A method for estimating seawater turbidity based on iterative reweighted least squares method

Abstract

The present invention discloses a method for estimating seawater turbidity based on iterative reweighted least squares method, which belongs to the field of water pollution detection technology. The method constructs a three-dimensional plane linear interpolation formula and an inverse distance weighted interpolation formula based on measured three-buoy data. Based on the iterative reweighted least squares principle, the calculation results of the target point through the three-dimensional plane linear interpolation method and the inverse distance weighted interpolation method are fused. Through repeated iterations, the weight distribution parameters are optimized, and the final fusion value is used as the seawater turbidity estimation value of the target point to improve the accuracy of the estimation result. The estimation accuracy of this method is higher than that of the 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 simplistic 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 inside the sea area.

Description

Technical Field

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

[0002] Measuring seawater turbidity is a crucial component of marine environmental monitoring. Turbidity reflects the concentration of suspended particulate matter in the water, directly impacting the health of marine ecosystems, underwater optical communications, pollutant dispersion assessments, and the safety of marine engineering projects. In recent years, with the continuous advancement of ocean observation technology, the use of buoy-mounted sensors to measure seawater parameters has gradually become a mainstream method in engineering practice. Its advantages lie in its real-time performance, long-term continuity, and wide-area coverage.

[0003] Traditional buoy measurement methods typically use single-buoy measurement, multi-buoy averaging, or multi-buoy linear interpolation to estimate the seawater turbidity of the target sea area. These methods have high accuracy when seawater parameters do not change much. However, in coastal waters such as nearshore waters within 10 nautical miles offshore, waters near river estuaries, and archipelago waters, seawater turbidity varies significantly, often exhibiting spatial variability and local differences. When processing data from such coastal waters with complex spatial distribution characteristics, traditional buoy measurement methods often result in large estimation errors, making it difficult to accurately reflect the true variation pattern of seawater turbidity, which in turn affects the normal development of scientific research activities in coastal waters. Summary of the Invention

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

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A method for estimating seawater turbidity based on iterative reweighted least squares method, comprising:

[0007] The buoy equipment is used to detect the seawater turbidity values ​​at three measurement points in the target sea area, and the geographical coordinates of the three measurement points are combined with the seawater turbidity values ​​of the measurement points to form the buoy data of the three measurement points;

[0008] Using the buoy data of three measurement points, a three-dimensional plane linear interpolation formula is constructed;

[0009] Select several estimation points, use the three-dimensional plane linear interpolation formula to calculate the estimated value of seawater turbidity at each estimation point, and combine the geographical coordinates of the estimation points to form several estimation point data;

[0010] Constructing an inverse distance weighted interpolation formula, using the buoy data of the three measurement points and the estimated point data as known point data in the formula;

[0011] Use the three-dimensional plane linear interpolation formula to calculate the target point P Planar linear interpolation of ;

[0012] Use the inverse distance weighted interpolation formula to calculate the target point P Inverse distance weighted interpolation of ;

[0013] Based on the iterative reweighted least squares principle, the target point P The plane linear interpolation and inverse distance weighted interpolation are fused to obtain the final fusion value;

[0014] The final fusion value is used as the target point P Estimated seawater turbidity.

[0015] In some embodiments of the present application, it is assumed that the buoy data of the three measurement points are ( x i , y i , z i ), i =1,2,3; among them, x i For the i The geographical easting direction of each measurement point, y i For the i The geographic north direction of the measurement point, z i For the i The seawater turbidity value of each measuring point; construct a three-dimensional plane linear interpolation formula: z=ax+by+c ; The buoy data of the three measurement points ( x i , y i , z i ) are substituted into the three-dimensional plane linear interpolation formula to calculate the unknown coefficients in the formula a, b, c The value of , and then the final three-dimensional plane linear interpolation formula is obtained.

[0016] In some embodiments of the present application, the three measurement points are configured to be distributed in a triangular shape in the target sea area to improve the accuracy of constructing the three-dimensional plane linear interpolation formula.

[0017] In some embodiments of the present application, the inverse distance weighted interpolation formula is:

[0018] ;

[0019] ;

[0020] ;

[0021] in, z i For the i The turbidity value of seawater at a known point; w i For the i The distance weight of each known point; d i The target point and i The Euclidean distance of known points; α is 1 or 2; n is the number of known points.

[0022] In some embodiments of the present application, the number of estimated points can be configured to be twice the number of measured points. That is, for the case of three measured points, six estimated point data can be provided as supplementary data by three-dimensional plane linear interpolation, that is, n =3+6=9, that is, nine known point data are used in the inverse distance weighted interpolation method to take into account the quality of the measurement dataset and the improvement of the spike phenomenon.

[0023] In some embodiments of the present application, a target point is selected within the target sea area. P After that, the following seawater turbidity value estimation process can be performed:

[0024] The target point P The geographical coordinates ( x , y ) is substituted into the three-dimensional plane linear interpolation formula to calculate the target point P Plane linear interpolation of z ( x , y );

[0025] The target point P The geographical coordinates ( x , y ) is substituted into the inverse distance weighted interpolation formula to calculate the target point P Inverse distance weighted interpolation ;

[0026] Establish the fusion equation:

[0027] ;

[0028] in, Indicates the target point ( x , y )’s fusion value; and is the weight parameter, and ;

[0029] Based on the iterative reweighted least squares algorithm, the weight parameters are adjusted by repeated iterations. and convergence;

[0030] The weight parameters after convergence and Substitute into the fusion equation and combine the target point P The geographical coordinates ( x , y ) calculates the final fusion value, which is the target point P The turbidity value of seawater.

[0031] In some embodiments of the present application, the following iterative process may be configured:

[0032] Calculate target point P Fusion value With its plane linear interpolation z ( x , y ) and inverse distance weighted interpolation The residual formula is:

[0033] ;

[0034] At the target point ( x , y ) around the neighborhood ( x’ , y’ ), select m neighborhood estimation points , j =1,2,……,m;

[0035] Using the fusion equation and residual formula, the residuals of the fusion values ​​of the m neighborhood estimation points and their plane linear interpolation are calculated respectively. , and the residual of the fusion value of m neighborhood estimation points and their inverse distance weighted interpolation ;

[0036] Calculate the mean of the two sets of residuals and ;

[0037] Compute the variance of the residuals within a neighborhood:

[0038] ;

[0039] Constructing the objective function S :

[0040] ;

[0041] Substitute the fusion equation into the objective function S Formula, transformed and simplified into neighborhood representation:

[0042] ;

[0043] For the objective function S about λ 1 Take the derivative and set it to zero, that is:

[0044] ;

[0045] The solution is: , ;

[0046] The calculated λ 1 and λ 2 is substituted into the fusion equation, and the iterative process is repeated. The weight parameters are adjusted by repeated iterations. λ 1 and λ 2Convergence.

[0047] In some embodiments of the present application, during the iterative process, the weight coefficient may be first λ 1 and λ 2. Assigning initial values ​​and calculating the initial fusion value using the fusion equation;

[0048] Configure the size of the local window and perform the weighting coefficient according to the iterative process. λ 1 and λ 2 iterative calculation until convergence;

[0049] Configure the local window to slide across the entire target space, complete the weight optimization of the entire target sea area, and determine the weight coefficients of all locations in the target sea area. λ 1 and λ 2, the seawater turbidity distribution of the target sea area is determined by the fusion equation.

[0050] Compared with existing technologies, the advantages and positive effects of the present invention are as follows: This method, based on the iteratively reweighted least squares principle, utilizes actual measurement data from three buoys, combines three-dimensional linear interpolation with inverse distance weighted interpolation, and optimizes weight distribution parameters through repeated iterations, ultimately estimating seawater turbidity values ​​with higher accuracy. This method achieves higher estimation accuracy and better results than traditional single-point methods, mean methods, and linear interpolation methods. It not only effectively addresses the oversimplification of localized spatial characteristics in traditional methods, but also allows for flexible weighting based on specific sea area conditions to more accurately reflect the parameter distribution within the sea area.

[0051] Other features and advantages of the present invention will become more apparent after reading the detailed description of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0053] Figure 1 This is an overall flow chart of an embodiment of a method for estimating seawater turbidity based on iterative reweighted least squares method proposed in the present invention;

[0054] Figure 2 It is the distribution diagram of the three-buoy data in the three-dimensional plane;

[0055] Figure 3 It is a seawater turbidity distribution diagram of each data point in the simulated data set in a three-dimensional plane;

[0056] Figure 4 It is the seawater turbidity distribution map of the target sea area estimated by three-dimensional plane linear interpolation method;

[0057] Figure 5 It is a seawater turbidity distribution map of the target sea area estimated by using the inverse distance weighted interpolation method with only the three buoy data as known points;

[0058] Figure 6 It is a seawater turbidity distribution map of 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;

[0059] Figure 7 It is the distribution map of the fusion results estimated based on the iterative reweighted least squares principle;

[0060] Figure 8 This is a comparison chart of the seawater turbidity error obtained by the estimation method of the present invention and the seawater turbidity error obtained by the traditional mean value method;

[0061] Figure 9 This is a comparison chart of the seawater turbidity error obtained by the estimation method of the present invention and the seawater turbidity error obtained by the traditional plane linear interpolation method;

[0062] Figure 10 This is a comparison diagram of the seawater turbidity error obtained by the estimation method of the present invention and the seawater turbidity error obtained by the traditional IDW interpolation method. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0064] The seawater turbidity estimation method of this embodiment measures the actual seawater turbidity values ​​of three different measurement points in the target sea area through a buoy-mounted sensor 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. The seawater turbidity estimation value of each estimation point is 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 final fusion result is used as the seawater turbidity estimation value of the target point. Simulation experiments can verify that the result has higher accuracy and better estimation effect than the estimation value obtained by the traditional method.

[0065] The following combination Figure 1 , the specific implementation process of the seawater turbidity estimation method of this embodiment is elaborated in detail.

[0066] S101. Obtain buoy data of three measurement points.

[0067] 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 triangle, such as Figure 2 As shown, this improves the accuracy of the subsequent three-dimensional plane linear interpolation formula construction.

[0068] Assume that the coordinates of the deployment points of the three buoy devices in the target sea area are ( x 1, y 1), ( x 2, y 2) ( x 3. y 3), the seawater turbidity values ​​measured by the turbidity sensors on each buoy device are z 1. z 2. z 3, thus forming three measurement points A, B, C Buoy data A ( x 1, y 1, z 1) B ( x 2,y 2, z 2) C ( x 3. y 3. z 3), and then construct a three-dimensional plane, such as Figure 2 As shown. Among them, x i Indicates the i The geographical easting direction of each measurement point, y i Indicates the i The geographic north direction of the measurement point, z i Indicates the i The seawater turbidity value at each measuring point, i =1,2,3.

[0069] S102. Construct a three-dimensional plane linear interpolation formula using the buoy data of the three measurement points.

[0070] The three-dimensional plane linear interpolation formula of this embodiment can be expressed as:

[0071] z=ax+by+c (1);

[0072] in, x is the geographical east direction of the target sea area; y is the geographic north direction of the target sea area; z is the seawater turbidity value at the corresponding location; a, b, c is the unknown coefficient.

[0073] The buoy data of the three measurement points A ( x 1, y 1, z 1) B ( x 2, y 2, z 2) C ( x 3. y 3. z 3) Substitute them into formula (1) to obtain the following equations:

[0074] ;

[0075] Solve the above equations to get the unknown coefficients a, b, c The specific value of .

[0076] The coefficient a, b, c Substituting the specific value of into formula (1), we can get the final three-dimensional plane linear interpolation formula.

[0077] S103 , selecting several estimation points and calculating the estimated value of seawater turbidity at each estimation point using a three-dimensional plane linear interpolation formula.

[0078] In the target sea area, several estimation points are randomly selected and their geographic coordinates are substituted into the three-dimensional plane linear interpolation formula (1) to calculate the estimated seawater turbidity value of each estimation point. The coordinates of each estimation point are combined with its estimated seawater turbidity value to form the data of several estimation points.

[0079] S104: Construct an inverse distance weighted interpolation formula, combining the buoy data of the three measurement points and the data of several estimated points to form the known point data in the formula.

[0080] Inverse distance weighted interpolation, or IDM, is an interpolation method based on the distance between measured points. Its logical root is the first law of geography, which states that all attribute values ​​on a geographic surface are interconnected, but that closer attribute values ​​are more strongly correlated than farther ones. Because of this property, IDW interpolation is widely used in data processing in physical space.

[0081] Assume that the geographic coordinates of the target point are ( x , y ), the seawater turbidity value is , the IDM interpolation method uses the weighted sum of the data of all known points in the region to estimate the value of the unknown point, which can be expressed by the formula:

[0082] (2);

[0083] (3);

[0084] (4);

[0085] in, z i For the i The turbidity value of seawater at a known point; w i For the i The distance weight of each known point; d i The target point and i The Euclidean distance of known points; α is 1 or 2; n is the number of known points.

[0086] The known points here include the buoy data of the three measurement points and the estimated point data calculated by the three-dimensional plane linear interpolation formula (1).

[0087] The IDW interpolation method is based on the first law of geography, reflecting the logical relationship between physical attributes and distance. It can effectively combine known regional information to estimate the spatial distribution of attribute values ​​and is highly robust. However, some issues still exist. The IDW interpolation method relies on the number of known points; the greater the number, the more accurate the estimation result. Using only three measurement data provided by three buoys can easily cause spikes near the maximum value. Therefore, this embodiment selects an appropriate amount of data 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.

[0088] It should be noted that the amount of supplementary data must be moderate. If too little is selected, it will have little effect on improving the spike phenomenon; if too much is selected, it will affect the quality of the measurement data set.

[0089] As a preferred embodiment, the supplementary data can be twice the measured 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 take into account both the quality of the measurement data set and the improvement of the spike phenomenon.

[0090] S105. Calculate target point P Planar linear interpolation of .

[0091] Select the target point in the target sea area P , assuming its geographic coordinates are ( x , y ). Set the target point P The geographical coordinates ( x , y ) is substituted into the three-dimensional plane linear interpolation formula (1) to calculate the target point P Plane linear interpolation of z ( x , y ).

[0092] S106. Calculate target point P Inverse distance weighted interpolation of .

[0093] The target point P The geographical coordinates ( x , y ) is substituted into the inverse distance weighted interpolation formula (2)-(4) to calculate the target point P Inverse distance weighted interpolation .

[0094] S107, based on the iterative reweighted least squares principle, the target point P The plane linear interpolation and inverse distance weighted interpolation are fused to obtain the final fusion value.

[0095] 3D linear interpolation can reflect the spatial variation trend of seawater turbidity, while IDW interpolation can effectively combine information from known regions to estimate the spatial distribution of attribute values. However, both methods have their own shortcomings. Therefore, this embodiment, based on the iterative reweighted least squares principle, combines the results calculated by 3D linear interpolation and IDW interpolation to obtain a more accurate estimate of seawater turbidity.

[0096] The fusion process is as follows:

[0097] Establish the fusion equation:

[0098] (5);

[0099] in, Indicates the target point ( x , y )’s fusion value; and is the weight parameter, and ;

[0100] Calculate target point P Fusion value With its plane linear interpolation and inverse distance weighted interpolation The residuals are:

[0101] (6).

[0102] At the target point ( x , y ) around the neighborhood ( x’ , y’ ), select m neighborhood estimation points , j =1,2,……,m. Using the above fusion equation (5) and residual formula (6), the fusion value of the m neighborhood estimation points and the residual of their plane linear interpolation are calculated respectively. , and the residual of the fusion value of the m neighborhood estimation points and its inverse distance weighted interpolation .

[0103] Compute the mean of the two sets of residuals:

[0104] ;

[0105] .

[0106] The local variance optimal strategy is used to calculate the variance of the residual in the neighborhood, that is:

[0107] ;

[0108] Among them, the variance and Independent of each other, that is, .

[0109] Using inverse variance weighting, the weighted residual sum of squares of the two is minimized to construct the objective function S , the expression is as follows:

[0110] (7).

[0111] Substituting the fusion equation (5) into the objective function formula (7), transforming and simplifying it into a neighborhood representation, we can obtain:

[0112] .

[0113] For the objective function S about λ 1 Take the derivative and set it to zero, that is:

[0114] ;

[0115] Then we can solve it and get:

[0116] ;

[0117] .

[0118] The calculated λ 1 and λ 2 is substituted into the fusion equation (5), and the above fusion process is repeated. The weight parameters are adjusted by repeated iterations. λ 1 and λ 2 Convergence (or reaching the maximum number of iterations), calculate the final fusion value.

[0119] S108, taking the final fusion value as the target point P Estimated seawater turbidity.

[0120] The weight parameters that converge after repeated iterations λ 1 and λ Substitute 2 into the fusion equation (5) to calculate the final fusion value. This fusion value is used as the target point P The seawater turbidity value is output to obtain the estimated seawater turbidity value of the target point.

[0121] In order to verify the feasibility and accuracy of the seawater turbidity estimation method proposed in this embodiment, the following simulation experiment is designed:

[0122] (1) Constructing a simulated dataset.

[0123] The spatial distribution of seawater turbidity is influenced by a variety of environmental factors, including water depth, ocean bottom topography, and marine meteorological conditions. In coastal waters, turbidity generally decreases with distance from shore, and this pattern of change is influenced by a variety of environmental factors.

[0124] Based on the above analysis, this embodiment selects an estimated space with a dimension of 10 km × 5 km as the target sea area, and simulates a number of original scattered data for constructing a simulation data set.

[0125] The denser the data points in the simulated dataset, the more accurately it can reflect the real situation. However, considering the workload and operability, it can only be constructed through the method of finite scattered points + ordinary kriging interpolation.

[0126] The construction strategy is as follows: First, 100 original scattered data points (10×10) are simulated in the target sea area. Then, ordinary kriging interpolation is used to generate 5,000 dense data points (100×50) as the real data for the sea area. The real data here consists of geographic coordinates and the seawater turbidity value at those coordinates.

[0127] Afterwards, three data points at different locations 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 follows Figure 3 shown.

[0128] (2) Use three-dimensional plane linear interpolation method to estimate the seawater turbidity distribution in the target sea area.

[0129] The three-dimensional plane linear interpolation formula is constructed using the selected three-buoy data. The coordinates of each data point in the simulation data set are substituted into the three-dimensional plane linear interpolation formula to estimate the seawater turbidity value at each location, forming the following: Figure 4 The turbidity distribution map of the target sea area is shown.

[0130] Depend on Figure 4 It can be seen that although the seawater turbidity value estimated by the three-dimensional plane linear interpolation method shows a trend of lower turbidity as the distance from the shore increases, this trend is linear and does not conform to the actual change law of seawater turbidity. Moreover, the slope of the turbidity change trend in the entire target sea area is greater than the actual situation, so the estimation result is not accurate enough.

[0131] (3) Use the inverse distance weighted interpolation method to estimate the seawater turbidity distribution in the target sea area.

[0132] The three buoy data are used as known points in the inverse distance weighted interpolation formula, and the estimated seawater turbidity value of each data point in the simulated data set is calculated using the inverse distance weighted interpolation formula, as shown in the following example: Figure 5 shown.

[0133] Depend on Figure 5 It can be seen that the seawater turbidity values ​​estimated using the inverse distance weighted interpolation method show a trend of decreasing with increasing distance from shore, and the nonlinear trend of seawater turbidity is closer to the actual situation. However, there are spikes near three measurement points, and because these three measurements are closer to the actual values, the slope of the overall turbidity trend is smaller than the actual situation.

[0134] In view of this, this embodiment selects several estimated point data from a large amount of estimated point data calculated using the three-dimensional plane linear interpolation method as supplementary data, and combines them with the three-buoy data to form more known point data for the inverse distance weighted interpolation formula.

[0135] Substituting the coordinates of each data point in the simulation data set into the inverse distance weighted interpolation formula, the seawater turbidity value at each location is estimated, which can be formed as follows: Figure 6 The turbidity distribution map of the target sea area is shown.

[0136] Depend on Figure 6 It can be seen that by increasing the number of known points, the peak phenomenon 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.

[0137] (4) Based on the iterative reweighted least squares principle, the estimation results of the three-dimensional plane linear interpolation method and the inverse distance weighted interpolation method are fused.

[0138] Assuming the initial weight coefficient 、 , use the fusion equation (5) to calculate the initial fusion value ,Right now:

[0139] .

[0140] Take the local window as 3×3, and perform weight coefficient according to the fusion process in this embodiment and Iterative calculation until convergence. k is the number of iterations.

[0141] Then, the window slides across the entire target space to complete the weight optimization of the entire target sea area to determine the weight coefficients of all locations in the target sea area. λ 1 and λ 2.

[0142] Determine the weight coefficients of all locations in the target sea area λ 1 and λ 2, the final fusion value can be estimated by fusion equation (5) The fusion result is as follows Figure 7 shown.

[0143] Depend on Figure 7 It can be seen that the estimation method based on the iterative reweighted least squares principle proposed in this embodiment can better capture the spatial distribution characteristics of the data when estimating the seawater turbidity value of the target sea area, especially when the data is sparse and there are outliers. It not only reflects the trend of high nearshore and low offshore, but also shows the relationship between seawater turbidity and distance factors.

[0144] 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. Figures 8-10 As shown. Among them, Figure 8 This 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 the traditional mean value method; Figure 9 1 is a comparison chart of the seawater turbidity error obtained by the estimation method of this embodiment and the seawater turbidity error obtained by the traditional plane linear interpolation method; Figure 10 1 is a comparison chart of the seawater turbidity error obtained by the estimation method of this embodiment and the seawater turbidity error obtained by the traditional IDW interpolation method.

[0145] Through simulations, we found that the 3D linear interpolation method can better capture the spatial distribution trend of seawater turbidity values ​​in localized waters, but its estimation accuracy is low in complex areas with strong nonlinearity. The IDW interpolation method can make reasonable estimates based on the distance between measurement points, but it lacks the use of background information, and its estimation accuracy is affected by the number of known measurement points, resulting in large estimation errors when used alone. By combining the two methods, we can fully utilize the large-scale background information provided by the 3D plane model and the distance-related advantages of the IDW interpolation method, thereby obtaining better estimation results.

[0146] Of course, the above embodiments are intended only to illustrate the technical solutions of the present invention, and are not intended to limit the same. Although the present invention has been described in detail with reference to the above embodiments, it is still possible for a person skilled in the art to modify the technical solutions described in the above embodiments, or to replace some of the technical features therein with equivalents; and such modifications or replacements do not deviate from the essence of the corresponding technical solutions from the spirit and scope of the technical solutions claimed for protection by the present invention.

Claims

1. A method for estimating seawater turbidity based on iterative reweighted least squares method, characterized in that: include: The buoy equipment is used to detect the seawater turbidity values ​​at three measurement points in the target sea area, and the geographical coordinates of the three measurement points are combined with the seawater turbidity values ​​of the measurement points to form the buoy data of the three measurement points; Using the buoy data of three measurement points, a three-dimensional plane linear interpolation formula is constructed; Select several estimation points, use the three-dimensional plane linear interpolation formula to calculate the estimated value of seawater turbidity at each estimation point, and combine the geographical coordinates of the estimation points to form several estimation point data; Constructing an inverse distance weighted interpolation formula, using the buoy data of the three measurement points and the estimated point data as known point data in the formula; Select the target point in the target sea area P , whose geographical coordinates are ( x , y ); The target point P The geographical coordinates ( x , y ) is substituted into the three-dimensional plane linear interpolation formula to calculate the target point P Planar linear interpolation of z ( x , y ); The target point P The geographical coordinates ( x , y ) is substituted into the inverse distance weighted interpolation formula to calculate the target point P Inverse distance weighted interpolation ; Establish the fusion equation: ； in, Indicates the target point ( x , y )’s fusion value; and is the weight parameter, and ; Calculate target point P Fusion value With its plane linear interpolation z ( x , y ) and inverse distance weighted interpolation The residual formula is: ； At the target point ( x , y ) around the neighborhood ( x’ , y’ ), select m neighborhood estimation points , j =1,2,……,m; Using the fusion equation and residual formula, the residuals of the fusion values ​​of the m neighborhood estimation points and their plane linear interpolation are calculated respectively. , and the residual of the fusion value of m neighborhood estimation points and their inverse distance weighted interpolation ; Calculate the mean of the two sets of residuals and ; Compute the variance of the residuals within a neighborhood: ； Constructing the objective function S : ； Substitute the fusion equation into the objective function S Formula, transformed and simplified into neighborhood representation: ； For the objective function S about λ 1 Take the derivative and set it to zero, that is: ； The solution is: , ; The calculated λ 1 and λ 2 is substituted into the fusion equation, and the weight parameter is adjusted by repeated iterations. λ 1 and λ 2. Convergence or reaching the maximum number of iterations, calculate the final fusion value; The final fusion value is used as the target point P Estimated seawater turbidity.

2. The method for estimating seawater turbidity based on iterative 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; among them, x i For the i The geographical easting direction of the measurement point, y i For the i The geographic north direction of the measurement point, z i For the i Seawater turbidity value at each measuring point; Construct a three-dimensional plane linear interpolation formula: z=ax+by+c ; The buoy data of the three measurement points ( x i , y i , z i ) are substituted into the three-dimensional plane linear interpolation formula to calculate the unknown coefficients in the formula a, b, c value.

3. The method for estimating seawater turbidity based on iterative reweighted least squares method according to claim 2, characterized in that: The three measurement points are distributed in a triangle shape in the target sea area.

4. The method for estimating seawater turbidity based on iterative reweighted least squares method according to claim 1, wherein: The inverse distance weighted interpolation formula is: ； ； ； in, z i For the i The turbidity value of seawater at a known point; w i For the i The distance weight of each known point; d i The target point and i The Euclidean distance of known points; α is 1 or 2; n is the number of known points.

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

6. The method for estimating seawater turbidity based on iterative reweighted least squares method according to any one of claims 1 to 5, characterized in that: In the iterative process, the weight coefficient is first λ 1 and λ 2. Assigning initial values ​​and calculating the initial fusion value using the fusion equation; Configure the size of the local window and adjust the weight coefficient according to the iterative process λ 1 and λ 2 iterative calculation until convergence; Configure the local window to slide across the entire target space, complete the weight optimization of the entire target sea area, and determine the weight coefficients of all locations in the target sea area. λ 1 and λ 2, the seawater turbidity distribution of the target sea area is determined by the fusion equation.

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