A method for positioning a seabed reference point based on a system error influence mechanism

Abstract

The application discloses a seabed reference point positioning method based on a system error influence mechanism, belongs to underwater positioning technology, and is used for seabed reference point positioning and comprising the following steps: constructing an observation equation of seabed reference point acoustic positioning; obtaining an observation value residual vector by adopting least square adjustment and extracting a residual vector direction system error; establishing a regression relationship between the residual vector direction system error and a corresponding angle of a side based on a local weighted regression method; calculating a solution vector direction system error by adopting the regression relationship; and substituting the obtained system error into the observation equation to perform system error compensation and high-precision seabed reference point positioning. The system error is obtained by the influence mechanism of the system error on a least square parameter solution, the positioning precision of the seabed reference point is significantly improved, and technical support can be provided for seabed reference network construction and maintenance, marine disaster monitoring, marine positioning services and the like.

Description

Technical Field

[0001] This invention discloses a seabed benchmark positioning method based on the mechanism of systematic error, belonging to underwater positioning technology. Background Technology

[0002] Due to the complex marine environment, precise positioning of seabed benchmarks faces numerous technical challenges. Among these, systematic errors are the most significant factor affecting the positioning accuracy. Systematic errors in acoustic positioning of seabed benchmarks mainly include sound velocity measurement errors and representativeness errors, hardware delay errors, GNSS positioning errors, equipment installation deviations, and transducer travel differences. Refined handling of systematic errors is a crucial problem that needs to be solved for high-precision positioning of seabed benchmarks. Currently, there are two main types of methods for handling systematic errors in seabed benchmark positioning: differential methods and model compensation methods. To reduce systematic errors between observations, a method using differential technology to position seabed benchmarks is proposed. In the case of a single transponder, the difference between observations from adjacent epochs can eliminate long-period systematic errors; if different transponders exist, positioning using a double-difference method can further eliminate short-period systematic errors. Considering the positional difference of the transponder at the time of transmission and reception, an underwater non-differential positioning method based on two-way acoustic paths is proposed. Subsequently, based on two-way acoustic paths, a two-way differential method is proposed. Although the differential algorithm can eliminate the influence of systematic errors and improve the accuracy of seabed benchmark positioning, it also has problems such as reduced number of equations and the observation equations being prone to ill-conditioned conditions.

[0003] In the study of model compensation for systematic errors, most research is based on sound velocity. To address the influence of time-varying sound velocity structures, polynomials or B-spline functions are used to fit the sound velocity error within a sliding time window, while simultaneously solving for the coordinates of the seabed reference point and the sound velocity correction parameters. Further research has proposed a GNSS-acoustic positioning model considering the horizontal gradient of sound velocity to eliminate the impact of sound velocity errors on horizontal positioning accuracy. Elastic observation models with time and distance deviation parameters, as well as elastic observation models with periodic error parameters, have been established to effectively compensate for the influence of systematic errors. A state-space equation has been constructed, and Kalman filtering has been used for sequential estimation of sound velocity errors, improving the estimation level. While the aforementioned model compensation methods for systematic errors have mitigated their impact to some extent, some systematic errors remain unestimated, and the accuracy of parameter solutions still needs improvement. Therefore, although significant progress has been made in the research of models and algorithms for systematic error handling in seabed reference point positioning, seabed reference point positioning observations exhibit complex and variable characteristics due to the influence of the complex marine environment. Systematic errors possess both systematic and random characteristics, making it difficult to completely eliminate systematic causes from the environmental perspective. Given the unclear mechanism by which systematic errors affect the least squares solution in least squares adjustment, in-depth analysis of the mechanism by which systematic errors affect the least squares solution and research on new methods for handling systematic errors in seabed benchmark positioning are key to improving the positioning accuracy of seabed benchmarks. Summary of the Invention

[0004] The purpose of this invention is to provide a seabed benchmark positioning method based on the mechanism of systematic error, so as to solve the problem that in the prior art, the positioning and observation of seabed benchmarks exhibits complex changing characteristics due to the influence of the complex marine environment. The systematic error has both systematic and random characteristics, and it is difficult to completely find systematic causes from the environment to eliminate them.

[0005] A method for locating seabed benchmarks based on the mechanism of systematic error includes:

[0006] S1. Determine the reference point, obtain the bidirectional propagation time of the acoustic signal from the sea surface acoustic transducer to the reference point, and use the sound velocity profile data to construct the observation equation from the sea surface acoustic transducer to the reference point. Use Taylor series expansion to obtain the linearized observation equation for all observation epochs.

[0007] S2. Solve for the coordinate correction of the reference point using the least squares method, calculate the residual vector of the observed value based on the coordinate correction, and extract the systematic error of the residual vector direction using the wavelet transform method.

[0008] S3. By utilizing the continuity of systematic errors in adjacent epochs and prior coordinates, constraints are imposed on the systematic errors and seabed reference point coordinates. A weighted fitting method is used to calculate the estimated systematic error. The systematic error in the direction of the residual vector is calculated by combining the systematic error in the direction of the residual vector. The angle of the opposite side of the residual vector is calculated based on the systematic error in the direction of the solution vector and the systematic error in the direction of the residual vector. A local weighted regression method is used to establish the regression relationship between the systematic error in the direction of the residual vector and the angle of the corresponding opposite side.

[0009] S4. For seabed reference points other than the reference reference point, based on the local weighted regression equation, calculate the systematic error of the residual vector direction for each seabed reference point, predict the corresponding angle vector, and calculate the systematic error of the solution vector direction.

[0010] S5. Calculate the systematic error vector of the seabed reference point using the systematic error of the residual vector direction and the systematic error of the solution vector direction, and correct the observation equation. Calculate the coordinate correction of the seabed reference point using the corrected observation equation, and calculate the corrected position of the seabed reference point by combining the initial coordinates of the seabed reference point.

[0011] S1 includes, S1.1, among seabed reference points with the same observation conditions, selecting one seabed reference point as the reference reference point, transmitting acoustic signals to the seabed using a surface acoustic transducer, and receiving the response acoustic signals from the reference reference point to obtain the two-way propagation time of the acoustic signals. Using the sound velocity profile data, constructing the observation equation from the surface acoustic transducer to the reference reference point:

[0012] ;

[0013] In the formula, , The total number of observed epochs. For the first The acoustic distance between the sea surface acoustic transducer and the reference point at each observation epoch. , This is the speed of sound. For the first The two-way propagation time of acoustic signals in each observation epoch. This represents the theoretical distance from the sea surface transducer to the reference point. It is the first The coordinates of the sea surface acoustic transducer at each observation epoch. The coordinates of the reference point, This is random error;

[0014] For the first Systematic error per observation epoch:

[0015] ;

[0016] In the formula, It is the first The systematic error caused by the seabed transponder delay in each observation epoch. It is the first The systematic error of sound velocity correlation for each observation epoch. It is the first Each observation epoch and External systematic errors.

[0017] S1 includes S1.2, and Taylor series expansion of the observation equations for the propagation distance from the sea surface acoustic transducer to the reference point, yielding the linearized observation equations for all observation epochs:

[0018] ;

[0019] In the formula, This is the difference between the acoustic ranging observation value and the theoretical distance. Design matrix for coordinate parameters, For the coordinate corrections of the unsolved reference datum point;

[0020] For observation error:

[0021] ;

[0022] In the formula, This is the transpose symbol.

[0023] S2 includes S2.1, and the solution based on least squares adjustment. :

[0024] ;

[0025] In the formula, The coordinate correction value for the reference datum point. The observation weight matrix;

[0026] S2 includes, S2.2, based on Calculate the residual vector of observations :

[0027] ;

[0028] S2 includes S2.3, which is extracted using wavelet transform. System error .

[0029] S3 includes S3.1, which constrains the systematic error and seabed benchmark based on the continuity of systematic errors in adjacent epochs and prior coordinates, and uses a weighted fitting method to calculate and obtain the estimated systematic error. ,Will and The difference is used to obtain the systematic error of the solution vector direction. :

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, For the estimated value vector, To design the matrix, , It is the identity matrix. For regularization matrix, For regularization parameters, To utilize the continuity of systematic errors between adjacent epochs The obtained system error weight matrix, , , It is a coordinate component weight matrix. = ;

[0034] S3 includes, S3.2, according to and calculate Angles of opposite sides :

[0035] .

[0036] S3 includes S3.3, which uses a locally weighted regression method to establish... and The regression relationships include constructing the dataset. , For the first Each observation epoch , for The corresponding angle, for each Construct a regression model at the target point The local weighted regression model at this point is:

[0037] ;

[0038] In the formula, A vector of independent variables. 1 represents the intercept term. Let be the order of the polynomial. for of Power of 1 For regression coefficients, It is a noise term.

[0039] S3 includes S3.4, which involves obtaining estimates of the regression coefficients using the weighted least squares method. :

[0040] ;

[0041] ;

[0042] In the formula, Let the vector be the dependent variable. , It is a diagonal weight matrix. To design the matrix, for of Power of 1.

[0043] S4 includes calculating the residual vector direction systematic error for each seabed reference point other than the reference reference point, based on the local weighted regression equation. And predict the corresponding angle vector And calculate the systematic error in the direction of the solution vector. :

[0044] .

[0045] S5 includes S5.1, based on and Calculate the system error vector :

[0046] ;

[0047] use Observation vectors of seabed reference points other than the reference reference point Make corrections:

[0048] ;

[0049] In the formula, This is the observation vector corrected for seabed reference points other than the reference reference point.

[0050] S5 includes S5.2, calculating the corrected coordinate correction vector. :

[0051] ;

[0052] In the formula, The design matrix for seabed datum points excluding the reference datum point. The weighted matrix of observation values ​​for seabed reference points other than the reference reference point;

[0053] S5 includes S5.3, which calculates the corrected positions of seabed reference points other than the reference reference point. :

[0054] ;

[0055] In the formula, These are the initial coordinates of the seabed reference points, excluding the reference reference point.

[0056] Compared with the prior art, the present invention has the following beneficial effects: The present invention obtains the systematic error through the influence mechanism of systematic error on the least squares parameter solution, which significantly improves the positioning accuracy of the seabed reference point and can provide technical support for the construction and maintenance of the seabed reference network, marine disaster monitoring and marine positioning services. Attached Figure Description

[0057] Figure 1 A schematic diagram illustrating the geometric interpretation of least squares;

[0058] Figure 2 This is a schematic diagram illustrating the mechanism by which systematic errors affect the least squares solution.

[0059] Figure 3 The results show the eastward positioning errors for seabed reference points T1, T2, and T3.

[0060] Figure 4 The results show the northward positioning errors for seabed reference points T1, T2, and T3.

[0061] Figure 5 The results show the celestial orientation positioning errors for seabed reference points T1, T2, and T3.

[0062] Figure 6 This is the residual result for the seabed reference point T1;

[0063] Figure 7 The residual results are for the seabed reference point T2;

[0064] Figure 8 This is the residual result for the seabed reference point T3. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0066] A method for locating seabed benchmarks based on the mechanism of systematic error includes:

[0067] S1. Determine the reference point, obtain the bidirectional propagation time of the acoustic signal from the sea surface acoustic transducer to the reference point, and use the sound velocity profile data to construct the observation equation from the sea surface acoustic transducer to the reference point. Use Taylor series expansion to obtain the linearized observation equation for all observation epochs.

[0068] S2. Solve for the coordinate correction of the reference point using the least squares method, calculate the residual vector of the observed value based on the coordinate correction, and extract the systematic error of the residual vector direction using the wavelet transform method.

[0069] S3. By utilizing the continuity of systematic errors in adjacent epochs and prior coordinates, constraints are imposed on the systematic errors and seabed reference point coordinates. A weighted fitting method is used to calculate the estimated systematic error. The systematic error in the direction of the residual vector is calculated by combining the systematic error in the direction of the residual vector. The angle of the opposite side of the residual vector is calculated based on the systematic error in the direction of the solution vector and the systematic error in the direction of the residual vector. A local weighted regression method is used to establish the regression relationship between the systematic error in the direction of the residual vector and the angle of the corresponding opposite side.

[0070] S4. For seabed reference points other than the reference reference point, based on the local weighted regression equation, calculate the systematic error of the residual vector direction for each seabed reference point, predict the corresponding angle vector, and calculate the systematic error of the solution vector direction.

[0071] S5. Calculate the systematic error vector of the seabed reference point using the systematic error of the residual vector direction and the systematic error of the solution vector direction, and correct the observation equation. Calculate the coordinate correction of the seabed reference point using the corrected observation equation, and calculate the corrected position of the seabed reference point by combining the initial coordinates of the seabed reference point.

[0072] S1 includes, S1.1, among seabed reference points with the same observation conditions, selecting one seabed reference point as the reference reference point, transmitting acoustic signals to the seabed using a surface acoustic transducer, and receiving the response acoustic signals from the reference reference point to obtain the two-way propagation time of the acoustic signals. Using the sound velocity profile data, constructing the observation equation from the surface acoustic transducer to the reference reference point:

[0073] ;

[0074] In the formula, , The total number of observed epochs. For the first The acoustic distance between the sea surface acoustic transducer and the reference point at each observation epoch. , This is the speed of sound. For the first The two-way propagation time of acoustic signals in each observation epoch. This represents the theoretical distance from the sea surface transducer to the reference point. It is the first The coordinates of the sea surface acoustic transducer at each observation epoch. The coordinates of the reference point, This is random error;

[0075] For the first Systematic error per observation epoch:

[0076] ;

[0077] In the formula, It is the first The systematic error caused by the seabed transponder delay in each observation epoch. It is the first The systematic error of sound velocity correlation for each observation epoch. It is the first Each observation epoch and External systematic errors.

[0078] S1 includes S1.2, and Taylor series expansion of the observation equations for the propagation distance from the sea surface acoustic transducer to the reference point, yielding the linearized observation equations for all observation epochs:

[0079] ;

[0080] In the formula, This is the difference between the acoustic ranging observation value and the theoretical distance. Design matrix for coordinate parameters, For the coordinate corrections of the unsolved reference datum point;

[0081] For observation error:

[0082] ;

[0083] In the formula, This is the transpose symbol.

[0084] S2 includes S2.1, and the solution based on least squares adjustment. :

[0085] ;

[0086] In the formula, The coordinate correction value for the reference datum point. The observation weight matrix;

[0087] S2 includes, S2.2, based on Calculate the residual vector of observations :

[0088] ;

[0089] S2 includes S2.3, which is extracted using wavelet transform. System error .

[0090] S3 includes S3.1, which constrains the systematic error and seabed benchmark based on the continuity of systematic errors in adjacent epochs and prior coordinates, and uses a weighted fitting method to calculate and obtain the estimated systematic error. ,Will and The difference is used to obtain the systematic error of the solution vector direction. :

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, For the estimated value vector, To design the matrix, , It is the identity matrix. For regularization matrix, For regularization parameters, To utilize the continuity of systematic errors between adjacent epochs The obtained system error weight matrix, , , It is a coordinate component weight matrix. = ;

[0095] S3 includes, S3.2, according to and calculate Angles of opposite sides :

[0096] .

[0097] S3 includes S3.3, which uses a locally weighted regression method to establish... and The regression relationships include constructing the dataset. , For the first Each observation epoch , for The corresponding angle, for each Construct a regression model at the target point The local weighted regression model at this point is:

[0098] ;

[0099] In the formula, A vector of independent variables. 1 represents the intercept term. Let be the order of the polynomial. for of Power of 1 For regression coefficients, It is a noise term.

[0100] S3 includes S3.4, which involves obtaining estimates of the regression coefficients using the weighted least squares method. :

[0101] ;

[0102] ;

[0103] In the formula, Let the vector be the dependent variable. , It is a diagonal weight matrix. To design the matrix, for of Power of 1.

[0104] S4 includes calculating the residual vector direction systematic error for each seabed reference point other than the reference reference point, based on the local weighted regression equation. And predict the corresponding angle vector And calculate the systematic error in the direction of the solution vector. :

[0105] .

[0106] S5 includes S5.1, based on and Calculate the system error vector :

[0107] ;

[0108] use Observation vectors of seabed reference points other than the reference reference point Make corrections:

[0109] ;

[0110] In the formula, This is the observation vector corrected for seabed reference points other than the reference reference point.

[0111] S5 includes S5.2, calculating the corrected coordinate correction vector. :

[0112] ;

[0113] In the formula, The design matrix for seabed datum points excluding the reference datum point. The weighted matrix of observation values ​​for seabed reference points other than the reference reference point;

[0114] S5 includes S5.3, which calculates the corrected positions of seabed reference points other than the reference reference point. :

[0115] ;

[0116] In the formula, These are the initial coordinates of the seabed reference points, excluding the reference reference point.

[0117] To investigate the mechanism by which systematic errors affect the least squares solution, it is first necessary to explain the geometric meaning of least squares. The matrix in the observation equation... The space formed by the column vectors is called a matrix. The range space is denoted as Therefore, the objective of least squares estimation is to estimate the range space. In the middle, find a vector This makes the observation vector arrive The distance is greater than The distances to other vectors in the vector are all short. Let... If the vector is the desired vector, then the least squares estimation criterion is:

[0118] ;

[0119] In the formula, It is the Euclidean norm of the vector, that is and The distance between them.

[0120] Based on the residual vector The least squares estimation criterion can be rewritten as:

[0121] ;

[0122] Because of the observation vector to the range space The shortest distance between vectors is along the perpendicular line. With range space Vertical, that is .

[0123] Therefore, in least squares estimation, the observation vector Decomposed into the range space vectors in Sum and range space Perpendicular residual vectors. In other words, It is the observation vector In the value range space Orthographic projection on, such as Figure 1 As shown, this is the geometric interpretation of least squares.

[0124] Since systematic errors exist in the observations, and based on the geometric interpretation of least squares, we can conclude that the influence of systematic errors in the observations on the least squares estimate is divided into two parts: part is absorbed by the solution vector and part is absorbed by the residual vector. Furthermore, the systematic errors in the solution vector direction and the systematic errors in the residual vector direction are perpendicular to each other. Figure 2 This is a schematic diagram illustrating the mechanism by which systematic errors affect the least squares solution. This refers to the systematic errors present in the observations. To solve for the systematic error in the vector direction, For the residual vector direction systematic error, The residual vector direction systematic error is the angle of the opposite side.

[0125] Theoretical derivation can further verify the influence mechanism of systematic errors on the least squares solution, and study the systematic error in the direction of the residual vector. The impact on the least squares solution. The least squares estimation criterion is... ,Right now:

[0126] ;

[0127] If systematic error exists in the residual vector ,make , For residual vectors Remove systematic errors The remaining random error components are then estimated using the least squares criterion. We can obtain:

[0128] ;

[0129] so:

[0130] ;

[0131] ;

[0132] Combination , It can be represented as:

[0133] ;

[0134] according to It can be known that:

[0135] ;

[0136] Combination It can be known ,so:

[0137] ;

[0138] In other words, the systematic error in the direction of the residual vector does not affect the final least squares parameter solution. The above analysis shows that solving for the systematic error in the direction of the solution vector is key to improving the positioning accuracy of seabed benchmarks. Therefore, it is necessary to further clarify the relationship between the systematic error in the direction of the least squares solution vector and the systematic error in the direction of the residual vector, based on the mechanism by which systematic errors affect the least squares solution.

[0139] like Figure 2 As shown, the systematic error of the solution vector direction Systematic error in residual vector direction If they are perpendicular to each other, the mathematical relationship between them can be expressed as:

[0140] ;

[0141] Obtaining high-precision seabed benchmark locations hinges on accurately determining the specific values ​​of systematic errors in the solution vector direction to eliminate their impact on the parameter solutions. It can be seen that if we want to obtain the systematic error of the solution vector direction... It is necessary to know the systematic error of the residual vector direction. And the systematic error of the residual vector direction is the angle of the opposite side. However, in actual measurements, the residual vector direction systematic error... It can be extracted from the residual vector, while the angle It's difficult to determine directly. Through analysis of... Studies have been conducted to investigate the patterns of change. and The changing patterns are highly similar. Utilizing this high similarity, a locally weighted regression method can be used to establish... and The regression relationship between them was obtained And then calculate In summary, determining the systematic error based on its influence mechanism on the least squares parameter solution is crucial for improving the positioning accuracy of seabed benchmarks.

[0142] This invention utilizes real observation data from underwater acoustic positioning. The prior coordinates of the seabed reference points used in calculating the design matrix are obtained through an inter-epoch differential positioning method. Based on the principle that among seabed reference points with similar or identical observation conditions, a seabed reference point with good observation geometry and a large number of observation epochs is selected as the standard reference point, four seabed reference points (T1, T2, T3, and T4) are established on the seabed. The systematic errors of the solution vector directions of the three seabed reference points (T1, T2, and T3) are calculated based on the regression relationship of the seabed reference point T4. Four methods were used for seabed reference point positioning, and the positioning results of these four methods were compared. Method 1 is a traditional method that does not consider systematic errors; Method 2 is a traditional method that compensates for the systematic errors in the residual vector directions; Method 3 is a new method that compensates for the systematic errors in the solution vector directions; and Method 4 is a new method that compensates for both the systematic errors in the residual vector directions and the systematic errors in the solution vector directions.

[0143] like Figure 3 , Figure 4 and Figure 5As shown, the new method has smaller positioning errors in both the horizontal and vertical directions compared to the traditional method, indicating its superior performance in seabed benchmark positioning. This difference is particularly significant in the vertical direction, where the new method improves the positioning error from the decimeter level to the centimeter level, significantly reducing the impact of vertical systematic errors and verifying the effectiveness of the proposed method in systematic error compensation. Furthermore, the positioning results of Method 1 and Method 2 are not significantly different, as are those of Method 3 and Method 4, indicating that the systematic error in the residual vector direction does not affect the solution of the seabed benchmark position parameters, consistent with the mechanism of systematic error influence on the least squares solution. The horizontal and three-dimensional positioning accuracy of the new method is consistently better than that of the traditional method. Taking Method 3 and Method 1 as examples, Method 3 improves the underwater positioning accuracy by 6.88% to 42.61% and the three-dimensional positioning accuracy by 45.50% to 68.10% compared to Method 1. These results demonstrate that the seabed benchmark positioning method based on the systematic error influence mechanism proposed in this invention can obtain accurate solution vector direction systematic errors, thereby achieving high-precision seabed benchmark positions. The statistical results of the positioning accuracy of different methods are shown in Table 1.

[0144] Table 1. Statistical analysis of positioning accuracy using different methods

[0145] .

[0146] Figure 6 , Figure 7 and Figure 8 The acoustic ranging residuals for positioning at seabed reference points T1, T2, and T3 are presented. Since methods 1 and 3 do not consider the influence of systematic errors in the residual vector direction, their residuals are higher than those of methods 2 and 4. By removing the extracted systematic errors in the residual vector direction from the observations, the residuals of methods 2 and 4 are smaller and show no systematic fluctuations. The relatively small difference between the residuals of methods 2 and 4 is because although method 4 compensates for the systematic errors in the solution vector direction from the observations, these systematic errors do not affect the residual results. Combining the positioning error and the residual results, this further demonstrates that good residual results are not equivalent to good parameter solutions. The underwater acoustic positioning method proposed in this invention, based on the influence mechanism of systematic errors on the least squares solution, is of great significance.

[0147] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for locating seabed benchmarks based on the mechanism of systematic error, characterized in that, include: S1. Determine the reference point, obtain the bidirectional propagation time of the acoustic signal from the sea surface acoustic transducer to the reference point, and use the sound velocity profile data to construct the observation equation from the sea surface acoustic transducer to the reference point. Use Taylor series expansion to obtain the linearized observation equation for all observation epochs. S2. Solve for the coordinate correction of the reference point using the least squares method, calculate the residual vector of the observed value based on the coordinate correction, and extract the systematic error of the residual vector direction using the wavelet transform method. S3. By utilizing the continuity of systematic errors in adjacent epochs and prior coordinates, constraints are imposed on the systematic errors and seabed reference point coordinates. A weighted fitting method is used to calculate the estimated systematic error. The systematic error in the direction of the residual vector is calculated by combining the systematic error in the direction of the residual vector. The angle of the opposite side of the residual vector is calculated based on the systematic error in the direction of the solution vector and the systematic error in the direction of the residual vector. A local weighted regression method is used to establish the regression relationship between the systematic error in the direction of the residual vector and the angle of the corresponding opposite side. S4. For seabed reference points other than the reference reference point, based on the local weighted regression equation, calculate the systematic error of the residual vector direction for each seabed reference point, predict the corresponding angle vector, and calculate the systematic error of the solution vector direction. S5. Calculate the systematic error vector of the seabed reference point using the systematic error of the residual vector direction and the systematic error of the solution vector direction, and correct the observation equation. Calculate the coordinate correction of the seabed reference point using the corrected observation equation, and calculate the corrected position of the seabed reference point by combining the initial coordinates of the seabed reference point. S1 includes S1.2, and Taylor series expansion of the observation equations for the propagation distance from the sea surface acoustic transducer to the reference point, yielding the linearized observation equations for all observation epochs: ； In the formula, This is the difference between the acoustic ranging observation value and the theoretical distance. Design matrix for coordinate parameters, For the coordinate corrections of the unsolved reference datum point; This is the observation error; S2 includes S2.1, and the solution based on least squares adjustment. : ； In the formula, The coordinate correction value for the reference datum point. The observation weight matrix; S2 includes, S2.2, based on Calculate the residual vector of observations : ； S2 includes S2.3, which is extracted using wavelet transform. System error ; S3 includes S3.1, which constrains the systematic error and seabed benchmark based on the continuity of systematic errors in adjacent epochs and prior coordinates, and uses a weighted fitting method to calculate and obtain the estimated systematic error. ,Will and The difference is used to obtain the systematic error of the solution vector direction. : ； ； ； In the formula, For the estimated value vector, To design the matrix, , It is the identity matrix. For regularization matrix, For regularization parameters, To utilize the continuity of systematic errors between adjacent epochs The obtained system error weight matrix, , , It is a coordinate component weight matrix. = ; S3 includes, S3.2, according to and calculate Angles of opposite sides : 。 2. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 1, characterized in that, S1 includes, S1.1, among seabed reference points with the same observation conditions, selecting one seabed reference point as the reference reference point, transmitting acoustic signals to the seabed using a surface acoustic transducer, and receiving the response acoustic signals from the reference reference point to obtain the two-way propagation time of the acoustic signals. Using the sound velocity profile data, constructing the observation equation from the surface acoustic transducer to the reference reference point: ； In the formula, , The total number of observed epochs. For the first The acoustic distance between the sea surface acoustic transducer and the reference point at each observation epoch. , This is the speed of sound. For the first The two-way propagation time of acoustic signals in each observation epoch. This represents the theoretical distance from the sea surface transducer to the reference point. It is the first The coordinates of the sea surface acoustic transducer at each observation epoch. The coordinates of the reference point, This is random error; For the first Systematic error per observation epoch: ； In the formula, It is the first The systematic error caused by the seabed transponder delay in each observation epoch. It is the first The systematic error of sound velocity correlation for each observation epoch. It is the first Each observation epoch and External systematic errors.

3. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 2, characterized in that, ； In the formula, This is the transpose symbol.

4. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 3, characterized in that, S3 includes S3.3, which uses a locally weighted regression method to establish... and The regression relationships include constructing the dataset. , For the first Each observation epoch , for The corresponding angle, for each Construct a regression model at the target point The local weighted regression model at this point is: ； In the formula, A vector of independent variables. 1 represents the intercept term. Let be the order of the polynomial. for of Power of 1 For regression coefficients, It is a noise term.

5. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 4, characterized in that, S3 includes S3.4, which involves obtaining estimates of the regression coefficients using the weighted least squares method. : ； ； In the formula, Let the vector be the dependent variable. , It is a diagonal weight matrix. To design the matrix, for of Power of 1.

6. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 5, characterized in that, S4 includes calculating the residual vector direction systematic error for each seabed reference point other than the reference reference point, based on the local weighted regression equation. And predict the corresponding angle vector And calculate the systematic error in the direction of the solution vector. : 。 7. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 6, characterized in that, S5 includes S5.1, based on and Calculate the system error vector : ； use Observation vectors of seabed reference points other than the reference reference point Make corrections: ； In the formula, This is the observation vector corrected for seabed reference points other than the reference reference point.

8. The seabed benchmark positioning method based on the influence mechanism of systematic errors according to claim 7, characterized in that, S5 includes S5.2, calculating the corrected coordinate correction vector. : ； In the formula, The design matrix for seabed datum points excluding the reference datum point. The weighted matrix of observation values ​​for seabed reference points other than the reference reference point; S5 includes S5.3, which calculates the corrected positions of seabed reference points other than the reference reference point. : ； In the formula, These are the initial coordinates of the seabed reference points, excluding the reference reference point.

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