Seawater turbidity estimation method based on iterative reweighted least square method

Abstract

The invention discloses a seawater turbidity estimation method based on an iteration reweighted least square method, and belongs to the technical field of water pollution detection.The method comprises the steps that a three-dimensional plane linear interpolation formula and an inverse distance weight interpolation formula are constructed based on actually-measured three-buoy data, and the three-dimensional plane linear interpolation formula and the inverse distance weight interpolation formula are calculated based on the iteration reweighted least square principle; the calculation results of the target point through the three-dimensional plane linear interpolation method and the inverse distance weight interpolation method are fused, weight distribution parameters are optimized through repeated iteration, and the finally obtained fusion value serves as the seawater turbidity estimation value of the target point so as to improve the accuracy of the estimation result. Compared with a traditional single-point method, a mean value method and a linear interpolation method, the method has the advantages that the estimation precision is higher, the estimation effect is better, the problem of simplification processing of local sea area spatial features in the traditional method can be effectively solved, and the weight can be flexibly set according to specific sea area conditions so as to more accurately reflect the parameter distribution condition in the sea area.

Description

Technical Field

[0001] The present invention belongs to the technical field of water pollution detection, and specifically relates to a seawater turbidity estimation method based on the iteratively reweighted least squares method. Background Art

[0002] The measurement of seawater turbidity is an important part of marine environmental monitoring. Turbidity reflects the content of suspended particulate matter in water, and directly affects the health of the marine ecosystem, underwater optical communication, pollutant diffusion assessment, and the safety of marine engineering. In recent years, with the continuous development of marine observation technology, the method of using buoys equipped with sensors to measure seawater parameters has gradually become the mainstream means in engineering practice, and its advantages lie in real-time, long-term continuity, and wide-area coverage.

[0003] Traditional buoy measurement methods usually use single-buoy measurement method, multi-buoy averaging method, or multi-buoy linear interpolation method to estimate the seawater turbidity of the target sea area. These methods have high accuracy when the seawater parameters do not change much. However, in coastal waters within 10 nautical miles from the shore, near river estuaries, archipelago waters and other coastal waters, the seawater turbidity changes greatly, usually showing spatial variability and local differences. When traditional buoy measurement methods are used to process data of coastal waters with complex spatial distribution characteristics, it often leads to large estimation errors and is difficult to accurately reflect the true change law of seawater turbidity, thus affecting the normal development of scientific research activities in coastal waters. Summary of the Invention

[0004] In order to solve the limitations of the existing buoy measurement methods when dealing with turbidity data of coastal waters, the present invention proposes a seawater turbidity estimation method based on the iteratively reweighted least squares method to adapt to the processing of turbidity data of waters with complex spatial distribution characteristics.

[0005] To solve the above technical problems, the present invention is implemented by the following technical solutions: A seawater turbidity estimation method based on the iteratively reweighted least squares method, comprising: Detecting the seawater turbidity values of three measurement points in the target sea area by using buoy equipment, and combining the geographical coordinates of the three measurement points with the seawater turbidity values of the measurement points to form buoy data of the three measurement points; Constructing a three-dimensional plane linear interpolation formula by using the buoy data of the three measurement points; Selecting several estimation points, calculating the estimated seawater turbidity values of each estimation point by using the three-dimensional plane linear interpolation formula, and combining the geographical coordinates of the estimation points to form data of several estimation points; Constructing an inverse distance weighted interpolation formula, and using the buoy data of the three measurement points and the data of the several estimation points as the known point data in the formula; Calculate the target point using the three-dimensional plane linear interpolation formula P for plane linear interpolation; Calculate the target point using the inverse distance weighted interpolation formula P for inverse distance weighted interpolation; Based on the iterative reweighted least squares principle, fuse the plane linear interpolation and inverse distance weighted interpolation of the target point P to obtain the final fused value; Use the final fused value as the estimated value of the seawater turbidity of the target point P .

[0006] In some embodiments of the present application, assume that the buoy data of the three measurement points are ( x i , y i , z i ), i i = 1, 2, 3; where x i is the geographic eastward direction of the i i-th measurement point, y i is the geographic northward direction of the i i-th measurement point, z i is the seawater turbidity value of the i i-th measurement point; construct the three-dimensional plane linear interpolation formula: z = ax + by + c ; Substitute the buoy data of the three measurement points ( x i , y i , z i ) into the three-dimensional plane linear interpolation formula respectively, and the value of the unknown coefficient a, b, c in the formula can be calculated, and then the final three-dimensional plane linear interpolation formula is obtained.

[0007] In some embodiments of the present application, configure the three measurement points to be triangularly distributed in the target sea area to improve the accuracy of constructing the three-dimensional plane linear interpolation formula.

[0008] In some embodiments of the present application, the inverse distance weighted interpolation formula is: ; ; ; where z i is the seawater turbidity value of the i i-th known point; wi is the distance weight of the i th known point; d i is the Euclidean distance between the target point and the i th known point; α takes 1 or 2; n is the number of known points.

[0009] In some embodiments of the present application, the number of estimated points can be configured to be twice the number of measurement points. That is, for the case of three measurement points, six estimated point data can be provided by three-dimensional plane linear interpolation method as supplementary data, that is n = 3 + 6 = 9, that is, nine known point data are used in the inverse distance weight interpolation method to balance the quality of the measurement data set and the improvement of the spike phenomenon.

[0010] In some embodiments of the present application, after selecting a target point in the target sea area P , the following seawater turbidity value estimation process can be executed: Substitute the geographical coordinates of the target point P ([[]] x , y ) into the three-dimensional plane linear interpolation formula to calculate the plane linear interpolation of the target point P ( z , x , y ); Substitute the geographical coordinates of the target point P ([[]] x , y ) into the inverse distance weight interpolation formula to calculate the inverse distance weight interpolation of the target point P ; ; Establish a fusion equation: ; where represents the fusion value of the target point ( x , y ); and are weight parameters, and ; Based on the iteratively reweighted least squares algorithm, the weight parameters and are converged by repeated iteration; Substitute the converged weight parameters and into the fusion equation, and combine the geographical coordinates of the target point P ([[]] x , y ) to calculate the final fusion value, and the fusion value is the target pointP The seawater turbidity value.

[0011] In some embodiments of the present application, the following iterative process may be configured: Calculate the fusion value of the target point P and its planar linear interpolation ( z ( x , y ) and the residual of the inverse distance weighted interpolation . The residual formula is: ; At the position of the target point ( x , y ), select m neighborhood estimation points x’ , y’ within the neighborhood ( , j = 1, 2, ……, m; Using the fusion equation and the residual formula, calculate the residuals of the fusion values of the m neighborhood estimation points and their planar linear interpolations , and the residuals of the fusion values of the m neighborhood estimation points and their inverse distance weighted interpolations ; Calculate the average values and of the two sets of residuals; Calculate the variance of the residuals within the neighborhood: ; Construct the objective function S : ; Substitute the fusion equation into the objective function S formula, transform and simplify it into a neighborhood representation: ; Derive the objective function S with respect to λ 1 and set it to zero, that is: ; Solve to get: , ; Substitute the calculated λ 1 and λ 2 into the fusion equation, repeat the iterative process, and make the weight parameters λ 1 and λ 2 converge through repeated iterations.

[0012] In some embodiments of the present application, during the iterative process, the weight coefficients λ 1 and λ 2 can be assigned initial values first, and the initial fusion value can be calculated using the fusion equation; Configure the size of the local window, and perform iterative calculations of the weight coefficients λ 1 and λ 2 according to the iterative process until convergence; Configure the local window to slide in the entire target space, complete the weight optimization of the entire target sea area, and determine the weight coefficients λ 1 and λ 2 at all positions in the target sea area. Then, the seawater turbidity distribution in the target sea area can be determined through the fusion equation.

[0013] Compared with the prior art, the advantages and positive effects of the present invention are as follows: The seawater turbidity estimation method proposed based on the iterative reweighted least squares principle uses the actual measurement data of three buoy devices, combines the three-dimensional plane linear interpolation method with the inverse distance weighted interpolation method, and optimizes the weight distribution parameters through repeated iterations to finally estimate a seawater turbidity value with higher accuracy. The estimation accuracy of this method is higher than that of traditional single-point method, mean method, and linear interpolation method, and the estimation effect is better. It can not only effectively solve the problem of simple processing of local sea area spatial characteristics by traditional methods, but also flexibly set weights according to specific sea area conditions to more accurately reflect the parameter distribution within the sea area.

[0014] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become clearer. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the following described drawings are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0016] Figure 1 is the overall flowchart of an embodiment of the seawater turbidity estimation method based on the iterative reweighted least squares method proposed by the present invention; Figure 2 is the distribution diagram of the three-buoy data in the three-dimensional plane; Figure 3 is the diagram of the seawater turbidity distribution of each data point in the simulation dataset in the three-dimensional plane; Figure 4 is the seawater turbidity distribution diagram of the target sea area estimated using the three-dimensional plane linear interpolation method; Figure 5It is the distribution map of seawater turbidity in the target sea area estimated by using the inverse distance weighted interpolation method with only the three-buoy data as known points; Figure 6 It is the distribution map of seawater turbidity in the target sea area estimated by using the inverse distance weighted interpolation method with the three-buoy data and the plane linear interpolation supplementary data as known points; Figure 7 It is the distribution map of the fusion result estimated based on the iterative reweighted least squares principle; Figure 8 It is the comparison chart of the seawater turbidity error obtained by using the estimation method of the present invention and the seawater turbidity error obtained by using the traditional mean method; Figure 9 It is the comparison chart of the seawater turbidity error obtained by using the estimation method of the present invention and the seawater turbidity error obtained by using the traditional plane linear interpolation method; Figure 10 It is the comparison chart of the seawater turbidity error obtained by using the estimation method of the present invention and the seawater turbidity error obtained by using the traditional IDW interpolation method. Specific Embodiment

[0017] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0018] The seawater turbidity estimation method of this embodiment measures the actual seawater turbidity values at three different measurement points in the target sea area through sensors carried by buoys to form three-buoy data; then, a three-dimensional plane linear interpolation formula is constructed using the three-buoy data, and several estimation points are selected, and the seawater turbidity estimation values of each estimation point are calculated through the constructed three-dimensional plane linear interpolation formula; n - 3 estimation point data are extracted and combined with the three-buoy data to construct an inverse distance weighted interpolation formula; finally, for the coordinates of the target point, based on the iterative reweighted least squares principle, the results calculated by the three-dimensional plane linear interpolation formula and the inverse distance weighted interpolation formula are fused, and the finally obtained fusion result is used as the seawater turbidity estimation value of the target point. Through simulation experiments, it can be verified that this result has higher accuracy and better estimation effect compared with the estimation values obtained by traditional methods.

[0019] Next, in combination with Figure 1 , the specific implementation process of the seawater turbidity estimation method of this embodiment will be elaborated in detail.

[0020] S101. Obtain the buoy data of three measurement points.

[0021] In this embodiment, three buoy devices are deployed in the target sea area. The deployment points of the three buoy devices should be distributed in a triangular shape, as Figure 2 shown, to improve the accuracy of constructing the subsequent three-dimensional plane linear interpolation formula.

[0022] Assume that the coordinates of the deployment points of the three buoy devices in the target sea area are respectively ( x 1, y 1), ( x 2, y 2), ( x 3, y 3). The seawater turbidity values measured by the turbidity sensors carried on each buoy device are respectively z 1, z 2, z 3. Thus, three measurement points A, B, C of buoy data A ( x 1, y 1, z 1), B ( x 2, y 2, z 2), C ( x 3, y 3, z 3) can be combined, and then a three-dimensional plane is constructed, as Figure 2 shown. Among them, x i represents the geographical eastward direction of the i th measurement point, y i represents the geographical northward direction of the i th measurement point, z i represents the seawater turbidity value of the i th measurement point, i = 1, 2, 3.

[0023] S102. Use the buoy data of the three measurement points to construct a three-dimensional plane linear interpolation formula.

[0024] The three-dimensional plane linear interpolation formula of this embodiment can be expressed as: z = ax + by + c (1); Among them, x is the geographical eastward direction of the target sea area; y is the geographical northward direction of the target sea area; z is the seawater turbidity value at the corresponding position; a, b, c is the unknown coefficient.

[0025] Substitute the buoy data of the three measurement pointsA ( x 1, y 1, z 1), B ( x 2, y 2, z 2), C ( x 3, y 3, z 3) are respectively substituted into formula (1) to obtain the following system of equations: ; Solving the above system of equations can obtain the specific values of the unknown coefficients a, b, c .

[0026] Substituting the specific values of the coefficients a, b, c into formula (1) can obtain the final three-dimensional plane linear interpolation formula.

[0027] S103. Select several estimated points and calculate the estimated values of seawater turbidity at each estimated point by using the three-dimensional plane linear interpolation formula.

[0028] In the target sea area, several estimated points are randomly selected, and the geographical coordinates of each estimated point are substituted into the three-dimensional plane linear interpolation formula (1) to calculate the estimated values of seawater turbidity at each estimated point. Combining the coordinates of each estimated point with its estimated value of seawater turbidity forms several sets of estimated point data.

[0029] S104. Construct an inverse distance weighted interpolation formula and combine the buoy data of three measurement points and several sets of estimated point data to form the known point data in the formula.

[0030] The inverse distance weighted interpolation method, i.e., the IDM interpolation method, is an interpolation method based on the distance of measurement points. Its logical root is the first law of geography, that is, all attribute values on the geographical surface are interrelated, but the attribute values closer in distance are more strongly correlated than those farther away. Due to this characteristic, the IDW interpolation method is widely used in the data processing of physical space.

[0031] Assume that the geographical coordinates of the target point are ( x , y ), and its seawater turbidity value is . The IDM interpolation method will use the weighted sum of the data of all known points in the area to estimate the value of the unknown point. Expressed by a formula, it is: (2); (3); (4); where, zi is the seawater turbidity value of the i th known point; w i is the distance weight of the i th known point; d i is the Euclidean distance between the target point and the i th known point; α takes 1 or 2; n is the number of known points.

[0032] The known points here include the buoy data of three measurement points and the estimated point data calculated by the three-dimensional plane linear interpolation formula (1).

[0033] The IDW interpolation method is based on the first law of geography, reflects the logical relationship between physical properties and distance, can effectively combine known regional information to estimate the spatial distribution of property values, and has strong robustness, but there are still some problems. The IDW interpolation method depends on the number of known points. The more the number, the more accurate the estimation result. Only using the three measurement data provided by three buoys is likely to cause peak phenomena near the maximum and minimum values. Therefore, in this embodiment, an appropriate amount of data is selected from the estimation results of the three-dimensional plane linear interpolation method as supplementary data to improve the estimation accuracy of the IDW interpolation method.

[0034] It should be noted that the quantity of supplementary data must be appropriate. If too little is selected, the improvement effect on the peak phenomenon is not significant; if too much is selected, it will affect the quality of the measurement data set.

[0035] As a preferred implementation manner, the supplementary data can be taken as twice the measurement data, that is, for the case of three measurement points, six estimated point data selected from the three-dimensional plane linear interpolation can be used as supplementary data to balance the quality of the measurement data set and the improvement of the peak phenomenon.

[0036] S105. Calculate the plane linear interpolation of the target point P .

[0037] Select the target point P in the target sea area, and assume its geographical coordinates are ( x , y ). Substitute the geographical coordinates ( P , x , y ) of the target point P into the three-dimensional plane linear interpolation formula (1) to calculate the plane linear interpolation z ( x , y ) of the target point

[0038] S106. Calculate the inverse distance weight interpolation of the target point P .

[0039] Substitute the geographical coordinates ( P , x , y ) of the target point into the inverse distance weighted interpolation formulas (2)-(4) to calculate the inverse distance weighted interpolation P of the target point. .

[0040] S107. Based on the iterative reweighted least squares principle, fuse the planar linear interpolation and the inverse distance weighted interpolation of the target point P to obtain the final fused value.

[0041] The three-dimensional planar linear interpolation method can reflect the spatial variation trend of seawater turbidity, and the IDW interpolation method can effectively combine the information of the known area to estimate the spatial distribution of the attribute value. However, both of them have their own disadvantages. Therefore, in this embodiment, based on the iterative reweighted least squares principle, the results calculated by the three-dimensional planar linear interpolation method and the IDW interpolation method are fused to obtain a more accurate estimated value of seawater turbidity.

[0042] The fusion process is as follows: Establish a fusion equation: (5); where represents the fused value of the target point ( x , y ); and are weight parameters, and ; Calculate the residual between the fused value P of the target point and its planar linear interpolation and its inverse distance weighted interpolation : (6). Within the neighborhood (

[0043] ) around the target point position ( x , y ), select m neighborhood estimation points x’ , y’ , , j = 1, 2, ……, m. Using the above fusion equation (5) and the residual formula (6), calculate the residuals between the fused values of these m neighborhood estimation points and their planar linear interpolations, and the residuals between the fused values of these m neighborhood estimation points and their inverse distance weighted interpolations.

[0044] Calculate the average value of the two sets of residuals: ; 。

[0045] Adopt the optimal local variance strategy to calculate the variance of the residuals within the neighborhood, that is: ; where the variance and are independent of each other, that is, 。

[0046] Adopt inverse variance weighting to jointly minimize the weighted sum of squared residuals of the two, and construct the objective function S , and the expression is as follows: (7).

[0047] Substitute the fusion equation (5) into the objective function formula (7), transform and simplify it into a neighborhood representation, and we can get: 。

[0048] For the objective function S with respect to λ 1, take the derivative and set it to zero, that is: ; Furthermore, the solution can be obtained as: ; 。

[0049] Substitute the calculated λ 1 and λ 2 into the fusion equation (5), repeat the above fusion process, and through repeated iteration, make the weight parameters λ 1 and λ 2 converge (or reach the maximum number of iterations), and calculate the final fusion value.

[0050] S108. Take the final fusion value as the estimated value of the seawater turbidity at the target point P .

[0051] Substitute the weight parameters λ 1 and λ 2 that converge after repeated iteration into the fusion equation (5), and the final fusion value can be calculated. Take this fusion value as the seawater turbidity value of the target point P output to obtain the estimated value of the seawater turbidity at the target point.

[0052] To verify the feasibility and accuracy of the seawater turbidity estimation method proposed in this embodiment, the following simulation experiment is designed: (I) Construct a simulation dataset.

[0053] The spatial distribution of seawater turbidity is affected by various environmental factors, mainly including water depth, seabed topography, marine meteorological conditions, etc. In coastal waters, the seawater turbidity generally shows a trend of decreasing with increasing distance from the shore, and its variation pattern is affected by multiple environments.

[0054] Based on the above analysis, in this embodiment, an estimation space with a dimension of 10 km × 5 km is selected as the target sea area, and a number of original scatter data are simulated for constructing a simulation dataset.

[0055] The denser the data points in the simulation dataset, the more accurately they can reflect the real situation. However, considering the workload and operability, it can only be constructed by the method of limited scatter points + ordinary Kriging interpolation.

[0056] The construction idea is as follows: First, 100 original scatter data of 10 × 10 are simulated in the target sea area; then, 5000 dense data of 100 × 50 are formed by ordinary Kriging interpolation as the real data of this sea area. The real data here consists of geographical coordinates and the seawater turbidity value at that coordinate position.

[0057] After that, three data at different positions are selected as the measurement data of three buoy devices to form three-buoy data. The three-dimensional plane distribution of each real data point is as Figure 3 shown.

[0058] (2) Estimate the seawater turbidity distribution in the target sea area by using the three-dimensional plane linear interpolation method.

[0059] Use the selected three-buoy data to construct a three-dimensional plane linear interpolation formula, substitute the coordinates of each data point in the simulation dataset into the three-dimensional plane linear interpolation formula, estimate the seawater turbidity value at each position, and form a seawater turbidity distribution map of the target sea area as Figure 4 shown.

[0060] It can be seen from Figure 4 that although the seawater turbidity values estimated by using the three-dimensional plane linear interpolation method show a trend of decreasing with increasing distance from the shore, this trend is linearly changing, which does not conform to the actual change law of seawater turbidity, and the slope of the turbidity change trend in the whole target sea area is greater than the actual situation. Therefore, the estimation result is not accurate enough.

[0061] (3) Estimate the seawater turbidity distribution in the target sea area by using the inverse distance weighting interpolation method.

[0062] Take the three-buoy data as the known points in the inverse distance weighting interpolation formula, and use the inverse distance weighting interpolation formula to calculate the seawater turbidity estimation values of each data point in the simulation dataset, as Figure 5 shown.

[0063] It can be seen from Figure 5 that the seawater turbidity values estimated by the inverse distance weighted interpolation method show a decreasing trend with the increase of the distance from the shore, and the non-linear change trend of seawater turbidity is closer to the actual situation. However, spike phenomena occur near the three measurement points, and since these three measured values are closer to the actual values, the slope of the entire turbidity change trend is smaller than the actual situation.

[0064] In view of this, in this embodiment, several data points are selected from a large number of estimated point data calculated by the three-dimensional plane linear interpolation method as supplementary data, and combined with the three buoy data to form more known point data for the inverse distance weighted interpolation formula.

[0065] Substitute the coordinates of each data point in the simulation dataset into the inverse distance weighted interpolation formula to estimate the seawater turbidity values at each position, and a seawater turbidity distribution map of the target sea area as shown in Figure 6 can be formed.

[0066] It can be seen from Figure 6 that by increasing the number of known points, the spike phenomena near the three measurement points can be effectively alleviated. However, the slope of the entire turbidity change trend is still smaller than the actual situation.

[0067] (4) Based on the principle of iteratively reweighted least squares, fuse the estimation results of the three-dimensional plane linear interpolation method and the inverse distance weighted interpolation method.

[0068] Assume the initial weight coefficients , , and calculate the initial fusion value using the fusion equation (5), that is: .

[0069] Take the local window as 3×3, and perform iterative calculations of the weight coefficients and according to the fusion process in this embodiment until convergence. Among them, k is the number of iterations.

[0070] Then, the window slides in the entire target space to complete the weight optimization of the entire target sea area to determine the weight coefficients λ 1 and λ 2 of all positions in the target sea area.

[0071] After determining the weight coefficients λ 1 and λ 2 of all positions in the target sea area, the final fusion value can be estimated through the fusion equation (5). The fusion result is as shown in Figure 7 .

[0072] It can be seen that the estimation method based on the principle of iterative reweighted least squares proposed in this embodiment can better capture the spatial distribution characteristics of data when estimating the seawater turbidity value in the target sea area. Especially in the case of sparse data and the presence of outliers, it not only reflects the trend of high near the shore and low in the open sea, but also shows the relationship between seawater turbidity and distance factors. Figure 7 Compared with the traditional mean method, linear method, and IDW interpolation method, the seawater turbidity estimation method of this embodiment significantly improves the accuracy of data processing, as

[0073] shown. Among them, Figures 8 - 10 is a comparison chart of the error between the seawater turbidity value estimated by the method of this embodiment and the true value, and the seawater turbidity error obtained by using the traditional mean method; Figure 8 is a comparison chart of the seawater turbidity error obtained by using the estimation method of this embodiment and the seawater turbidity error obtained by using the traditional planar linear interpolation method; Figure 9 is a comparison chart of the seawater turbidity error obtained by using the estimation method of this embodiment and the seawater turbidity error obtained by using the traditional IDW interpolation method. Figure 10

[0074] Through simulation, it is found that the three-dimensional planar linear interpolation method can better capture the spatial distribution trend of seawater turbidity values in a local sea area, but its estimation accuracy is low in complex areas with strong nonlinearity; while the IDW interpolation method can make a reasonable prediction based on the distance of measurement points, but it lacks the utilization of background information, and the estimation accuracy is affected by the number of known measurement points. Therefore, the estimation error is also large when used alone. By combining the two methods, the advantages of the large-range background information provided by the three-dimensional planar model and the distance-related advantages of the IDW interpolation method can be fully utilized, so as to obtain a better estimation result.

[0075] Of course, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, for those of ordinary skill in the art, it is still possible to modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions required to be protected by the present invention.​

Claims

1. A seawater turbidity estimation method based on iterative reweighted least squares method, characterized in that Including: Detecting the seawater turbidity values at three measurement points in the target sea area by using buoy devices, combining the geographical coordinates of the three measurement points with the seawater turbidity values of the measurement points to form buoy data of the three measurement points; Constructing a three-dimensional plane linear interpolation formula by using the buoy data of the three measurement points; Selecting several estimation points, calculating the estimated seawater turbidity values of each estimation point by using the three-dimensional plane linear interpolation formula, and combining the geographical coordinates of the estimation points to form data of several estimation points; Constructing an inverse distance weighted interpolation formula, and taking the buoy data of the three measurement points and the data of the several estimation points as the known point data in the formula; Calculate the planar linear interpolation of the target point using the three-dimensional planar linear interpolation formula P for planar linear interpolation; Use the inverse distance weighting interpolation formula to calculate the inverse distance weighting interpolation of the target point P ; Based on the principle of iterative reweighted least squares, for the target point P perform the fusion of planar linear interpolation and inverse distance weighted interpolation to obtain the final fusion value; Use the final fusion value as the target point P for the estimated value of seawater turbidity.

2. The seawater turbidity estimation method based on the iteratively reweighted least squares method according to claim 1, characterized in that The buoy data of the three measurement points are ( x i , y i , z i ), i = 1, 2, 3; where x i is the geographic east direction of the i th measurement point, y i is the geographic north direction of the i th measurement point, z i is the seawater turbidity value of the i th measurement point; Construct a three-dimensional plane linear interpolation formula: z = ax + by + c ; Substitute the buoy data of the three measurement points ( x i , y i , z i ) into the three-dimensional plane linear interpolation formula respectively to calculate the value of the unknown coefficient a, b, c in the formula.

3. The seawater turbidity estimation method based on the iterative reweighted least squares method according to claim 2, wherein The three measurement points are distributed in a triangle in the target sea area.

4. The seawater turbidity estimation method based on the iteratively reweighted least squares method according to claim 1, characterized in that The inverse distance weighted interpolation formula is: ； ； ； wherein, z i is the seawater turbidity value of the i th known point; w i is the distance weight of the i th known point; d i is the Euclidean distance between the target point and the i th known point; α takes 1 or 2; n is the number of known points.

5. The method for estimating seawater turbidity based on the iterative reweighted least squares method according to claim 1, characterized in that The number of the estimation points is twice the number of the measurement points.

6. The seawater turbidity estimation method based on the iteratively reweighted least squares method according to any one of claims 1 to 5, characterized in that Select a target point within the target sea area P , whose geographical coordinates are ( x , y ); Substitute the geographical coordinates of the target point P ( x , y ) into the three-dimensional plane linear interpolation formula to calculate the plane linear interpolation of the target point P z ( x , y );​ Substitute the geographical coordinates of the target point P ( x , y ) into the inverse distance weighted interpolation formula to calculate the inverse distance weighted interpolation of the target point P ; ; Establishing a fusion equation: ； Among them, represents the fusion value of the target point ( x , y ); and are weight parameters, and ; Based on the iterative reweighted least squares algorithm, the weight parameters are made to converge by repeated iteration and converge; Substitute the converged weight parameters and into the fusion equation, and combine with the geographical coordinates of the target point P ( x , y ) to calculate the final fusion value.

7. The method for estimating seawater turbidity based on the iteratively reweighted least squares method according to claim 6, characterized in that, The iterative process includes: Calculate the target point P of the fusion value and its planar linear interpolation z ( x , y ) and the inverse distance weighted interpolation of the residuals, and the residual formula is: ； At the target point position ( x , y ), within the neighborhood ( x’ , y’ ) around it, select m neighborhood estimation points , j where i = 1, 2, ……, m; Calculate the residuals between the fusion values of the m neighborhood estimation points and their planar linear interpolations, respectively, using the fusion equation and the residual formula , and the residuals between the fusion values of the m neighborhood estimation points and their inverse distance weighted interpolations ; Calculate the average value of two sets of residuals and ; Calculating the variance of the residuals in the neighborhood: ； Construct the objective function S : ； Substitute the fusion equation into the objective function S The formula is transformed and simplified into a neighborhood representation: ； For the objective function S with respect to λ 1, take the derivative and set it to zero, i.e.: ； The solution is: , ; Substitute the calculated λ 1 and λ 2 into the fusion equation, repeat the iterative process, and converge the weight parameters λ 1 and λ 2 by repeated iteration.

8. The seawater turbidity estimation method based on the iterative reweighted least squares method according to claim 7, wherein In the iterative process, first, initial values are assigned to the weight coefficients λ 1 and λ 2, and the initial fusion value is calculated using the fusion equation; Configure the size of the local window and perform iterative calculations of the weight coefficients λ 1 and λ 2 until convergence; Configure the local window to slide in the entire target space, complete the weight optimization of the entire target sea area, and determine the weight coefficients of all positions in the target sea area λ 1 and λ After 2, the seawater turbidity distribution in the target sea area is determined through the fusion equation

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