External magnetic field tracking detection method and system based on cascade state observer
By using a cascaded state observer control method, the time delay and noise amplification problems of optically pumped magnetometers in a wide frequency band were solved, achieving highly stable external magnetic field tracking and meeting the needs of precision measurement and engineering applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-07
- Publication Date
- 2026-04-03
AI Technical Summary
Existing optically pumped magnetometers suffer from time delay and noise amplification issues in tracking and detecting external magnetic fields over a wide frequency band, affecting system stability and measurement accuracy, and making it difficult to meet the needs of precision measurement and engineering applications.
A control method based on cascaded state observers is adopted. By designing first-stage and second-stage state observers, the controller output is improved, the time delay caused by the lock-in amplifier is reduced, and the magnetic field tracking speed and measurement bandwidth are increased.
Without affecting the magnetometer's sensitivity, the measurement bandwidth of the magnetometer was expanded, the impact of internal time delay was reduced, and the system's stability and measurement accuracy were improved.
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Figure CN121784627A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of magnetic measurement sensor technology, and more specifically to an external magnetic field tracking and detection method and system based on a cascaded state observer. Background Technology
[0002] Currently, optically pumped magnetometers, as a type of quantum magnetic field sensor, possess advantages such as high sensitivity and room-temperature operation, and have become an important research direction in the field of precision magnetic field measurement. Based on the different magnetic moment components of the detected atoms, optically pumped magnetometers are generally divided into two types: Mz and Mx. Among them, the phase-stabilized mode Mx-type optically pumped magnetometer detects the transverse magnetic moment of atoms, exhibiting faster response speed and wider dynamic range, making it more suitable for broadband magnetic field measurement. It has broad prospects in applications such as biomagnetic field signal detection, geomagnetic compensation, target detection, and navigation. The phase-stabilized mode Mx-type optically pumped magnetometer achieves real-time tracking of the external magnetic field by detecting the phase difference between the excitation radio frequency signal and the atomic response signal and locking it at the Larmor frequency.
[0003] However, to extract phase information from the response signal, a lock-in amplifier (LPA) is typically used for demodulation and filtering. The finite impulse response (FIR) filter in the LPA inevitably introduces a time delay, weakening the system's phase margin and limiting the closed-loop bandwidth. Simultaneously, increasing the loop gain to improve disturbance rejection significantly amplifies high-frequency noise, leading to decreased system stability and measurement accuracy. Currently, the most common control method is proportional-integral (PI) control. This method is simple in structure and easy to implement, but its control performance is severely limited in the presence of significant time delays.
[0004] Therefore, how to achieve highly stable external magnetic field tracking in a wide frequency band using an optically pumped magnetometer to meet the needs of precision measurement and engineering applications is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0005] In view of the above problems, the present invention is proposed to provide an external magnetic field tracking and detection method and system based on a cascaded state observer to overcome or at least partially solve the above problems, thereby realizing highly stable external magnetic field tracking of an optically pumped magnetometer in a wide frequency band, and thus meeting the needs of precision measurement and engineering applications.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for tracking and detecting external magnetic fields based on a cascaded state observer includes: Obtaining the Bloch equation based on the geometry of the target optically pumped magnetometer; The phase of the output signal of the target optically pumped magnetometer is obtained by transforming and linearizing the Bloch equation. The transfer function from the controller output to the lock-in amplifier output is obtained based on the phase of the output signal; Based on the transfer function, the system state-space equation is obtained and a first-level state observer is designed. The first-level transformation equation is obtained based on the first-level state observer; Design a second-level state observer based on the first-level transformation equation and obtain the second-level transformation equation; The overall control law is derived based on the observation values output from the first-level transformation equation and the second-level transformation equation, which is used to control the target optically pumped magnetometer to achieve external magnetic field tracking and detection.
[0007] In one embodiment, the Bloch equation is obtained as follows: The total magnetic field is obtained based on the geometry of the target optically pumped magnetometer; Based on the total magnetic field, the evolution formula of the first magnetic moment in the ambient magnetic field is obtained; Based on the aforementioned evolution formula, a new coordinate system is introduced, and the system rotates around the z-axis at a preset angular velocity to obtain the second magnetic moment in the rotating coordinate system. The Bloch equation is obtained based on the second magnetic moment combined with the relaxation process.
[0008] In one embodiment, the method for obtaining the output signal phase is as follows: Based on the component differential equations in the Bloch equation, a Laplace transform is performed to obtain the differential transformation equation; The output signal phase is obtained by linearizing the differential transformation equation at the detuning frequency of zero.
[0009] In one embodiment, the method for obtaining the system state-space equations is as follows: Based on the transfer function, the differential equation is converted into a differential equation and combined with the Larmor frequency to obtain the differential equation of the lock-in amplifier output; The system state-space equation is obtained based on the differential equation output by the lock-in amplifier.
[0010] In one embodiment, the method for obtaining the first-level state observer is as follows: Based on the system state-space equations, the controller output is delayed, and combined with measurement noise, a first-level model-assisted extended state observer is obtained as the first-level state observer: ; Where Γ=1 / T 2, T 2 represents the lateral relaxation time. z 1 and z2 represents the estimates of the lock-in amplifier output and the external magnetic field from the first-stage state observer, respectively. and They represent z 1 and z The differential of 2, b =360, u Indicates the controller output. t Indicates time, t d Indicates the delay time. β 1 and β 2 represents the gain of the first observer and the gain of the second observer, respectively. y δ This represents the phase information extracted by the lock-in amplifier after taking into account measurement noise.
[0011] In one embodiment, the method for obtaining the first transformation equation is as follows: Based on setting the two poles of the first-stage state observer to constant values - oh o1 The first observer gain and the second observer gain are obtained. Substituting the first observer gain and the second observer gain into the first-level state observer, the first-level transformation equation is obtained.
[0012] In one embodiment, the method for obtaining the second-level state observer is as follows: Based on the external environment estimate and the lock-in amplifier output estimate obtained from the first-level transformation equation, the second-level model-assisted extended state observer is obtained as the second-level state observer: ; in, s 1 and s 2 represents the precise estimate of the lock-in amplifier and the value at which the phase-locked amplifier is in operation. z Based on 2, the estimated value of the remaining amount, β 3 and β 4 represents the gain of the third observer and the gain of the fourth observer, respectively.
[0013] In one embodiment, the method for obtaining the second transformation equation is as follows: The two poles of the second-stage state observer are set to constant values. oh o2 The third observer gain and the fourth observer gain are obtained. Substituting the gains of the third and fourth observers into the second-level state observer, the second-level transformation equation is obtained.
[0014] In one embodiment, the overall control lawu z Specifically: ; in, u 0 indicates the output of the feedback controller.
[0015] An external magnetic field tracking and detection system based on a cascaded state observer includes: a Bloch equation construction module, a signal phase acquisition module, a transfer function acquisition module, a first observer construction module, a second observer construction module, and a total control law output module; The Bloch equation construction module is used to obtain the Bloch equation based on the geometry of the target optically pumped magnetometer. The signal phase acquisition module is used to perform transformation and linearization based on the Bloch equation to obtain the output signal phase of the target optically pumped magnetometer. The transfer function acquisition module is used to obtain the transfer function from the controller output to the lock-in amplifier output based on the phase of the output signal; The first observer construction module is used to obtain the system state-space equations based on the transfer function and design a first-level state observer; and to obtain the first-level transformation equations based on the first-level state observer. The second observer construction module is used to design a second-level state observer based on the first-level transformation equation and obtain the second-level transformation equation; The total control law output module is used to obtain the total control law based on the observation values output by the first-level transformation equation and the second-level transformation equation, and is used to control the target optical pump magnetometer to achieve external magnetic field tracking and detection.
[0016] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses an external magnetic field tracking and detection method and system based on a cascaded state observer. Without affecting the sensitivity of the magnetometer, the present invention improves the tracking speed of the optically pumped magnetometer on the external magnetic field by improving the control method, expands the measurement bandwidth of the magnetometer, and reduces the impact of time delay caused by the internal lock-in amplifier of the system. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0018] Figure 1The flowchart of an external magnetic field tracking and detection method based on a cascaded state observer provided by the present invention is shown.
[0019] Figure 2 A schematic diagram of the phase-stabilized mode Mx-type optically pumped magnetometer provided by the present invention.
[0020] Figure 3 This is a schematic diagram of the geometric structure of the Mx-type optically pumped magnetometer provided by the present invention.
[0021] Figure 4 The structural diagram of the closed-loop system of the phase-stabilized mode Mx type optically pumped magnetometer provided by the present invention.
[0022] Figure 5 The block diagram of the cascaded model-assisted extended state observer provided by the present invention.
[0023] Figure 6 A schematic diagram comparing the frequency response of the magnetometer under different control methods provided by this invention.
[0024] Figure 7 This is a schematic diagram of the time-domain waveform and frequency-domain sensitivity of the magnetometer measurement results under different control methods provided by the present invention. Detailed Implementation
[0025] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0026] Example 1 like Figure 1 As shown, this embodiment of the invention discloses an external magnetic field tracking and detection method based on a cascaded state observer, including the following steps. For ease of description, these steps are numbered S1 to S7, and these numbers are not used to limit the sequential relationship between the various steps of this invention: S1 obtains the Bloch equation based on the geometry of the target optically pumped magnetometer.
[0027] Furthermore, the target optically pumped magnetometer in this invention is a phase-stabilized mode Mx-type optically pumped magnetometer, the structure of which is as follows: Figure 2 As shown, the Mx-type optically pumped magnetometer uses optical radio frequency resonance technology to measure the strength of the ambient magnetic field by detecting the Larmor precession frequency of the alkali metal atom ensemble. oh L The relationship between the ambient magnetic field strength |B| and the magnetic field strength is as follows: oh L = c|B|, where c Indicates the gyromagnetic ratio of an atom; A circularly polarized laser tuned to the D1 transition passes through an atomic gas cell, optically pumping the atomic spins along the direction of light propagation and creating spin polarization. The corresponding magnetization intensity is at the Larmor frequency. oh L Circumferential external magnetic field B 0 precession, applying a radio frequency magnetic field in a direction parallel to the optical axis. B 1. When the radio frequency field frequency oh rf and oh L Upon approach, the same-direction rotational component of the radio frequency field coherently drives the magnetic resonance and applies phase to the precession spin. f The driven magnetization generates an oscillating magnetization component along the optical axis, which periodically alters the optical absorption properties of the medium, thereby modulating the transmitted light intensity. The phase of the modulated light intensity is extracted using a photodiode and a lock-in amplifier. f The controller actively uses phase information to... oh rf Locked at the Lamo frequency oh L This allows the magnetometer to track changes in the magnetic field in a phase-coherent manner.
[0028] Furthermore, the Bloch equation is obtained as follows: The total magnetic field is obtained based on the geometry of the target optically pumped magnetometer; The evolution formula of the first magnetic moment in the ambient magnetic field is obtained based on the total magnetic field. A new coordinate system is introduced based on the evolution formula, and the second magnetic moment in the rotating coordinate system is obtained by rotating around the z-axis at a preset angular velocity. Based on the second magnetic moment combined with the relaxation process, the Bloch equation is obtained.
[0029] Furthermore, the geometry of the Mx-type optically pumped magnetometer is as follows: Figure 3 As shown, radio frequency field B 1 can be divided into two components, only the one perpendicular to the external magnetic field. B The 0 component will induce magnetic resonance, therefore... Considering it as an effective radio frequency field and ignoring the other radio frequency field component in the z direction, the total magnetic field B is: .
[0030] Furthermore, the first magnetic moment M The evolution formula in the environmental magnetic field is: ; Based on this evolution formula, a new coordinate system is introduced, with radio frequency as the reference. oh rfRotating about the z-axis and using the rotating wave approximation, the magnetic field in the rotating coordinate system can be expressed as: The second magnetic moment in the rotating coordinate system This can be further expressed as: ; set up Combining the relaxation process, we obtain the Bloch equation: ; in, These represent the three components of the magnetic moment in the rotating coordinate system. The detuning amount, Ω = represents the radio frequency. cB 1 represents the Rabi frequency, which is determined by the amplitude of the radio frequency field. M 0 represents the steady-state value of the longitudinal magnetic moment. T 1 and T 2 represents the longitudinal relaxation time and the transverse relaxation time, respectively.
[0031] S2 is transformed and linearized based on the Bloch equation to obtain the output signal phase of the target optically pumped magnetometer.
[0032] Furthermore, the method for obtaining the phase of the output signal is as follows: Based on the Bloch equation Performing a Laplace transform on the component differential equations, let Γ=1 / T 2. The differential transformation equation is obtained: ; Where s represents the complex frequency, Δ f Indicates the detuning frequency; based on Substituting into the above differential transformation equation and at the detuning frequency Δ f Linearization is performed at the zero point to obtain the phase of the output signal. f : ; According to the above formula, the Mx-type optically pumped magnetometer can be regarded as a first-order low-pass filter. Its cutoff frequency is determined by the transverse relaxation state of atoms, and the phase of the magnetometer's output signal is determined by the detuning frequency Δ. f Instead of radio frequency oh rf .
[0033] S3 obtains the transfer function from the controller output to the lock-in amplifier output based on the phase of the output signal.
[0034] Furthermore, the phase-stabilized mode Mx-type optically pumped magnetometer closed-loop system, such as Figure 4 As shown, it utilizes laser powerP With detuning frequency Δ f The change in the external magnetic field is measured by a photodiode, which detects the laser power and converts it into a current signal. A transimpedance amplifier then converts the current signal into a voltage signal, and a lock-in amplifier extracts the laser power signal with frequency [value missing]. oh rf The controller obtains the phase information of the signal based on the output phase of the lock-in amplifier. f Calculate the new radio frequency oh rf Then, a frequency of is generated using direct digital synthesis (DDS) technology. oh rf A sinusoidal signal is applied to an RF coil to generate an RF field. Ultimately, f Locked to 0, oh rf Closed-loop tracking of Larmor frequency oh L This enables magnetic field measurement.
[0035] In the magnetometer system, the coil and photodiode are integrated inside the sensor probe. The lock-in amplifier, DDS, and controller are implemented using a field-programmable gate array (FPGA), while the transimpedance amplifier is an analog circuit. Neither the DDS nor the coil affects the signal frequency. oh rf Therefore, they can be considered unity-gain elements. Furthermore, the bandwidth of the photodiode and transimpedance amplifier is much higher than the Larmor frequency (approximately 350 kHz for 87Rb atoms under the Earth's magnetic field), meaning they have almost no effect on the signal phase. Therefore, they can also be simplified to unity-gain elements. Based on the aforementioned derivation, the sensor probe can be modeled as a first-order inertial element. The FIR filter in the lock-in amplifier has linear phase characteristics, and its cutoff frequency is higher than that of the sensor probe; therefore, it can be modeled as a time delay. t d The specific transfer function is as follows: ; ; in, and These represent the transfer functions of the magnetometer probe and the lock-in amplifier, respectively. Based on the phase of the output signal f according to Figure 4 Assume the controller output is u The output of the lock-in amplifier is y Then from u arrive y The transfer function is: .
[0036] S4 obtains the system state-space equations based on the transfer function and designs the first-level state observer.
[0037] Furthermore, the method for obtaining the system state-space equations is as follows: The differential equation of the lock-in amplifier output is obtained by converting the transfer function into a differential equation and combining it with the Larmor frequency. The system state-space equation is obtained from the differential equation based on the output of the lock-in amplifier.
[0038] Furthermore, by setting b = 360, the transfer function is transformed into a differential equation, and this is combined with the Larmor frequency. oh L The effect of this leads to the differential equation of the lock-in amplifier output: ; in, This indicates the magnitude of the external magnetic field and is related to the Larmor frequency.
[0039] Furthermore, in order to measure the Larmor frequency, it is necessary to obtain the values of the variables. m Accurate estimation, therefore, m Expand to new system state variables, and assume m It is continuously differentiable, and its derivative is ,definition x 1 = y , x 2=- m Based on the differential equation of the lock-in amplifier output, the system state-space equation is obtained as follows: .
[0040] Furthermore, the method for obtaining the first-level state observer is as follows: The controller output is delayed based on the system state-space equations, and a first-level model-assisted extended state observer is obtained by combining the measurement noise. ; Where Γ=1 / T 2, T 2 represents the lateral relaxation time. z 1 and z 2 represents the estimates of the lock-in amplifier output and the external magnetic field from the first-stage state observer, respectively. and They represent z 1 and z The differential of 2, b =360, u Indicates the controller output. t Indicates time, td Indicates the delay time. β 1 and β 2 represents the gain of the first observer and the gain of the second observer, respectively. y δ = y + d This represents the phase information extracted by the lock-in amplifier after taking into account measurement noise.
[0041] Furthermore, based on the system state-space equations, an extended state observer (ESO) is designed, and known model information is incorporated into the ESO to handle the input. u Perform a length of t d Considering the time delay and measurement noise, a first-level model-aided extended state observer (MESO) is designed as the first-level state observer.
[0042] S5 derives the first-level transformation equation based on the first-level state observer.
[0043] Furthermore, the method for obtaining the first transformation equation is as follows: The two poles of the first-stage state observer are set to a constant value -ω. o1 The gain of the first observer is obtained. β 1 = 2ω o1 -Γ and second observer gain ; Based on the first observer gain β 1 and second observer gain β Substitute 2 into the first-level state observer and let The first-order transformation equation is obtained: .
[0044] S6 designs a second-level state observer based on the first-level transformation equation and obtains the second-level transformation equation.
[0045] The method for obtaining the second-level state observer is as follows: Estimated external magnetic field obtained based on the first-order transformation equation z 2. And output the estimated value using a lock-in amplifier. z 1 replaces y δ To reduce the amplification of measurement noise, a second-level model-assisted extended state observer is obtained as the second-level state observer: ; in, s 1 and s 2 represents the precise estimate of the lock-in amplifier and the value at which the phase-locked amplifier is in operation. z Based on 2, the estimated value of the remaining amount,β 3 and β 4 represents the gain of the third observer and the gain of the fourth observer, respectively.
[0046] Furthermore, the method for obtaining the second transformation equation is as follows: The two poles of the second-stage state observer are set to constant values. oh o2 The gain of the third observer is obtained. β 3 = 2ω o2 -Γ and fourth observer gain ; Based on the third observer gain β Gain of the 3rd and 4th observers β 4. Substitute into the second-level state observer, and let The second-order transformation equation is obtained: .
[0047] S7 derives the overall control law from the observation values output by the first-order and second-order transformation equations, which is used to control the target optical pump magnetometer to achieve external magnetic field tracking and detection.
[0048] Furthermore, the block diagram of the Cascaded Model-Assisted Extended State Observer (CMESO) is as follows: Figure 5 As shown, the output observations of the first-order transformation equation and the second-order transformation equation are combined into a total observation. The feedback controller uses proportional control; therefore, the overall control law is... u z Represented as: ; in, u 0 indicates the output of the feedback controller.
[0049] Furthermore, The control target is r = 0. k p This represents the gain parameter of the controller.
[0050] Example 2 The effectiveness of the CMESO control method of this invention was verified by applying it to a phase-stabilized Mx-type optically pumped magnetometer. like Figure 6As shown, the frequency response of the magnetometer is illustrated when applying PI, MESO, and CMESO control methods respectively. In the amplitude-frequency response graph, the measurement error is less than 0.1 dB in the low-frequency range below 30 Hz for all three curves. The amplitude-frequency response with the PI controller shows a significant attenuation starting from 50 Hz, exceeding 0.5 dB at its maximum, and then drops sharply above 300 Hz, finally attenuating to -19 dB at 1.5 kHz. By considering the system's time delay and model information, improvements to ESO significantly enhance the measurement bandwidth.
[0051] MESO can guarantee an amplitude error of less than 0.3dB within the frequency band up to 700Hz, attenuating to -15dB at 1.5kHz. The CMESO of this invention, by introducing a cascaded structure, improves the flatness within the passband, achieving an amplitude error of less than 0.2dB within 700Hz. Furthermore, compared to MESO, it exhibits a faster decay rate above 700Hz, attenuating to -18dB at 1.5kHz, approaching the performance of a PI controller. Regarding phase frequency response, both MESO and CMESO reduce the phase lag of the measured values within the passband, improving the measurement accuracy of the magnetometer.
[0052] like Figure 7 As shown, the time-domain waveforms and frequency-domain sensitivity of the magnetometer measurement results under three control methods are illustrated. Sensitivity reflects the power distribution of the measured signal in different frequency bands and can characterize the noise level of the sensor.
[0053] When using a PI controller, the magnetometer loses mid-to-high frequency information, resulting in the narrowest time-domain waveform. In the 10-100Hz range, the magnetometer sensitivities for PI control, MESO control, and CMESO control are 380, 384, and 377 fT / Hz, respectively. 1 / 2 Experimental results show that the three control methods have comparable noise levels within the passband, but above 700 Hz, the noise level of the measurement data obtained by CMESO is significantly lower than that of MESO. When the frequency exceeds 1.5 kHz, the noise level approaches that of the PI controller. This characteristic is reflected in the time-domain waveform, where the CMESO measurement results are narrower than those of MESO. Experiments demonstrate that applying CMESO can extend the measurement bandwidth of the magnetometer while avoiding excessive amplification of high-frequency measurement noise.
[0054] Example 3 Based on the same inventive concept, the present invention also provides an external magnetic field tracking and detection system based on a cascaded state observer, comprising: a Bloch equation construction module, a signal phase acquisition module, a transfer function acquisition module, a first observer construction module, a second observer construction module, and a total control law output module; The Bloch equation building module is used to obtain the Bloch equation based on the geometry of the target optically pumped magnetometer. The signal phase acquisition module is used to perform transformation and linearization based on the Bloch equation to obtain the output signal phase of the target optically pumped magnetometer. The transfer function acquisition module is used to obtain the transfer function from the controller output to the lock-in amplifier output based on the phase of the output signal; The first observer construction module is used to obtain the system state-space equations based on the transfer function and design the first-level state observer; the first-level transformation equations are obtained based on the first-level state observer. The second observer construction module is used to design the second-level state observer based on the first-level transformation equation and obtain the second-level transformation equation. The overall control law output module is used to obtain the overall control law based on the observation values output from the first-level transformation equation and the second-level transformation equation, and is used to control the target optical pump magnetometer to achieve external magnetic field tracking and detection.
[0055] Furthermore, in this embodiment, the functional implementation methods of each functional module correspond one-to-one with the methods described above, and will not be repeated here.
[0056] Example 4 Based on the same inventive concept, the present invention also provides an electronic device, which includes a processor and a memory, wherein the memory stores instructions, characterized in that the instructions are loaded and executed by the processor to implement an external magnetic field tracking and detection method based on a cascaded state observer as described in Embodiment 1.
[0057] Based on the same inventive concept, the present invention also provides a computer device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; When the processor executes the program stored in the memory, it can implement an external magnetic field tracking and detection method based on a cascaded state observer, as shown in Example 1.
[0058] The electronic device may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions in the memory to execute the external magnetic field tracking and detection method based on a cascaded state observer as described in Embodiment 1.
[0059] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0060] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for tracking and detecting external magnetic fields based on a cascaded state observer, characterized in that, include: Obtaining the Bloch equation based on the geometry of the target optically pumped magnetometer; The phase of the output signal of the target optically pumped magnetometer is obtained by transforming and linearizing the Bloch equation. The transfer function from the controller output to the lock-in amplifier output is obtained based on the phase of the output signal; Based on the transfer function, the system state-space equation is obtained and a first-level state observer is designed. The first-level transformation equation is obtained based on the first-level state observer; Design a second-level state observer based on the first-level transformation equation and obtain the second-level transformation equation; The overall control law is derived based on the observation values output from the first-level transformation equation and the second-level transformation equation, which is used to control the target optically pumped magnetometer to achieve external magnetic field tracking and detection.
2. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 1, characterized in that, The method for obtaining the Bloch equation is as follows: The total magnetic field is obtained based on the geometry of the target optically pumped magnetometer; Based on the total magnetic field, the evolution formula of the first magnetic moment in the ambient magnetic field is obtained; Based on the aforementioned evolution formula, a new coordinate system is introduced, and the system rotates around the z-axis at a preset angular velocity to obtain the second magnetic moment in the rotating coordinate system. The Bloch equation is obtained based on the second magnetic moment combined with the relaxation process.
3. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 1, characterized in that, The method for obtaining the phase of the output signal is as follows: Based on the component differential equations in the Bloch equation, a Laplace transform is performed to obtain the differential transformation equation; The output signal phase is obtained by linearizing the differential transformation equation at the detuning frequency of zero.
4. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 1, characterized in that, The method for obtaining the system state-space equations is as follows: Based on the transfer function, the differential equation is converted into a differential equation and combined with the Larmor frequency to obtain the differential equation of the lock-in amplifier output; The system state-space equation is obtained based on the differential equation output by the lock-in amplifier.
5. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 1, characterized in that, The method for obtaining the first-level state observer is as follows: Based on the system state-space equations, the controller output is delayed, and combined with measurement noise, a first-level model-assisted extended state observer is obtained as the first-level state observer: ； Where Γ=1 / T 2, T 2 represents the lateral relaxation time. z 1 and z 2 represents the estimates of the lock-in amplifier output and the external magnetic field from the first-stage state observer, respectively. and They represent z 1 and z The differential of 2, b =360, u Indicates the controller output. t Indicates time, t d Indicates the delay time. β 1 and β 2 represents the gain of the first observer and the gain of the second observer, respectively. y δ This represents the phase information extracted by the lock-in amplifier after taking into account measurement noise.
6. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 5, characterized in that, The method for obtaining the first transformation equation is as follows: Based on setting the two poles of the first-stage state observer to constant values - ω o1 The first observer gain and the second observer gain are obtained. Substituting the first observer gain and the second observer gain into the first-level state observer, the first-level transformation equation is obtained.
7. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 5, characterized in that, The method for obtaining the second-level state observer is as follows: Based on the external environment estimate and the lock-in amplifier output estimate obtained from the first-level transformation equation, the second-level model-assisted extended state observer is obtained as the second-level state observer: ； in, s 1 and s 2 represents the precise estimate of the lock-in amplifier and the value at which the phase-locked amplifier is in operation. z Based on 2, the estimated value of the remaining amount, β 3 and β 4 represents the gain of the third observer and the gain of the fourth observer, respectively.
8. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 7, characterized in that, The method for obtaining the second transformation equation is as follows: The two poles of the second-stage state observer are set to constant values. ω o2 The third observer gain and the fourth observer gain are obtained. Substituting the gains of the third and fourth observers into the second-level state observer, the second-level transformation equation is obtained.
9. The external magnetic field tracking and detection method based on a cascaded state observer according to claim 7, characterized in that, The overall control law u z Specifically: ； in, u 0 indicates the output of the feedback controller.
10. An external magnetic field tracking and detection system based on a cascaded state observer, used to execute the external magnetic field tracking and detection method based on a cascaded state observer as described in any one of claims 1-9, characterized in that, include: The module includes a Bloch equation construction module, a signal phase acquisition module, a transfer function acquisition module, a first observer construction module, a second observer construction module, and a total control law output module. The Bloch equation construction module is used to obtain the Bloch equation based on the geometry of the target optically pumped magnetometer. The signal phase acquisition module is used to perform transformation and linearization based on the Bloch equation to obtain the output signal phase of the target optically pumped magnetometer. The transfer function acquisition module is used to obtain the transfer function from the controller output to the lock-in amplifier output based on the phase of the output signal; The first observer construction module is used to obtain the system state-space equation based on the transfer function and design a first-level state observer; The first-level transformation equation is obtained based on the first-level state observer; The second observer construction module is used to design a second-level state observer based on the first-level transformation equation and obtain the second-level transformation equation; The total control law output module is used to obtain the total control law based on the observation values output by the first-level transformation equation and the second-level transformation equation, and is used to control the target optical pump magnetometer to achieve external magnetic field tracking and detection.