A method for constructing a high-precision aeromagnetic map based on sparse magnetic field data

Abstract

The application provides a method for constructing a high-precision aerial magnetic map based on sparse magnetic field data, and belongs to the technical field of aerial magnetic map construction. A flight route composed of multiple parallel survey lines and cutting lines intersecting the survey lines is planned and flown, survey line data and cutting line data are collected, and denoising and deduplication processing are performed; the preprocessed survey line data is first interpolated along each survey line direction to regularize the data in the survey line; then interpolation is performed between adjacent regularized survey lines to generate pseudo survey lines, and all survey line data is converted into a regular two-dimensional magnetic field matrix; a sparse constraint survey line bias inversion leveling method based on flight-magnetic map interface residual is used to level and correct the two-dimensional magnetic field matrix according to the cutting line data; and an aerial magnetic map is generated based on the leveled and corrected two-dimensional magnetic field matrix. The application can be applied to various aerial magnetic survey platforms such as vertical take-off fixed-wing unmanned aerial vehicles and rotor unmanned aerial vehicles, and has good universality.

Description

Technical Field

[0001] This invention relates to the field of aeronautical magnetic map construction technology, and specifically to a method for constructing high-precision aeronautical magnetic maps based on sparse magnetic field data. Background Technology

[0002] Airborne magnetic mapping technology, belonging to the field of airborne geophysical exploration and magnetic anomaly target detection, is a key technique for dynamically measuring the geomagnetic field along a flight path using magnetic measurement equipment mounted on airborne platforms (including vertical takeoff and landing fixed-wing UAVs and rotary-wing UAVs). This data is then processed to reconstruct the spatial distribution of the regional magnetic field. This technology has significant application value in mineral resource exploration, underground structure analysis, and unexploded ordnance detection. Its basic principle is to acquire discrete magnetic field data along a pre-set survey line, and combine this data with positioning information. Through data correction, leveling, and spatial reconstruction, the discrete measurement results are transformed into a continuous two-dimensional magnetic field distribution map, thus reflecting the spatial distribution characteristics of underground magnetic bodies.

[0003] Existing methods for constructing aerobatic magnetic maps mainly include reconstruction methods based on regular grid interpolation, surface fitting methods based on smoothing constraints, and spatial interpolation methods based on statistical models. Among these, the regular grid method performs interpolation calculations after resampling the survey line data at a uniform resolution; the minimum curvature method and spline function method generate continuous magnetic field surfaces by introducing smoothing constraints; and methods such as inverse distance weighted interpolation and Kriging interpolation estimate the magnetic field data based on spatial correlation. In addition, some studies have attempted to introduce machine learning methods to fit the magnetic field distribution to improve the modeling ability of complex regions. However, most of these methods are based on the assumption that the data distribution is relatively uniform or that the noise approximately follows a Gaussian distribution, which limits their adaptability to actual aerobatic survey data.

[0004] In actual airborne magnetic surveys, due to factors such as flight costs, operating environment, and mission constraints, magnetic field data typically exhibits sparse characteristics, including large spacing between survey lines and uneven sampling distribution. Simultaneously, influenced by instrument drift, platform attitude changes, and the external electromagnetic environment, the acquired data generally contains non-Gaussian distributed colored noise and systematic biases between survey lines. Furthermore, traditional methods often employ unidirectional leveling or local correction strategies when processing survey line and cutting line data, which are insufficient to effectively eliminate survey line banding effects and cross-errors. In the data standardization and interpolation process, there is a lack of full utilization of survey line structure information, leading to problems such as decreased reconstruction accuracy and distortion of anomalous information in sparse regions. Therefore, existing technologies struggle to simultaneously achieve magnetic map reconstruction accuracy, computational efficiency, and result stability under sparse sampling conditions. Summary of the Invention

[0005] To address the problems of low reconstruction accuracy, significant strip errors, poor noise adaptability, and insufficient utilization of survey line structure in existing airborne magnetic map construction methods under sparse sampling conditions, this invention provides a method for constructing high-precision airborne magnetic maps based on sparse magnetic field data.

[0006] The technical solution adopted in this invention is as follows: This invention proposes a method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data, comprising the following steps: S1. Plan and fly a flight path consisting of multiple parallel survey lines and at least three intersecting cutting lines, and collect magnetic field data and position data on the survey lines and cutting lines respectively to form survey line data and cutting line data. S2. Perform noise reduction and deduplication processing on the measured line data and cutting line data; S3. For the preprocessed survey line data, first interpolate along the direction of each survey line to regularize the data within the survey line; then interpolate between adjacent regularized survey lines to generate pseudo survey lines, and convert all survey line data into a regular two-dimensional magnetic field matrix. S4. The sparse constraint survey line offset inversion leveling method based on the flight-magnetic map intersection residual is used to level and correct the two-dimensional magnetic field matrix according to the cutting line data. S5. Generate an aeronautical magnetic map based on the leveled and corrected two-dimensional magnetic field matrix.

[0007] Further, in step S2, the denoising process employs an adaptive denoising method constrained by wavelet-Kalman filtering, including: S21. Perform wavelet decomposition on the original magnetic field data to obtain the detail coefficients of each layer; S22. Apply a soft thresholding function to the detail coefficients of each layer for thresholding. S23. Use the detail coefficients after thresholding to perform wavelet reconstruction and obtain candidate denoising results; S24. Establish a state-space model of the geomagnetic signal, use the candidate noise reduction results as the observations of the Kalman filter, and calculate the innovative residuals; S25. Based on the innovative residual and signal energy retention rate, construct a comprehensive evaluation function, traverse the parameter space of wavelet basis, decomposition level and threshold factor, and select the parameter combination that makes the comprehensive evaluation function optimal. S26. Perform wavelet denoising again using the optimal parameter combination to obtain the final denoising result.

[0008] Furthermore, the establishment of the state-space model for the geomagnetic signal includes: Define a system state vector, which is composed of the true value of the geomagnetic signal and the rate of change of the geomagnetic signal; Define a state equation and an observation equation. The state equation uses a state transition matrix to map the system state vector from the previous time step to the current time step, and adds process noise. The observation equation uses an observation matrix to map the system state vector to the predicted observation value, and adds measurement noise. The observation matrix is ​​used to extract the true value component of the geomagnetic signal in the system state vector, and the true observation value is taken as the candidate denoising result after wavelet denoising. Based on the state equation, the system state estimate of the previous time step is used to calculate the predicted system state value of the current time step; based on the observation equation, the predicted system state value of the current time step is used to calculate the predicted observation value of the current time step; the difference between the actual observation value of the current time step and the predicted observation value is calculated to obtain the innovation residual of the current time step.

[0009] Furthermore, the formula for calculating the signal energy retention rate is as follows: ; Where k is the sampling time and N is the total number of sampling points. The square of the magnetic field value at the k-th sampling point is the candidate denoising result. It is the square of the magnetic field value at the kth sampling point of the original magnetic field data.

[0010] Further, in step S2, the deduplication process includes: converting latitude and longitude coordinates into geocentric rectangular coordinates, calculating the spatial distance between all sampling points, and removing duplicate points whose distance is less than a first set threshold.

[0011] Furthermore, the regularization of the data within the survey line includes: automatically determining the direction of the survey line, constructing a regular coordinate sequence with uniform resolution along the main direction of the survey line, and calculating the magnetic field value at the regular coordinate point through linear interpolation.

[0012] Furthermore, the interpolation between adjacent regularized survey lines is performed as linear interpolation at a preset second resolution.

[0013] Furthermore, the sparse-constrained survey line offset inversion and leveling method based on flight-magnetic map handover residuals includes: S41. For each valid intersection point of the cutting lines, record its latitude and longitude as follows: The measured magnetic field value is The interpolated magnetic field value at this point is calculated using two-dimensional linear interpolation. The flight-magnetic map residuals of the measured magnetic field value and the interpolated magnetic field value are calculated. The flight-magnetic map residuals of all effective intersection points of the cutting lines constitute the flight-magnetic map residual vector. ,in The total number of valid intersection points of the cutting line; S42. The system bias of each measurement line in the two-dimensional magnetic field matrix is ​​used as the parameter to be inverted, and the bias of the q-th measurement line is denoted as... The offsets of all survey lines constitute the offset parameter vector. ,in This represents the total number of survey lines. S43. Establish a sparse linear mapping relationship between the flight-magnetic map residual vector and the bias parameter vector. ,in It is a sparse mapping matrix. The residual vector; S44. Introduce the continuity constraint of the survey line and construct the objective function. ,in It is a first-order difference matrix. To smooth the weight coefficients; solve for the bias parameter vector that minimizes the objective function. ; S45. Using the bias parameter vector obtained from the solution The magnetic field value of each measurement line in the two-dimensional magnetic field matrix is ​​compensated and corrected: for the p-th sampling point on the q-th measurement line, the corrected magnetic field value is... ,in The original measured magnetic field value before calibration. This is the offset corresponding to the survey line.

[0014] Furthermore, in step S42, the sparse mapping matrix The construction methods include: For each valid intersection of the cutting lines, its longitude is Calculate the distance between the longitude and the representative longitude of each survey line, where the representative longitude is the average of the longitudes of all sampling points on the survey line; Select the two survey lines with the closest longitude distance. and , representing longitude respectively and ;like The weights are calculated using the following formula: ; ; in, and These are two survey lines. and The weights; like Then let ; Find the two survey lines that are closest to the point in longitude, calculate the weights based on the longitude distance between the point and the two survey lines, and assign the weights to the corresponding row and column positions in the sparse mapping matrix.

[0015] Weight and Assigned to sparse mapping matrix The i-th row of the middle Column and number The position of the first column is set, and the positions of the remaining columns are set to 0.

[0016] Furthermore, the route is a "bow" shaped route, and the cutting line is perpendicular to the direction of the measuring line and is evenly distributed in the magnetic map area.

[0017] The beneficial effects of this invention are: This invention generates pseudo-survey lines through interpolation between survey lines and performs matrix standardization, effectively compensating for information loss caused by data sparsity, improving the spatial resolution of magnetic maps, and thus enhancing reconstruction accuracy under sparse data conditions. Simultaneously, it combines a wavelet-Kalman filter-constrained denoising method to reduce the impact of non-Gaussian noise on the magnetic map construction results, enhancing adaptability to non-Gaussian colored noise and improving data stability. Furthermore, it corrects systematic deviations in the survey line direction through sparse constraint survey line offset inversion and leveling using the flight-magnetic map handover residuals, effectively eliminating striping effects and significantly reducing striping errors and systematic biases. In addition, it converts discrete survey line data into a regular matrix form, facilitating subsequent processing and visualization, improving overall computational efficiency, and achieving regularized data representation and efficient processing. This invention can be applied to various airborne magnetic survey platforms such as vertical takeoff and landing fixed-wing UAVs and rotary-wing UAVs, demonstrating good versatility. Attached Figure Description

[0018] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the process for constructing a high-precision aerospace magnetic map based on sparse magnetic field data according to the present invention.

[0020] Figure 2 This is a schematic diagram of the "bow"-shaped magnetic map acquisition route in this invention.

[0021] Figure 3 This is a flowchart of the denoising process based on wavelet-Kalman filter constraints in this invention.

[0022] Figure 4This is the leveling method for sparse constraint survey line offset inversion based on flight-magnetic map junction residuals in this invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive activity are within the scope of protection of this application.

[0024] like Figure 1 As shown, this invention discloses a method for constructing high-precision airborne magnetic maps based on sparse magnetic field data, which mainly includes steps such as route acquisition, data preprocessing, magnetic field data matrix standardization, survey line leveling, magnetic map construction and visualization.

[0025] In this embodiment, an aerial platform (including a vertical takeoff and landing fixed-wing UAV or a rotary-wing UAV) is used to carry magnetic field measurement equipment for magnetic field data acquisition, with a sampling frequency of 10Hz. The flight path planning adopts a regular structured design, satisfying the following requirements: ① Multiple parallel measurement lines are set up, with a spacing generally between 5m and 200m, serving as the main measurement direction; ② Multiple intersecting lines are set up as cross-constraint directions; ③ The number of intersecting lines is no less than 3; ④ Each measurement line intersects with at least three intersecting lines. During flight, latitude and longitude information, altitude information, and magnetic field strength information are simultaneously collected along the above-mentioned flight path. The collected magnetic field data includes non-Gaussian distributed colored noise introduced by environmental factors, electromagnetic interference, and equipment factors.

[0026] like Figure 2 As shown, the magnetic map acquisition route is a "bow" shaped route. After the magnetic map acquisition flight is completed, a cutting line flight is carried out in the direction perpendicular to the survey line, with ≥3 cutting lines evenly distributed in the magnetic map area, and each survey line intersecting with the cutting line at ≥3 points. During actual flight, there are turning, acceleration, and unstable flight phases, requiring the extraction of effective flight segments from the raw data. First, it is necessary to identify abrupt changes in flight direction based on the characteristics of the flight path changes. The continuous trajectory can be divided into multiple sub-segments based on the location of these abrupt changes, with each segment being a survey line / cutting line. Invalid flight segments with a length less than a preset threshold are discarded. For example, continuous trajectory segments with fewer than 500 sampling points are retained, and effective survey lines and cutting line data are formed during the stable flight phase.

[0027] For the magnetic field data of the survey line and the cutting line, a denoising method based on wavelet-Kalman filtering constraint is used to remove high-frequency interfering magnetic fields and extract low-frequency geomagnetic signals, such as... Figure 3 As shown.

[0028] Suppose the original geomagnetic measurement sequence is as follows: in, These are geomagnetic measurements. This is a real geomagnetic signal. This is a noise signal. Sampling time, , This represents the total number of sampling points.

[0029] The candidate wavelet basis is selected as follows: in, The number of candidate wavelet bases, For the first Small wavelet bases.

[0030] Let the number of decomposition layers be . Discrete wavelet transform is performed on the original signal. in, Indicates the first Layer approximation coefficients (low-frequency components). Indicates the first Layer detail factor: According to wavelet theory: Among them, the approximation coefficient It mainly includes geomagnetic variation trends and detail coefficients. It mainly contains high-frequency disturbance information.

[0031] For the Layer detail factor A soft threshold function is used: in, This is the coefficient index for this layer. To extract symbols, For the first Layer threshold, the threshold is: in, As a threshold adjustment factor, The length of the original data. For the first The estimated standard deviation of layer noise is calculated as follows: Wavelet reconstruction using the detail coefficients after thresholding: in, These are the candidate denoising results.

[0032] To evaluate whether the noise reduction results retain the true characteristics of geomagnetic changes, a state-space model of the geomagnetic signal is established.

[0033] Define system state: in, This is the geomagnetic value. This represents the rate of change of the Earth's magnetic field.

[0034] Define the state equation: in, Here is the state transition matrix. The sampling period is For process noise , Let be the process noise covariance matrix.

[0035] Define the observation equation: in, , That is, the result after wavelet denoising is used as the observation value. To measure noise , To measure the noise covariance matrix.

[0036] Kalman predictions: in for Time-state vector The estimated value.

[0037] Predicted observations: Innovation residual: in, For the first Constantly innovate residuals.

[0038] Calculate the root mean square of the innovation residual: .

[0039] Considering residual constraints The smaller the better, define the energy signal: Original signal energy: Signal energy retention rate: Define fidelity metrics: Final evaluation function: in, For residual weights, To ensure accuracy and weight, .

[0040] Traversing the parameter space ,in For wavelet basis, The number of decomposition layers, This is the threshold factor.

[0041] For each set of parameters ,calculate ,choose The optimal parameter combination is obtained.

[0042] Using optimal parameters Wavelet denoising was performed again to obtain the true geomagnetic signal. The estimated value : in, This is a wavelet noise reduction operation.

[0043] After wavelet denoising of the survey line magnetic field data and the tangent line magnetic field data, to avoid the impact of overly dense sampling points on interpolation stability, deduplication based on spatial distance is performed on the trajectory points. Specifically, the latitude and longitude coordinates are first transformed to the geocentric coordinate system: in, For the Earth's radius, Latitude data For longitude data, The coordinates represent the distance to the east. The coordinates are the northward distance coordinates. The coordinates are height and distance. The spatial distance between all sampling points is calculated. If the distance between points is less than a set threshold (e.g., 0.15 m), the points are identified as duplicates and removed. This reduces redundant data while preserving the geometric characteristics of the trajectory, and improves the efficiency and stability of subsequent interpolation calculations.

[0044] To convert discrete survey line data into regular grid data, the magnetic field data needs to be matrix-normalized. The average longitude and latitude variations of the first 500 sampling points of the survey line are calculated. If the latitude variation is greater than the longitude variation, it is considered a north-south survey line; otherwise, it is considered an east-west survey line.

[0045] For each survey line, the main direction coordinate range is extracted. For example, for a north-south survey line, the sampling points with the largest and smallest latitudes are selected as the main direction coordinate range. A regular coordinate sequence is constructed according to a preset first resolution (1 / 2 or 1 / 4 of the spacing between consecutive sampling points on the survey line). Within the main direction coordinate range, several latitude and longitude points are interpolated according to the preset first resolution as regular coordinate sequences. The magnetic field values ​​at the regular coordinate points are calculated using a linear interpolation method, thus completing the regularized representation of the survey line data. Between regularized adjacent survey lines, linear interpolation is performed according to a preset second resolution (1 / 2 or 1 / 4 of the spacing between survey lines) to generate several pseudo-survey lines, thereby constructing a discrete data distribution with a preset second resolution between the survey lines, forming a two-dimensional magnetic field matrix. The corresponding latitude and longitude coordinate matrix is: in, It can be considered as a low-precision magnetic map before leveling.

[0046] If a contour magnetic map is directly constructed based on the regularized survey line magnetic field matrix, the resulting magnetic map may exhibit significant banding. This banding could be attributed to sensor measurement bias, flight attitude changes, systematic errors caused by external environmental factors, and geomagnetic variations. Therefore, continuous cut-line data is needed to eliminate this inter-line bias. Figure 4 As shown, this embodiment proposes a leveling method for sparse constraint survey line offset inversion based on flight-magnetic map intersection residuals. This method utilizes the continuous residual field formed by the intersection region of the flight trajectory and the low-precision magnetic map, establishes a linear relationship between the flight residuals and the survey line offset parameters through a sparse mapping matrix, and introduces a priori constraints for survey line smoothing to achieve survey line-level offset inversion.

[0047] Assuming a low-precision magnetic map consists of several north-south survey lines, the magnetic map grid is represented as follows: in, Indicates the sampling point number within the survey line. Indicates the survey line number. This represents the number of sampling points for a single survey line in a low-precision magnetic map. This represents the total number of low-precision magnetic survey lines. Indicates the first The first survey line The longitude of each point Indicates the first The first survey line The latitude of each point This indicates the corresponding magnetic field value.

[0048] The flight path is represented as follows: in, Indicates the sampling point number of the flight trajectory. Indicates the number of valid handover points. Indicates the longitude of the flight point. Indicates the latitude of the flight point. This indicates the magnetic field value measured during flight.

[0049] On a low-precision magnetic map, the magnetic field value at the flight trajectory point is calculated using two-dimensional linear interpolation. , This represents a two-dimensional linear interpolation operator.

[0050] Define the flight-magnetic map residual: in, Indicates the first The residuals at the junction points.

[0051] Let the residual vector be: Dimensions .

[0052] Assume that the error in the magnetic map mainly stems from the fixed biases present in each survey line. Definition Indicates the first The bias of a survey line. The parameter vector formed by the bias of the survey line is: Dimensions , This represents the total number of survey lines.

[0053] The corrected magnetogram is then represented as: in, This indicates the corrected magnetic field.

[0054] definition For the first Each survey line represents a longitude, and the represented longitude is the average of the longitudes of all sampling points on that survey line; This represents the number of valid points for the survey line.

[0055] For flight point Find the two survey lines with the shortest longitude distance. and That is, satisfying and Minimum.

[0056] set up Then the definition is: in, Indicates the measured line of the flight point Influence weight, Indicates the measured line of the flight point Influence weight, if it happens to occur In the case of... .

[0057] Then the residual: The residuals of all flight points are expressed in matrix form: in It is a sparse mapping matrix.

[0058] The elements can be described as: Therefore, each row has at most two non-zero elements.

[0059] The sparsity is approximately: When the number of survey lines is large It exhibits significant sparsity characteristics.

[0060] If solved directly Inter-line oscillations may occur, therefore a line continuity constraint is introduced.

[0061] Define a first-order difference matrix The format is: Constraints: Represented as: That is, the offset change of adjacent survey lines should be smooth and continuous.

[0062] Construct the objective function: Among them, the first item This is the transfer residual fitting term, used to ensure that the flight data and magnetic data are consistent. Figure 1 To. Item Two This is a line smoothing constraint term used to suppress high-frequency oscillations in the bias field. This represents the smoothing weighting coefficient.

[0063] make We can obtain: Calculated Then, uniform compensation was applied to each survey line: The final leveled magnetogram is obtained as follows: Based on the leveled magnetic field matrix data, the final aerospace magnetic map can be generated by using contour line filling for visualization.

[0064] The above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data, characterized in that, Includes the following steps: S1. Plan and fly a flight path consisting of multiple parallel survey lines and at least three intersecting cutting lines, and collect magnetic field data and position data on the survey lines and cutting lines respectively to form survey line data and cutting line data. S2. Perform noise reduction and deduplication processing on the measured line data and cutting line data; S3. For the preprocessed survey line data, first interpolate along the direction of each survey line to regularize the data within the survey line; then interpolate between adjacent regularized survey lines to generate pseudo survey lines, and convert all survey line data into a regular two-dimensional magnetic field matrix. S4. The sparse constraint survey line offset inversion leveling method based on the flight-magnetic map intersection residual is used to level and correct the two-dimensional magnetic field matrix according to the cutting line data. S5. Generate an aeronautical magnetic map based on the leveled and corrected two-dimensional magnetic field matrix.

2. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, In step S2, the denoising process employs an adaptive denoising method constrained by wavelet-Kalman filtering, including: S21. Perform wavelet decomposition on the original magnetic field data to obtain the detail coefficients of each layer; S22. Apply a soft thresholding function to the detail coefficients of each layer for thresholding. S23. Use the detail coefficients after thresholding to perform wavelet reconstruction and obtain candidate denoising results; S24. Establish a state-space model of the geomagnetic signal, use the candidate noise reduction results as the observations of the Kalman filter, and calculate the innovative residuals; S25. Based on the innovative residual and signal energy retention rate, construct a comprehensive evaluation function, traverse the parameter space of wavelet basis, decomposition level and threshold factor, and select the parameter combination that makes the comprehensive evaluation function optimal. S26. Perform wavelet denoising again using the optimal parameter combination to obtain the final denoising result.

3. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 2, characterized in that, The establishment of the state-space model for the geomagnetic signal includes: Define a system state vector, which is composed of the true value of the geomagnetic signal and the rate of change of the geomagnetic signal; Define a state equation and an observation equation. The state equation uses a state transition matrix to map the system state vector from the previous time step to the current time step, and adds process noise. The observation equation uses an observation matrix to map the system state vector to the predicted observation value, and adds measurement noise. The observation matrix is ​​used to extract the true value component of the geomagnetic signal in the system state vector, and the true observation value is taken as the candidate denoising result after wavelet denoising. Based on the state equation, the system state estimate of the previous time step is used to calculate the predicted system state value of the current time step; based on the observation equation, the predicted system state value of the current time step is used to calculate the predicted observation value of the current time step; the difference between the actual observation value of the current time step and the predicted observation value is calculated to obtain the innovation residual of the current time step.

4. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 2, characterized in that, The formula for calculating the signal energy retention rate is as follows: ； Where k is the sampling time and N is the total number of sampling points. The square of the magnetic field value at the k-th sampling point is the candidate denoising result. It is the square of the magnetic field value at the kth sampling point of the original magnetic field data.

5. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, In step S2, the deduplication process includes: converting latitude and longitude coordinates into geocentric rectangular coordinates, calculating the spatial distance between all sampling points, and removing duplicate points whose distance is less than a first set threshold.

6. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, The regularization of data within the survey line includes: automatically determining the direction of the survey line, constructing a regular coordinate sequence with uniform resolution along the main direction of the survey line, and calculating the magnetic field value at the regular coordinate point through linear interpolation.

7. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, The interpolation between adjacent regularized survey lines is performed by linear interpolation at a preset second resolution.

8. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, The sparse-constrained survey line offset inversion and leveling method based on flight-magnetic map handover residuals includes: S41. For each valid intersection point of the cutting lines, record its latitude and longitude as follows: The measured magnetic field value is The interpolated magnetic field value at this point is calculated using two-dimensional linear interpolation. The flight-magnetic map residuals of the measured magnetic field value and the interpolated magnetic field value are calculated. The flight-magnetic map residuals of all effective intersection points of the cutting lines constitute the flight-magnetic map residual vector. ,in The total number of valid intersection points of the cutting line; S42. The system bias of each measurement line in the two-dimensional magnetic field matrix is ​​used as the parameter to be inverted, and the bias of the q-th measurement line is denoted as... The offsets of all survey lines constitute the offset parameter vector. ,in This represents the total number of survey lines. S43. Establish a sparse linear mapping relationship between the flight-magnetic map residual vector and the bias parameter vector. ,in It is a sparse mapping matrix. The residual vector; S44. Introduce the continuity constraint of the survey line and construct the objective function. ,in It is a first-order difference matrix. To smooth the weight coefficients; solve for the bias parameter vector that minimizes the objective function. ; S45. Using the bias parameter vector obtained from the solution The magnetic field value of each measurement line in the two-dimensional magnetic field matrix is ​​compensated and corrected: for the p-th sampling point on the q-th measurement line, the corrected magnetic field value is... ,in The original measured magnetic field value before calibration. This is the offset corresponding to the survey line.

9. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 8, characterized in that, In step S42, the sparse mapping matrix The construction methods include: For each valid intersection of the cutting lines, its longitude is Calculate the distance between the longitude and the representative longitude of each survey line, where the representative longitude is the average of the longitudes of all sampling points on the survey line; Select the two survey lines with the closest longitude distance. and , representing longitude respectively and ;like The weights are calculated using the following formula: ； ； in, and These are two survey lines. and The weights; like Then let ; Find the two survey lines that are closest to the point in longitude, calculate the weights based on the longitude distances between the point and the two survey lines, and assign the weights to the corresponding row and column positions in the sparse mapping matrix; Weight and Assigned to sparse mapping matrix The i-th row of the middle Column and number The position of the first column is set, and the positions of the remaining columns are set to 0.

10. The method for constructing high-precision aerobatic magnetic maps based on sparse magnetic field data according to claim 1, characterized in that, The flight path is a "bow" shaped flight path, and the cutting lines are perpendicular to the direction of the measuring line and are evenly distributed in the magnetic map area.

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