A method for in-situ calibration and error decoupling of gradient coils in a SERF inertial measurement device based on tensor eigenvalue decomposition

Abstract

The application discloses a method for in-situ calibration and error decoupling of a gradient coil in a spin-exchange relaxation free (SERF) inertial measurement device based on tensor eigenvalue decomposition. In view of the systematic deviation problem caused by the strong coupling between mechanical alignment error and coil constant in the in-situ calibration process of the gradient compensation coil in the SERF inertial measurement device, the method first acquires a measured magnetic field gradient tensor containing mechanical alignment error and measurement noise; the measured tensor is preprocessed by using the symmetry and trace characteristics of Maxwell equations to effectively suppress the antisymmetric noise and common mode drift; the tensor eigenvalue decomposition theory is introduced, and the invariance of eigenvalues under orthogonal transformation is used to eliminate the cosine projection attenuation in principle, thereby realizing the effective decoupling of the coil constant and the installation error; an automatic matching criterion based on the projection of the eigenvector space is constructed to realize the accurate mapping of the eigenvalue and the physical coil constant, and the in-situ installation error angle is inversely quantitatively calculated by the analytical corrected eigenvector matrix. The method can effectively eliminate the cross talk between the gradient coil axes and realize the high-precision in-situ calibration of the constant, and can be used for improving the precise construction and active compensation accuracy of the extremely weak magnetic environment in the SERF inertial measurement device.

Description

Technical Field

[0001] This invention relates to the field of quantum precision measurement and inertial navigation technology, specifically to a method for in-situ calibration and error decoupling of gradient compensation coils in a SERF inertial measurement device based on magnetic field gradient tensor eigenvalue decomposition. Background Technology

[0002] Inertial measurement units based on the SERF mechanism exhibit extremely high sensitivity in fields such as quantum precision measurement. To maintain the SERF state, the atomic gas cell must be placed in an extremely low and highly uniform magnetic field environment. Tiny residual magnetic field gradients in space can lead to a shortening of the atomic spin transverse relaxation time and a severe broadening of the magnetic resonance linewidth, significantly reducing the system's sensitivity. Therefore, actively compensating by generating a high-precision reverse gradient field using triaxial gradient compensation coils is essential, and accurately obtaining the gradient coil constants is a prerequisite for achieving high-precision compensation.

[0003] Traditional gradient coil calibration methods typically employ uniaxial measurement and fitting. However, during in-situ installation, factors such as assembly tolerances, frame deformation, and probe positioning deviations inevitably lead to three-dimensional mechanical alignment errors between the coil's physical principal axis and the sensitive axis of the measuring probe. This geometric alignment error causes leakage of principal axis gradient energy to off-diagonal crosstalk components, resulting in cosine projection attenuation. Traditional methods directly read the principal diagonal elements as coil constants, ignoring the deep coupling between mechanical errors and coil constants, leading to severe systematic biases in the calibration results. Directly using this bias constant to calculate the compensation current will cause "overcompensation" or "undercompensation," resulting in a surge in residual gradient. Summary of the Invention

[0004] The technical problem solved by this invention is to address the deep coupling between mechanical alignment errors and coil constants during in-situ installation of gradient compensation coils in SERF inertial measurement units, leading to spindle gradient energy leakage, severe inter-axis crosstalk, and failure of traditional single-axis calibration. This invention provides a tensor eigenvalue decomposition-based in-situ gradient coil calibration and error decoupling method that can completely eliminate inter-axis crosstalk and achieve precise decoupling of constants and attitude. This method can overcome interference from complex mechanical installation deflection while achieving high-precision in-situ acquisition of gradient coil constants, effectively suppressing residual magnetic field gradients and maintaining the SERF state of atoms.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for in-situ calibration and error decoupling of gradient coils in a SERF inertial measurement device based on tensor eigenvalue decomposition, characterized by comprising the following steps:

[0007] Step S1: Obtain the measured magnetic field gradient tensor. In the in-situ environment, apply an excitation signal to the triaxial gradient compensation coil to be calibrated. Use a magnetic field measuring device to perform spatial scanning measurements in the target area to obtain the measured magnetic field gradient tensor matrix, which includes mechanical alignment errors and measurement noise. .

[0008] Step S2: Tensor preprocessing based on physical constraints. Utilizing the irrotational and passive physical constraints of Maxwell's equations, the measured magnetic field gradient tensor is preprocessed. Symmetry and zero-tracking are performed to filter out antisymmetric noise and common-mode drift, resulting in a preprocessed tensor matrix. .

[0009] The symmetrization and zero-trace operations are as follows:

[0010]

[0011]

[0012] in, For the measured magnetic field gradient tensor, Let be the transpose of the measured magnetic field gradient tensor. It is a symmetric tensor. To preprocess tensors, For the trace operator of a matrix, It is a 3×3 identity matrix.

[0013] Step S3: Tensor eigenvalue decomposition and error decoupling. This involves processing the preprocessed tensor matrix... Perform eigenvalue decomposition to obtain three eigenvalues. and the corresponding feature vectors By utilizing the property that the eigenvalues ​​of a real symmetric matrix remain unchanged under orthogonal similarity transformation, the cosine projection attenuation caused by mechanical installation errors is eliminated, thus achieving decoupling between the coil constant and the installation posture.

[0014] Step S4: Automatic matching based on feature vector space projection. Define the three orthonormal bases of the in-situ coordinate system as follows: Calculate the absolute value of the projection of each eigenvector onto the standard orthogonal basis. The eigenvalue corresponding to the eigenvector with the largest absolute projection value onto a given standard orthogonal basis is mapped to the true gradient coil constant of the physical principal axis of that basis. .

[0015] The specific matching criteria are as follows:

[0016]

[0017] in, , For the target physical axis The corresponding true gradient coil constant, For the matched feature values, The first in the set of feature vectors 1 eigenvector The standard orthogonal basis corresponding to the target physical axis.

[0018] Step S5: In-situ installation error angle inversion. Based on the matching results of step S4, the feature vectors are rearranged according to the physical axis order to form a feature vector matrix. Furthermore, a sign correction function is introduced to eliminate mathematical ambiguity; the corrected eigenvector matrix is... Equivalent to a three-dimensional rotation matrix The in-situ installation error angle of the gradient coil is analyzed using inverse trigonometric functions, providing quantitative guidance for the mechanical leveling of the system.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. Strong robustness: This invention innovatively introduces physical constraints of symmetry and zero-trace characteristics, which effectively suppresses antisymmetric noise and common-mode drift in low signal-to-noise ratio environments.

[0021] 2. Effective decoupling: This invention cleverly utilizes the invariance of tensor eigenvalues ​​under orthogonal transformation, thereby eliminating the cosine projection attenuation of traditional methods in principle. The calibration results are no longer limited by the spatial installation orientation of the coil.

[0022] 3. Automatic matching: The spatial projection matching criterion proposed in this invention can achieve fully automatic and robust mapping of feature values ​​to physical axes without any prior knowledge about gradient magnitude.

[0023] 4. Provides quantitative guidance: This invention can accurately invert the in-situ installation error angle, providing a quantitative basis for the mechanical closed-loop leveling of quantum precision measurement devices. Attached Figure Description

[0024] Figure 1 This is a flowchart of a gradient coil in-situ calibration and error decoupling method in a SERF inertial measurement device based on tensor eigenvalue decomposition according to the present invention.

[0025] Figure 2 This is a schematic diagram illustrating the in-situ calibration environment and error mechanism of a triaxial gradient coil in an embodiment of the gradient coil in-situ calibration and error decoupling method in a SERF inertial measurement device based on tensor eigenvalue decomposition according to the present invention.

[0026] Figure 3This is a comparison curve of calibration error between the present invention's SERF inertial measurement device based on tensor eigenvalue decomposition and the traditional method under different installation angles. Detailed Implementation

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0028] Example:

[0029] like Figure 1 The diagram shows a flowchart of a gradient coil in-situ calibration and error decoupling method in a SERF inertial measurement device based on tensor eigenvalue decomposition, according to the present invention. Figure 2 As shown, during the actual in-situ calibration of the SERF inertial measurement unit, due to factors such as coil frame assembly tolerances, deformation, and probe positioning deviations, a three-dimensional mechanical alignment error inevitably exists between the intrinsic coordinate system of the coil and the in-situ measurement coordinate system. Mathematically, this error is equivalent to a coefficient of performance determined by Euler angles. Parametric 3D rotation matrix .

[0030] To eliminate the above-mentioned errors, the specific steps of this embodiment are as follows:

[0031] Step S1: Obtain the measured magnetic field gradient tensor. For example... Figure 1 As shown, in an in-situ environment, an excitation signal is applied to the triaxial gradient compensation coil to be calibrated, and a magnetic field measuring device is used to perform spatial scanning measurements in the target area. The measured magnetic field gradient tensor matrix, including mechanical alignment errors and measurement noise, is obtained through least-squares linear fitting. Its mathematical model satisfies:

[0032]

[0033] in, It is a three-dimensional rotation matrix. For an ideal intrinsic magnetic field gradient tensor, This is the combined noise matrix.

[0034] Step S2: Tensor preprocessing based on physical constraints. According to Maxwell's curl and divergence theorems, the magnetic field in the source-free region satisfies irrotation and source-free properties. Based on this, tensor preprocessing is performed... Perform filter preprocessing:

[0035] First, a forced symmetry operation is performed to eliminate the antisymmetric noise component introduced by the positioning deviation, resulting in a symmetric tensor. :

[0036]

[0037] Then, a zero-trace operation is performed to subtract the mean trace deviation on the main diagonal, suppressing common-mode diagonal noise caused by environmental drift, resulting in a preprocessed tensor.

[0038]

[0039] in, For the measured magnetic field gradient tensor, Let be the transpose of the measured magnetic field gradient tensor. It is a symmetric tensor. To preprocess tensors, For the trace operator of a matrix, It is a 3×3 identity matrix.

[0040] Step S3: Tensor eigendecomposition and error decoupling. For example... Figure 1 As shown, for the preprocessed tensor Perform eigenvalue decomposition:

[0041]

[0042] Three eigenvalues ​​were obtained With the corresponding feature vector Since the eigenvalues ​​of a real symmetric matrix remain unchanged under orthogonal similarity transformations, the three eigenvalues ​​obtained by solving are numerically exactly equal to the intrinsic gradient constant of the coil. This fundamentally eliminates the need for rotation matrices. The resulting cosine projection attenuation achieves decoupling between the constant and the attitude.

[0043] Step S4: Automatic matching based on feature vector space projection. For example... Figure 1 As shown, the three orthogonal bases of the in-situ coordinate system are defined as follows: For any target physical axis Calculate the absolute value of the projection of each eigenvector onto the corresponding orthogonal basis, and uniquely determine the eigenvalue corresponding to the eigenvector with the largest absolute projection value as the true gradient coil constant of the physical axis of the target:

[0044]

[0045] in, For the target physical axis The corresponding true gradient coil constant, For the matched feature values, The first in the set of feature vectors 1 eigenvector The standard orthogonal basis corresponding to the target physical axis.

[0046] Step S5: Inversion of in-situ installation error angle. For example... Figure 1 As shown, the feature vectors matched in step S4 are processed according to... The physical axes are rearranged to form an eigenvector matrix. Introducing a sign correction function Ensure that the elements on the main diagonal are positive to obtain the correction matrix. .Will Equivalent to a three-dimensional rotation matrix The in-situ installation deflection angle is determined analytically using the four-quadrant arctangent function.

[0047]

[0048]

[0049]

[0050] in, These are the Euler angles corresponding to the in-situ installation error angles. The third in the three-dimensional spatial rotation matrix Line number Column elements, This is the arctangent function in the four quadrants. The calculated Euler angles can be fed back to the mechanical adjustment mechanism to guide the physical closed-loop leveling of the coil frame.

[0051] Effect verification:

[0052] like Figure 3 The figure shows a comparison curve of calibration errors between a traditional method and an embodiment of the gradient coil in-situ calibration and error decoupling method in a SERF inertial measurement device based on tensor eigenvalue decomposition according to the present invention, under different installation angles. Figure 3 It is known that the error of traditional measurement fitting calibration methods increases monotonically with the increase of the deflection angle, resulting in severe cosine projection attenuation. However, using the method of this invention, the error curve remains flat throughout the entire scanning range and stabilizes at an extremely low level. This proves that the present invention successfully achieves complete elimination of geometric system errors and significantly improves the calibration accuracy of the gradient coil constant.

[0053] In summary, this embodiment ultimately provides a method for in-situ calibration and error decoupling of gradient compensation coils for SERF inertial measurement units. The calibration method proposed in this invention effectively resolves the contradiction between mechanical alignment errors and the deep coupling of coil constants in the in-situ calibration of SERF devices, completely eliminating inter-axis crosstalk of the gradient coils, and providing a reliable solution for the precise construction and active compensation of extremely weak magnetic environments for high-precision atomic sensors.

[0054] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A method for in-situ calibration and error decoupling of gradient coils in a SERF inertial measurement device based on tensor eigenvalue decomposition, characterized in that, Includes the following steps: Step S1: Apply an excitation signal to the gradient compensation coil to be calibrated, and use a magnetic field measuring device to perform spatial scanning measurement to obtain the measured magnetic field gradient tensor of the gradient compensation coil to be calibrated in the in-situ environment of the SERF inertial measurement device. Step S2: Based on the physical constraints of Maxwell's equations, the measured magnetic field gradient tensor is preprocessed to obtain a preprocessed tensor. Step S3: Perform eigenvalue decomposition on the preprocessed tensor to obtain a set of eigenvalues ​​and a set of corresponding eigenvectors. Use the set of eigenvalues ​​to eliminate the cosine projection attenuation caused by mechanical installation errors, thereby decoupling the coil constant from the installation posture. Step S4: Construct a matching criterion based on feature vector space projection, and map the feature values ​​in the feature value set to the real gradient coil constants of the corresponding physical principal axes; Step S5: Based on the feature vector set and the matching criterion, perform in-situ installation error angle inversion to parse out the in-situ installation error angle of the gradient coil.

2. The method according to claim 1, characterized in that, In step S2, based on the physical constraints of Maxwell's equations, the measured magnetic field gradient tensor is preprocessed to obtain a preprocessed tensor, specifically including: The measured magnetic field gradient tensor is symmetricized using irrotational constraints to eliminate the antisymmetric noise component introduced by the positioning deviation, thus obtaining a symmetric tensor. The symmetric tensor is zero-traced using passive constraints to subtract the mean trace deviation on the main diagonal and suppress common-mode diagonal noise, thus obtaining the preprocessed tensor.

3. The method according to claim 2, characterized in that, The mathematical expressions for the symmetry and zero-tracking operations are as follows: in, For the measured magnetic field gradient tensor, Let be the transpose of the measured magnetic field gradient tensor. It is a symmetric tensor. To preprocess tensors, For the trace operator of a matrix, It is a 3×3 identity matrix.

4. The method according to claim 1, characterized in that, In step S4, a matching criterion based on feature vector space projection is constructed, mapping the feature values ​​in the feature value set to the true gradient coil constants corresponding to the physical principal axes. Specifically, this includes: Define the three orthonormal bases of the in-situ coordinate system as follows: ; For any target physical axis Calculate the absolute value of the projection of each eigenvector onto the corresponding orthogonal basis; The eigenvalue corresponding to the eigenvector with the largest absolute value of the projection is uniquely determined as the true gradient coil constant of the physical axis of the target.

5. The method according to claim 4, characterized in that, The formula for determining the true gradient coil constant is: in, For the target physical axis The corresponding true gradient coil constant, For the matched feature values, The first in the set of feature vectors 1 eigenvector The standard orthogonal basis corresponding to the target physical axis.

6. The method according to claim 1, characterized in that, In step S5, based on the feature vector set and the matching criterion, the in-situ installation error angle is inverted to parse the in-situ installation error angle of the gradient coil, specifically including: According to the matching criteria, the feature vectors in the feature vector set are rearranged in physical axis order to form a feature vector matrix; A sign correction function is introduced to correct the eigenvector matrix so that the elements on the main diagonal of the corrected matrix are positive. The corrected matrix is ​​equivalent to a three-dimensional spatial rotation matrix, and the in-situ installation error angle of the gradient coil is obtained by analyzing the inverse trigonometric function.

7. The method according to claim 6, characterized in that, The analytical formula for the in-situ installation error angle includes: in, These are the Euler angles corresponding to the in-situ installation error angles. The third in the three-dimensional spatial rotation matrix Line number Column elements, It is the arctangent function in the four quadrants.

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