A vector magnetic field measurement method based on extended Kalman filter

Abstract

The present invention discloses a vector magnetic field measurement method based on an extended Kalman filter, comprising the following steps: Step 1, establishing a model, establishing a nonlinear system evolution model and a detection model in an atomic magnetometer; Step 2, establishing an extended Kalman filter to estimate the magnetic field vector. The accuracy of traditional vector detection schemes depends largely on the mathematical model for extracting the magnetic field direction from experimental signals, and also requires a bias field with very high magnitude and direction accuracy, which is time-consuming and labor-intensive. The present invention overcomes the defect that the original atomic magnetometer vector magnetic field estimation requires the additional setting of a bias magnetic field, thereby obtaining the vector information of the magnetic field more accurately.

Description

Technical Field

[0001] The present invention relates to the field of vector magnetic field measurement, and in particular to a vector magnetic field measurement method based on extended Kalman filtering. Background Art

[0002] Vector magnetic field measurement plays a vital role in practical engineering applications such as geological exploration, biomedicine, nondestructive testing, and military defense. With the advancement of science and technology, engineering applications are placing increasing demands on magnetic detection accuracy and complexity. Therefore, the research and development of high-precision, high-resolution vector magnetic field measurement instruments and technologies are of paramount importance.

[0003] Atomic magnetometers, currently among the most sensitive magnetometers, typically require a tiny bias field or radio frequency field superimposed on the original magnetic field for vector measurement. This effectively modulates the magnetic field along orthogonal axes and demodulates the magnetic resonance frequency to achieve vector measurement. However, the accuracy of this approach relies heavily on the mathematical model used to extract the magnetic field direction from the experimental signal. This also requires a bias field with very high precision in both magnitude and direction. Therefore, a solution is needed that can achieve high-precision vector magnetic field measurements without a bias field. Summary of the Invention

[0004] In response to the shortcomings of existing technologies, this paper proposes a method for measuring vector magnetic fields based on an extended Kalman filter. This solution uses extended Kalman filtering technology and combines it with three-axis orthogonal detection light to successfully measure vector magnetic fields without the need for an additional bias magnetic field.

[0005] In order to solve the above technical problems, the technical solution of the present invention is:

[0006] A vector magnetic field measurement method based on extended Kalman filtering comprises the following steps:

[0007] Step 1: Determine the vector direction under the magnetic field, then establish a vector magnetic field in any direction through the rotation matrix, establish the xyz coordinate axis, and then obtain the angular momentum of the xyz coordinate axis;

[0008] Step 2: determining a spin evolution model using the Bloch equation for atoms under a magnetic field based on the determined vector direction, and estimating parameter information of the vector magnetic field using the spin evolution model, wherein the parameter information includes the direction and magnitude of the vector magnetic field;

[0009] Step 3: Establish an evolution model of the vector magnetic field to be estimated according to the change of the magnetic field over time;

[0010] Step 4: establishing a nonlinear system evolution model based on the spin evolution model obtained in step 2 and the evolution model of the vector magnetic field to be estimated obtained in step 3;

[0011] Step 5: Obtain a three-axis orthogonal detection light polarization rotation angle model based on the established nonlinear system evolution model, obtain the angular momentum vector on the xyz coordinate axis by rotating the detection light polarization angle, and then obtain the detection light signal on the three axes xyz on the coordinate axis through the three-axis orthogonal detection light polarization rotation angle model;

[0012] Step 6: Use the xyz three-axis detection light signal as input to estimate the magnetic field vector through the extended Kalman filter.

[0013] Preferably, in step 1, the expression of the rotation matrix is ​​as follows:

[0014] ;

[0015] Among them, θ and ψ represent the direction angles in the rotation matrix.

[0016] Preferably, in step 1, the method for establishing the coordinate axis is:

[0017] The three-axis vertical detection direction of the atomic magnetometer is used as the xyz axis, and the initial magnetic field is assumed to be in the z direction. Then the magnetic field is rotated clockwise by an angle of θ around the x-axis, and then by an angle of ψ around the z-axis. The new coordinate axis is established with the rotated magnetic field, and the magnetic field direction is the z' axis.

[0018] Preferably, the spin evolution model is expressed as follows:

[0019]

[0020]

[0021] Where, T2 represents the transverse relaxation time, T1 represents the longitudinal relaxation time, A is the one-step transfer matrix, ω0 represents the Larmor frequency, and its relationship with the magnetic field is ω0 = γB, and J represents the angular momentum vector on the xyz coordinate axis. refers to the rate of change of J over time, Refers to the thermal noise of the atomic angular momentum in the xyz direction.

[0022] Preferably, the evolution model of the vector magnetic field to be estimated is expressed as follows:

[0023]

[0024] in, It means that the magnitude of the magnetic field does not change with time. Indicates that the direction of the magnetic field does not change with time.

[0025] Preferably, the nonlinear system evolution model is expressed as follows:

[0026]

[0027] θ is the angle at which the z-axis magnetic field first rotates clockwise around the x-axis, and ψ is the angle at which the magnetic field then rotates clockwise around the z-axis.

[0028] Preferably, the three-axis orthogonal detection light polarization rotation angle model is expressed as follows:

[0029]

[0030] Where I(t) is the detection light signal of the xyz three axes, is the coupling coefficient between light and atomic spin, and R0 is the observation noise variance.

[0031] Preferably, step 6 includes the following sub-steps:

[0032] Step 6.1: Establish the time update part of the extended Kalman filter in the atomic magnetometer, calculate the prior estimation information of the spin signal and the vector magnetic field; calculate the mean square error of the prior estimation of the spin signal and the magnetic field vector;

[0033] Step 6.2 establishes the extended Kalman filter measurement update part in the atomic magnetometer, calculates the Kalman gain, calculates the a posteriori estimation information of the spin signal and the magnetic field vector; calculates the mean square error of the a posteriori estimation of the spin signal and the magnetic field vector.

[0034] Preferably, in step 6.1, the extended Kalman filter time update part is expressed as follows:

[0035]

[0036] in, is the prior estimated state quantity at time k; is the posterior estimated state quantity at time k-1; is the state transfer matrix at time k-1; is the prior estimated covariance matrix at time k; is the posterior estimated covariance matrix at time k-1; is the state transfer partial derivative matrix at time k-1; is the covariance matrix of the state noise at time k-1.

[0037] Preferably, in step 6.2, the extended Kalman filter measurement update part is expressed as follows:

[0038]

[0039] in, is the Kalman gain at time k; is the covariance matrix of the observation noise at time k; is the observation matrix; is the true value of observation at the kth moment; is the observed value predicted at the kth moment.

[0040] Preferably, the a priori estimated state quantity at time k and the a posteriori estimated state quantity at time k-1 are expressed as follows:

[0041] ,

[0042] Preferably, the state transition partial derivative matrix at time k-1 is expressed as follows:

[0043]

[0044] in, is the one-step transfer matrix at time k-1, is the rotation matrix at time k-1, is the angular momentum vector at time k-1, dt is the time difference from time k-1 to time k, are matrix pair parameters Find the derivative.

[0045] Preferably, the observation matrix is ​​expressed as follows:

[0046]

[0047] in, is the coupling coefficient between light and spin.

[0048] The present invention has the following characteristics and beneficial effects:

[0049] First, this invention pioneered the use of an extended Kalman filter (EKF) method in an atomic magnetometer to estimate vector magnetic fields. This method, unlike vector magnetic field measurement methods that add a bias magnetic field, facilitates more accurate magnetic field source location and analysis of the vector magnetic field gradient in space.

[0050] Second, the accuracy of traditional vector magnetic field detection schemes relies heavily on mathematical models for extracting magnetic field direction from experimental signals. This also requires a bias field with very high magnitude and direction accuracy, which is time-consuming and labor-intensive. This invention overcomes the drawback of traditional atomic magnetometers, which require an additional bias field for spatial magnetic field estimation, thereby obtaining more accurate vector magnetic field information.

[0051] 3. The extended Kalman filter can effectively suppress noise by updating the state estimation error covariance matrix in real time and combining theoretical model predictions with experimental observations, thereby maintaining high-precision vector magnetic field estimation under noise interference.

[0052] 4. In actual environments, the magnetic field may change over time. The extended Kalman filter can update the vector magnetic field state estimation in real time, track the dynamic changes of the magnetic field, and maintain measurement accuracy.

[0053] 5. The proposed xyz three-axis detection light is used to detect the spin signal, which avoids the defect of being unable to accurately obtain vector magnetic field information due to single-axis detection light.

[0054] 6. The extended Kalman filter-based vector magnetic field measurement method is general. For different variations in the vector magnetic field, the change in the vector magnetic field can be accurately estimated by simply changing the corresponding nonlinear evolution model of the atomic magnetometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0056] Figure 1 Flowchart of an embodiment of the present invention.

[0057] Figure 2 Schematic diagram of the vector direction of the magnetic field according to an embodiment of the present invention.

[0058] Figure 3 Schematic diagram of the magnetic field parameter ω0 estimation result according to an embodiment of the present invention.

[0059] Figure 4 Schematic diagram of the magnetic field parameter θ estimation result according to an embodiment of the present invention.

[0060] Figure 5 Schematic diagram of the magnetic field parameter ψ estimation result according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0062] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0063] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0064] The present invention provides a vector magnetic field estimation method for use in an atomic magnetometer, such as Figure 1 As shown, the following steps are included:

[0065] Step 1: Establish the vector direction of the magnetic field in the atomic magnetometer. Use the three-axis orthogonal detection light direction to establish the coordinate axis. The rotation matrix from the z-axis to any direction is:

[0066]

[0067] like Figure 2 As shown, a vector magnetic field in any direction can be established by rotating the direction angles θ and ψ in the matrix.

[0068] Step 2: In establishing an atomic magnetometer, the spin evolution model is determined using the Bloch equation for the behavior of atoms under a magnetic field using the determined vector direction. The spin evolution model is used to estimate the parameter information of the vector magnetic field, including the direction and magnitude of the vector magnetic field. In this embodiment, the spin evolution is as follows:

[0069]

[0070] Step 3: Establish an evolution model of the vector magnetic field to be estimated in the atomic magnetometer. For the vector estimation of the static magnetic field, the direction and magnitude of the magnetic field do not change with time. The evolution model of the vector magnetic field to be estimated is expressed as: .

[0071] Step 4: Considering the influence of the vector magnetic field on the spin, the nonlinear system evolution model in the atomic magnetometer is formed by combining the obtained spin evolution model and the evolution model of the vector magnetic field to be estimated. The spin angular momentum is combined with the three parameters ω0, θ, and ψ of the vector magnetic field to form a vector form. The coefficients of the vector are obtained from the differential equations of the time-varying spin angular momentum and the vector magnetic field in steps 2 and 3, and finally the thermal noise of the spin angular momentum and the noise of the estimated parameters are added to obtain the nonlinear system evolution model in the atomic magnetometer. In the vector parameter estimation of the static magnetic field, the nonlinear system evolution model of the atomic magnetometer in this embodiment is in the following form:

[0072]

[0073] in, , R is the rotation matrix, T2 represents the transverse relaxation time, T1 represents the longitudinal relaxation time, ω0 represents the Larmor frequency, which is related to the magnetic field by ω0 = γB, and J represents the angular momentum vector on the xyz coordinate axes. θ is the angle of the z-axis magnetic field's initial clockwise rotation about the x-axis, and ψ is the angle of the subsequent clockwise rotation about the z-axis.

[0074] Step 5. In the atomic magnetometer, a three-axis orthogonal detection light polarization rotation angle model is obtained based on the angular momentum J of the established nonlinear system evolution model. Due to the Faraday rotation effect, the polarization direction of the detection light is deflected. We use a polarization beam splitter to differentiate the signal. At this time, the signal intensity is proportional to the angular momentum, and the coefficient is the coupling coefficient between the light and the atomic spin. Adding the noise in the detection process, we obtain a three-axis orthogonal detection light polarization rotation angle model. The spin signal is detected by rotating the polarization angle of the detection light. The detection model established in this embodiment specifically adopts the following form:

[0075]

[0076] Where I(t) is the detection light signal of the xyz three axes, is the coupling coefficient between light and atomic spin, and R0 is the observation noise variance. In this embodiment, the three-axis detection directions all use the same detection light intensity and the same detector.

[0077] Step 6: Establish an extended Kalman filter to estimate the vector magnetic field.

[0078] Step 6.1: Based on the models in steps 4 and 5, the extended Kalman filter time update portion of the atomic magnetometer is established to calculate the prior estimation information of the spin signal and the magnetic field vector. The mean square error of the prior estimation of the spin signal and the magnetic field vector is calculated. In this embodiment, the discretization method commonly used in engineering is used to establish the extended Kalman filter time update portion. The prior estimation equation is as follows:

[0079]

[0080] in, is the prior estimated state quantity at time k, and its specific form is: ; is the posterior estimated state quantity at time k-1, and its specific form is: ; is the state transfer matrix at time k-1, and its specific form is: ; is the prior estimated covariance matrix at time k; is the posterior estimated covariance matrix at time k-1; is the state transfer partial derivative matrix at time k-1, and its specific form is: ;

[0081] ; is the process noise covariance matrix at time k-1.

[0082] Step 6.2 establishes the extended Kalman filter measurement update portion of the atomic magnetometer, calculates the Kalman gain, and calculates the a posteriori estimates of the spin signal and magnetic field vector. Calculate the mean square error of the a posteriori estimates of the spin signal and magnetic field vector. The extended Kalman filter measurement update portion is as follows:

[0083]

[0084] in, is the Kalman gain matrix at time k; is the covariance matrix of the observation noise at time k; is the observation matrix, which is expressed in the extended Kalman filter as: Since there are three-axis xyz detection light signals, and in this embodiment, the measurement matrix and the state quantity are in a linear relationship, the measurement matrix is ​​expressed as . is the true value of observation at the kth moment; is the Kalman filter observation value at the kth moment.

[0085] Apply the above embodiment to simulate, through Figure 3-Figure 5It can be seen that by applying the embodiment of the present invention to estimate the vector magnetic field, the three parameters ω0, θ, and ψ of the magnetic field will gradually approach the true value and fluctuate over time, thereby proving that the embodiment of the present invention can accurately estimate the change of the vector magnetic field.

[0086] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions, and variations of these embodiments, including components, without departing from the principles and spirit of the present invention are still within the scope of protection of the present invention.

Claims

1. A vector magnetic field measurement method based on extended Kalman filtering, characterized in that: The steps include: Step 1: Determine the vector direction under the magnetic field, then establish a vector magnetic field in any direction through the rotation matrix, establish the xyz coordinate axis, and then obtain the angular momentum of the xyz coordinate axis; Step 2: determining a spin evolution model using the Bloch equation for atoms under a magnetic field based on the determined vector direction, and estimating parameter information of the vector magnetic field using the spin evolution model, wherein the parameter information includes the direction and magnitude of the vector magnetic field; Step 3: Establish an evolution model of the vector magnetic field to be estimated according to the change of the magnetic field over time; Step 4: establishing a nonlinear system evolution model based on the spin evolution model obtained in step 2 and the evolution model of the vector magnetic field to be estimated obtained in step 3; Step 5: Obtain a three-axis orthogonal detection light polarization rotation angle model based on the established nonlinear system evolution model, obtain the angular momentum vector on the xyz coordinate axis by rotating the detection light polarization angle, and then obtain the detection light signal on the three axes xyz on the coordinate axis through the three-axis orthogonal detection light polarization rotation angle model; Step 6: Use the xyz three-axis detection light signals as input to estimate the vector magnetic field through the extended Kalman filter.

2. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 1, wherein: In step 1, the expression of the rotation matrix is ​​as follows: ； Among them, θ and ψ represent the direction angles in the rotation matrix.

3. The vector magnetic field measurement method based on extended Kalman filtering according to claim 1, characterized in that: In step 1, the method for establishing the coordinate axis is: The three-axis vertical detection direction of the atomic magnetometer is used as the xyz axis, and the initial magnetic field is assumed to be in the z direction. Then the magnetic field is rotated clockwise by an angle of θ around the x-axis, and then by an angle of ψ around the z-axis. The new coordinate axis is established with the rotated magnetic field, and the magnetic field direction is the z' axis.

4. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 2, wherein: The spin evolution model is expressed as follows: ； ； Wherein, T2 represents the transverse relaxation time, T1 represents the longitudinal relaxation time, ω0 represents the Larmor frequency, and its relationship with the magnetic field is ω0 = γB, and J represents the angular momentum vector on the xyz coordinate axis. refers to the rate of change of J over time, Refers to the thermal noise of the atomic angular momentum in the xyz direction.

5. The vector magnetic field measurement method based on extended Kalman filtering according to claim 1, characterized in that: The evolution model of the vector magnetic field to be estimated is expressed as follows: ； in, It means that the magnitude of the magnetic field does not change with time. Indicates that the direction of the magnetic field does not change with time.

6. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 4, wherein: The nonlinear system evolution model is expressed as follows: ； θ is the angle at which the z-axis magnetic field first rotates clockwise around the x-axis, and ψ is the angle at which the magnetic field then rotates clockwise around the z-axis.

7. The vector magnetic field measurement method based on extended Kalman filtering according to claim 6, characterized in that: The three-axis orthogonal detection light polarization rotation angle model is expressed as follows: ； Where I(t) is the detection light signal of the xyz three axes, is the coupling coefficient between light and atomic spin, and R0 is the observation noise variance.

8. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 7, wherein: The step 6 includes the following sub-steps: Step 6.1: Establish the time update part of the extended Kalman filter in the atomic magnetometer, calculate the prior estimation information of the spin signal and the vector magnetic field; calculate the mean square error of the prior estimation of the spin signal and the vector magnetic field; Step 6.2 establishes the extended Kalman filter measurement update part in the atomic magnetometer, calculates the Kalman gain, calculates the a posteriori estimation information of the spin signal and the vector magnetic field; calculates the mean square error of the a posteriori estimation of the spin signal and the vector magnetic field.

9. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 8, wherein: In step 6.1, the extended Kalman filter time update part is expressed as follows: ； in, is the prior estimated state quantity at time k; is the posterior estimated state quantity at time k-1; is the state transfer matrix at time k-1; is the prior estimated covariance matrix at time k; is the posterior estimated covariance matrix at time k-1; is the state transfer partial derivative matrix at time k-1; is the covariance matrix of the state noise at time k-1.

10. The vector magnetic field measurement method based on extended Kalman filtering according to claim 9, characterized in that: In step 6.2, the extended Kalman filter measurement update part is expressed as follows: ； in, is the Kalman gain at time k; is the covariance matrix of the observation noise at time k; is the observation matrix; is the true value of observation at the kth moment; is the observed value predicted at the kth moment.

11. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 10, wherein: The a priori estimated state quantity at time k and the a posteriori estimated state quantity at time k-1 are expressed as follows: ， 。 12. The method for measuring a vector magnetic field based on an extended Kalman filter according to claim 11, wherein: The state transfer partial derivative matrix at time k-1 is expressed as follows: ； in, is the one-step transfer matrix at time k-1, is the rotation matrix at time k-1, is the angular momentum vector at time k-1, dt is the time difference from time k-1 to time k, are matrix pair parameters Find the derivative.

13. The method for measuring vector magnetic field based on extended Kalman filtering according to claim 10, characterized in that: The observation matrix is ​​expressed as follows: ； in, is the coupling coefficient between light and spin.

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