmonic analysis module further includes a judgment unit for judging whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope according to the harmonic analysis results and triggering the second closed-loop compensation module to work only when it is determined that there is transverse residual magnetism. The method for judging whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope in the judgment unit can be any of the methods provided in the foregoing embodiments.

[0036] The above is only the preferred embodiment of the present application, and the protection scope of the present application is not limited to the above-mentioned embodiments. Any technical solution falling within the concept of the present application shall fall within the protection scope of the present application. It should be noted that some improvements and refinements made by ordinary skilled in the art without departing from the principles of the present application shall be considered as falling within the protection scope of the present application.

Claims

1. A method for magnetic field compensation of nuclear magnetic resonance gyroscopes based on Xe atomic frequency harmonic signals, characterized in that, Includes the following steps: S1, measure the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope, and feed the measurement result back to the transverse magnetic field coil to maintain the stable precession of the Xe atom transverse magnetic moment, forming the first closed loop; S2, perform harmonic analysis on the frequency components of the Xe atom magnetic moment precession signal measured in S1, and obtain the amplitude of the harmonic signal oscillating at the Xe atom resonance frequency contained in the frequency components. S3 uses the harmonic signal amplitude as a reference to adjust the output of the magnetic field transverse coil of the nuclear magnetic resonance gyroscope, so as to minimize the harmonic signal amplitude and form a second closed loop for compensating for transverse residual magnetism.

2. The method for nuclear magnetic resonance gyroscope magnetic field compensation based on Xe atomic frequency harmonic signals according to claim 1, characterized in that, In S1, the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope is measured, including measuring the phase, frequency and amplitude of the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope through a phase-locked loop, and feeding the phase, frequency and amplitude of the Xe atom magnetic moment precession signal into the measurement results and feeding them back to the transverse magnetic field coil to maintain the stable precession of the Xe atom transverse magnetic moment.

3. The method for nuclear magnetic resonance gyroscope magnetic field compensation based on Xe atomic frequency harmonic signals according to claim 1 or 2, characterized in that, S2 includes determining whether there is transverse remanence in the nuclear magnetic resonance gyroscope based on the harmonic analysis results. If transverse remanence is determined to exist, S3 is executed.

4. The method for nuclear magnetic resonance gyroscope magnetic field compensation based on Xe atomic frequency harmonic signals according to claim 3, characterized in that, In S2, harmonic analysis is performed on the frequency components of the Xe atomic magnetic moment precession signal measured in S1 to determine whether the frequency components of the Xe atomic magnetic moment precession signal contain frequencies... If the oscillating harmonic signal is present, then transverse remanence is determined to exist; otherwise, it is determined that transverse remanence is not present. This is the zeroth-order solution for the phase of the transverse component of the Xe atomic magnetic moment.

5. The method for nuclear magnetic resonance gyroscope magnetic field compensation based on Xe atomic frequency harmonic signals according to claim 1, 2, or 4, characterized in that, In S3, a PID closed-loop feedback control method is used to adjust the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope. Based on the deviation between the harmonic signal amplitude and the preset target value, a compensation control signal is generated to adjust the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope.

6. The method for nuclear magnetic resonance gyroscope magnetic field compensation based on Xe atomic frequency harmonic signals according to claim 5, characterized in that, The transverse magnetic moment precession of Xe atoms in the nuclear magnetic resonance gyroscope satisfies the following Bloch equation: in This represents the amplitude of the transverse component of the magnetic moment of the Xe atom. This indicates the phase of the transverse component of the Xe atomic magnetic moment. Represents the longitudinal component of the magnetic moment of the Xe atom. , Representing the longitudinal and transverse relaxation rates of the Xe atom's magnetic moment, respectively. Represents the steady-state magnetic moment of the Xe atom. , , These represent the equivalent angular frequencies in the x, y, and z directions caused by the magnetic field and rotation, respectively. , Indicates the gyromagnetic ratio.

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