Nuclear magnetic resonance gyro magnetic field compensation method based on xe atomic frequency harmonic signal

Abstract

The application provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals. First, the phase-locked loop is used to measure the Xe atomic magnetic moment precession signals in the nuclear magnetic resonance gyroscope, and the measurement results are fed back to the magnetic field transverse coil to maintain the stable precession of the Xe atomic transverse magnetic moment. Then, the frequency components of the measured Xe atomic magnetic moment precession signals are analyzed, and the harmonic signal amplitude oscillating at the Xe atomic resonance frequency contained in the frequency components 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. With the harmonic signal amplitude as a reference quantity, the output of the magnetic field transverse coil of the nuclear magnetic resonance gyroscope is adjusted to minimize the harmonic signal amplitude, and the online monitoring and closed-loop compensation of the transverse residual magnetism are realized. The 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.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of inertial sensing and quantum precision measurement, specifically a method for magnetic field compensation of nuclear magnetic resonance gyroscopes based on Xe atomic frequency harmonic signals. Background Technology

[0002] As the core measurement component of an inertial navigation system, the high-precision gyroscope directly determines the positioning accuracy and long-term stability of the system. With the continuous upgrading of equipment intelligence and miniaturization requirements, traditional mechanical and optical gyroscopes, limited by bottlenecks such as large size and power consumption and strong environmental sensitivity, can no longer meet the application requirements of long-endurance and high-precision navigation scenarios.

[0003] Nuclear Magnetic Resonance Gyroscopes (NMRGs), based on the principles of quantum precision measurement, have become a key direction for breaking through foreign technological blockades and achieving independent control of high-end inertial navigation equipment, thanks to the inherent anti-interference properties of nuclear spin ensembles, low-angle random walks, and miniaturization potential. Compared to other atomic spin gyroscopes, NMRGs not only possess the advantages of long nuclear spin relaxation time and high measurement accuracy, but also feature small size, low power consumption, and easy integration, and are widely recognized as one of the most promising micro-miniature high-precision gyroscope technologies for engineering applications.

[0004] However, in the process of transforming nuclear magnetic resonance gyroscopes from laboratory research to engineering applications, transverse remanent magnetization interference has always been one of the main bottlenecks restricting the improvement of their accuracy. The core working principle of nuclear magnetic resonance gyroscopes is to invert the carrier rotation information by detecting the closed-loop precession frequency of the nuclear spin of Xe atoms (or other inert gas atoms). However, the unavoidable transverse remanent magnetization in the system (such as the additional magnetic field introduced by the tilt of the z-axis coil, the residual magnetic field of magnetic shielding, etc.) will directly disturb the precession state of the Xe atom magnetic moment, causing its precession axis to deflect and the closed-loop resonance frequency to fluctuate, thereby introducing gyroscope measurement errors and reducing navigation accuracy.

[0005] To address the issue of transverse remanence interference, existing technologies generally employ a compensation scheme using an embedded alkali metal magnetometer. This involves assessing the magnitude of transverse remanence by detecting the transverse bias of the spin signal of alkali metal atoms (such as Rb and Cs), and then adjusting the current in the magnetic field coil based on this assessment to compensate for the transverse remanence. However, this scheme has several practical problems: First, the magnetic field information measured by alkali metal atoms may differ from the magnetic field sensed by Xe atoms, affecting the accuracy of magnetic compensation. Second, the amplitude information of the alkali metal atom spin signal is easily affected by the state of the embedded alkali metal magnetometer; factors such as temperature, light intensity, demodulation phase, and carrier frequency can all influence this amplitude information. Furthermore, this scheme requires additional extraction of the alkali metal magnetometer bias information, which may increase the complexity of signal processing. These issues ultimately limit the engineering application of nuclear magnetic resonance gyroscopes in high-precision navigation scenarios. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides a method for magnetic field compensation of nuclear magnetic resonance gyroscopes based on Xe atomic frequency harmonic signals.

[0007] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0008] On one hand, this invention provides a method for magnetic field compensation of a nuclear magnetic resonance gyroscope based on Xe atomic frequency harmonic signals, comprising the following steps:

[0009] 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;

[0010] 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.

[0011] 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.

[0012] Furthermore, 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.

[0013] On the other hand, a nuclear magnetic resonance gyroscope magnetic field compensation system based on Xe atomic frequency harmonic signals is provided, comprising:

[0014] The first closed-loop control module is used to measure the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope and feed the measurement result back to the magnetic field transverse coil to maintain the stable precession of the Xe atom transverse magnetic moment.

[0015] The harmonic analysis module is connected to the first closed-loop control module and is used to perform harmonic analysis on the frequency components of the Xe atom magnetic moment precession signal measured by the first closed-loop control module, and to obtain the amplitude of the harmonic signal oscillating at the Xe atom resonance frequency contained in the frequency components.

[0016] The second closed-loop compensation module is connected to the harmonic analysis module and the transverse magnetic field coil. It is used to adjust the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope with the harmonic signal amplitude as a reference, so as to minimize the harmonic signal amplitude and achieve compensation for transverse remanence.

[0017] Furthermore, the harmonic analysis module also includes a judgment unit, which is used to determine whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope based on the harmonic analysis results, and triggers the second closed-loop compensation module to work only when transverse residual magnetism is determined to exist.

[0018] This invention provides a magnetic field compensation method for nuclear magnetic resonance gyroscopes based on Xe atom frequency harmonic signals. First, the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope is measured using a phase-locked loop, and the measurement result is fed back to the transverse magnetic field coil to maintain stable precession of the Xe atom's transverse magnetic moment. Then, harmonic analysis is performed on the frequency components of the measured Xe atom magnetic moment precession signal to obtain the amplitude of the harmonic signal oscillating at the Xe atom resonant frequency. The amplitude of the harmonic signal is directly caused by transverse remanence, and its presence and magnitude characterize the transverse remanence state. Using the harmonic signal amplitude as a reference, the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope is adjusted to minimize the harmonic signal amplitude, achieving online monitoring and closed-loop compensation of transverse remanence. This invention can effectively suppress the influence of transverse remanence on the accuracy of the nuclear magnetic resonance gyroscope, improving the long-term stability and measurement accuracy of the nuclear magnetic resonance gyroscope. Compared with the prior art, the beneficial effects of this invention are as follows:

[0019] The magnetic field compensation scheme for nuclear magnetic resonance gyroscopes proposed in this invention is directly based on the harmonic signal of Xe atom frequency, reflecting the transverse magnetic field change felt by Xe atoms. It is less affected by the state of alkali metal atoms and the non-ideal characteristics of alkali metal magnetometers, and is of great significance for improving the accuracy of magnetic compensation in nuclear magnetic resonance gyroscopes.

[0020] The magnetic field compensation method based on the harmonic signal of Xe atom frequency proposed in this invention reflects the magnitude of remanence through the frequency signal, and has stronger anti-interference ability compared with the signal amplitude measured by the traditional embedded alkali metal magnetometer.

[0021] The magnetic field compensation method based on the harmonic signal of Xe atom frequency proposed in this invention directly extracts the remanent magnetization information from the closed-loop frequency signal of Xe atom in nuclear magnetic resonance gyroscopes without the need for redundant hardware structures and control algorithms. This method has positive significance for simplifying gyroscope signal processing and improving integration. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0023] Figure 1 This is a flowchart of a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals in one embodiment;

[0024] Figure 2 This is a simulation curve showing the effect of transverse remanence on the time-domain frequency signal of Xe atoms in one embodiment;

[0025] Figure 3 This is a Fourier spectrum analysis diagram of the transverse remanence to the Xe atom frequency signal in one embodiment;

[0026] Figure 4 This is a schematic diagram of the transverse remanence compensation process using the Xe atomic frequency harmonic signal in one embodiment. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0028] In a nuclear magnetic resonance gyroscope, the transverse magnetic moment precession of Xe atoms satisfies the following Bloch equation:

[0029] (1)

[0030] 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. , for vector form, include , , Three components, It is the gyromagnetic ratio. The vector form representing the main magnetic field B. Represents the angular frequency of the gyroscope. The vector form.

[0031] Consider a nuclear magnetic resonance gyroscope with transverse remanence; its magnetic field components in the x, y, and z directions are:

[0032] (2)

[0033] in To maintain the transverse feedback excitation magnetic field for the precession of the transverse magnetic moment of Xe atoms To provide feedback on the amplitude of the excitation magnetic field, This represents the precession phase of the transverse magnetic moment of the Xe atom. To provide feedback on the phase difference between the excitation magnetic field and the precession of the magnetic moment of the Xe atoms, This is the main magnetic field along the z-direction. , These represent the x and y components of transverse remanence, respectively.

[0034] Substituting the triaxial magnetic field in formula (2) into formula (1), and assuming that the transverse remanence is small, we use a first-order perturbation to let:

[0035] (3)

[0036] in For small quantity notation, the superscripts (0) and (1) represent the zeroth-order solution and the first-order solution, respectively. , These represent the zeroth-order and first-order solutions to the transverse component amplitude of the Xe atomic magnetic moment, respectively. , These represent the zeroth-order and first-order solutions of the phase of the transverse component of the Xe atomic magnetic moment, respectively. , These represent the zeroth-order and first-order solutions of the longitudinal component of the Xe atomic magnetic moment, respectively.

[0037] Substituting equation (3) into equation (1), we obtain the equation satisfied by the zeroth-order perturbation, i.e., equation (4), and the equation satisfied by the first-order perturbation, i.e., equation (5):

[0038] (4)

[0039] (5)

[0040] in , , , Meanwhile, the second harmonic term was ignored.

[0041] For the equation satisfied by the zeroth-order perturbation, i.e., formula (4), its steady-state result can be obtained directly:

[0042] (6)

[0043] Substituting formula (6) into formula (5) yields the first-order perturbation result.

[0044] Substituting the first-order perturbation result into formula (3) yields the analytical formula that considers the influence of transverse remanence on the closed-loop precession of Xe atoms.

[0045] It can be found from formula (5) that the first-order perturbation of the Xe atom precession frequency contains ,in , The physical meaning of this term is that when non-zero transverse remanence exists, the precession frequency of Xe atoms will contain [a certain value]. The oscillating harmonic signal. Conversely, this signal can be used to determine whether transverse remanence exists in the NMRG.

[0046] Based on the above analysis, one embodiment provides a nuclear magnetic resonance gyroscope magnetic field compensation method based on Xe atomic frequency harmonic signals to accurately extract transverse remanence information and achieve closed-loop compensation, including the following steps:

[0047] S1, measure the precession signal of the magnetic moment of Xe atoms in the nuclear magnetic resonance gyroscope, and feed the measurement result back to the transverse magnetic field coil to maintain the precession of the transverse magnetic moment of Xe atoms, forming the first closed loop;

[0048] 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.

[0049] 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.

[0050] Specifically, in S1 of the above embodiment, measuring the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope includes 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 (PLL), and feeding the phase, frequency and amplitude of the precession signal of the Xe atom magnetic moment into the measurement results and feeding them back to the transverse magnetic field coil to maintain the stable precession of the transverse magnetic moment of the Xe atom.

[0051] In another embodiment, a method for compensating the magnetic field of a nuclear magnetic resonance gyroscope based on Xe atomic frequency harmonic signals is provided, comprising the following steps:

[0052] 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;

[0053] S2, perform harmonic analysis on the frequency component of the Xe atom magnetic moment precession signal measured in S1, and determine whether there is transverse remanence in the nuclear magnetic resonance gyroscope based on the harmonic analysis results. When transverse remanence is determined to exist, obtain the amplitude of the harmonic signal oscillating at the Xe atom resonance frequency contained in the frequency component, and execute S3.

[0054] 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.

[0055] The above embodiments, combining the correlation mechanism between transverse remanence and the amplitude of the Xe atom frequency harmonic signal, can use a PID control algorithm to close-loop regulate the transverse coil current of the nuclear magnetic resonance gyroscope's magnetic field, locking the harmonic signal amplitude to the lowest level to cancel transverse magnetic field interference. This method can solve the problems of traditional nuclear magnetic resonance gyroscope magnetic field compensation, such as the influence of alkali metal atomic states, weak anti-interference ability, and complex hardware structure.

[0056] In S2 of one embodiment, harmonic analysis is performed on the frequency components of the Xe atom magnetic moment precession signal measured in S1 to determine whether the frequency components of the Xe atom magnetic moment precession signal contain harmonics. If the oscillating harmonic signal is present, then transverse remanence is determined to exist; otherwise, transverse remanence is determined to be absent. Based on the foregoing analysis, the amplitude of the harmonic signal is related to the first-order perturbation of the Xe atom precession frequency caused by transverse remanence, and this first-order perturbation includes… ,in , , , These represent the equivalent angular frequencies corresponding to the transverse remanence in the x and y directions multiplied by the gyromagnetic ratio, respectively. , These represent the x and y components of transverse remanence, respectively. Indicates the gyromagnetic ratio, This is the zero-order solution of the phase of the transverse component of the Xe atomic magnetic moment; when transverse remanence exists in the nuclear magnetic resonance gyroscope, the frequency component of the Xe atomic magnetic moment precession signal will contain... The oscillating harmonic signal allows us to determine whether transverse remanence exists in the nuclear magnetic resonance gyroscope by performing harmonic analysis on the frequency components of the Xe atom magnetic moment precession signal measured by S1.

[0057] In S3 of any of the above embodiments, the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope is adjusted by a closed-loop feedback control method such as PID. Based on the deviation between the harmonic signal amplitude and the preset target value, a compensation control signal for adjusting the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope is generated.

[0058] The above embodiments utilize the relationship between transverse remanence and the harmonics of the closed-loop resonant frequency of Xe atoms derived from the Bloch equation of the Xe atom magnetic moment and the perturbation iterative method. The amplitude of the harmonic oscillation of the frequency signal is extracted as a criterion for transverse remanence, and a PID control algorithm is combined to regulate the transverse coil current to achieve closed-loop compensation. This method improves the accuracy of magnetic compensation by avoiding interference from the non-ideal characteristics of alkali metals; enhances anti-interference capability by utilizing the characteristics of the frequency signal; and simplifies system integration without requiring additional hardware. It effectively solves the problem of Xe atom frequency fluctuations caused by transverse remanence, providing key technical support for the high-precision measurement and engineering application of nuclear magnetic resonance gyroscopes.

[0059] like Figure 2 As shown, simulation curves illustrating the effect of transverse remanence on the time-domain frequency signal of Xe atoms are presented. The parameters set in the simulation experiment are as follows: , , , , The dashed line in the figure represents the Xe atom resonant frequency versus time when the transverse remanence is 10 nT, while the solid line represents the Xe atom resonant frequency versus time when there is no transverse remanence. It is evident that transverse remanence increases the fluctuation of the Xe atom resonant frequency. This verifies the correctness of the theoretical analysis result of formula (5) and also provides the basic principle for measuring transverse remanence using Xe atom frequency harmonic signals. By measuring the amplitude of the Xe atom frequency harmonic signal, the transverse remanence of the system can be characterized.

[0060] Figure 3 Fourier spectrum analysis of the transverse remanence with respect to the Xe atom frequency signal is presented. The simulation parameters are... Figure 2The configuration is the same. The dashed line represents the spectral analysis result of the Xe atom resonance frequency changing with time when there is 10 nT of transverse remanence, and the solid line represents the spectral analysis result of the Xe atom resonance frequency changing with time when there is no transverse remanence. From the dashed line, it can be found that when there is 10 nT of transverse remanence, the Xe atom resonance frequency does indeed contain a harmonic signal that fluctuates at the resonance frequency (118.6 Hz), while the result without transverse remanence, represented by the solid line, does not contain this harmonic signal. These results are consistent with the prediction results of formula (5), which once again verifies the correctness of the theoretical analysis.

[0061] Figure 4 The results of compensating for transverse remanence by controlling the current in the transverse magnetic field coil under similar conditions are presented. As can be seen from the figure, by adjusting the coil magnetic field and continuously canceling the transverse remanence, the amplitude of the Xe atomic frequency harmonic signal continuously decreases. When the transverse remanence is almost completely canceled, the amplitude of this harmonic signal also decreases to zero, thus verifying the feasibility of the nuclear magnetic resonance gyroscope magnetic field compensation method based on the Xe atomic frequency harmonic signal proposed in this invention.

[0062] Another embodiment provides a nuclear magnetic resonance gyroscope magnetic field compensation system based on Xe atomic frequency harmonic signals, comprising:

[0063] The first closed-loop control module is used to measure the precession signal of the Xe atom magnetic moment in the nuclear magnetic resonance gyroscope and feed the measurement result back to the magnetic field transverse coil to maintain the stable precession of the Xe atom transverse magnetic moment.

[0064] The harmonic analysis module is connected to the first closed-loop control module and is used to perform harmonic analysis on the frequency components of the Xe atom magnetic moment precession signal measured by the first closed-loop control module, and to obtain the amplitude of the harmonic signal oscillating at the Xe atom resonance frequency contained in the frequency components.

[0065] The second closed-loop compensation module is connected to the harmonic analysis module and the transverse magnetic field coil. It is used to adjust the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope with the harmonic signal amplitude as a reference, so as to minimize the harmonic signal amplitude and achieve compensation for transverse remanence.

[0066] Furthermore, the harmonic analysis module also includes a judgment unit, used to determine whether there is transverse remanence in the nuclear magnetic resonance gyroscope based on the harmonic analysis results, and to trigger the second closed-loop compensation module to operate only when transverse remanence is determined to exist. The method used by the judgment unit to determine whether there is transverse remanence in the nuclear magnetic resonance gyroscope can be any of the methods provided in the aforementioned embodiments.

[0067] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A nuclear magnetic resonance gyromagnetic field compensation method based on Xe atomic frequency harmonic signals, characterized in that, The method comprises the following steps: S1, measuring the Xe atom magnetic moment precession signal in the nuclear magnetic resonance gyroscope and feeding back the measurement result to the magnetic field transverse coil to maintain the stable precession of the Xe atom transverse magnetic moment, forming a first closed loop, wherein measuring the Xe atom magnetic moment precession signal in the nuclear magnetic resonance gyroscope comprises measuring the phase, frequency and amplitude of the Xe atom magnetic moment precession signal in the nuclear magnetic resonance gyroscope by a phase-locked loop, and feeding back the phase, frequency and amplitude of the Xe atom magnetic moment precession signal to the magnetic field transverse coil to maintain the stable precession of the Xe atom transverse magnetic moment; S2, performing harmonic analysis on the frequency component of the Xe atomic magnetic moment precession signal measured by S1, based on the harmonic analysis result, judging whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope, when it is judged that there is transverse residual magnetism, obtaining the harmonic signal amplitude contained in the frequency component oscillating at the Xe atomic resonance frequency, and performing S3, wherein the method for judging whether there is transverse residual magnetism in the nuclear magnetic resonance gyroscope is: judging whether the frequency component of the Xe atomic magnetic moment precession signal contains a harmonic signal oscillating at if yes, it is judged that there is transverse residual magnetism, and if not, it is judged that there is no transverse residual magnetism, is the zero-order solution of the phase of the Xe atomic magnetic moment transverse 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 gyroscope by a PID closed-loop feedback control method, generating a compensation control signal for adjusting the output of the transverse magnetic field coil of the nuclear magnetic resonance gyroscope according to the deviation of the harmonic signal amplitude from the preset target value, and minimizing the harmonic signal amplitude, forming a second closed loop for compensating the transverse residual magnetism.

2. The Xe atomic frequency harmonic signal-based nuclear magnetic resonance gyro magnetic field compensation method according to claim 1, characterized in that, The Xe atom transverse magnetic moment precession 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. , for vector form, include , , Three components, Indicates the gyromagnetic ratio, The vector form representing the main magnetic field B. Represents the angular frequency of the gyroscope. The vector form.

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