A robust waveform matching based underground vehicle speed measurement method and system

Abstract

This invention discloses a method and system for underground vehicle speed measurement based on robust waveform matching. The method includes the following steps: constructing multiple magnetometer baseline pairs, extracting the magnetic field waveform sequences of the front and rear magnetometers for each baseline pair; dividing the magnetic field waveform sequences into multiple sliding windows along the time axis, and determining a target sliding window containing the time to be measured; within the target sliding window, performing waveform matching using a robust dynamic time warping algorithm based on the magnetic field waveform sequence corresponding to each magnetometer baseline pair, and calculating the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair based on the matching results; and weighted fusing the local vehicle speed estimates of each magnetometer baseline pair based on the matching weights to obtain the target vehicle speed estimate. This method improves the ability of magnetic field waveforms to stably match in underground engineering environments, achieving accurate measurement of underground vehicle speeds.

Description

Technical Field

[0001] This invention relates to the field of underground engineering vehicle technology, and in particular to an underground vehicle speed measurement method and system based on robust waveform matching. Background Technology

[0002] In underground engineering vehicle operations, due to the lack of satellite signals and the complex environment, speed estimation using geomagnetic characteristics has become an important technical means. Existing technologies often employ magnetic field waveform matching to estimate the speed of underground vehicles. This method utilizes a magnetometer array installed on the vehicle to collect magnetic field waveforms along the vehicle's travel path. Speed ​​is estimated based on the sample delay generated during waveform matching between the magnetic field waveforms and the individual waveforms in the magnetometer array.

[0003] However, existing speed estimation methods based on magnetic field waveform matching have certain limitations in practical applications. Underground engineering environments are typically harsh, and the signals acquired by magnetometers are highly susceptible to factors such as local ferromagnetic structures, temporary construction equipment, high-voltage cables, vehicle motors, sensor noise, installation errors, and individual differences in magnetometers. This results in a large amount of random noise and outliers being mixed into the acquired magnetic field waveform. Traditional waveform matching algorithms use Euclidean distance for dynamic time warping, which is highly sensitive to these noises and outliers. During waveform matching, the matching point is prone to drift, leading to significant errors in the calculated sample delay, ultimately affecting the accuracy and stability of vehicle speed estimation. Summary of the Invention

[0004] This invention addresses the problem that existing dynamic time warping algorithms, which use Euclidean distance, are sensitive to noise and outliers during waveform matching, easily causing matching point drift and thus seriously affecting the speed measurement accuracy of underground engineering vehicles. It provides an underground vehicle speed measurement method and system based on robust waveform matching.

[0005] The technical solution of the present invention is as follows: Firstly, a robust waveform matching-based method for underground vehicle speed measurement includes the following steps: Multiple magnetometer baseline pairs are constructed. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. The magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair are extracted respectively. The magnetic field waveform sequence is divided into multiple sliding windows along the time axis, and a target sliding window containing the moment of velocity to be measured is determined. Within the target sliding window, based on the magnetic field waveform sequences of the front and rear magnetometers corresponding to each magnetometer baseline pair, a robust dynamic time warping algorithm is used for waveform matching. Based on the matching results, the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair are calculated. The local vehicle speed estimates of each magnetometer baseline pair are weighted and fused based on the matching weights to obtain the target vehicle speed estimate.

[0006] This application, within the target sliding window, utilizes a robust dynamic time warping algorithm to perform waveform matching based on the magnetic field waveform sequences of the front and rear magnetometers of each magnetometer baseline pair. Based on the matching results, the local vehicle speed estimate and its corresponding matching weight are calculated for each magnetometer baseline pair. In this method, the robust dynamic time warping algorithm reduces the weight of outliers in the matching process, resulting in more accurate matching. This effectively suppresses the impact of magnetic field signal distortion in complex underground environments on speed measurement accuracy, improving the reliability of single-baseline speed measurement. Furthermore, based on more accurate matching results, the local vehicle speed estimate is more accurate, leading to a more accurate target vehicle speed estimate. In addition, by introducing matching weights for weighted fusion, the negative impact of poor-quality magnetometer baselines can be mitigated, fully utilizing the redundancy of multi-baseline data and further improving the robustness and stability of vehicle speed measurement in complex underground environments.

[0007] As an feasible approach, waveform matching is performed using a robust dynamic time warping algorithm, including: Within the target sliding window, a robust matching cost function is constructed based on the magnetic field waveform sequences of the front and rear magnetometers in each magnetometer baseline pair. The optimal matching path for the magnetic field waveform sequence in each magnetometer baseline pair is then searched using a dynamic time warping method. Based on the optimal waveform matching path, the local vehicle speed estimate and matching weight of the magnetometer baseline pair are calculated.

[0008] This application utilizes a robust dynamic time warping-based waveform matching method to effectively overcome nonlinear distortion and local anomaly interference of magnetic field signals in complex underground environments, ensuring the accuracy and stability of path matching between the magnetic field waveform sequences of the front and rear magnetometers. Furthermore, the local vehicle speed estimate calculated based on this optimal matching path can more realistically reflect the actual vehicle speed, while the matching weight can accurately characterize the reliability of the baseline for the current speed measurement result, providing accurate input for subsequent weighted fusion of multiple baseline vehicle speeds. Ultimately, this significantly improves the robustness and speed measurement accuracy of this speed measurement method under complex working conditions.

[0009] Optionally, constructing a robust matching cost function specifically involves: , In the formula, The local matching cost between the i-th front magnetometer sampling point and the j-th back magnetometer sampling point within the k-th sliding window is the q-th magnetometer baseline pair. For the magnetic field observations of the front magnetometer; For the magnetic field observations of the post-magnetic meter; This represents the trend of magnetic field change in the previous magnetometer; This represents the trend of magnetic field change after the magnetometer is activated; This is the weighting coefficient for the magnetic field amplitude residual term; The weighting coefficients for the residual term representing the magnetic field change trend are: This is the robust loss function.

[0010] This application constructs a robust matching cost function through a robust loss function. The difference between the magnetic field observations of the front and rear magnetometers, and the difference between the magnetic field change trends of the front and rear magnetometers, take into account both the matching degree of magnetic field amplitude and the consistency of waveform change trends. This can more comprehensively reflect the similarity of the two magnetic field waveforms, thereby further improving the accuracy of waveform matching and making the subsequent local vehicle speed estimate and matching weight calculated based on the optimal matching path more reliable.

[0011] Optionally, the robust loss function adopts the Tukey double-weight loss function, the expression of which is: , In the formula, r is the local residual during the magnetic field waveform matching process; c is the robust adjustment threshold. This represents the value of the Tukey double-weighted loss function.

[0012] This application adopts Tukey's dual-weight loss function as a robust loss function, which effectively suppresses the influence of outliers on the matching cost, significantly improves the robustness and matching accuracy of the dynamic time warping algorithm in the complex underground magnetic field environment, and ensures the reliability of the final calculated local vehicle speed estimate and matching weight.

[0013] As one feasible approach, calculating the local vehicle speed estimate for the magnetometer baseline pair based on the optimal matching path includes: Based on the optimal matching path in each magnetometer baseline pair, the sample delay between the magnetic field waveform sequences of the front and rear magnetometers is calculated; based on the sample delay, magnetometer baseline length, and magnetic field sampling frequency, the vehicle speed estimate for each magnetometer baseline pair is calculated.

[0014] This application calculates the sample delay based on the optimal matching path and derives the local vehicle speed estimate accordingly. Since the optimal matching path is obtained through the aforementioned robust dynamic time warping algorithm, this path accurately reflects the true correspondence between the magnetic field waveforms of the front and rear magnetometers on the time axis. Therefore, the calculated sample delay can accurately characterize the actual time interval required for the vehicle to pass the magnetometer baseline, avoiding delay estimation errors caused by local waveform distortion or noise interference. Furthermore, by combining the known magnetometer baseline length and high-precision magnetic field sampling frequency, a high-confidence local vehicle speed estimate can be calculated, which can adapt to speed fluctuations during vehicle operation and provide an accurate single-baseline speed for subsequent multi-baseline vehicle speed fusion based on matching weights.

[0015] As one feasible approach, the calculation of the matching weight of the magnetometer baseline pair based on the optimal matching path includes: Based on the number of matching points and the local matching cost in the optimal matching path, the average matching residual of each magnetometer baseline pair is calculated; based on the average matching residual of each magnetometer baseline pair, the matching weight of each magnetometer baseline pair is determined.

[0016] This application calculates the average matching residual based on the number of matching points in the optimal matching path and the local matching cost, and determines the matching weight of each magnetometer baseline pair based on the average matching residual. The average matching residual quantifies the overall error level of each magnetometer baseline pair in the waveform matching process. The smaller the average matching residual, the higher the matching degree between the magnetic field waveform sequence of the preceding magnetometer and the magnetic field waveform sequence of the following magnetometer, and the more reliable the corresponding local vehicle speed estimate. Based on this average matching residual, the matching weight is determined so that magnetometer baseline pairs with high matching degree and small error have a larger weight in the subsequent multi-magnetometer baseline pair fusion calculation of vehicle speed, while the weight of magnetometer baseline pairs with low matching degree and large error is reduced accordingly. This realizes adaptive weighting of the speed measurement results of different magnetometer baseline pairs, effectively suppresses the error in the final vehicle speed estimation caused by low-quality magnetometer baseline pairs, and significantly improves the robustness and accuracy of vehicle speed testing.

[0017] As one feasible approach, determining the matching weight of each magnetometer baseline pair based on the average matching residual of each magnetometer baseline pair includes: Find the minimum average matching residual among all magnetometer baseline pairs; The matching weight is calculated based on the difference between the average matching residual of each magnetometer baseline pair and the minimum average matching residual.

[0018] This application finds the minimum average matching residual among all magnetometer baseline pairs and calculates the matching weight based on the average matching residual of each magnetometer baseline pair and this minimum average matching residual, enabling adaptive adjustment of the reliability of different baseline pairs. Specifically, the minimum average matching residual represents the best matching quality among all magnetometer baseline pairs at the current moment. By calculating the difference between the average matching residual of other magnetometer baseline pairs and this value, the deviation of each magnetometer baseline pair from the optimal state can be quantified: the closer the difference is to zero, the smaller the deviation, indicating a higher waveform matching quality for that baseline pair, and the closer its corresponding local vehicle speed estimate is to the true value, thus it is assigned a higher weight; conversely, the larger the deviation, the lower the weight. This method does not require a preset fixed threshold but dynamically adjusts the matching weight of each magnetometer baseline pair based on real-time data, effectively overcoming the problem of local baseline pair matching failure caused by metal interference or magnetic field anomalies in underground environments. It can still filter out high-confidence speed measurement data in complex underground alleyway or tunnel scenarios, thereby significantly improving the speed measurement stability and positioning accuracy of vehicles in underground confined spaces.

[0019] As an feasible approach, the matching weight is calculated based on the average matching residual of each magnetometer baseline as follows: , In the formula, The array fusion weights for the q-th magnetometer baseline pair within the k-th sliding window; Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; The minimum average local matching residual for all magnetometer baseline pairs within the k-th sliding window; is the weight sensitivity coefficient; Q is the number of magnetometer baseline pairs participating in the fusion.

[0020] This application employs an exponential weighting formula, introducing a weight sensitivity coefficient to perform an exponential operation on the difference between the average matching residual and the minimum residual. The exponential function has non-linear amplification characteristics, significantly enhancing even small differences in the matching residual. This ensures that the magnetometer baseline pair with extremely high matching quality has a large weight in the final vehicle speed fusion, guaranteeing the accuracy and stability of vehicle speed measurement results in confined underground spaces.

[0021] As an feasible approach, the average matching residual for each magnetometer baseline pair is calculated as follows: , In the formula, Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; This represents the number of matching points in the optimal waveform matching path. The optimal waveform matching path; This represents the cost of local matching.

[0022] This application determines the average matching residual of each magnetometer baseline pair by statistically analyzing the local matching cost of all matching points on the optimal waveform matching path and calculating its average value. The average matching residual obtained by normalizing by dividing by the number of matching points eliminates the dimensional influence caused by different path lengths, improves the adaptability to waveform stretching or compression at different driving speeds, and can effectively overcome common local signal distortion or transient noise interference in complex underground magnetic field environments.

[0023] Secondly, the present invention provides an underground vehicle speed measurement system based on robust waveform matching, comprising: The acquisition module is used to construct multiple magnetometer baseline pairs. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. The magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair are extracted respectively. The window division module is used to divide the magnetic field waveform sequence into multiple sliding windows according to the time axis, and to determine the target sliding window that includes the moment to be measured. The local speed measurement module is used to perform waveform matching using a robust dynamic time warping algorithm based on the magnetic field waveform sequences of the front and rear magnetometers corresponding to each magnetometer baseline pair within the target sliding window. Based on the matching results, the module calculates the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair. The calculation module is used to perform weighted fusion of the local vehicle speed estimates of each magnetometer baseline pair based on the matching weights to obtain the target vehicle speed estimate.

[0024] Optionally, in the system described above, a robust dynamic time warping algorithm is used for waveform matching, and the local velocity measurement module is specifically used for: Within the target sliding window, a robust matching cost function is constructed based on the magnetic field waveform sequences of the front and rear magnetometers in each magnetometer baseline pair. The optimal matching path for the magnetic field waveform sequence in each magnetometer baseline pair is then searched using a dynamic time warping method. Based on the optimal waveform matching path, the local vehicle speed estimate and matching weight of the magnetometer baseline pair are calculated.

[0025] This invention, by adopting the above technical solutions, has significant technical effects: This invention introduces a robust loss function to construct a waveform matching cost function, enabling the magnetic field waveform to be stably matched in complex underground engineering environments, thus achieving accurate velocity measurement.

[0026] The system of this invention has the same beneficial effects as the method embodiments described above, and will not be repeated here. Attached Figure Description

[0027] 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.

[0028] Figure 1 This is a flowchart illustrating an underground vehicle speed measurement method based on robust waveform matching provided by the present invention. Figure 2 This is a flowchart of a local velocity measurement method based on robust waveform matching according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of an underground vehicle speed measurement system based on robust waveform matching according to the present invention. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0030] Currently, the method of speed estimation by matching magnetic field waveforms enables underground engineering vehicles to measure their own speed in environments lacking satellite signals.

[0031] To address the problem that existing technologies using Euclidean distance are sensitive to noise and outliers during waveform matching, easily causing matching point drift and thus severely affecting the speed measurement of underground engineering vehicles, this invention provides an underground vehicle speed measurement method and system based on robust waveform matching. The aim is to construct a waveform matching cost function by introducing a robust loss function, enabling the magnetic field waveform to be stably matched in complex underground engineering environments, thereby achieving accurate speed measurement.

[0032] like Figure 1 As shown, it includes the following steps: S101. Construct multiple magnetometer baseline pairs. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. Extract the magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair respectively.

[0033] For example, the vehicle-mounted magnetometer array is a 2×2 rectangular array distributed front and back along the vehicle's driving direction, including a front and rear first magnetometer and a second magnetometer located on the left side of the vehicle, and a front and rear third magnetometer and a fourth magnetometer located on the right side of the vehicle. The magnetometer baseline pair may include a left baseline pair consisting of a first magnetometer and a second magnetometer, and a right baseline pair consisting of a third magnetometer and a fourth magnetometer.

[0034] It should be noted that the magnetometer baseline pair includes front and rear magnetometer combinations with a non-zero projected length along the vehicle's direction of travel. The projected length of the upper left and lower left magnetometers is the front-to-back distance, forming a valid combination; the projected length of the upper right and lower right magnetometers is the front-to-back distance, forming a valid combination; the projected length of the upper left and lower right magnetometers, as well as the upper right and lower left magnetometers, is the component of the front-to-back distance in the direction of travel, also forming valid combinations; however, the combinations of the upper left and upper right magnetometers, and the lower left and lower right magnetometers, have zero projected length because they have no positional difference in the direction of travel, and are therefore excluded from the baseline pair.

[0035] Understandably, by acquiring a sufficient number of magnetic field waveform sequences and constructing multiple magnetometer baseline pairs distributed along the vehicle's direction of travel, the spatial density is increased compared to single-baseline speed measurement, further improving the accuracy of the final output vehicle speed at the target moment.

[0036] S102. Divide the magnetic field waveform sequence into multiple sliding windows according to the time axis, and determine the target sliding window that includes the moment when the velocity to be measured.

[0037] To achieve continuous monitoring of vehicle speed, the waveform sequence is divided into multiple consecutive sliding windows. Each sliding window corresponds to a specific moment in the vehicle's movement on the time axis. Since the time it takes for the vehicle to pass the magnetometer baseline is extremely short, the vehicle can be approximated as being in uniform motion within the time range of this sliding window.

[0038] Therefore, there is a one-to-one mapping between the target sliding window and the instantaneous state of the vehicle. When it is necessary to obtain the vehicle speed at a specific moment, it is only necessary to extract the waveform data within the target sliding window corresponding to that moment.

[0039] It should be noted that, for each pair of magnetic baselines, the process of constructing a waveform matching cost function based on a preset robust loss function is as follows: each magnetic field waveform sequence is divided into windows, and a robust matching cost function is constructed within the sliding window of each magnetic field waveform sequence.

[0040] For each magnetometer baseline pair, the process of extracting the magnetic field waveform sequence of its preceding and following magnetometers within each sliding window can be represented as: , In the formula, The magnetic field waveform sequence of the magnetometer before the baseline of the q-th magnetometer is aligned with the k-th sliding window. The magnetic field waveform sequence of the magnetometer within the k-th sliding window after the baseline of the q-th magnetometer is aligned; N is the length of the sliding window; the magnetic field waveform sequence is the magnetic field magnitude, uniaxial magnetic field component, or multiaxial magnetic field combination.

[0041] It should be noted that the value of the sliding window length must meet the following requirements: it should be able to cover the number of sampling points corresponding to the maximum time difference generated when the front and rear magnetometers pass through the same geomagnetic feature when the vehicle is traveling at the lowest expected speed; at the same time, the sliding window length should not be too large to avoid waveform distortion caused by vehicle speed changes or changes in the geomagnetic environment.

[0042] S103. In the target sliding window, based on the magnetic field waveform sequences of the front and rear magnetometers of each magnetometer baseline pair, a robust dynamic time warping algorithm is used to perform waveform matching. Based on the matching results, the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair are calculated respectively.

[0043] S1031. In the target sliding window, based on the magnetic field waveform sequence of the front magnetometer and the magnetic field waveform sequence of the rear magnetometer in each magnetometer baseline pair, a robust matching cost function is constructed, and the optimal matching path of the magnetic field waveform sequence in each magnetometer baseline pair is searched by the dynamic time warping method.

[0044] It should be noted that, for the target sliding window, the process of dynamic time warping based on the robust waveform matching cost function includes: First, based on the robust magnetic field waveform matching cost, the corresponding dynamic time warping cost matrix within each sliding window is generated.

[0045] Specifically, a dynamic time warping cost matrix is ​​generated based on the robust magnetic field waveform matching cost between the front and rear magnetometer sampling points within the target sliding window.

[0046] It should be noted that the robust magnetic field waveform matching cost is calculated by the robust loss function from the magnetic field amplitude residual term and the magnetic field change trend residual term, rather than simply using the Euclidean distance.

[0047] Understandably, calculating the robust magnetic field waveform matching cost using a robust loss function can effectively suppress the negative impact of outliers caused by metal interference or sensor noise in underground environments on the matching results. Traditional Euclidean distance is very sensitive to outliers, and drastic fluctuations at individual sampling points can easily lead to a sharp increase in the matching cost, resulting in mismatches. Introducing a robust loss function can reduce the weight of outliers with large residuals, allowing the matching algorithm to retain the contribution of normal waveform features while ignoring the interference of abrupt noise, thereby significantly improving the positioning robustness and matching accuracy in complex and strong magnetic interference environments.

[0048] Secondly, based on the dynamic time warping cost matrix, the optimal waveform matching path of the target sliding window is searched.

[0049] Specifically, the optimal waveform matching path that minimizes the cumulative matching cost, based on boundary conditions, monotonicity constraints, and continuity constraints, can be expressed as: , In the formula, The optimal waveform matching path for the q-th magnetometer baseline pair within the k-th sliding window; Matching paths for candidate waveforms; This represents the local matching cost between corresponding sampling points.

[0050] Understandably, the search process for the optimal waveform matching path described above is essentially about finding an "optimal curved path" that minimizes the accumulated matching cost, while satisfying boundary conditions, monotonicity constraints, and continuity constraints. The monotonicity constraint ensures that the matching order conforms to the temporal causality of vehicle movement, while the continuity constraint prevents jumps in matching points, ensuring the coherence of the waveform shape. Furthermore, because a robust loss function is introduced when constructing the local matching cost, this search process can suppress the misleading influence of abnormal magnetic field interference in the underground environment on the path search while performing dynamic programming optimization. Therefore, even with changes in vehicle speed or the presence of local magnetic interference, it can still accurately align the front and rear magnetometer magnetic field waveform sequences within the same magnetometer baseline pair.

[0051] Specifically, a robust matching cost function can be constructed as follows: , In the formula, The local matching cost between the i-th front magnetometer sampling point and the j-th back magnetometer sampling point within the k-th sliding window is the q-th magnetometer baseline pair. For the magnetic field observations of the front magnetometer; For the magnetic field observations of the post-magnetic meter; This represents the trend of magnetic field change in the previous magnetometer; This represents the trend of magnetic field change after the magnetometer is activated; This is the weighting coefficient for the magnetic field amplitude residual term; The weighting coefficients for the residual term representing the magnetic field change trend are: This is the robust loss function.

[0052] It should be noted that the weighting coefficients of the magnetic field amplitude residual term and the magnetic field change trend residual term are adaptively adjusted based on the degree of magnetic field amplitude fluctuation, the stability of the magnetic field change trend, and the proportion of local anomalies within the target sliding window. If the magnetic field amplitude change is stable and the proportion of anomalies is low within the target sliding window, the weight of the magnetic field amplitude residual term is increased. If there are local magnetic anomalies, abrupt amplitude changes, sensor amplitude bias, or poor amplitude consistency between different magnetometers within the target sliding window, the weight of the magnetic field change trend residual term is increased to reduce the impact of simple magnetic field amplitude differences on the waveform matching path.

[0053] Understandably, in specific implementations, a robust loss function is used to construct the waveform matching cost function, which further improves the accuracy of magnetic field waveform sequence matching, reduces the impact of environmental noise or outliers on the matching results, and provides accurate preconditions for subsequent matching of magnetic field waveform sequences using the dynamic time warping algorithm.

[0054] Optionally, the robust loss function adopts the Tukey double-weight loss function, the expression of which is: , In the formula, r is the local residual during the magnetic field waveform matching process; c is the robust adjustment threshold. This represents the value of the Tukey double-weighted loss function.

[0055] It should be noted that the robust adjustment threshold is adaptively determined based on the dispersion of the magnetic field waveform residual within the current sliding window. It is used to characterize the influence of local magnetic anomalies, metal structure interference, cable electromagnetic interference, vehicle motor interference, and sensor noise on the magnetic field waveform matching in the current underground environment. If the residual fluctuation is large, the proportion of outliers is high, or the magnetic field waveform distortion is obvious within the current sliding window, the robust adjustment threshold is increased to avoid excessive suppression of normal waveform changes. If the residual fluctuation is small and the magnetic field waveform is relatively stable within the current sliding window, the robust adjustment threshold is decreased to enhance the suppression of local outliers.

[0056] The robust adjustment threshold is adaptively determined based on the median absolute deviation of the residuals within the sliding window, and its expression is: , In the formula, This is the residual scale estimate of the q-th magnetometer baseline pair within the k-th sliding window; The i-th local residual within the target sliding window; The robust threshold coefficient; Let q be the robust adjustment threshold corresponding to the q-th magnetometer baseline pair within the k-th sliding window. This represents the median of the local residuals within the target sliding window.

[0057] It should be noted that the robust threshold coefficient is determined based on the intensity of magnetic field interference, the proportion of local anomalies, the degree of magnetic field waveform distortion, and the continuity of magnetic field characteristics in the underground environment. The proportion of local anomalies is the ratio of the number of sampling points in the current sliding window whose local residuals exceed a preset multiple of the residual scale estimate to the total number of sampling points in the target sliding window. When the vehicle is located in an area with dense metal support, near high-voltage cables, near electromechanical equipment, in an area with strong vehicle motor interference, or in an area with a high concentration of local magnetic anomalies, the robust threshold coefficient is reduced to enhance the Tukey double-weight loss function's suppression of outlier residuals. When the vehicle is located in an area with stable magnetic field changes, good waveform continuity, and a low proportion of anomalies, the robust threshold coefficient is increased to preserve the contribution of normal magnetic field waveform changes to the matching path.

[0058] Understandably, the robust matching cost function constructed using the Tukey dual-weight loss function approximates a squared loss when the local residuals in the magnetic field waveform matching process are small, preserving the contribution of normal data to the matching cost. When the local residuals in the magnetic field waveform matching process are large, the loss function's growth tends to level off or even truncate, effectively suppressing the influence of outliers on the matching cost and improving the robustness of the vehicle speed estimation method in complex interference environments. In underground magnetic field matching and positioning, this function can adaptively reduce the weight of abnormal magnetic field sampling points caused by metal structures, high-voltage equipment, etc., preventing them from dominating the matching results and ensuring the stability and accuracy of path matching.

[0059] In addition, the robust loss function can be selected as Huber function, Cauchy function, Geman-McClure function or Welsch function, etc., depending on the noise characteristics of the actual application scenario.

[0060] S1032. Based on the optimal waveform matching path, calculate the local vehicle speed estimate and matching weight of the magnetometer baseline pair.

[0061] First, based on the optimal matching path in each magnetometer baseline pair, the sample delay between the magnetic field waveform sequences of the front and rear magnetometers is calculated.

[0062] For example, the method for calculating the sample delay between the front and rear magnetometers based on the optimal waveform matching path is as follows: In the formula, Let (i,j) be the sample delay of the q-th magnetometer baseline pair within the k-th sliding window; (i,j) is the optimal waveform matching path. The set of matching sampling point indices; ji represents the index delay of the subsequent magnetometer sampling point relative to the previous magnetometer sampling point; This represents the median of the index differences among all matching points in the optimal waveform matching path.

[0063] It should be noted that the median of the index differences among all matching points in the optimal waveform matching path is used to calculate the sample delay, further improving the robustness of the algorithm. Although the optimal matching path has eliminated most outliers, there may still be non-ideal matching points at the start and end of the waveform due to waveform amplitude flatness or local noise. The index differences of these points may cause significant deviations. The median reflects the central tendency of most matching points in the path, thus accurately extracting the true physical time delay between the front and rear magnetometer signals, ensuring the stability of subsequent velocity calculations.

[0064] Secondly, based on the sample delay, magnetometer baseline length, and magnetic field sampling frequency, the vehicle speed estimate for each magnetometer baseline pair is calculated.

[0065] For example, since the vehicle is within the target sliding window, it can be approximated as being in uniform motion. Therefore, the method for calculating the vehicle velocity estimate in a single magnetometer baseline pair can be expressed as follows: , In the formula, This is the estimated vehicle speed for the q-th magnetometer baseline pair within the k-th sliding window. Let be the baseline length of the q-th magnetometer baseline pair; This refers to the sampling frequency of the magnetic field data. Let be the sample delay of the q-th magnetometer baseline pair within the k-th sliding window.

[0066] It should be noted that, on the one hand, the baseline length is a known geometric parameter obtained through offline calibration after the vehicle magnetometer is installed, reflecting the physical distance between the front and rear magnetometers in the vehicle's driving direction; the sampling frequency is a preset constant parameter of the data acquisition system, controlled by a hardware clock to ensure the synchronization of multi-channel sampling. Both of these parameters are deterministic known quantities of the system and do not change with the vehicle's driving state.

[0067] On the other hand, the velocity estimate of the target magnetometer baseline is used to indicate the projected component of the vehicle's speed relative to the ground in the direction of the magnetometer baseline.

[0068] Although the above steps can be used to calculate local vehicle speed estimates based on a single magnetometer baseline, in actual underground parking environments, magnetic field signals are highly susceptible to environmental noise.

[0069] At certain times, a particular magnetometer baseline pair may happen to be in a region of signal distortion or low signal-to-noise ratio, resulting in a large error in the local vehicle speed estimate calculated based on that magnetometer baseline pair. If the speed measurement results of all magnetometer baseline pairs are simply averaged arithmetically, these data with large errors will severely reduce the accuracy of the final speed measurement.

[0070] Therefore, in order to eliminate the negative impact of large-error vehicle speed estimates on the overall speed measurement results, this embodiment introduces the concept of matching weight. By evaluating the matching weight of each magnetometer baseline pair in the target sliding window, the local vehicle speed estimates of multiple magnetometer baseline pairs are weighted and fused to obtain a more robust and accurate target vehicle speed estimate.

[0071] Based on the optimal matching path, the matching weights of the magnetometer baseline pair are calculated, including: First, based on the number of matching points in the optimal matching path and the local matching cost, the average matching residual of each magnetometer baseline pair is calculated.

[0072] For example, the average matching residual for each magnetometer baseline pair within the target sliding window is calculated as follows: , In the formula, Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; This represents the number of matching points in the optimal waveform matching path. The optimal waveform matching path; This represents the cost of local matching.

[0073] Understandably, by statistically analyzing the local matching costs of all matching points on the optimal waveform matching path and calculating their average value, the average matching residual of each magnetometer baseline pair is determined. The average matching residual obtained by normalizing by dividing by the number of matching points eliminates the dimensional influence caused by different path lengths, improves the adaptability to waveform stretching or compression at different driving speeds, and can effectively overcome common local signal distortion or transient noise interference in complex underground magnetic field environments.

[0074] Secondly, the matching weight of each magnetometer baseline pair is determined based on the average matching residual of each magnetometer baseline pair.

[0075] Specifically, based on the average matching residual of each magnetometer baseline pair, the matching weight of each magnetometer baseline pair is determined, including: First, find the minimum average matching residual among all magnetometer baseline pairs.

[0076] The expression for the minimum average local matching residual of all magnetometer baseline pairs within the target sliding window is: , In the formula, Q represents the number of magnetometer baseline pairs participating in the fusion within the k-th sliding window. Let be the average local matching residual corresponding to the q-th magnetometer baseline pair.

[0077] It should be noted that the process of finding the minimum average matching residual among all magnetometer baseline pairs is as follows: First, calculate the average local matching residual of each valid magnetometer baseline pair within the current sliding window; then select the result with the smallest value as the minimum average local matching residual of all magnetometer baseline pairs within the target sliding window, which is used to relatively normalize the matching weight of the magnetometer baseline pairs participating in the velocity fusion calculation.

[0078] Secondly, the matching weight is calculated based on the difference between the average matching residual and the minimum average matching residual for each magnetometer baseline pair.

[0079] In one alternative implementation, the matching weight is calculated based on the average matching residual of each magnetometer baseline as follows: , In the formula, The array fusion weights for the q-th magnetometer baseline pair within the k-th sliding window; Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; The minimum average local matching residual for all magnetometer baseline pairs within the k-th sliding window; is the weight sensitivity coefficient; Q is the number of magnetometer baseline pairs participating in the fusion.

[0080] Understandably, an exponential weighting formula is used, introducing a weight sensitivity coefficient to exponentially calculate the difference between the average matching residual and the minimum residual. The exponential function has non-linear amplification characteristics, significantly enhancing even small differences in the matching residual. This ensures that the magnetometer baseline pair with extremely high matching quality has a large weight in the final vehicle speed fusion, guaranteeing the accuracy and stability of vehicle speed measurement results in confined underground spaces.

[0081] S104. Based on the matching weight, the local vehicle speed estimates of each magnetometer baseline pair are weighted and fused to obtain the target vehicle speed estimate.

[0082] In one alternative implementation, the method for calculating the target vehicle speed estimate can be expressed as: In the formula, v is the estimated target vehicle speed, and w k v represents the matching weight of the k-th magnetometer baseline pair within the target sliding window; kis the local vehicle speed estimate for the k-th magnetometer baseline pair within the target sliding window; M represents the number of magnetometer baseline pairs within the target sliding window.

[0083] Understandably, by calculating the local vehicle speed estimate using the aforementioned weighted fusion formula, a matching weight-based screening mechanism is implemented. In this step, using the matching weight as an indicator of the reliability of each magnetometer baseline pair's data can suppress outliers. For baseline pairs severely affected by magnetic field interference or with poor waveform matching, their corresponding matching residuals are large, and the calculated matching weights approach zero. Therefore, the negative impact on the final speed estimate during the fusion process is minimal, and the final vehicle speed estimation result is not contaminated. This significantly improves the robustness and accuracy of vehicle speed estimation in complex magnetic environments.

[0084] It should be noted that the embodiments of this application mainly take a specific sliding window as an example to illustrate in detail the calculation process of the target vehicle speed estimate within the target sliding window. The target vehicle speed estimate represents the speed estimate at the corresponding moment of the target sliding window, but the method of this application is not limited to this. In practical applications, by moving along the time axis or selecting different sliding windows, the above waveform matching and weighted fusion steps can be repeated to obtain the instantaneous speed estimate of the vehicle at different moments.

[0085] Furthermore, by arranging the aforementioned instantaneous speed estimates in chronological order, a complete vehicle speed curve can be reconstructed. This curve not only reflects the overall speed level of the vehicle as it passes through the detection area, but also precisely depicts the dynamic changes of the vehicle within a specific time period, thereby achieving continuous and high-precision monitoring of the vehicle's motion state.

[0086] To verify the effectiveness of the proposed robust waveform matching-based underground vehicle speed measurement method, multiple comparative experiments were conducted on an actual vehicle testing platform. The experiments included calculations using both the traditional Euclidean distance-based matching method and the proposed robust waveform matching-based method. In this embodiment, the calculations were performed along a 42-meter underground or indoor straight vehicle route.

[0087] The experiment employed an onboard magnetometer array, an inertial measurement unit (IMU), and a reference positioning system as experimental equipment. The onboard magnetometer array was used to collect multi-channel magnetic field data during the operation of the underground engineering vehicle. The IMU was used to collect the vehicle's angular velocity and acceleration data. The reference positioning system was used to provide a reference trajectory for the underground engineering vehicle during its operation and to obtain the reference velocity by differentiating the reference positions at adjacent time points.

[0088] Experimental results show that, compared with traditional dynamic time warping methods based on Euclidean distance, the robust magnetic field waveform matching cost constructed by this invention using the Tukey dual-weight loss function reduces the impact of local magnetic anomalies, sensor noise, and waveform distortion on the matching path, making the sample delay estimation more stable. For short, medium, and long baseline installation distances, the root mean square error of vehicle speed estimation is reduced by approximately 42.83%, 40.18%, and 37.43%, respectively, after applying the robust magnetic field waveform matching method of this invention. This result demonstrates that this invention can effectively suppress the interference of abnormal magnetic field points on the dynamic time warping path and improve the stability of single-baseline magnetic field waveform speed estimation.

[0089] Table 1 shows the performance parameters of the magnetometer used in the experiment.

[0090] Table 1 As shown in Table 1, the magnetometer used in this experiment has high sensitivity and low nonlinear error. This means that the sensor can accurately capture the subtle changes in the geomagnetic field during vehicle operation, and the output signal distortion is extremely low.

[0091] Table 2 shows the performance parameters of the gyroscope and accelerometer in the experiment.

[0092] Table 2 Table 2 shows that the gyroscope and accelerometer used in this experiment have extremely low zero-bias stability and random walk coefficients. This indicates that the inertial measurement unit (IMU) can provide high-precision attitude and displacement calculations in a short time, and its own drift error grows slowly. Combined with the wide range characteristics of the gyroscope and accelerometer, it can accurately cover the vehicle's motion state under various driving conditions. These high-performance parameters ensure that the inertial navigation system can still provide reliable auxiliary positioning information when the magnetic field signal is missing or interfered with, verifying the hardware feasibility of the multi-source fusion scheme of this invention.

[0093] Table 3 shows the root mean square error results of the speed estimation. The methods used are a robust waveform matching-based underground vehicle speed measurement method and an Euclidean distance-based matching method provided by this invention to estimate the underground vehicle speed.

[0094] Table 3 As shown in Table 3, after adopting the underground vehicle speed measurement method based on robust waveform matching of the present invention, the root mean square error of the average speed estimation in the five sets of tests decreased from 0.1912 m / s to 0.1439 m / s, an average reduction of 0.0473 m / s, representing a reduction of approximately 24.7%. This result indicates that the array fusion weighting method based on matching residuals can effectively weaken the influence of low-quality baseline matching results on the final speed estimation, making the fused speed result smoother and more consistent with the reference speed.

[0095] The experimental results above demonstrate the effectiveness and correctness of the method provided by this invention. The method provided by this invention enables vehicle speed estimation using the magnetometer array mounted on the underground engineering vehicle, without relying on satellite signals, UWB base stations, QR code markers, or external cooperative targets. Compared with traditional dynamic time-warped magnetic field waveform matching methods, the method provided by this invention effectively improves the robustness of magnetic field waveform alignment; compared with single magnetometer baseline speed estimation methods, this invention can utilize multiple sets of magnetometer baselines to achieve adaptive weighted fusion, thereby improving the stability and reliability of underground engineering vehicle speed estimation.

[0096] This invention also provides an underground vehicle speed measurement system based on robust waveform matching, comprising: The acquisition module 301 is used to construct multiple magnetometer baseline pairs. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. The magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair are extracted respectively. The window division module 302 is used to divide the magnetic field waveform sequence into multiple sliding windows according to the time axis and determine the target sliding window containing the moment to be measured. The local speed measurement module 303 is used to perform waveform matching in the target sliding window based on the magnetic field waveform sequences of the front and rear magnetometers of each magnetometer baseline pair using a robust dynamic time warping algorithm, and calculate the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair according to the matching results. The calculation module 304 is used to perform weighted fusion of the local vehicle speed estimates of each magnetometer baseline pair based on the matching weights to obtain the target vehicle speed estimate.

[0097] Optionally, in the system described above, a robust dynamic time warping algorithm is used for waveform matching, and the local velocity measurement module 303 is specifically used for: Within the target sliding window, a robust matching cost function is constructed based on the magnetic field waveform sequences of the front and rear magnetometers in each magnetometer baseline pair. The optimal matching path for the magnetic field waveform sequence in each magnetometer baseline pair is then searched using a dynamic time warping method. Based on the optimal waveform matching path, the local vehicle speed estimate and matching weight of the magnetometer baseline pair are calculated.

[0098] As the system implementation is basically similar to the method implementation, it is described in a relatively simple way. For relevant details, please refer to the description of the method implementation.

[0099] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0100] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0101] This invention is described with reference to flowchart illustrations and / or block diagrams of the method, terminal device (system), and computer program product according to the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0102] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0103] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0104] It should be noted that: The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

Claims

1. A method for underground vehicle speed measurement based on robust waveform matching, characterized in that, Includes the following steps: Multiple magnetometer baseline pairs are constructed. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. The magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair are extracted respectively. The magnetic field waveform sequence is divided into multiple sliding windows along the time axis, and a target sliding window containing the moment of velocity to be measured is determined. Within the target sliding window, based on the magnetic field waveform sequences of the front and rear magnetometers corresponding to each magnetometer baseline pair, a robust dynamic time warping algorithm is used for waveform matching. Based on the matching results, the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair are calculated. The local vehicle speed estimates of each magnetometer baseline pair are weighted and fused based on the matching weights to obtain the target vehicle speed estimate.

2. The underground vehicle speed measurement method based on robust waveform matching according to claim 1, characterized in that, Waveform matching is performed using a robust dynamic time warping algorithm, including: Within the target sliding window, a robust matching cost function is constructed based on the magnetic field waveform sequences of the front and rear magnetometers in each magnetometer baseline pair. The optimal matching path for the magnetic field waveform sequence in each magnetometer baseline pair is then searched using a dynamic time warping method. Based on the optimal waveform matching path, the local vehicle speed estimate and matching weight of the magnetometer baseline pair are calculated.

3. The underground vehicle speed measurement method based on robust waveform matching according to claim 2, characterized in that, The specific steps for constructing a robust matching cost function are as follows: ， In the formula, The local matching cost between the i-th front magnetometer sampling point and the j-th back magnetometer sampling point within the k-th sliding window is the q-th magnetometer baseline pair. For the magnetic field observations of the front magnetometer; For the magnetic field observations of the post-magnetic meter; This represents the trend of magnetic field change in the previous magnetometer; This represents the trend of magnetic field change after the magnetometer is activated; This is the weighting coefficient for the magnetic field amplitude residual term; The weighting coefficients for the residual term representing the magnetic field change trend are: This is the robust loss function.

4. The underground vehicle speed measurement method based on robust waveform matching according to claim 3, characterized in that, The robust loss function adopted is the Tukey double-weight loss function, the expression of which is: ， In the formula, r is the local residual during the magnetic field waveform matching process; c is the robust adjustment threshold. This represents the value of the Tukey double-weighted loss function.

5. The underground vehicle speed measurement method based on robust waveform matching according to claim 2, characterized in that, The calculation of the local vehicle speed estimate for the magnetometer baseline pair based on the optimal matching path includes: Based on the optimal matching path in each magnetometer baseline pair, calculate the sample delay between the magnetic field waveform sequences of the front and rear magnetometers. Based on the sample delay, magnetometer baseline length, and magnetic field sampling frequency, the vehicle speed estimate for each magnetometer baseline pair is calculated.

6. The underground vehicle speed measurement method based on robust waveform matching according to claim 2, characterized in that, Based on the optimal matching path, the matching weight of the magnetometer baseline pair is calculated, including: Based on the number of matching points and the local matching cost in the optimal matching path, the average matching residual of each magnetometer baseline pair is calculated. The matching weight of each magnetometer baseline pair is determined based on the average matching residual of each magnetometer baseline pair.

7. The underground vehicle speed measurement method based on robust waveform matching according to claim 6, characterized in that, The determination of the matching weight of each magnetometer baseline pair based on the average matching residual of each magnetometer baseline pair includes: Find the minimum average matching residual among all magnetometer baseline pairs; The matching weight is calculated based on the difference between the average matching residual of each magnetometer baseline pair and the minimum average matching residual.

8. The underground vehicle speed measurement method based on robust waveform matching according to claim 7, characterized in that, The method for calculating the matching weight based on the average matching residual of each magnetometer baseline is as follows: ， In the formula, The array fusion weights for the q-th magnetometer baseline pair within the k-th sliding window; Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; The minimum average local matching residual for all magnetometer baseline pairs within the k-th sliding window; This is the weight sensitivity coefficient; Q represents the number of magnetometer baseline pairs participating in the fusion.

9. The underground vehicle speed measurement method based on robust waveform matching according to claim 8, characterized in that, The method for calculating the average matching residual for each magnetometer baseline pair is as follows: ， In the formula, Let be the average local matching residual of the q-th magnetometer baseline pair within the k-th sliding window; This represents the number of matching points in the optimal waveform matching path. The optimal waveform matching path; This represents the cost of local matching.

10. An underground vehicle speed measurement system based on robust waveform matching, characterized in that, include: The acquisition module is used to construct multiple magnetometer baseline pairs. Each magnetometer baseline pair includes a front magnetometer and a rear magnetometer arranged along the vehicle's driving direction. The magnetic field waveform sequences of the front magnetometer and the rear magnetometer of each baseline pair are extracted respectively. The window division module is used to divide the magnetic field waveform sequence into multiple sliding windows according to the time axis, and to determine the target sliding window that includes the moment to be measured. The local speed measurement module is used to perform waveform matching using a robust dynamic time warping algorithm based on the magnetic field waveform sequences of the front and rear magnetometers corresponding to each magnetometer baseline pair within the target sliding window. Based on the matching results, the module calculates the local vehicle speed estimate and its corresponding matching weight for each magnetometer baseline pair. The calculation module is used to perform weighted fusion of the local vehicle speed estimates of each magnetometer baseline pair based on the matching weights to obtain the target vehicle speed estimate.

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