A water depth interpolation method considering the precision and distribution difference of original water depth data

Abstract

The application provides a water depth interpolation method considering the precision and distribution difference of original water depth data, and belongs to the technical field of marine surveying and mapping. The method comprises the following steps: obtaining original water depth data; obtaining the coordinates of a point to be interpolated; dividing the surrounding area of the point to be interpolated into four sub-areas at an angle of 90 degrees, and finding four original water depth points closest to the point to be interpolated in each sub-area as reference points; constructing a multi-factor fusion water depth interpolation model: constructing a variogram model to quantify spatial variability, combining inverse distance weighting method to calculate distance factor, calculating the precision, direction and distribution of water depth data; fusing the three factors, and using weighted average method to calculate the water depth of the interpolation point combined with the multi-factor weight. The application overcomes the deficiency that the traditional method does not fully consider the distribution and precision difference of water depth data when processing the water depth data, effectively considers the characteristics of the precision and distribution difference of the original water depth by fusing the multi-factor weight, and effectively improves the interpolation precision.

Description

Technical Field

[0001] This invention belongs to the field of marine surveying and mapping technology, and relates to a water depth interpolation method that takes into account the accuracy and distribution differences of the original water depth data. Background Technology

[0002] Water depth interpolation refers to the process of estimating water depth values ​​at unmeasured locations within a study area using known discrete water depth data and certain mathematical methods or algorithms. Choosing an appropriate interpolation method can effectively improve the accuracy and reliability of water depth data, providing strong support for navigation safety, marine engineering construction, and other fields. Numerous scholars abroad have conducted a series of related research studies on water depth interpolation methods.

[0003] In the study of interpolation methods, Amoroso pointed out through comparative analysis with other interpolation methods that Kriging interpolation is one of the best choices for interpolation of heterogeneous spatial data due to its strong adaptability (Amoroso PP, Aguilar FJ, Parente C, et al. Statistical Assessment of Some Interpolation Methods for Building Grid Format Digital Bathymetric Models [J]. Remote Sensing, 2023, 15(8): 2072.). Maleika significantly improved the accuracy of water depth interpolation by optimizing the inverse distance weighting method (Maleika W. Inverse distance weighting method optimization in the process of digitalterrain model creation based on data collected from a multibeam Echosounder[J]. Applied Geomatics, 2020, 12(4): 397–407.). In domestic research, Shi Chaojian proposed a method to obtain continuous depth values ​​by interpolating discrete and irregularly distributed nautical chart depth data using neural network technology (Shi Chaojian. Research on Depth Interpolation Based on Neural Network [J]. China Navigation, 2003, (04).). Wang Huaiji, targeting areas with complex seabed topography, combined the spatial correlation between sample depth points and constructed an IDW interpolation that takes into account the redistribution of distances of characteristic depth points, effectively improving the accuracy of depth interpolation (Wang Huaiji, Zhu Junhui, Hu Ying, Wang Ruifu. Inverse Distance Weighted Interpolation Algorithm Taking into Account the Redistribution of Distances of Characteristic Depth Points [J]. Marine Bulletin, 2022, (01): 9-18.). Commonly used spatial interpolation methods include the classic inverse distance weighted average (IDW), natural neighborhood method, spline function method, etc., among which the IDW algorithm is widely used due to its simple principle. Among the methods mentioned above, Kriging interpolation is highly adaptable, but parameter selection is complex and computationally intensive for large-scale heterogeneous data. Traditional IDW and some of its optimization methods fail to fully consider the measurement accuracy and spatial distribution differences of the original water depth data, and are prone to large errors when the data is sparse or unevenly distributed. Neural network interpolation is highly dependent on training samples and has poor model interpretability. Although IDW, which takes into account the redistribution of distances to feature water depth points, improves accuracy, it does not take into account the characteristics of other water depth data. Summary of the Invention

[0004] To overcome the impact of inconsistent quality and uneven distribution of raw water depth data on interpolation accuracy, this invention proposes a water depth interpolation method that considers both the accuracy and distribution differences of the raw water depth data. This method introduces four types of weighted factors: distance, distribution, accuracy, and orientation. By taking into account the quality and spatial distribution characteristics of the raw water depth data, a comprehensive weighting approach is used to improve the accuracy and reliability of the interpolation results. Existing experiments have shown that the method described in this invention takes into account the characteristics of the raw water depth and improves the accuracy of interpolation.

[0005] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0006] A water depth interpolation method that takes into account the accuracy and distribution differences of the original water depth data includes the following steps:

[0007] Step S1: Obtain the original water depth points and record the coordinates, water depth value, measurement accuracy, and survey line direction information for each original water depth point;

[0008] Step S2: Obtain the coordinates of the point to be inserted. Divide the area around the point to be inserted into 4 sub-regions at 90° angles, with the point to be inserted as the center. In each sub-region, find the 4 original water depth points closest to the point to be inserted as reference points.

[0009] Step S3: Construct a variogram model, calculate the experimental variogram based on the original water depth point, fit it using a spherical variogram model, and determine the optimal parameters of the model using the least squares method;

[0010] Step S4: Obtain the distance factor weights by fitting a spherical variogram model and combining it with the inverse distance weighted average method. ;

[0011] Step S5: By counting the number of neighboring reference points within a certain radius for each reference point, and using point density to characterize the distribution, the distribution factor weights are obtained. ;

[0012] Step S6: Calculate the accuracy factor weights based on the measurement accuracy index of the reference point. ;

[0013] Step S7: Based on the angle between the direction of the line connecting the reference point and the point to be inserted and the direction of the survey line. The orientation factor weights are obtained. ;

[0014] Step S8: Based on the four factors calculated above, calculate the interpolation point water depth value using the weighted average interpolation method. By harmonizing the weights of the four factors, calculate the interpolated grid water depth value.

[0015] In step S3, the experimental variability function value of the original water depth point is first calculated using the following formula:

[0016]

[0017] in, For the experimental variability function, For the number of points at water depth, Here are the coordinates of the two water depth points. This represents the distance between two water depth points. These represent the water depth values ​​corresponding to the two water depth points. After obtaining the experimental variogram calculation results, a spherical variogram model is used for fitting, and the calculation formula is as follows:

[0018]

[0019] in, This represents the fitted variogram value; The distance between two water depth points; The value is the nugget value, representing variability on a small scale; The sill value represents the maximum variability within the region; The effective distance range for representing spatial correlation is given by the variable range method. Finally, the parameters are determined using the least squares method, and the calculation formula is:

[0020]

[0021] in, The distance is The experimental variogram value, The parameter is The spherical variogram model at distance The predicted value at that location, It is the number of water depth points in the experimental variogram. Given a vector of parameters to be estimated, find a set of such parameters. This makes the spherical variogram model at distance Predicted value at location Compared with experimental variability function values The sum of squared errors between them is minimized.

[0022] In step S4, the distance factor weight The calculation formula is:

[0023]

[0024] in, The distance between the point to be inserted and the reference point. Distance The corresponding variogram value, This is the base value.

[0025] In step S5, the distribution factor weights The calculation formula is:

[0026]

[0027] For each selected reference point, the distance between it and other selected reference points is calculated, and the distances between the reference points and their center radii are counted. The number of reference points within a certain range, which serves as the point density of that reference point. .

[0028] In step S6, the precision factor weight The calculation formula is:

[0029]

[0030] in, Indicates reference point The measurement accuracy index. The higher the accuracy, the greater the weight, thus ensuring that high-quality bathymetry data plays a greater role in the interpolation process.

[0031] In step S7, the orientation factor The calculation formula is:

[0032]

[0033] in, The angle between the line connecting the reference point and the point to be inserted and the direction of the survey line where the reference point is located.

[0034] In step S8, the final weight calculation formula is:

[0035]

[0036] in, For a certain reference point, For distance factor weights, For the distribution factor weights, For the precision factor weight, For directional factor weights, This is an index representing the degree of influence of the distance factor. This is an index representing the degree of influence of the distribution factor. This is an index indicating the degree of influence of the accuracy factor; the index indicating the degree of influence of the distance factor can be adjusted. To ensure a reasonable contribution of spatial proximity to interpolation, adjust the influence index of the distribution factor. To balance the interference of data density differences on interpolation, adjust the degree of influence of the precision factor index. Avoid overemphasizing accuracy and reducing the influence of spatial features such as distance and distribution on interpolation.

[0037] Based on the final weights, the water depth at the interpolation point is calculated using the following formula:

[0038]

[0039] in, The water depth at the interpolation point, interpolation point The coordinates are The reference point is , The distance between the interpolation point and the reference point. This is the final weight.

[0040] The beneficial effects of this invention are as follows: The water depth interpolation method proposed in this invention takes into account the differences in the distribution and accuracy of the original water depth data. Existing experiments have shown that the method described in this invention can effectively consider the characteristics of water depth and improve the accuracy of the constructed water depth interpolation. Attached Figure Description

[0041] Figure 1 This is a flowchart of the water depth interpolation method of the present invention that takes into account the accuracy and distribution differences of the original water depth data. Detailed Implementation

[0042] The technical solution of the present invention will be further described below with reference to specific examples and accompanying drawings.

[0043] This invention proposes a water depth interpolation method that takes into account the accuracy and distribution differences of the original water depth data. The implementation process involves constructing a spherical variogram model and calculating the distance factor weight using an inverse distance weighted average method. Subsequently, the weights of four factors—distribution, accuracy, and orientation—are calculated separately. Finally, a weighted average interpolation method is used to harmonize the weights of the four factors to calculate the interpolated water depth, thereby improving the accuracy of the interpolation. An interpolation point is set... The coordinates are The coordinates of the reference point are The interpolation calculation using the method described in this invention includes the following steps (such as...). Figure 1 (as shown)

[0044] Step S1: Obtain raw water depth data and record the coordinates, water depth value, measurement accuracy, and survey line direction information for each raw water depth point;

[0045] Step S2: Obtain the coordinates of the point to be inserted. Divide the area around the point to be inserted into 4 sub-regions at 90° angles, with the point to be inserted as the center. In each sub-region, find the 4 original water depth points closest to the point to be inserted as reference points.

[0046] Step S3: Construct a variogram model, calculate the experimental variogram based on the original water depth point, fit it using a spherical variogram model, and determine the optimal parameters of the model using the least squares method;

[0047] Step S4: Calculate the weights of the distance factor, distribution factor, accuracy factor, and orientation factor. Then, based on the multi-factor comprehensive weights calculated above, combine them with the weighted average interpolation method to calculate the interpolated point depth value. By harmonizing the weights of the four factors, the interpolated depth value is obtained. The calculation formula is as follows:

[0048]

[0049] Among them, the multi-factor comprehensive weight For a certain reference point, interpolation point water depth, The distance between the interpolation point and the reference point. The interpolated water depth at the interpolation point can be obtained through the above calculations.

[0050] Step S5: Following the steps above, perform water depth interpolation calculations for a specific interpolation point. The weighting results of the selected reference point are shown in the table below:

[0051]

[0052] The interpolated depth was calculated to be 360.17 meters using the interpolation formula, while the actual depth was 365.33 meters. According to the hydrographic surveying standard GB12327-2022, the relative error of the interpolated depth of 1.41% is less than the 3% comparison limit, meeting the accuracy standards for depth data in hydrographic surveying and demonstrating the rationality of the method presented in this invention.

Claims

1. A water depth interpolation method that takes into account the accuracy and distribution differences of the original water depth data, characterized in that, Includes the following steps: Step S1: Obtain the original water depth points and record the coordinates, water depth value, measurement accuracy, and survey line direction information for each original water depth point; Step S2: Obtain the coordinates of the point to be inserted. Divide the area around the point to be inserted into 4 sub-regions at 90° angles, with the point to be inserted as the center. In each sub-region, find the 4 original water depth points closest to the point to be inserted as reference points. Step S3: Construct a variogram model, calculate the experimental variogram based on the original water depth point, fit it using a spherical variogram model, and determine the optimal parameters of the model using the least squares method; Step S4: Obtain the distance factor weights by fitting a spherical variogram model and combining it with the inverse distance weighted average method. ; Step S5: By counting the number of neighboring reference points within a certain radius for each reference point, and using point density to characterize the distribution, the distribution factor weights are obtained. ; Step S6: Calculate the accuracy factor weights based on the measurement accuracy index of the reference point. ; Step S7: Based on the angle between the direction of the line connecting the reference point and the point to be inserted and the direction of the survey line. The orientation factor weights are obtained. ; Step S8: Based on the four factors calculated above, calculate the interpolation point water depth value using the weighted average interpolation method. By harmonizing the weights of the four factors, calculate the interpolated grid water depth value.

2. The water depth interpolation method according to claim 1, which takes into account the accuracy and distribution differences of the original water depth data, is characterized in that, In step S3, the experimental variability function value of the original water depth point is first calculated using the following formula: in, For the experimental variability function, For the number of points at water depth, Here are the coordinates of the two water depth points. This represents the distance between two water depth points. Here are the water depth values ​​corresponding to the two water depth points; after obtaining the experimental variogram calculation results, a spherical variogram model is used for fitting, and the calculation formula is as follows: in, This represents the fitted variogram value; The distance between two water depth points; The value is the nugget value, representing variability on a small scale; The sill value represents the maximum variability within the region; The effective distance range for spatial correlation is represented by the range variation; finally, the least squares method is used to determine the parameters, and the calculation formula is as follows: in, The distance is The experimental variogram value, The parameter is The spherical variogram model at distance The predicted value at that location, It is the number of water depth points in the experimental variogram. Given a vector of parameters to be estimated, find a set of such parameters. This makes the spherical variogram model at distance Predicted value at location Compared with experimental variability function values The sum of squared errors between them is minimized.

3. The water depth interpolation method according to claim 1, which takes into account the accuracy and distribution differences of the original water depth data, is characterized in that... In step S4, the distance factor weight The calculation formula is: in, The distance between the point to be inserted and the reference point. Distance The corresponding variogram value, This is the base value.

4. The water depth interpolation method according to claim 1, which takes into account the accuracy and distribution differences of the original water depth data, is characterized in that... In step S5, the distribution factor weights The calculation formula is: For each selected reference point, the distance between it and other selected reference points is calculated, and the distances between the reference points and their center radii are counted. The number of reference points within a certain range, which serves as the point density of that reference point. .

5. The water depth interpolation method according to claim 1, taking into account the accuracy and distribution differences of the original water depth data, is characterized in that... In step S6, the precision factor weight The calculation formula is: in, Indicates reference point The measurement accuracy index.

6. The water depth interpolation method according to claim 1, taking into account the accuracy and distribution differences of the original water depth data, is characterized in that... In step S7, the orientation factor The calculation formula is: in, The angle between the line connecting the reference point and the point to be inserted and the direction of the survey line where the reference point is located.

7. The water depth interpolation method according to claim 1, taking into account the accuracy and distribution differences of the original water depth data, is characterized in that... In step S8, the final weight calculation formula is: in, For a certain reference point, For distance factor weights, For the distribution factor weights, For the precision factor weight, For directional factor weights, This is an index representing the degree of influence of the distance factor. This is an index representing the degree of influence of the distribution factor. This is an index representing the degree of influence of the accuracy factor. Based on the final weights, the water depth at the interpolation point is calculated using the following formula: in, The water depth at the interpolation point, interpolation point The coordinates are The reference point is The distance between the interpolation point and the reference point. This is the final weight.

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