Method for improving underwater obstacle detection precision based on support vector regression gravity gradient

Abstract

The application relates to a method for improving underwater obstacle detection precision based on support vector regression gravity gradient. The underwater gravity gradient detection technology is beneficial to the safety of the navigation process of a submarine. In order to improve the underwater obstacle detection precision based on the gravity gradient detection technology, the application obtains a gravity gradient difference ratio (GGDR) equation related to only the position of an obstacle by using a difference method and a ratio method on the basis of a gravity gradient calculation formula, proposes a new support vector regression-gravity gradient joint method (SGJM), and verifies the reliability of the new SGJM in detecting underwater obstacles. Experimental results show that the positioning precision in the x and z directions in the obstacle position calculation based on the new SGJM is improved by 88% and 85% respectively. The new SGJM provides a theoretical and method reference for detecting underwater obstacles based on the gravity gradient in the future.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of underwater navigation and marine surveying, and in particular to a method for improving the accuracy of underwater obstacle detection based on support vector regression gravity gradient. Background Technology

[0002] Underwater vehicles, with their high stealth and maneuverability, have been widely used in national defense and scientific fields, such as underwater warfare, oceanographic research, and mineral exploration. Ensuring the safe underwater navigation of these vehicles is crucial for their successful implementation in both military and civilian applications. However, since the 20th century, nearly 500 accidents involving underwater vehicles have occurred, approximately 20% of which were collision-induced sinkings, resulting in the sinking of 84 vehicles. Due to the highly complex seabed environment, the inadequacy of existing detection methods is a significant contributing factor to these numerous accidents. When performing certain special missions, underwater vehicles need to remain concealed, rendering some detection methods that easily reveal their position (such as active sonar) unusable. If obstacles are not detected in time when seabed topography is incorrect or new terrain features appear, collisions are highly likely. Therefore, breakthroughs in real-time, accurate, and passive underwater obstacle detection technology are essential for ensuring the safe underwater navigation of underwater vehicles.

[0003] Underwater obstacle detection is a crucial component of underwater navigation safety. Underwater obstacle detection technologies utilize acoustic signals, optical signals, electromagnetic signals, and gravity gradient signals to detect underwater obstacles. Acoustic signal methods primarily estimate the location and distance of underwater obstacles by recording the propagation time and phase difference of acoustic signals using sonar. They offer advantages such as a large operating range and insensitivity to water turbidity. However, the active emission of signals by acoustic signals exposes the submersible's position, limiting their practical application. Optical signal methods acquire environmental information by receiving ambient light, offering high resolution and refresh rates. However, underwater lighting conditions are complex (e.g., light absorption and scattering), limiting the detection range of optical signal methods. Electromagnetic sensor methods can estimate underwater distances. However, environmental electromagnetic fields can interfere with measurement accuracy. Each of these underwater obstacle detection technologies has its advantages and disadvantages, requiring researchers to combine multiple technologies in practice to complete various underwater obstacle detection tasks. Based on this, the gravity gradient signal method, as a passive detection method, has the characteristics of high sensitivity, good concealment, all-weather and real-time performance, which meets the requirements of safe navigation of submersibles under covert conditions and has important application value.

[0004] Gravity gradients reflect subtle changes in the gravitational field. For high-density objects, their mass can be accurately estimated by measuring the resulting gravity gradient. For obstacle detection in unknown sea areas (such as those with missing or insufficiently resolved gravity gradient reference maps), a gravity gradient differential ratio method without a reference map is proposed. This method establishes a gravity gradient differential ratio (GGDR) equation that depends only on the obstacle's location and uses the Newton-Raphson method (NRM) to solve the GGDR equation to obtain the obstacle's location. However, if the initial values ​​chosen when using NRM to solve the GGDR equation are inappropriate, the calculation results may not converge, leading to low detection accuracy. Summary of the Invention

[0005] This application provides a method for obstacle detection, a method for training an obstacle detection model, and an electronic device, with the aim of improving the accuracy of obstacle localization.

[0006] Firstly, a method for obstacle detection is provided, including:

[0007] Obtain the gravity gradient difference ratio function of the obstacle;

[0008] The gravity gradient difference ratio function is input into the obstacle detection model to predict the location or mass of the obstacle, wherein the obstacle detection model satisfies:

[0009]

[0010] λ i and Represents the Lagrange multipliers. m i Let φ(m) be the gravity gradient difference ratio function. i ) represents the input space m i The high-dimensional feature space of nonlinear mappings; f(m i ) is the kernel function The corresponding predicted value.

[0011] In conjunction with the first aspect, in some implementations of the first aspect, the gravity gradient difference ratio function satisfies:

[0012] rΔT=ΔT (t) / ΔT (t+1) =(To (t+1) -To (t) ) / (To (t+2) -To (t+1) )

[0013] To represents the gravitational gradient caused by the obstacle.

[0014] In conjunction with the first aspect, in some implementations of the first aspect, the obstacle detection model is used to output position detection information in the target direction, and the gravity gradient difference ratio function includes the gravity gradient related to the target direction.

[0015] In conjunction with the first aspect, in some implementations of the first aspect, the method further includes:

[0016] Based on the obstacle's location detection information, the mass of the obstacle is determined, wherein the location detection information and the mass satisfy any one of the following:

[0017] ΔT xx (t) =Gmr t+1 -5 (3x t+1 2 -r t+1 2 )-Gmr -5 (3x t 2 -r t 2 )

[0018] ΔT yy (t) =Gmr t+1 -5 (3y t+1 2 -r t+1 2 )-Gmr -5 (3y t 2 -r t 2 )

[0019] ΔT zz (t) =Gmr t+1 -5 (3z t+1 2 -r t+1 2 )-Gmr -5 (3z t 2 -r t 2 )

[0020] ΔT xy (t) =3Gmr t+1 -5 x t+1 yt+1 -3Gmr t -5 x t y t

[0021] ΔT xz (t) =3Gmr t+1 -5 x t+1 z t+1 -3Gmr t -5 x t z t

[0022] ΔT yz (t) =3Gmr t+1 -5 y t+1 z t+1 -3Gmr t -5 y t z t

[0023] G represents the gravitational constant, m represents the mass of the obstacle, (x t ,y t ,z t () represents the coordinates of point P, the position of the submersible, during the t-th measurement.

[0024] In conjunction with the first aspect, in some implementations of the first aspect, the kernel function K(m) i ,m i ( ) Meets at least one of the following:

[0025]

[0026]

[0027]

[0028]

[0029] In conjunction with the first aspect, in some implementations of the first aspect, The value of is [-50,0) or (0,50], and the value of l is [-50,50].

[0030] Secondly, a method for training an obstacle detection model is provided, including:

[0031] Multiple samples are acquired, each sample including a gravity gradient difference ratio function and corresponding real detection information, wherein the real detection information is position detection information or mass detection information;

[0032] The multiple samples are fed into the obstacle detection model, and the obstacle detection model satisfies... And for the obstacle detection model The optimization of l is performed to ensure that the predicted value of each sample and the corresponding true detection information satisfy the following conditions: The minimum value is found, where λ i and Represents the Lagrange multipliers. m i Let φ(m) be the gravity gradient difference ratio function. i ) represents the input space m i The high-dimensional feature space of the nonlinear mapping, f(m i y is the predicted value of the sample. i This represents the actual detection information, ξ and Let ξ and ξ be slack variables. At least one is 0, ε is the pipe size, C is the penalty term parameter, and C > 0.

[0033] In conjunction with the second aspect, in some implementations of the second aspect, the real detection information of the multiple samples includes the position detection information of the target direction, and the obstacle detection model is the detection model of the target direction.

[0034] In conjunction with the second aspect, in some implementations of the second aspect, the acquisition of multiple samples includes:

[0035] The Median Deviation (MAD) algorithm is used to remove outliers whose deviation from the median exceeds a preset range.

[0036] In conjunction with the second aspect, in some implementations of the second aspect, the kernel function K(m) i ,m i ( ) Meets at least one of the following:

[0037]

[0038]

[0039]

[0040]

[0041] Thirdly, an electronic device is provided for performing the method as described in any of the implementations of the first aspect above.

[0042] Compared with the prior art, the solution provided in this application has at least the following beneficial technical effects:

[0043] Kernel functions help researchers handle feature spaces of arbitrary dimensions without explicitly calculating the mapping φ(m); any function satisfying the Mercer condition can be used as a kernel function. This invention establishes the intrinsic relationship between the gravity gradient difference ratio and the obstacle position, implicitly explaining their mathematical relationship.

[0044] The mean absolute error and root mean square error (RMSE) of the positioning results were obtained by comparing the calculated and actual values ​​of underwater obstacle locations. The SGJM's mean absolute error and RMSE are both lower than those of the NRM. In the y-direction, the SGJM's mean absolute error and RMSE are slightly better than the NRM, while in the x and z directions, the SGJM's mean absolute error and RMSE are significantly better than the NRM. Specifically, the accuracy in the x-direction is improved by 88%, the y-direction by 6%, and the z-direction by 85%. The improvement in y-direction positioning accuracy is relatively low because the NRM has higher positioning accuracy in the y-direction. The positioning error of the SGJM is significantly better than that of the NRM. The positioning error of the SGJM in each direction increases with distance but remains within the range of -4 to 4 meters. The new SGJM effectively improves the positioning accuracy of the traditional NRM. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of a hyperplane.

[0046] Figure 2 The flowchart shows the new support vector regression-gravity gradient joint method.

[0047] Figure 3 This is an obstacle model.

[0048] Figure 4 This is a plane diagram of the full tensor gravity gradient of the simulation model.

[0049] Figure 5 The relationship between the gravity gradiometer and distance. (a) Gravity gradient varies with distance on different planes. (b) Gravity gradient accuracy varies with distance.

[0050] Figure 6 The process of building a difference ratio dataset.

[0051] Figure 7 This is a schematic diagram showing the distribution of survey lines and the location of obstacles.

[0052] Figure 8 This represents the error distribution of the positioning results.

[0053] Figure 9 This represents the variation of relative error and signal-to-noise ratio with distance.

[0054] Figure 10 Error diagram of SGJM positioning results.

[0055] Figure 11 Error diagram of NRM positioning results.

[0056] Figure 12 This represents the change in signal-to-noise ratio.

[0057] Figure 13 For comparison of relative errors.

[0058] Figure 14 This is a comparison chart of the relative errors of NRM and SGJM. Detailed Implementation

[0059] The present application will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0060] The Earth is an irregularly shaped ellipsoid with uneven density distribution across its surface, resulting in variations in gravity gradients across different locations. For example, the vertical gravity gradient can be divided into two parts: a normal vertical gravity gradient, assumed to be caused by a rotating ellipsoid with uniform density distribution; and an anomaly in the vertical gravity gradient, caused by the difference between the actual vertical gravity gradient induced by the Earth and the normal vertical gravity gradient. Similarly, the difference in density between an underwater obstacle and its surrounding environment creates differences in gravity gradients, which contain information such as the obstacle's location and mass. Therefore, given sufficiently high accuracy of the gravity gradiometer, it is feasible to detect underwater obstacles by analyzing the gravity gradients they cause.

[0061] The gravity gradient differential ratio method transforms obstacle detection into a problem of solving high-order nonlinear equations. Assume a uniformly dense obstacle and a submersible equipped with a gravity gradiometer exist in a seawater environment. Establish a Cartesian coordinate system (right-handed) with the obstacle's centroid as the origin, the x-axis parallel to the submersible's path and with the submersible's direction of motion as positive. Then, the obstacle's centroid coordinates in the Cartesian coordinate system are O(0,0,0), and the submersible's position coordinates are P(x,y,z) (the coordinates of the gravity gradiometer measurement point relative to the obstacle's centroid, reflecting the obstacle's position). The t-th gravity gradient recorded by the submersible at point P can be described as:

[0062]

[0063] Where To represents the gravitational gradient caused by the obstacle. This represents the component of the gravitational gradient caused by the obstacle in the direction D. The value of underwater ambient noise in the D direction is represented by Tn, G represents the gravitational constant, and m represents the mass of the obstacle. t,y t ,z t () represents the coordinates of point P, the position of the submersible, during the t-th measurement. This represents the distance from point P, the position of the submersible, to point O, the center of the obstacle, during the t-th measurement.

[0064] If gravity gradient data are recorded twice within a short period during the underwater navigation of a submersible, the difference between these two data points can be considered to be mainly caused by the relative positional change between the submersible and the underwater obstacle. Therefore, subtracting the two short-term gravity gradient data points can eliminate the underwater environmental noise Tn, thereby isolating the submersible and the obstacle from the surrounding environment. The gravity gradient difference ΔT is calculated as follows:

[0065]

[0066] in, This represents the component of the gravitational gradient difference in the D direction.

[0067] As shown in formula (2), the gravity gradient difference ΔT after eliminating environmental noise still includes the mass of the obstacle. Since the mass of the obstacle cannot be determined in advance, the influence of the obstacle mass is eliminated by a ratio, which requires quotienting the two gravity gradient differences to obtain the gravity gradient difference ratio function that is only related to the position of the obstacle:

[0068]

[0069] Where rΔT represents the gravity gradient difference ratio. This represents the component of the gravity gradient difference ratio in the D direction.

[0070] Expanding equation (3) further into integral form, we obtain the gravity gradient difference ratio integral function, which depends only on the position of the obstacle:

[0071]

[0072] Wherein, the integration region of the integral function is the space enclosed by the outline of the obstacle, and (a,b,c) are the coordinates of the obstacle volume element; If Δs is the distance interval recorded by the gravity gradient, then x t+1 =x t +Δs;y t =y t+1 , z t =z t+1 .

[0073] Moving the integral of equation (4) from the right side to the left side of the equation and setting the right side to 0, we obtain the GGDR equation consisting of higher-order nonlinear equations with unknowns x, y, and z:

[0074]

[0075] The GGDR equation (formula (5)) is a high-order nonlinear equation. For solving high-order nonlinear equations, the traditional NRM is generally used. The mass of the obstacle can also be obtained by substituting the obstacle position obtained from the solution into formula (2). However, NRM is an iterative algorithm, and the selection of initial values ​​is very important. Inappropriate initial values ​​will lead to non-convergence of calculation results and low detection accuracy.

[0076] This invention proposes a novel Support Vector Regression-Gravity Gradient Joint Method (SGJM), such as... Figure 2 As shown, the novel SGJM transforms the obstacle detection problem into a high-order nonlinear equation problem using the gravity gradient differential ratio method, and then determines the underwater obstacle location by calculating a regression function. First, gravity gradient differential ratio data induced by simulated obstacles is calculated using the gravity gradient differential ratio method. The gravity gradient differential ratio data and the corresponding obstacle location (and / or obstacle mass) are used as input and output to construct a differential ratio dataset. Then, based on the differential ratio dataset, parameter optimization (training), testing, and reliability verification of the regression function are performed. This application also compares the underwater obstacle detection results of SGJM and NRM under the same experimental environment, verifying the improvement in obstacle localization accuracy achieved by the SGJM of this invention.

[0077] This application uses one embodiment as an example to illustrate the parameter optimization process of the novel obstacle detection method provided in this application embodiment.

[0078] Simulated obstacles were constructed using protruding seabed rocks as a reference. The simulated obstacles were solid cubic prisms, 50m × 50m × 50m in size, with uniform density distribution. The density was set to σ = 2.7 t / m³, referencing the density of the seabed crust. 3 ,like Figure 3 As shown. The gravity gradient data simulation area is 1000m×1000m×200m, and the centroid of the model is located at the center of the vertical projection of the data simulation area. Each point can generate a set of gravity gradient difference ratio data independently according to formula (4). Assume that the sensitivity of the gravity gradiometer is 10. -5 E. Therefore, when verifying the reliability of the new SGJM, a root mean square error of 10 was added to the simulated gravity gradient data. -5 E's environmental noise.

[0079] Combining formula (1), the gravity gradient distribution caused by the simulated obstacle (cubic prism) on the z = 100m plane is obtained, as follows: Figure 4As shown, the gravity gradient caused by the simulated obstacle at a horizontal plane 100m directly above it exhibits a very regular distribution characteristic, showing different trends for different gravity gradient components. The maximum value of the gravity gradient anomaly is 44.5E, the minimum is -22.3E, and the average is -6 × 10⁻⁶. -8 E, with a resolution of 10m × 10m. When the submersible travels towards the obstacle along a direction parallel to the x-axis, there will always be instances where the submersible's x-coordinate relative to the obstacle is negative. Therefore, it is only necessary to establish the relationship between the gravity gradient characteristics of the obstacle in the negative x-axis direction and the obstacle's position. Assuming the obstacle is located to the left of the submersible's forward direction, gravity gradient difference ratio data generated from points with coordinates in the ranges x∈[-500,-130], y∈[-200,-10], and z∈[10,200] are selected as data for the reliability verification experiment, such as... Figure 4 The area enclosed by the dotted line is the area for selecting experimental data.

[0080] To more intuitively understand the relationship between the detection accuracy and detection distance of a gravity gradiometer, the vertical gravity gradient generated by a simulated obstacle at different straight-line distances was calculated, thus obtaining the relationship between the accuracy of the vertical gravity gradient and the detection distance. Figure 5 As shown. According to Figure 5 (b) It can be seen that when the accuracy of the gravity gradiometer is 10... -2 The gravity gradient-based underwater obstacle detection method can detect underwater obstacles at a slant distance of up to 700m, when the gravity gradiometer accuracy is 10. -3 At speed E, underwater obstacles can be detected at a slant distance of up to 1200m, when the gravity gradiometer accuracy is 10. -4 At time E, underwater obstacles can be detected at a slant distance of up to 1700m. Therefore, 10 -5 The gravity gradient data caused by simulated obstacles of E-precision meets the accuracy requirements for underwater obstacle detection methods based on gravity gradients to detect obstacles within a slant distance of 700m.

[0081] The simulated gravity gradient data is converted into gravity gradient difference ratios using formula (3). A difference ratio dataset is constructed using the gravity gradient difference ratios as input and the corresponding obstacle positions as outputs, preparing for the subsequent obstacle detection model training. The difference ratio dataset contains 15200 samples, each containing 6 features (components of the gravity gradient in the directions D = xx, yy, zz, xy, xz, yz) and 3 expected values ​​(x, y, z). The method for constructing the difference ratio dataset for obstacle detection model training is as follows: Figure 6 As shown. The first step is to simulate gravity gradient data. The full tensor gravity gradient anomaly caused by the simulated obstacle is calculated using formula (1), with a root mean square error of 10. -5E's environmental noise; the second step is to calculate the gravity gradient difference ratio rΔT, input the gravity gradient data into formula (3) to output the gravity gradient difference ratio, which corresponds to the coordinates of the calculation point; the third step is to divide the difference ratio dataset into three datasets according to different coordinate components, and combine rΔT with x, y and z respectively to obtain dataset 1 (for training the x-direction detection model), dataset 2 (for training the y-direction detection model) and dataset 3 (for training the z-direction detection model).

[0082] In the above embodiment, rΔT = ΔT (t) / ΔT (t+1) =(To (t+1) -To (t) ) / (To (t+2) -To (t+1) In other embodiments, rΔT can be constructed from any two distinct gravitational gradient differences within a short period of time, where the gravitational gradient difference can be any two gravitational gradients within that short period of time. For example,

[0083] rΔT=ΔT (t) / ΔT (t+1) =2*(To (t+1) -To (t) ) / (To (t+2) -To (t) For example,

[0084] rΔT=ΔT (t) / ΔT (t+1) =2*(To (t+1) -To (t) ) / (To (t+3) -To (t+2) This application does not limit the scope of the embodiments. Constructing rΔT by combining multiple gravity gradients over a period of time is beneficial for increasing the amount of data and also for improving the compatibility of parameter optimization.

[0085] In some embodiments, datasets 1, 2, and 3 can be identical, i.e., rΔT can be used as the input φ(m) of the obstacle detection model. i ).

[0086] In other embodiments, the dataset 1 described above can remove data in rΔT that is irrelevant to the x-direction (see formula (3)) and retain only rΔT. xx (t) 、rΔT xy (t) 、rΔT xz (t) φ(m) as the input obstacle detection model iThe dataset 2 above can remove data in rΔT that are irrelevant to the y-direction (see formula (3)), retaining only rΔT. yy (t) 、rΔT xy (t) 、rΔT yz (t) φ(m) as the input obstacle detection model i The dataset 3 above can be used to remove data in rΔT that are irrelevant to the z-direction (see formula (3)), retaining only rΔT. zz (t) 、rΔT xz (t) 、rΔT yz (t) φ(m) as the input obstacle detection model i ).

[0087] The reliability of underwater obstacle detection based on the novel SGJM was verified through simulation experiments. Four survey lines were designed based on whether the underwater obstacle was in the path of travel. The gravity gradient difference ratio generated on the four survey lines was input into the obstacle detection model (including three detection models in the x, y, and z directions) to obtain the obstacle position. Then, the reliability of the novel SGJM was verified by comparing the actual value and the calculated value of the obstacle position.

[0088] During data simulation, the gravity gradient values ​​spanned multiple orders of magnitude. The quotient of large-order-of-magnitude gravity gradient differences with small-order-of-magnitude differences can lead to outliers in the gravity gradient difference ratio calculation. These outliers negatively impact the regression results of the obstacle detection model. To obtain a better training model, the data needs to be kept within a stable range. First, the gravity gradient difference ratio data is analyzed, and an initial threshold is selected to remove larger outliers. Then, the Median Absolute Deviation (MAD) algorithm is used to determine outliers by judging whether the deviation of each element from the median is within a reasonable range, and these outliers are then removed. The specific calculation formula for the Median Absolute Deviation algorithm is as follows:

[0089] MAD = median|rΔT i -median|rΔT|| (6)

[0090] Where median(Ψ) represents the median of all elements in Ψ.

[0091] The data was adjusted using MAD as follows:

[0092]

[0093] Where ν represents a parameter, and its value is 3.

[0094] The difference ratio dataset is divided into training, validation, and test sets: the training set is used to train the intrinsic parameters of the obstacle detection model; the validation set is typically used to tune hyperparameters, determining which set of hyperparameters has the best performance based on the performance of several models on the validation set; and the test set is used to evaluate the model's generalization ability. This invention extracts four test lines from the difference ratio dataset as the test set, randomly extracts 80% of the remaining data as the training set, and uses the remaining 20% ​​as the validation set.

[0095] In this embodiment, the obstacle detection model described above can be represented as follows:

[0096]

[0097] Where, λ i and Represents the Lagrange multipliers.

[0098] This represents the kernel function, where the value of the kernel is equal to the feature space φ(m). i ) T and φ(m) i Two vectors in ) and M i The inner product, i.e. m i =rΔT i In other words, dataset kernel functions help researchers handle feature spaces of arbitrary dimensions without explicitly calculating the mapping φ(m). i Any function that satisfies the Mercer condition can be used as a kernel function. The solution can be approximated using any of the methods shown in Table 1.

[0099] Table 1. Common Kernel Function Types and Expressions

[0100] Kernel function type Kernel function expression linear <![CDATA[K(x i ,x j )=x i T x j ]]> polynomial <![CDATA[K(x i ,x j )=(γx i T x j +r) d ,γ>0]]> Radial basis functions (RBF) <![CDATA[K(x i ,x j )=exp(-γ||x i -x j || 2 ),γ>0]]> Sigmod <![CDATA[K(x i ,x j )=tanh(γx i T x j +r)]]>

[0101] f(m i ) represents the kernel function The corresponding expected value. In this embodiment, f(m) i The position information in the x / y / z directions can be used. Inputting the position information in the x / y / z directions into formula (2) above can also yield the mass information of the obstacle. In other embodiments, f(m) i It can also be information about the quality of obstacles.

[0102] Equation (8) establishes the intrinsic relationship between the gravity gradient difference ratio and the obstacle position / mass, implicitly explaining their mathematical relationship. In the trained obstacle detection model, and l are the optimized parameters. The obstacle detection method provided in this application obtains the corresponding obstacle position / mass by substituting the new gravity gradient difference ratio into formula (8). The principle of the above obstacle detection model is explained below.

[0103] Let the sample set A = {(x i ,y i Let x = |i = 1, 2, ..., n}, where x i Represents the input vector; y i Represents the output vector (usually 1-dimensional); x∈R v , where v represents the dimension of the sample dataset. Let the regression model be:

[0104] y = f(x) = ω T φ(x)+l (9)

[0105] Here, φ(x) represents the high-dimensional feature space of the nonlinear mapping of the input space x. ω and l are model parameters.

[0106] Support Vector Regression (SVR) algorithms have unique advantages over traditional regression algorithms. Traditional regression models calculate loss only when the output value f(x) is not equal to the true value y. Support Vector Regression (SVR) algorithms, on the other hand, do not calculate loss when the absolute value of the difference between f(x) and y is not greater than the "tube size" parameter ε; they only calculate loss when the absolute value of the difference between f(x) and y is greater than ε.

[0107] according to Figure 1 As can be seen, assuming there exist two hyperplanes (as shown by the dashed line in the figure) parallel to hyperplane h0, and the region enclosed by the two hyperplanes is called the "spacer zone", then the geometrical space between the two hyperplanes can be expressed as:

[0108]

[0109] Based on the idea of ​​maximizing the margin and minimizing the loss in support vector machines, to obtain an optimal hyperplane, we need to maximize the margin and minimize the loss calculation. Therefore, the coefficients ω and b are estimated by minimizing equation (11):

[0110]

[0111] In practice, it's often impossible to directly find a suitable ε that ensures most data falls within the "interval band." To allow more data to fall within the "interval band," slack variables ξ and ε are added. Some samples are allowed to be outside the interval band, but must meet the following conditions: It is worth noting that for any sample x i When it is on or inside the spacer band, ξ = 0; when it is above the spacer band, ξ > 0. When below the gap band, ξ = 0.

[0112] Formula (11) is a convex optimization problem, which introduces Lagrange multipliers. The calculation is performed using the Lagrange multiplier method. The Lagrange function can be written as follows:

[0113]

[0114] With respect to the independent variables ω, b, ξ of the Lagrange function, Taking the partial derivative and setting it to 0, we get:

[0115]

[0116] Substituting equation (13) into equation (12) yields the dual problem:

[0117]

[0118] In some embodiments, the dual problem described above can satisfy KKT constraints:

[0119]

[0120] By analyzing the above formula, we can deduce that when f(x) i )-y i -ε-ξ i =0 when λ i It can be a non-zero value, when y i -f(x i )-ε-ξ i =0 It can be a non-zero value. Since the above two equations cannot both be true simultaneously, therefore, λ i and At least one of them has a value of 0.

[0121] Solving formula (11), we obtain the following expression:

[0122]

[0123] In the sample set, the condition that satisfies... The samples can be viewed as support vectors for a support vector regression machine, with these points falling outside the interval band. In this case, the support vectors of the support vector regression machine still exhibit sparsity, which is different from the support vector classifier.

[0124] From the KKT constraints in formula (15), it can be seen that for each sample, (C-λ) i )ξ i =0 and λ i (f(x i )-y i -ε-ξ i ) = 0, therefore, if 0 < λ i If <C, then ξ must exist. i =0, thus obtaining the formula for calculating l:

[0125]

[0126] Finally, a kernel function is introduced, and φ(x) is used to replace x, resulting in the final obstacle detection model:

[0127]

[0128] This application also provides an electronic device for performing the above-described obstacle detection method, and / or for performing the above-described obstacle detection model training method.

[0129] In one embodiment, Figure 7 The gravity gradient difference ratio data from the four survey lines shown are sequentially input into the obstacle detection model to obtain the obstacle position calculation results. The mean absolute error and root mean square error of the positioning error are obtained by statistically analyzing the calculated and actual obstacle positions. The minimum and maximum coefficients of determination for the x-direction detection model of the four survey lines are 0.993 and 0.999, respectively, demonstrating a high degree of model fit. Because the coordinates in the y and z directions remain unchanged in each survey line, the coefficients of determination for the y and z directions of the detection model cannot be calculated. The positioning errors of the obstacle detection in the three directions for each survey line are as follows: Figure 8 As shown, the signal-to-noise ratio and relative error are as follows: Figure 9 As shown.

[0130] The mean absolute error of the underwater obstacle detection results for survey lines 1-4 is approximately 2.25m, with a range of 0.71-5.39m. Specifically, the maximum mean absolute error in the x-direction is 2.52m, and the minimum is 1.34m; the maximum mean absolute error in the y-direction is 5.39m, and the minimum is 1.43m; and the maximum mean absolute error in the z-direction is 3.39m, and the minimum is 0.71m. The mean root mean square error (RMSE) of the underwater obstacle detection results for survey lines 1-4 is approximately 3.48m, with a range of 0.99-7.58m. The mean absolute error of the traditional acoustic underwater positioning algorithm is 7.05m. Therefore, the positioning accuracy of the new SGJM is superior to that of traditional underwater positioning methods.

[0131] according to Figure 8It can be seen that the detection errors in the x, y, and z directions of survey lines 1 to 4 are mostly between -5 and 5 meters. For example... Figure 8 (a)~(d), survey lines 1~2 have better positioning effects in the x and z directions; such as Figure 8 (g)~(h), the positioning effect of survey line 4 in the y direction is better; such as Figure 8 (e) to (f), the positioning results of survey line 3 are relatively worse than those of survey lines 1, 2, and 4, but the positioning error is still within the obstacle size range, and the obstacle position can still be accurately located. Therefore, Figure 8 The positioning results demonstrate the effectiveness and reliability of the new SGJM.

[0132] according to Figure 9 From (a) to (d), it can be seen that the relative errors in underwater obstacle positioning for survey lines 1-4 in the x-direction, survey lines 1-2 in the z-direction, and survey line 4 in the y-direction are within 4% when the distance is less than 500m; the relative error in the y-direction of survey line 1 is within 8% when the distance is less than 500m; the relative errors in other directions are larger, with the maximum relative error being 24.6%. Figure 9 As can be seen from (e) to (h), the signal-to-noise ratio decreases as the distance increases, while the impact of environmental noise increases.

[0133] In summary, the novel SGJM exhibits superior detection accuracy compared to traditional acoustic underwater obstacle detection methods. The varying positioning accuracy across different survey lines is attributed to their different locations. Survey line 3, being closer to the boundary of the differential ratio dataset used for training, performs worse in this regard compared to survey line 1, which is closer to the simulated data center. Similarly, survey lines 2 (y-direction) and 4 (z-direction) are also close to the dataset boundary; this data imbalance results in relatively poor positioning in these directions. The larger relative errors in some directions of survey lines 2-4 are due to the smaller true values ​​of y and z in these lines, leading to larger relative errors.

[0134] The novel SGJM was applied to underwater obstacle detection, and a traditional NRM was used as a control, demonstrating that the SGJM has better detection accuracy. A simulation experiment was conducted, assuming the underwater obstacle was a rectangular prism of 80m × 40m × 20m with a density of 2.7t / m³. 3 A Cartesian coordinate system (right-handed) was established with the obstacle's center of mass as the origin. The submersible's motion direction was parallel to the positive x-axis, with the initial coordinates at (-400m, 70m, -60m) and a velocity of 10m / s. The gravity gradiometer recorded data once per second. A root mean square error of 10 was added to the simulated gravity gradient data. -5 E's environmental noise.

[0135] The mean absolute error and root mean square error of the positioning results are obtained by comparing the calculated and actual values ​​of the underwater obstacle locations. The positioning error of the new SGJM is as follows: Figure 10 As shown. The positioning error of traditional NRM is as follows. Figure 11 As shown. The signal-to-noise ratio of SGJM and NRM is as follows. Figure 12 As shown, the relative error comparison is as follows: Figure 13 and Figure 14 As shown.

[0136] The mean absolute error and root mean square error (RMSE) of SGJM are both smaller than those of NRM. In the y-direction, the mean absolute error and RMSE of SGJM are slightly better than those of NRM, while in the x and z directions, the mean absolute error and RMSE of SGJM are significantly better than those of NRM. Specifically, the accuracy in the x-direction is improved by 88%, the accuracy in the y-direction by 6%, and the accuracy in the z-direction by 85%. The improvement in y-direction positioning accuracy is relatively low because NRM has higher positioning accuracy in the y-direction.

[0137] according to Figure 10 and Figure 11 It can be seen that the positioning error of SGJM is significantly better than that of NRM. The positioning error of SGJM in each direction increases with the increase of distance, but still remains within the range of -4 to 4m. Figure 12 It can be seen that the signal-to-noise ratio decreases with increasing distance, while the impact of environmental noise increases. According to... Figure 13 and Figure 14 It can be seen that the obstacle location accuracy (RE) of NRM is within 6% at a distance of less than 360m, while that of SGJM is within 4% at a distance of less than 410m and within 2% at a distance of less than 290m. SGJM has higher obstacle location accuracy than NRM. Therefore, the new SGJM effectively improves the positioning accuracy of traditional NRM.

[0138] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims of the present invention.

Claims

1. A method for obstacle detection, characterized in that, include: Obtain the gravity gradient difference ratio function of the obstacle; The gravity gradient difference ratio function is input into the obstacle detection model to predict the location or mass of the obstacle, wherein the obstacle detection model satisfies: and Represents the Lagrange multipliers. , ; , The gravity gradient difference ratio function is... Indicates input space The high-dimensional feature space of nonlinear mapping; For kernel function The corresponding predicted value; The gravity gradient difference ratio function satisfies: This represents the gravitational gradient caused by the obstacle.

2. The method according to claim 1, characterized in that, The obstacle detection model is used to output position detection information in the target direction, and the gravity gradient difference ratio function includes the gravity gradient related to the target direction.

3. The method according to claim 1, characterized in that, The method further includes: Based on the obstacle's location detection information, the mass of the obstacle is determined, wherein the location detection information and the mass satisfy any one of the following: Represents the gravitational constant. Indicates the mass of the obstacle. Indicates the first Submarine position during the second measurement The coordinates of the point .

4. The method according to claim 1, characterized in that, The kernel function Meet at least one of the following: ； ； ； 。 5. The method according to claim 1, characterized in that, The value can be [-50, 0) or (0, 50]. l The value of is [-50, 50].

6. A method for training an obstacle detection model, characterized in that, include: Multiple samples are acquired, each sample including a gravity gradient difference ratio function and corresponding real detection information, wherein the real detection information is position detection information or mass detection information; The multiple samples are fed into the obstacle detection model, and the obstacle detection model satisfies... and for the obstacle detection model and l The goal is to find the optimal value for each sample so that the predicted value and the corresponding real detection information satisfy the following conditions: , The minimum value is found in the following case: and Represents the Lagrange multipliers. , , For kernel function, The gravity gradient difference ratio function is... Indicates input space The high-dimensional feature space of nonlinear mapping, For the predicted value of the sample, y i This represents the actual detection information. and As slack variables, and At least one is 0, ε is the pipe size, and C is the penalty term parameter. ; The gravity gradient difference ratio function satisfies: This represents the gravitational gradient caused by the obstacle.

7. The method according to claim 6, characterized in that, The real detection information of the multiple samples includes the position detection information of the target direction, and the obstacle detection model is the detection model of the target direction.

8. The method according to claim 6, characterized in that, The acquisition of multiple samples includes: The Median Deviation (MAD) algorithm is used to remove outliers whose deviation from the median exceeds a preset range.

9. The method according to claim 6 or 7, characterized in that, The kernel function Meet at least one of the following: ； ； ； 。 10. An electronic device, characterized in that, The electronic device is used to perform the method as described in any one of claims 1 to 9.

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