Anti-singularity method for surveying and mapping in real time and reconstructing magnetic map

Abstract

The invention belongs to the technical field of magnetic map surveying and mapping, and discloses an anti-singularity method, system, equipment and program product for surveying and mapping and reconstructing a magnetic map in real time, the method comprises the following steps: surveying and mapping magnetic nodes in real time, reconstructing the magnetic map in real time by adopting an interpolation method based on the magnetic nodes, defining a plurality of evaluation indexes, and judging whether the reconstructed magnetic map has a singularity problem or not, if the singular problem does not exist, magnetic map reconstruction is completed, and otherwise, the magnetic map is reconstructed based on noise disturbance or compensation based on path planning or compensation based on data screening and multiplexing; the system and the equipment are used for implementing the method. The program product comprises a computer program for implementing the method; the problem of singularity in real-time mapping and reconstruction of the magnetic map is solved, the interpolation success rate and the map reconstruction precision are remarkably improved, and the method has the advantages of being high in compatibility and low in calculation complexity.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of magnetic map surveying and mapping, and particularly relates to an anti-singularity method for real-time surveying and mapping and reconstructing a magnetic map. BACKGROUND

[0002] The magnetic map technology can provide spatial positioning services for various mobile carriers in satellite signal limited environments, and is hailed as a strategic reserve technology for future positioning and navigation. The main architecture of the current positioning and navigation based on the magnetic map usually adopts a two-stage research, namely offline surveying and mapping and online matching positioning. Many researchers focus on constructing the magnetic map by using the offline crowdsourcing technology, that is, using the magnetic sensor data collected by the public users through terminals such as smart phones in daily activities such as natural walking, offline processing and constructing the magnetic map. In addition, the classical interpolation methods include geostatistical methods, cubic spline interpolation, inverse distance weighted interpolation, polynomial interpolation and radial basis function interpolation, which all use rough nodes surveyed to reconstruct a fine magnetic map. In addition, there is a series of methods using various advanced artificial intelligence methods to further refine the magnetic map. These methods mainly focus on offline construction, that is, using all the offline collected data to construct the magnetic map. However, in rescue tasks, military scenarios or other large-scale magnetic map applications, unmanned aerial vehicles or other carriers are required to be equipped with magnetic sensors to survey and reconstruct the magnetic map in real time or quasi-real time, such as the unmanned aerial vehicle collecting magnetic nodes while reconstructing the magnetic map within a certain range during flight.

[0003] The reconstruction of the magnetic map by using the interpolation method is greatly restricted by the known magnetic nodes surveyed, and this restriction is manifested in the topological relationship. When the known magnetic nodes are strictly or approximately collinear on a two-dimensional or three-dimensional projection plane, the interpolation task becomes difficult or even cannot be effectively performed, which is manifested in that the entire target area cannot be completely reconstructed and the reconstruction error is large, that is, the singularity problem of real-time surveying and reconstructing the magnetic map. An inevitable problem of real-time surveying and reconstructing the magnetic map is that the motion trajectory of the unmanned aerial vehicle or other equipment is always a straight line or a quasi-straight line in a period of time, so the magnetic nodes are always strictly or approximately collinear on a two-dimensional or three-dimensional projection plane, thereby the singularity problem inevitably occurs. SUMMARY

[0004] In order to overcome the above-mentioned shortcomings of the prior art, the purpose of the present application is to provide an anti-singularity method, system, device and program product for real-time surveying and reconstructing a magnetic map, which characterizes and solves the singularity problem in real-time surveying and reconstructing the magnetic map by introducing a topological loss and a topological compensation model based on noise disturbance, thereby expanding the reconstructable range and improving the reconstruction accuracy.

[0005] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: An anti-singularity method for real-time surveying and reconstructing a magnetic map, comprising the following steps: Step 1: Real-time mapping of magnetic nodes, and real-time reconstruction of the magnetic map based on the magnetic nodes using interpolation. Step 2: Define multiple evaluation metrics to determine whether the reconstructed magneto map has singularities; Step 3: If there are no singular issues, complete the magnetic map reconstruction; otherwise, return to Step 1 and reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation.

[0006] In step 1, the interpolation methods include linear interpolation, cubic interpolation, natural nearest neighbor interpolation, nearest neighbor interpolation, Kriging interpolation, biharmonic spline interpolation, modified Shepard interpolation, and inverse distance interpolation; Kriging interpolation includes ordinary Kriging interpolation or generalized Kriging interpolation.

[0007] In step 2, the multiple evaluation metrics include the Degree of Topological Loss (DTL), interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error. The construction process of these metrics is as follows: Based on Shannon's information theory, as shown in Equation (1), a topological loss index is defined to quantify the loss of magnetic field information caused by the sensor's position distribution during the reconstruction process: (1) In formula (1), This represents the Euclidean distance between the two farthest magnetic nodes in the set of magnetic nodes mapped in real time in step 1. This indicates the number of magnetic nodes in the set of magnetic nodes; This represents the Euclidean distance from each node to the straight line; the more strictly the magnetic nodes are distributed along the straight line, the greater the topological loss and the greater the topological loss index; based on formula (1) and the distribution of the surveyed magnetic nodes, the topological loss of this set of magnetic nodes is quantified. The greater the topological loss, the more severe the singularity problem in the magnetic map reconstruction. By calculating and comparing the magnitude of the topology loss before and after topology compensation, we can assess whether the topology loss has been effectively compensated. If the topology loss index decreases after noise disturbance, it indicates that the topology loss has been effectively compensated. In real-time mapped and reconstructed magnetic maps, the singularity problem caused by topological loss leads to two scenarios: Case 1: The magnetic nodes in the target area are not fully estimated, i.e., the interpolation results are incomplete; Case 2: Although the magnetic nodes in the target area are fully estimated, the normalized root mean square error index of the magnetic fingerprint is >1, that is, the interpolation result is inaccurate. Number of magnetic nodes successfully interpolated Total number of magnetic nodes interpolated with the target The ratio of the interpolation result to the interpolation ratio is used to assess the degree of incompleteness of the interpolation result, and is defined as the interpolation success rate index: (2) The normalized root mean square error (RMSE) of the magnetic field magnitude, the normalized RMSE of the location stamp, and the normalized RMSE of the magnetic fingerprint are used to assess the degree of inaccuracy of the interpolation results. The normalization method for the RMSE of the magnetic field magnitude uses the average value of the magnetic field magnitude of the reference magnetic map as the standard, and its definition is as follows: (3) in, This represents the total number of magnetic nodes to be evaluated. This represents the average magnetic field magnitude of all magnetic nodes in a standard magnetic map. For each magnetic node to be evaluated, the magnetic field magnitude is... The average magnetic field magnitude of reference magnetic nodes within a given search radius is centered on the location stamp of each magnetic node to be evaluated. The normalized root mean square error index of the location stamp is normalized using the average magnetic field location marker granularity of the reference magnetic map as the standard, and is defined as follows: (4) in, This represents the total number of magnetic nodes to be evaluated. To determine the granularity of the magnetic map to be evaluated. Let x be the x-coordinate of each magnetic node to be evaluated. Let be the ordinate of each magnetic node to be evaluated. , These are the horizontal and vertical coordinates of the standard magnetic node whose magnetic field magnitude is closest to that of the magnetic node to be evaluated, centered on the location stamp of each magnetic node to be evaluated, within a given search radius. The normalization method for the normalized root mean square error index of magnetic fingerprints is to combine the normalized root mean square error index of the magnetic field magnitude and the normalized root mean square error index of the location stamp with equal weights, that is: (5) The reference magnetic map was constructed using ordinary kriging based on offline measured magnetic nodes; The normalized root mean square error index of the magnetic field modulus and the normalized root mean square error index of the location stamp depend on the matching search radius between the reconstructed magnetic map and the reference magnetic map. The search radius is set to 1-10 times the granularity of the reference magnetic map. Based on the normalized root mean square error index and the interpolation success rate index η of magnetic fingerprint, a normalized magnetic fingerprint error index is proposed to comprehensively evaluate the incompleteness and inaccuracy of the interpolation results. The index is defined as follows: (6) in, η is the normalized root mean square error index for magnetic fingerprints. The smaller the value of η, the greater the incompleteness or inaccuracy of the interpolation results, thus affecting the accuracy of the results. and A non-linear trade-off is achieved between them.

[0008] Step 2 determines whether the reconstructed magnetic map has singularities based on the threshold set for the specific task. If any one of the following indicators—interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error—is higher than the threshold required by the specific task, then the reconstructed magnetic map has singularities.

[0009] The steps for reconstructing the magnetic map based on noise perturbation in step 3 are as follows: Add uniform white noise of a certain magnitude to the location stamps of the real-time mapped magnetic nodes to make the real-time mapped magnetic nodes deviate from the original straight or quasi-straight distribution, thereby compensating for the topological loss of the real-time mapped magnetic nodes. The magnitude of the added uniform white noise is 0.1-10 times that of the longer side of the target reconstruction range.

[0010] The steps of step 3, which involves reconstructing the magnetic map based on path planning and compensation, are as follows: During the execution of a surveying mission, if the topological loss of the current set of magnetic nodes exceeds the set threshold, the surveying system is controlled to deviate from the original straight trajectory and fly forward in an S-shaped curve or approximately S-shaped curve in the plane, maintaining the original surveying frequency and collecting measurement points that deviate from the original track to enhance the spatial distribution diversity of magnetic nodes, thereby improving the overall topology before continuing the original route surveying.

[0011] The steps in step 3, which involve data filtering and reuse to reconstruct the magnetic map, are as follows: By selecting magnetic nodes whose spatial location is within the target reconstruction range from historical mapping data or adjacent tracks of the current mapping route, and merging them with the current real-time mapping set of magnetic nodes, a hybrid magnetic node set with lower topological loss is constructed for subsequent magnetic map reconstruction processing.

[0012] A singularity-resistant system for real-time mapping and reconstruction of magnetic maps includes: The magnetic map reconstruction module measures magnetic nodes in real time and reconstructs the magnetic map in real time using interpolation based on the magnetic nodes. The singularity evaluation module defines multiple evaluation indicators to determine whether the magnetic map reconstructed by the magnetic map reconstruction module has singularities. The singularity problem resolution module completes the magnetic map reconstruction if the singularity problem evaluation module determines that there are no singularities. Otherwise, it returns to the magnetic map reconstruction module to reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation.

[0013] An anti-singularity device for real-time mapping and reconstruction of magnetic maps, comprising: Memory: Used to store computer programs that implement anti-singularity methods for real-time mapping and reconstruction of magnetic maps; Processor: An anti-singularity method for implementing real-time mapping and reconstructing of magnetic maps when executing the computer program.

[0014] A computer program product includes a computer program that, when executed by a processor, implements an anti-singularity method for real-time mapping and reconstruction of magnetic maps.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention fundamentally solves a long-standing but unrecognized technical bottleneck, achieving a breakthrough from "unusable" to "usable".

[0016] 1) Technical problem: Solve the singularity problem caused by the quasi-linear distribution of survey points in the real-time mapping and reconstruction of magnetic maps. This problem has caused many interpolation reconstruction methods to completely fail.

[0017] 2) Technical Solution: This invention reveals for the first time that the essence of this singularity problem is "topological loss," and scientifically characterizes it by introducing the quantitative index of topological loss degree. Furthermore, through an innovative method of applying uniform white noise perturbation along the minor axis of the measurement point, the topological loss is actively compensated, fundamentally eliminating the conditions for the generation of singularity.

[0018] 3) Specific effects: As shown in the experiment, for methods such as linear interpolation and natural neighbor interpolation, the present invention can improve the interpolation success rate from 0% to nearly 100%, making real-time map reconstruction under quasi-linear aerial survey paths change from "complete failure" to "stable and reliable".

[0019] 2. This invention significantly improves the accuracy and reliability of reconstructed magnetic maps, solving the problem of transitioning from "usable" to "easy to use".

[0020] 1) Technical issues: Singularity problems not only lead to interpolation failures, but also produce huge reconstruction errors even in some cases where results can be output (such as partial kriging), making the results unreliable.

[0021] 2) Technical solution: The present invention optimizes the topology of the measurement points through noise disturbance, thereby solving the matrix ill-conditioning problem in the subsequent interpolation calculation and making the interpolation process more stable.

[0022] 3) Specific effects: While successfully solving the singularity problem, this invention can stabilize the comprehensive error index of the reconstruction results—the normalized magnetic fingerprint error index—at a low level below 0.18. This means that this invention not only ensures the integrity of the reconstruction but also its accuracy, producing a high-precision and reliable magnetic map.

[0023] 3. This invention has strong versatility and compatibility, protects existing resources and reduces deployment costs.

[0024] 1) Technical issues: This problem is prevalent in many mainstream interpolation methods. Developing a separate solution for each method would be costly and inefficient.

[0025] 2) Technical Solution: The topology loss and compensation model proposed in this invention is an independent front-end processing module. It does not modify or replace the specific interpolation algorithm, but rather performs "preprocessing" on the input measurement data.

[0026] 3) Specific effects: This model is seamlessly compatible with various interpolation methods that are sensitive to topology, such as polynomial interpolation, natural nearest neighbor interpolation, and Kriging interpolation. Users do not need to change their familiar or optimized backend reconstruction algorithms; they only need to add this preprocessing step to make it resistant to singularities, which greatly saves development costs and the complexity of system modification.

[0027] 4. The solution to the singularity problem in this invention is efficient and lightweight, and is particularly suitable for real-time operation on resource-constrained embedded platforms.

[0028] 1) Technical issues: Airborne computing resources of drones and other carriers are limited, and complex solutions are difficult to meet the needs of real-time mapping and reconstruction of magnetic maps.

[0029] 2) Technical Solution: The core operations of this invention—topology loss calculation and uniform white noise generation—have low computational complexity and do not involve complex iterative optimization or large-scale matrix operations. The noise perturbation operation itself is a simple addition operation, with minimal overhead to the system.

[0030] 3) Specific effects: This solution has low computational burden and fast response speed, and can be easily integrated into the flight control system or data processing unit of UAVs to realize real-time processing and singularity elimination of magnetic measurement data, which strongly supports the practical engineering application of magnetic maps in harsh environments.

[0031] 5. This invention provides a scientific, closed-loop systematic evaluation framework, ensuring the verifiability and optimizability of the solution.

[0032] 1) Technical issues: There is a lack of unified metrics to quantify the severity of singularity problems and the effectiveness of solutions.

[0033] 2) Technical solution: This invention not only provides a solution, but also constructs a complete multi-index evaluation system.

[0034] 3) Specific effects: This system allows engineers to quantitatively diagnose problems, precisely control the amplitude of noise disturbances, and scientifically evaluate the final results. For example, by monitoring the change curve of the normalized magnetic fingerprint error index with the noise amplitude, the optimal disturbance parameters can be quickly found, realizing the observability, controllability, and optimizability of the entire process.

[0035] In summary, this invention successfully solves the singularity problem in real-time magnetic mapping by introducing a quantitative index of topological loss and a noise perturbation method, significantly improving interpolation success rate and map reconstruction accuracy. This invention is highly compatible, seamlessly integrating multiple interpolation methods, and has low computational complexity, making it suitable for resource-constrained embedded platforms. A scientific evaluation system ensures the verifiability and optimizability of the solution, thus providing an efficient and reliable technical solution and driving breakthrough progress in magnetic mapping technology. Attached Figure Description

[0036] Figure 1 This is a flowchart of the topology loss and compensation process of the present invention.

[0037] Figure 2 This is a graph showing how the simulation topology loss index of this invention changes with the noise level.

[0038] Figure 3 This invention uses a linear interpolation method to simulate and study the normalized root mean square error index of location stamps under different noise disturbance levels.

[0039] Figure 4 This invention uses the normalized root mean square error index of the magnetic field modulus under different noise disturbance levels to simulate and study the magnetic field modulus.

[0040] Figure 5This invention uses linear interpolation to study the interpolation success rate and normalized magnetic fingerprint error under different noise disturbance levels.

[0041] Figure 6 This invention uses a cubic interpolation method to simulate the normalized root mean square error index of location stamps under different noise disturbance levels.

[0042] Figure 7 This invention uses a cubic interpolation method to study the normalized magnetic fingerprint error index of the magnetic field modulus under different noise disturbance levels.

[0043] Figure 8 This invention uses a cubic interpolation method to study the interpolation success rate and normalized magnetic fingerprint error under different noise disturbance levels.

[0044] Figure 9 This invention simulates the normalized root mean square error index of location stamps under different noise disturbance levels using the natural nearest neighbor interpolation method.

[0045] Figure 10 This invention uses the natural nearest neighbor interpolation method to simulate and study the normalized root mean square error index of the magnetic field modulus under different noise disturbance levels.

[0046] Figure 11 This invention uses the natural nearest neighbor interpolation method to study the interpolation success rate and normalized magnetic fingerprint error under different noise disturbance levels.

[0047] Figure 12 This invention simulates the normalized root mean square index of location stamps under different noise levels using a generalized kriging interpolation method with the covariance function as the exponential covariance function.

[0048] Figure 13 This invention simulates the normalized root mean square error index of the magnetic field modulus under different noise levels using the universal Kriging interpolation method with the covariance function as the exponential covariance function.

[0049] Figure 14 This invention uses the ordinary Kriging interpolation method with a covariance function of Gaussian to study the normalized root mean square error index of the magnetic field modulus under different noise levels.

[0050] Figure 15 The simulation results demonstrate the interpolation success rate under different noise disturbance intensities and with varying interpolation widths in this invention.

[0051] Figure 16 This invention simulates the interpolation success rate under different noise disturbance intensities and with varying interpolation widths using cubic interpolation.

[0052] Figure 17 This invention simulates the interpolation success rate index using natural nearest neighbor interpolation with different interpolation widths and noise disturbance intensities. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings.

[0054] like Figure 1 As shown, a method for resisting singularities in real-time mapping and reconstruction of magnetic maps includes the following steps: Step 1: Real-time mapping of magnetic nodes, and real-time reconstruction of the magnetic map based on the magnetic nodes using interpolation. Step 2: Define multiple evaluation metrics to determine whether the reconstructed magneto map has singularities; Step 3: If there are no singular issues, complete the magnetic map reconstruction; otherwise, return to Step 1 and reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation.

[0055] In step 1, the interpolation methods include linear interpolation, cubic interpolation, natural nearest neighbor interpolation, nearest neighbor interpolation, Kriging interpolation, biharmonic spline interpolation, and modified Shepard interpolation (Renka, RJ (1988). Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Softw., 14(2), 139-148. https: / / doi.org / 10.1145 / 45054.45055 ) or inverse distance interpolation; Kriging interpolation includes ordinary Kriging interpolation or generalized Kriging interpolation.

[0056] In step 2, the multiple evaluation metrics include the Degree of Topological Loss (DTL), interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error. The construction process of these metrics is as follows: The topology loss metric must meet the following four conditions: Condition 1: The topological loss is independent of the choice and rotation of the Cartesian coordinate system; Condition 2: The topology loss is independent of the size and scale of the mapped magnetic node data, but depends on the relative position of the magnetic nodes; Condition 3: The topological loss can describe the clustering degree of magnetic nodes and is sensitive to the outlier values ​​of the magnetic node's location stamp. Condition 4: The mathematical form of topological loss is simple and its computational complexity is controllable.

[0057] Based on conditions 1-4 and Shannon's information theory, as shown in formula (1), a topological loss index is defined to quantify the loss of magnetic field information caused by the sensor position distribution during the reconstruction process: (1) In formula (1), This represents the Euclidean distance between the two farthest magnetic nodes in the set of magnetic nodes mapped in real time in step 1. This represents the number of magnetic nodes in the set of magnetic nodes. After applying the least squares method to linearly fit the positions of the magnetic nodes, the denominator is obtained by calculating the average Euclidean distance from each magnetic node to the fitted line. This represents the Euclidean distance from each node to the straight line; the more strictly the magnetic nodes are distributed along the straight line, the greater the topological loss and the greater the topological loss index; based on formula (1) and the distribution of the surveyed magnetic nodes, the topological loss of this set of magnetic nodes is quantified. The greater the topological loss, the more severe the singularity problem in the magnetic map reconstruction. By calculating and comparing the magnitude of the topology loss before and after topology compensation, we can assess whether the topology loss has been effectively compensated. If the topology loss decreases after noise disturbance, it indicates that the topology loss has been effectively compensated. In real-time mapping and reconstruction of magnetic maps, the singularity problem caused by topological loss leads to two scenarios: Case 1: The magnetic nodes in the target area are not fully estimated, i.e., the interpolation results are incomplete; Case 2: Although the magnetic nodes in the target area are fully estimated, the normalized root mean square error index of the magnetic fingerprint is >1, that is, the interpolation result is inaccurate. Number of magnetic nodes successfully interpolated Total number of magnetic nodes interpolated with the target The ratio of the interpolation result to the interpolation success rate is used to assess the degree of incompleteness of the interpolation result. (2) The normalized root mean square error (RMSE) of the magnetic field magnitude, the normalized RMSE of the location stamp, and the normalized RMSE of the magnetic fingerprint are used to assess the degree of inaccuracy of the interpolation results. The normalization method for the RMSE of the magnetic field magnitude uses the average value of the magnetic field magnitude of the reference magnetic map as the standard, and its definition is as follows: (3) in, This represents the total number of magnetic nodes to be evaluated. This represents the average magnetic field magnitude of all magnetic nodes in a standard magnetic map. For each magnetic node to be evaluated, the magnetic field magnitude is... The average magnetic field magnitude of reference magnetic nodes within a given search radius is centered on the location stamp of each magnetic node to be evaluated. The normalized root mean square error index of the location stamp is normalized using the average magnetic field location marker granularity of the reference magnetic map as the standard, and is defined as follows: (4) in, This represents the total number of magnetic nodes to be evaluated. To determine the granularity of the magnetic map to be evaluated. Let x be the x-coordinate of each magnetic node to be evaluated. Let be the ordinate of each magnetic node to be evaluated. , These are the horizontal and vertical coordinates of the standard magnetic node whose magnetic field magnitude is closest to that of the magnetic node to be evaluated, centered on the location stamp of each magnetic node to be evaluated, within a given search radius. The normalization method for the normalized root mean square error index of magnetic fingerprints is to combine the normalized root mean square error index of the magnetic field magnitude and the normalized root mean square error index of the location stamp with equal weights, that is: (5) The reference magnetic map was constructed using ordinary kriging based on offline measured magnetic nodes; It is important to note that the normalized root mean square error (RMSE) of the magnetic field modulus and the normalized RMSE of the location stamp depend on the matching search radius between the reconstructed magnetic map and the reference magnetic map. If the search radius is set too small, the evaluation results may be distorted, resulting in the same reconstruction error for different interpolation methods. Conversely, if the search radius is too large, the evaluation error will be exaggerated, making the results unreliable. After comprehensive consideration, the search radius is set to 1-10 times the granularity of the reference magnetic map. Based on the normalized root mean square error index of magnetic fingerprint and the interpolation success rate η, a normalized magnetic fingerprint error index is proposed to comprehensively evaluate the incompleteness and inaccuracy of the interpolation results. The index is defined as follows: (6) in, The normalized root mean square error (RMSE) of the magnetic fingerprint is given. The physical significance of the normalized magnetic fingerprint error index lies in its ability to sensitively capture nonlinear changes in η. When the value approaches 1, the normalized magnetic fingerprint error index degenerates into the normalized root mean square error index of the magnetic field magnitude; while when When the deviation from 1 occurs, the squared term accelerates the perception and amplifies the overall error. In other words, the smaller η is, the greater the incompleteness or inaccuracy of the interpolation result, thus affecting... and A non-linear trade-off is achieved between them. By introducing a normalized magnetic fingerprint error index, the changing trend of the severity of singularity problems can be tracked more intuitively.

[0058] Step 2 determines whether the reconstructed magnetic map has singularities based on the threshold set for the specific task. If any one of the following indicators—interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error—is higher than the threshold required by the specific task, then the reconstructed magnetic map has singularities.

[0059] The steps for reconstructing the magnetic map based on noise perturbation in step 3 are as follows: Uniform white noise of a certain magnitude is added to the location stamps of the real-time mapped magnetic nodes to deviate from the original straight or quasi-straight distribution of the magnetic nodes, thus compensating for the topological loss of the real-time mapped magnetic nodes. The noise used to compensate for the topological loss must be white noise, not colored noise. The essence of noise perturbation is to disrupt the location markings of the magnetic nodes within a certain range to improve the topological structure. Colored noise will introduce significant deviations, resulting in a significant error between the location markings of the magnetic fingerprint and the actual location markings. Gaussian white noise follows a normal distribution, and the perturbed magnetic nodes are still concentrated near the original straight line. Although Gaussian white noise still has some effect, it is not as effective as uniform white noise. The magnitude of the added uniform white noise is 0.1-10 times the magnitude of the longer side of the target reconstruction range.

[0060] The steps of step 3, which involves reconstructing the magnetic map based on path planning and compensation, are as follows: During the execution of a surveying mission, if the topological loss of the current set of magnetic nodes exceeds the set threshold, the surveying system is controlled to deviate from the original straight trajectory and fly forward in an S-shaped curve or approximately S-shaped curve in the plane, maintaining the original surveying frequency and collecting measurement points that deviate from the original track to enhance the spatial distribution diversity of magnetic nodes, thereby improving the overall topology before continuing the original route surveying.

[0061] The steps in step 3, which involve data filtering and reuse to reconstruct the magnetic map, are as follows: By selecting magnetic nodes whose spatial location is within the target reconstruction range from historical mapping data or adjacent tracks of the current mapping route, and merging them with the current real-time mapping set of magnetic nodes, a hybrid magnetic node set with lower topological loss is constructed for subsequent magnetic map reconstruction processing.

[0062] A singularity-resistant system for real-time mapping and reconstruction of magnetic maps includes: The magnetic map reconstruction module measures magnetic nodes in real time and reconstructs the magnetic map in real time using an interpolation method based on the magnetic nodes, which is used to implement step 1 of the anti-singularity method for real-time measurement and reconstruction of the magnetic map; The singularity problem evaluation module defines multiple evaluation indicators to determine whether the magnetic map reconstructed by the magnetic map reconstruction module has singular problems, and is used to implement step 2 of the anti-singularity method for real-time mapping and reconstruction of magnetic maps; The singularity problem resolution module completes the magnetic map reconstruction if the singularity problem evaluation module determines that there is no singularity problem; otherwise, it returns to the magnetic map reconstruction module to reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation. This is used to implement step 3 of the anti-singularity method for real-time mapping and reconstruction of magnetic maps.

[0063] An anti-singularity device for real-time mapping and reconstruction of magnetic maps, comprising: Memory: Used to store computer programs that implement anti-singularity methods for real-time mapping and reconstruction of magnetic maps; Processor: An anti-singularity method for implementing real-time mapping and reconstructing of magnetic maps when executing the computer program.

[0064] A computer program product includes a computer program that, when executed by a processor, implements an anti-singularity method for real-time mapping and reconstruction of magnetic maps.

[0065] Simulation Experiment First, let's verify the topological loss. For example... Figure 2 As shown, the topology loss initially decreases rapidly with increasing noise levels. This verifies that noise disturbances can compensate for the topology loss to a certain extent.

[0066] Secondly, the feasibility and applicability of this invention are verified by commonly used interpolation methods in eight major categories and nine subcategories. The dataset used in this study was collected through field experiments conducted in the eastern coastal region of China using a drone equipped with a magnetic sensor. The geomagnetic measurement achieved an accuracy of 0.1 nT, covering an area of ​​tens of square kilometers.

[0067] The specific steps of the experimental procedure are as follows: (1) Constructing a test scenario: Select a drone flight trajectory from the dataset and process its measurement points to be strictly distributed along a straight line, thus artificially creating an extreme test scenario with severe topological loss.

[0068] (2) Use multiple interpolation methods to reconstruct the magnetic map of the above scene and record the reconstruction results without processing.

[0069] (3) Application of the present invention: Apply a series of 15 different amplitudes (from 10) along the minor axis direction (latitude direction) of the measurement point. -5 Up to 10 -1 Uniformly distributed white noise.

[0070] (4) Quantitative evaluation of the effect: For each noise disturbance amplitude, the topology loss is recalculated and the magnetic map reconstruction is performed again. Finally, the completeness and accuracy of the reconstruction results are quantitatively evaluated using the evaluation index system defined in this invention—interpolation success rate index, normalized root mean square error index of magnetic field magnitude, normalized root mean square error index of location stamp, normalized root mean square error index of magnetic fingerprint, and normalized magnetic fingerprint error index.

[0071] (5) Eliminating random effects: In order to eliminate the uncertainty of noise disturbances generated by random numbers, the above steps are repeated five times with different random number seeds and the average is taken to obtain the trend.

[0072] First, using normalized root mean square error (RMSE) for evaluation is incomplete before the successful interpolation rate reaches a certain threshold. As the number of successfully interpolated data increases, oscillations will occur at certain critical points. Therefore, an increase in error does not necessarily indicate the negative impact of introduced noise.

[0073] First, analyze linear interpolation, cubic interpolation, and natural nearest neighbor interpolation methods that produce incomplete interpolations. Observe... Figure 5 , Figure 8 , Figure 11 It was found that the noise micro-fingerprint result curves generated by the three methods using different random numbers were consistent. The triangular curve represents the interpolation success rate, and the "*" curve represents the normalized magnetic fingerprint error index: when the noise level increases from 10... -3 Increase to 10 -2.3 At that time, the interpolation success rate of the above three methods increased from 20% to nearly 100%, and the normalized magnetic fingerprint error curve generally showed a downward trend, stabilizing around 0.18. Further analysis Figure 3 , Figure 6 , Figure 9The dark blue lines represent the average normalized root mean square error (RMSE) of the location stamps under noise perturbation caused by five different random numbers, reflecting the overall trend. The other curves represent the perturbation results caused by noise from different random numbers. It can be seen that the RMSE of the location stamps converges to around 0.33. Further analysis... Figure 4 , Figure 7 , Figure 10 The dark blue line represents the average value of the normalized root mean square error (RMSE) of the magnetic field modulus under noise perturbations generated by five different random numbers, reflecting the overall trend of change. The other curves represent the perturbation results of noise generated by different random numbers, and it can be seen that the RMSE of the magnetic field modulus is stable at around 0.018. It is easy to conclude that the improved interpolation success rate is due to the noise interference making the magnetic nodes more dispersed, compensating for topological loss and facilitating the triangulation process. Therefore, more magnetic nodes can find their corresponding triangles and successfully perform interpolation.

[0074] The reconstruction singularity of the pan-kriging method is manifested by a large reconstruction error, as observed... Figure 13 The dark blue lines represent the average value of the normalized root mean square error index of the magnetic field modulus under noise perturbations generated by five different random numbers, reflecting the overall trend of change. The other curves represent the results of perturbations caused by noise generated by different random numbers. Under the influence of noise perturbations, the normalized root mean square error index of the magnetic field modulus decreases from around 5-15 to near 0. Figure 12 The location stamp error index fluctuates within a small range. The dark blue line represents the average value of the normalized root mean square error index of the location stamp under noise perturbation generated by five different random numbers in the figure, which reflects the overall trend. The other curves represent the perturbation results of noise generated by different random numbers, which also verifies the feasibility of the invention.

[0075] Another important point to note is that the core of the ordinary kriging method lies in the choice of the covariance function. Essentially, it uses a specific function to map distance to covariance. During this process, the topological loss is simultaneously transformed. For example, the distance between two originally closely spaced magnetic nodes might be amplified by the covariance function, or conversely, the transformed distance might be drastically reduced, leading to even closer clustering of magnetic nodes and thus exacerbating the topological loss. Because the covariance function has a significant impact on the topological loss, kriging interpolation is highly sensitive to the choice of covariance function. Models using exponential covariance significantly outperform those using Gaussian covariance, such as... Figure 14As shown, the dark blue lines represent the average value of the normalized root mean square error index of the magnetic field magnitude under noise perturbation generated by five different random numbers, reflecting the overall trend of change. The other curves represent the perturbation results of noise generated by different random numbers. Although the normalized root mean square error index of the magnetic field magnitude decreases significantly, it is still difficult to return to the normal value again through topological compensation of noise using the interpolation method of Gaussian covariance function.

[0076] The above experiments were all based on a given interpolation width. However, the required interpolation width varies in different application scenarios, so the proposed model was further validated. It can be inferred that the reasonable extrapolation range for a given set of magnetic nodes is inherently finite. If the range is too large, it will inevitably lead to larger errors. Therefore, we only focus on the incomplete interpolation problem in the aforementioned singularity problem and analyze whether the noise perturbation method has universality under different interpolation widths. The experiments selected a series of ten interpolation widths from 0.002 to 0.020, and further investigated three interpolation methods (cubic interpolation, linear interpolation, and natural neighbor interpolation) under different noise perturbation intensities. The experimental results for the three methods are consistent, as shown in... Figure 15 As shown in Figure 17, the vertical axis represents the successful interpolation rate, the horizontal axis represents the magnitude of noise perturbation, and the different curves represent the half-width of the interpolation range in different tasks, ranging from 0.001 to 0.010, with a total of ten lines. It can be seen that in interpolation tasks with different interpolation range widths, the reconstructed magnetic nodes after noise perturbation can almost completely cover the entire plane, where the required noise magnitude corresponds to the width of the interpolation range—the larger the plane, the larger the required noise magnitude, which further confirms the reliability of the model.

[0077] Table 1. Classification and resolution results of singular problems in different interpolation methods The final results of the above experiments are summarized in Table 1, distinguishing between singular and non-singular reconstruction methods. The data in Table 1 show the metrics of reconstruction methods with singular problems when achieving the lowest normalized magnetic fingerprint error, and the metrics of reconstruction methods without singular problems at the point of most severe topological loss. It is particularly important to note that the singularity problem of ordinary kriging interpolation needs to be discussed separately. In Table 1, Y represents methods that will exhibit singularity in real-time mapping and reconstruction, and N represents methods that will not exhibit singularity in real-time mapping and reconstruction. linear represents linear interpolation, cubic represents cubic interpolation, natural represents natural nearest neighbor interpolation, Ukriging represents universal kriging interpolation, Okriging1 represents ordinary kriging interpolation using a Gaussian covariance model, Okriging2 represents ordinary kriging interpolation using an exponential covariance model, IDW represents inverse distance interpolation, MSM represents improved Shepard interpolation, Nearest represents nearest neighbor interpolation, and V4 represents biharmonic spline interpolation. NRMSE1 represents the normalized root mean square error index of the magnetic field magnitude, and NRMSE2 represents the normalized root mean square error index of the location stamp. Table 1 shows that even with significant topological loss, the singularity-free method can successfully complete the reconstruction task. Interpolation methods encountering singularity problems can recover normally under noise perturbation. The ordinary kriging method needs to be discussed separately. The η value of the first three methods is not 100% because the experiment only compensated for noise in the longitudinal direction, and there are small areas on both sides of the latitude where interpolation cannot be completed. In practical applications, noise can be added in the latitude direction to achieve 100% interpolation.

Claims

1. A method for resisting singularities in real-time mapping and reconstruction of magnetic maps, characterized in that, Includes the following steps: Step 1: Real-time mapping of magnetic nodes, and real-time reconstruction of the magnetic map based on the magnetic nodes using interpolation. Step 2: Define multiple evaluation metrics to determine whether the reconstructed magneto map has singularities; Step 3: If there are no singular issues, complete the magnetic map reconstruction; otherwise, return to Step 1 and reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation.

2. The method according to claim 1, characterized in that, In step 1, the interpolation methods include linear interpolation, cubic interpolation, natural nearest neighbor interpolation, nearest neighbor interpolation, Kriging interpolation, biharmonic spline interpolation, modified Shepard interpolation, and inverse distance interpolation; Kriging interpolation includes ordinary Kriging interpolation and generalized Kriging interpolation.

3. The method according to claim 1, characterized in that, In step 2, the multiple evaluation metrics include the Degree of Topological Loss (DTL), interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error. The construction process of these metrics is as follows: Based on Shannon's information theory, as shown in Equation (1), a topological loss index is defined to quantify the loss of magnetic field information caused by the sensor's position distribution during the reconstruction process: （1） In formula (1), This represents the Euclidean distance between the two farthest magnetic nodes in the set of magnetic nodes measured in real time in step 1. This represents the number of magnetic nodes in the set of magnetic nodes; This represents the Euclidean distance from each node to the straight line; the more strictly the magnetic nodes are distributed along the straight line, the greater the topological loss and the greater the topological loss index; based on formula (1) and the distribution of the surveyed magnetic nodes, the topological loss of this set of magnetic nodes is quantified. The greater the topological loss, the more severe the singularity problem in the magnetic map reconstruction. By calculating and comparing the magnitude of the topology loss before and after topology compensation, we can assess whether the topology loss has been effectively compensated. If the topology loss decreases after noise disturbance, it indicates that the topology loss has been effectively compensated. In real-time mapped and reconstructed magnetic maps, the singularity problem caused by topological loss leads to two scenarios: Case 1: The magnetic nodes in the target area are not fully estimated, i.e., the interpolation results are incomplete; Case 2: Although the magnetic nodes in the target area are fully estimated, the normalized root mean square error index of the magnetic fingerprint is >1, that is, the interpolation result is inaccurate. Number of magnetic nodes successfully interpolated Total number of magnetic nodes interpolated with the target The ratio of the interpolation result to the interpolation ratio is used to assess the degree of incompleteness of the interpolation result, and is defined as the interpolation success rate index: （2） The normalized root mean square error (RMSE) of the magnetic field magnitude, the normalized RMSE of the location stamp, and the normalized RMSE of the magnetic fingerprint are used to assess the degree of inaccuracy of the interpolation results. The normalization method for the RMSE of the magnetic field magnitude uses the average value of the magnetic field magnitude of the reference magnetic map as the standard, and its definition is as follows: （3） in, This represents the total number of magnetic nodes to be evaluated. This represents the average magnetic field magnitude of all magnetic nodes in a standard magnetic map. For each magnetic node to be evaluated, the magnetic field magnitude is... The average magnetic field magnitude of reference magnetic nodes within a given search radius is centered on the location stamp of each magnetic node to be evaluated. The normalized root mean square error index of the location stamp is normalized using the average magnetic field location marker granularity of the reference magnetic map as the standard, and is defined as follows: （4） in, This represents the total number of magnetic nodes to be evaluated. The granularity of the magnetic map to be evaluated. Let x be the x-coordinate of each magnetic node to be evaluated. Let be the ordinate of each magnetic node to be evaluated. , These are the horizontal and vertical coordinates of the standard magnetic node whose magnetic field magnitude is closest to that of the magnetic node to be evaluated, centered on the location stamp of each magnetic node to be evaluated, within a given search radius. The normalized root mean square error index of magnetic fingerprints is obtained by combining the normalized root mean square error index of the magnetic field magnitude and the normalized root mean square error index of the location stamp with equal weights, that is: （5） The reference magnetic map was constructed using ordinary kriging based on offline measured magnetic nodes; The normalized root mean square error index of the magnetic field modulus and the normalized root mean square error index of the location stamp depend on the matching search radius between the reconstructed magnetic map and the reference magnetic map. The search radius is set to 1-10 times the granularity of the reference magnetic map. Based on the normalized root mean square error (RMSE) index and the interpolation success rate index η of magnetic fingerprinting, a normalized magnetic fingerprint error index is proposed to comprehensively evaluate the incompleteness and inaccuracy of the interpolation results. The index is defined as follows: （6） in, η is the normalized root mean square error index for magnetic fingerprints. The smaller the value of η, the greater the incompleteness or inaccuracy of the interpolation results, thus affecting... and A non-linear trade-off is achieved between them.

4. The method according to claim 1, characterized in that, Step 2 determines whether the reconstructed magnetic map has singularities based on the threshold set for the specific task. If any one of the following indicators—interpolation success rate, normalized root mean square error of magnetic field magnitude, normalized root mean square error of location stamp, normalized root mean square error of magnetic fingerprint, and normalized magnetic fingerprint error—is higher than the threshold required by the specific task, then the reconstructed magnetic map has singularities.

5. The method according to claim 1, characterized in that, The steps for reconstructing the magnetic map based on noise perturbation in step 3 are as follows: Add uniform white noise of a certain magnitude to the location stamps of the real-time mapped magnetic nodes to make the real-time mapped magnetic nodes deviate from the original straight or quasi-straight distribution, thereby compensating for the topological loss of the real-time mapped magnetic nodes. The magnitude of the added uniform white noise is 0.1-10 times that of the longer side of the target reconstruction range.

6. The method according to claim 1, characterized in that, The steps of step 3, which involves reconstructing the magnetic map based on path planning and compensation, are as follows: During the execution of a surveying mission, if the topological loss of the current set of magnetic nodes exceeds the set threshold, the surveying system is controlled to deviate from the original straight trajectory and fly forward in an S-shaped curve or approximately S-shaped curve in the plane, maintaining the original surveying frequency and collecting measurement points that deviate from the original track to enhance the spatial distribution diversity of magnetic nodes, thereby improving the overall topology before continuing the original route surveying.

7. The method according to claim 1, characterized in that, The steps in step 3, which involve data filtering and reuse to reconstruct the magnetic map, are as follows: By selecting magnetic nodes whose spatial location is within the target reconstruction range from historical mapping data or adjacent tracks of the current mapping route, and merging them with the current real-time mapping set of magnetic nodes, a hybrid magnetic node set with lower topological loss is constructed for subsequent magnetic map reconstruction processing.

8. A singularity-resistant system for real-time mapping and reconstructing magnetic maps based on the method of any one of claims 1-7, characterized in that, include: The magnetic map reconstruction module measures magnetic nodes in real time and reconstructs the magnetic map in real time using interpolation based on the magnetic nodes. The singularity evaluation module defines multiple evaluation indicators to determine whether the magnetic map reconstructed by the magnetic map reconstruction module has singularities. The singularity problem resolution module completes the magnetic map reconstruction if the singularity problem evaluation module determines that there are no singularities. Otherwise, it returns to the magnetic map reconstruction module to reconstruct the magnetic map based on noise disturbance, path planning compensation, or data filtering and reuse compensation.

9. A singularity-resistant device for real-time mapping and reconstruction of magnetic maps, characterized in that, include: Memory: for storing a computer program that implements the method as described in any one of claims 1-7; Processor: for implementing the method as described in any one of claims 1-7 when executing the computer program.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-7.

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