Attitude error magnetic compensation method based on vector T-L model

Abstract

The invention discloses an attitude error magnetic compensation method based on a vector T-L model, and the method comprises the steps: firstly carrying a three-component magnetometer and an optical pump magnetometer for navigation, and collecting two kinds of magnetometer data and attitude sensor data; secondly, obtaining an improved vector T-L model according to a traditional T-L model; then, independent correction terms and cross terms of attitude angles in attitude sensor data are introduced into the vector T-L model, and an attitude error compensation model is established; and finally, according to the attitude error compensation model, calculating a compensation coefficient matrix, calculating total interference by using the compensation coefficient matrix, and compensating the data of the optical pump magnetometer. According to the method, the direction characteristics of magnetic field interference are accurately described, the attitude related errors of the three-component magnetic sensor are effectively eliminated, and the precision of attitude error compensation and the adaptability of the model are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of geomagnetic interference compensation, and particularly relates to an attitude error magnetic compensation method based on a vector T-L model. Background Technique

[0002] Magnetic compensation technology is a method based on correcting and optimizing magnetic field measurement data, and is widely applied in fields such as navigation, geomagnetic exploration, aerospace, and marine exploration. In a complex environment, magnetic field measurement is easily affected by geomagnetic anomalies, local magnetic objects, or other interference sources, resulting in a decrease in measurement accuracy. Magnetic compensation technology can significantly improve the accuracy of magnetic field measurement by correcting sensor errors and eliminating environmental interference.

[0003] In the field of geomagnetic measurement, the Tolles-Lawson (T-L) model is a classical magnetic measurement interference compensation method. This model effectively compensates for the magnetic field interference generated by the carrier itself by modeling hard magnetic interference, soft magnetic interference, and eddy current interference. However, with the complication of application scenarios and the improvement of accuracy requirements, the limitations of the T-L model in attitude error compensation are gradually emerging, and it is difficult to meet the requirements of high-precision magnetic measurement. On the other hand, the T-L model outputs a scalar error, that is, the total error of the magnetic field intensity, and it is impossible to distinguish the components of the magnetic field interference in the x, y, and z directions. This scalar form is difficult to accurately describe the direction characteristics of the interference. Especially when the attitude of the carrier changes, the direction dependence of the interference cannot be accurately modeled. Summary of the Invention

[0004] In order to overcome the limitations of the traditional T-L model, the present invention proposes an attitude error magnetic compensation method based on a vector T-L model. This method effectively reduces the attitude error of the three-component magnetometer by representing the error in vector form and combining attitude angle information, and significantly improves the accuracy and robustness of interference compensation.

[0005] It mainly includes the following steps:

[0006] s1: The carrier is equipped with a three-component magnetometer and an optically pumped magnetometer to sail, and data of the two magnetometers and attitude sensor data are collected.

[0007] s2: Improve the traditional T-L model to a vector T-L model.

[0008] s3: Introduce independent correction terms and cross terms of attitude angles into the vector T-L model. Among them, the three attitude angles respectively represent the yaw angle, pitch angle, and roll angle of the carrier attitude. An attitude error compensation model is established according to the three attitude angles:

[0009]

[0010] Where Represents the independent correction term of the attitude angle, Represents the cross term of the attitude angle and the magnetic field component.

[0011] S4: Introduce the data of the three-component magnetometer and the optically pumped magnetometer, as well as the three attitude angle data, into the attitude error compensation model, calculate the compensation coefficient matrix, and use the compensation coefficient matrix to calculate the total interference and compensate the optically pumped magnetometer data.

[0012] Further, step S1 is specifically as follows: The navigation refers to the vehicle traveling underwater at a certain distance from the shore along a specified route for a fixed time, and during the navigation process, repeated maneuvers such as vehicle sinking, pitching, and rolling are performed; the navigation data includes the measurement values of the optically pumped magnetometer and the three-component magnetometer, and the attitude sensor data.

[0013] Further, step S2 is specifically as follows: The traditional T-L model decomposes the magnetic field noise H generated by the carrier I into three parts: the permanent magnetic field H generated by the ferromagnetic material of the carrier itself per , the induced magnetic field H generated by the magnetization of the soft iron material of the carrier itself ind , and the eddy current magnetic field H generated by the carrier moving in the magnetic field and cutting the magnetic induction line eddy , and the formula is expressed as:

[0014] H I =H per +H ind +H eddy

[0015]

[0016] Among them, p i , a ij , b ij are the compensation coefficients of the T-L model, c i , c j are the cosine values of the angles between the vehicle coordinate system and the geomagnetic coordinate system, c'i is the derivative of c i , and the cosine coefficients c i , c j are expressed as:

[0017]

[0018] Among them, h1, h2, and h3 are the magnetic field components in three directions obtained from the three-component magnetometer and are measured by the three-component magnetometer.

[0019] The measurement value H of the optically pumped magnetometer total is the superposition of the interference magnetic field H I and the geomagnetic field H f :

[0020] Htotal = H f + H I

[0021] Improve the T-L model, decompose the magnetic field noise H I into components in three directions, and represent the error in vector form. The expression is:

[0022]

[0023] where p ix , a ijx , b ijx , p iy , a ijy , b ijy , p iz , a ijz , b ijz represent the compensation coefficients of the model in the x, y, and z directions respectively.

[0024] Furthermore, step s3 is specifically: introduce independent correction terms and cross terms of the attitude angle in the vector T-L model. The three attitude angles are defined as α, β, and γ, which represent the yaw angle, pitch angle, and roll angle of the carrier attitude respectively. Establish an attitude error compensation model based on the three attitude angles:

[0025]

[0026] where d kx , d ky , d kz are the independent correction coefficients of the attitude angle, e ikx , e iky , e ikz are the cross-term coefficients of the attitude angle and the magnetic field components, h i is the measured value of the three-component magnetometer, and f k (α, β, γ) is the correlation function of the attitude angle:

[0027] f1 = sinα, f2 = cosα, f3 = sinβ, f4 = cosβ, f5 = sinγ, f6 = sinγ

[0028] Furthermore, step s4 is specifically: introduce the two magnetometer data H total and h1, h2, h3 as well as the three attitude angles α, β, γ into the attitude error compensation model obtained in s3, perform zero-phase filtering on the initial geomagnetic field H total . Since the attitude error compensation model is in matrix form and its modulus is represented by the Frobenius norm, the LM nonlinear fitting algorithm is used to calculate the compensation coefficient matrix, and the total interference is calculated using the compensation coefficient matrix and the optically pumped magnetometer data is compensated.

[0029] Compared with the prior art, the present invention proposes an attitude error magnetic compensation method based on a vector T-L model, which innovates the scalar error analysis method of the traditional T-L model. By improving the T-L model, introducing an independent correction term for the attitude angle and its cross term with the magnetic field components, and adopting a vector error analysis method, this method accurately describes the directional characteristics of magnetic field interference, effectively eliminates the attitude-related errors of the three-component magnetic sensor, and significantly improves the accuracy of attitude error compensation and the adaptability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be further described below in conjunction with the drawings and embodiments. In the drawings:

[0031] Figure 1 is a flowchart of an attitude error magnetic compensation method based on a vector T-L model according to an embodiment of the present invention;

[0032] Figure 2 is a diagram of the relationship between the vehicle coordinate system and the geomagnetic field according to an embodiment of the present invention;

[0033] Figure 3 is a diagram of the three-dimensional space definition of the attitude angle according to an embodiment of the present invention;

[0034] Figure 4 is a schematic diagram of the compensation effect of the attitude error compensation model according to an embodiment of the present invention (route L1);

[0035] Figure 5 is a schematic diagram of the compensation effect of the attitude error compensation model according to an embodiment of the present invention (route L2). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] In order to have a clearer understanding of the technical features, objectives, and effects of the present invention, the specific embodiments of the present invention will now be described in detail with reference to the drawings.

[0037] An embodiment of the present invention provides an attitude error magnetic compensation method based on a vector T-L model.

[0038] Please refer to Figure 1 , Figure 1 which is a flowchart of an attitude error magnetic compensation method based on a vector T-L model according to an embodiment of the present invention, and specifically includes the following steps:

[0039] First, the vehicle sails with a three-component magnetometer and an optically pumped magnetometer, and collects data from the two magnetometers and the attitude sensor data.

[0040] This navigation experiment means that the ship sails on the sea surface 600 m and 800 m away from the shore along the specified route for a fixed time. During the navigation process, the carrier repeats maneuvering actions such as sinking, pitching, and rolling; the navigation data includes the measured values of the optically pumped magnetometer and the three-component magnetometer, and the attitude sensor data.

[0041] In the second step, the traditional T-L model is improved to a vector T-L model to further utilize the directional characteristics of magnetic field interference.

[0042] The T-L model decomposes the magnetic field noise generated by the carriers into three parts: the permanent magnetic field H per generated by the ferromagnetic material of the carriers themselves, the induced magnetic field h ind magnetized by the soft iron material of the carriers themselves, and the eddy current magnetic field H eddy generated by the carriers moving in the magnetic field and cutting the magnetic induction lines. The interference field H I is the linear superposition of the permanent field H per , the induced field h ind , and the eddy current field H eddy . The T-L magnetic compensation model is

[0043] H I =H per +H ind +H eddy

[0044] Among them, H I is the total noise analyzed by the T-L model. The three parts of the magnetic field noise can be related to the direction cosines between the three axes of the carrier coordinate system and the geomagnetic field, reflecting the attitude information of the carrier. Please refer to Figure 2 , Figure 2 which is the relationship diagram between the carrier coordinate system and the geomagnetic field in the embodiment of the present invention. The origin O of the carrier coordinate system is the position of the optically pumped magnetometer and the three-axis fluxgate magnetometer. The O-XY plane is parallel to the horizontal plane of the carrier, and H E represents the geomagnetic field vector, and N points to the geomagnetic north pole. There is a linear relationship between the three kinds of noise and the cosine coefficient matrix:

[0045]

[0046] Among them, the cosine coefficients c i , c j represent the cosine coefficients of the angles between the X, Y, and Z axes and H E , c′ i represents the derivative of the cosine coefficient c i , and p i , a ij , b ij represent the T-L model compensation coefficients. The expressions of the cosine coefficients c i , c j are:

[0047]

[0048] Among them, h1, h2, and h3 are the magnetic field components in three directions obtained by a three-component magnetometer. The total magnetic field value H measured by an optically pumped magnetometer total is the interference magnetic field H I superimposed with the geomagnetic field H f :

[0049] H total =H f +H I

[0050] Improve the T-L model, decompose the magnetic field noise H I into components in three directions, and represent the error in vector form. Its expression is:

[0051]

[0052] Among them, A is the cosine coefficient matrix, coef is the interference compensation coefficient matrix p ix , a ijx , b ijx , pi , x, α ijx , b ijx , p ix , a ijx , b ijx are the compensation coefficients of the model in the three directions of x, y, and z. Thus, the improved T-L model is realized.

[0053] In the third step, introduce the independent correction coefficient and cross-term coefficient of the attitude angle into the vector error model (vector T-L model) to dynamically correct the vector components of the magnetic field interference and establish an attitude error compensation model.

[0054] Introduce the independent correction term and cross-term of the attitude angle into the vector error model. Among them, the three attitude angles are defined as the yaw angle α, the pitch angle β, and the roll angle γ. Please refer to Figure 3 , Figure 3 , which is the three-dimensional space definition diagram of the attitude angle in the embodiment of the present invention. The three attitude angles defined by it respectively represent the rotation angles of the carrier around the coordinate axes Z, X, and Y, and the illustrated coordinate axis rotation direction is the positive direction. The two errors caused by the attitude change are the independent correction error H d and the cross error H e . The independent correction error represents the direct influence of the carrier attitude angle on the fixed magnetic interference, and the cross error between the attitude angle and the magnetic field component represents the coupling effect between the attitude angle and the magnetic field component. Their expressions are:

[0055]

[0056] where d kx , d ky , d kz are the independent correction coefficients of the attitude angles, e ikx , e iky , e ikz are the cross-term coefficients of the attitude angles and the magnetic field components, h i is the measured value of the three-component magnetometer, f k (α, β, γ) is the correlation function of the attitude angles:

[0057] f1 = sinα, f2 = cosα, f3 = sinβ, f4 = cosγ, f5 = sinγ, f6 = cosγ

[0058] According to the vector T-L model in the second step, the two errors are decomposed into components in three directions. According to the three attitude angles, the total interference is:

[0059]

[0060] where A t is the attitude cosine coefficient matrix, coef t is the attitude error model compensation coefficient matrix. Thus, the attitude error compensation model is realized.

[0061] In the fourth step, the data of the three-component magnetometer and the optically pumped magnetometer, as well as the data of the three attitude angles, are introduced into the attitude error compensation model to calculate the compensation coefficient matrix. The total interference is calculated using the compensation coefficient matrix, and the data of the optically pumped magnetometer are compensated. Thus, the standard deviations of the data of the optically pumped magnetometer before and after compensation are obtained and the improvement ratio is compared;

[0062] As can be seen from the second and third steps, the total magnetic field H total is composed of the geomagnetic field H f and the total interference H I added together. According to the Frobenius norm of the matrix, H total can be expressed as:

[0063]

[0064] where the geomagnetic field H f can be filtered out by a zero-phase band-pass filter:

[0065] bpf(H total ) = bpf(H f ) + bpf(H I ) = 0 + bpf(H I ) = bpf(H I )

[0066] Introduce the three-component magnetometer and optically pumped magnetometer data, as well as the three attitude angle data, into the attitude error compensation model:

[0067] bpf(H I ) = coef t ·bpf(A t )

[0068] Thus, the compensation coefficient matrix coef can be obtained by fitting according to the LM algorithm t , and its iterative formula is:

[0069] X k+1 = X k + Δ x Δ x = -(J T J + μI) -1 g k

[0070] where X k is the parameter vector of the k-th iteration, J is the Jacobian matrix, representing the partial derivative of the objective function with respect to the parameters, g k is the residual matrix of the objective function, and μ is the damping factor used to control the step size in the iterative process.

[0071] The Jacobian matrix J is:

[0072]

[0073] The residual matrix g k of the objective function is:

[0074] g k = H I - coef t ·A t

[0075] Iterate repeatedly until ‖Δ x ‖ ≤ φ, where φ is the judgment condition threshold, set to 1e-8. After the iteration is completed, calculate the total interference H I using the fitted compensation coefficient matrix:

[0076] H I = coef t ·A t

[0077] Compensate the optically pumped magnetometer data according to the total interference H I :

[0078]

[0079] The standard deviations of the magnetic data of the optically pumped magnetometer before and after compensation can be obtained and the improvement ratio can be compared. The calculation formulas for the standard deviation and the improvement ratio are as follows:

[0080]

[0081] where n represents the number of samples, and x i represents the scalar data of the optically pumped magnetometer. The improvement effect is measured by comparing the improvement ratios IR of the first compensation and the second compensation. H a and H b represent the total field values before and after compensation respectively.

[0082] The experimental data set is from the measurement results of the sensor in the first step. The collected data of the navigation routes L1 and L2 are selected as the verification data set of the attitude error compensation model. Among them, L1 represents one of the underwater vehicle navigation routes 600 meters away from the shore, and L2 represents one of the navigation routes 800 meters away from the shore. Please refer to Figure 4 and Figure 5 , Figure 4 and Figure 5 which are the schematic diagrams of the compensation effects of the attitude error compensation model in the embodiments of the present invention.

[0083] It can be seen from the compensation results of the T-L model that this model can effectively reduce the noise generated by the movement of the carrier, but there is still a certain amount of residual noise. These residual noises may be due to dynamic magnetic field interference or the influence of the sensor installation method. By introducing the attitude error compensation model, this part of the residual noise can be further compensated, significantly improving the compensation effect. From Figure 4 it can be seen that after using the attitude error compensation model, the residual noise during the movement of the carrier is significantly suppressed, further improving the accuracy of magnetic field measurement.

[0084] The results of the two experiments are shown in Table 1 below:

[0085] Table 1

[0086]

[0087] The experimental results show that, taking STD as the measurement standard, compared with the traditional T-L model, the compensation effect of this method has been improved by nearly 13.3%-30.9%. This indicates that on the basis of the T-L model compensation, the present invention effectively further reduces the noise, improves the signal-to-noise ratio of the magnetic anomaly signal, and a higher signal-to-noise ratio is also more conducive to the development of subsequent magnetic anomaly detection algorithms.

Claims

1. A magnetic compensation method for attitude error based on a vector T-L model, characterized in that, It includes the following steps: S1: The carrier is equipped with a three-component magnetometer and an optically pumped magnetometer to navigate, and data from the two magnetometers and an attitude sensor are collected; S2: According to the traditional T-L model, an improved vector T-L model is obtained; S3: An independent correction term and a cross term of the attitude angle in the attitude sensor data are introduced into the vector T-L model to establish an attitude error compensation model; S4: According to the attitude error compensation model, a compensation coefficient matrix is calculated, and the total interference is calculated using the compensation coefficient matrix to compensate the magnetometer data.

2. The attitude error magnetic compensation method based on the vector T-L model according to claim 1, wherein In step S1, the carrier repeatedly performs sinking, pitching, and rolling motions during navigation; the navigation data includes the measured values of the optically pumped magnetometer and the three-component magnetometer and the attitude sensor data.

3. The attitude error magnetic compensation method based on the vector T-L model according to claim 2, characterized in that The specific implementation process of step S2 is as follows: The traditional T-L model decomposes the magnetic field noise H generated by carriers I into three parts: the permanent magnetic field H generated by the ferromagnetic material of the carriers themselves per , the induced magnetic field H generated by the magnetization of the soft iron material of the carriers themselves ind , and the eddy current magnetic field H generated by the carriers moving in the magnetic field and cutting the magnetic induction lines eddy : Among them, p i , a ij , b ij are the compensation coefficients of the T-L model, c i , c j is the cosine value of the angle between the carrier coordinate system and the geomagnetic coordinate system, c′ i is the derivative of c i , c i , c j are the cosine coefficients; Measured value H of the optically pumped magnetometer total is the interference magnetic field H I superposed with the geomagnetic field H f Improve the T-L model, decompose the magnetic field noise H I into components in three directions, and the error is expressed in vector form. Its expression is: where p ix , a ijx , b ijx , p iy , a ijy , b ijy , p iz , a ijz , b ijz respectively represent the compensation coefficients of the model in the x, y, and z directions.

4. The attitude error magnetic compensation method based on the vector T-L model according to claim 3, characterized in that The specific implementation process of establishing the attitude error compensation model is as follows: An independent correction term and a cross term of the attitude angle are introduced into the vector T-L model, where the three attitude angles are defined as α, β, and γ, representing the yaw angle, pitch angle, and roll angle of the carrier attitude respectively, and an attitude error compensation model is established based on the three attitude angles: where d kx , d ky , d kz are independent correction coefficients of the attitude angle, e ikx , e iky , e ikz are cross-term coefficients of the attitude angle and the magnetic field components, h i is the measured value of the three-component magnetometer, f k (α, β, γ) is the correlation function of the attitude angle: f1 = sinα, f2 = cosα, f3 = sinβ, f4 = cosβ, f5 = sinγ, f6 = sinγ.

5. The attitude error magnetic compensation method based on the vector T-L model according to claim 4, wherein, The specific implementation of the step S4 is as follows: introducing the magnetometer data H total and h i as well as three attitude angles α, β, and γ into the attitude error compensation model, performing zero-phase filtering on H total The attitude error compensation model is in matrix form, and its modulus value is represented by the Frobenius norm. The LM nonlinear fitting algorithm is used to calculate the compensation coefficient matrix, and the total interference is calculated using the compensation coefficient matrix to compensate the optically pumped magnetometer data.

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