A long-distance submarine route surveying milepost determination method

Abstract

This invention provides a method for determining mileage markers in long-distance seabed route surveys, belonging to the field of seabed route survey technology. It establishes a database by acquiring the geodetic coordinates of each inflection point of a long-distance seabed route. Using an inverse kilometer marker algorithm, the actual distance and azimuth of the route segment between adjacent inflection points are calculated through Mercator projection asymptotic latitude difference and longitude / latitude difference. The total route mileage is obtained by accumulating the distances of each segment. The spacing between mileage markers is determined based on the scale of the survey map, and standard parameters for their placement are established. The geodetic coordinates of each route inflection point are converted to planar coordinates using Mercator projection. The midpoint plane coordinates are iteratively calculated between the two endpoints of the route segment using the midpoint equal division iterative method. After being converted back to geodetic coordinates using Mercator projection, the actual distance to the starting point of each route segment is calculated using an inverse kilometer marker algorithm. This distance is compared with the preset mileage marker distance to calculate the distance difference. When the distance difference is less than a set threshold, the accurate location of the preset mileage marker is determined.

Description

Technical Field

[0001] This invention belongs to the field of submarine route survey technology, and more specifically, relates to a method for determining mileage markers in long-distance submarine route survey. Background Technology

[0002] Submarine route surveying is a crucial step in marine engineering construction. In projects such as submarine cable laying, submarine pipeline construction, and marine geological exploration, accurate mileage marker positioning is essential for construction navigation, quantity calculation, and quality control. For short-distance submarine route surveys using projections with minimal distortion, such as the Gauss-Kruger projection, mileage marker determination primarily employs straight-line distance calculations and simple coordinate transformation techniques. Mileage markers are placed by segmenting the route and directly calculating distances using a plane coordinate system. However, for long-distance submarine route surveys using the Mercator projection, the above methods neglect the influence of Mercator projection length distortion and Earth's curvature on distance calculations. This leads to an inaccurate reflection of actual distances on the Earth's surface, resulting in increased cumulative errors in mileage marker calculations. While existing technologies can use the conformal forward algorithm to calculate the actual location of mileage markers using azimuth angles and preset distances, the actual calculation process requires repeated application of both conformal forward and inverse algorithms and Mercator projection forward and inverse algorithms. The conformal forward algorithm, in particular, involves complex latitude iteration calculations and relies on highly accurate azimuth angle calculations, significantly increasing the overall computational difficulty and time. Furthermore, due to the lack of precise calculation methods that consider the characteristics of the Earth's ellipsoid, existing technologies suffer from systematic biases in determining mileage marker locations during long-distance seabed route surveys. These errors accumulate with increasing route distance, severely impacting the reliability of survey results and the accuracy requirements of engineering implementation. In other words, existing technologies suffer from insufficient accuracy in determining mileage marker locations during long-distance seabed route surveys. Summary of the Invention

[0003] In view of this, the present invention provides a novel method for determining the mileage markers of long-distance seabed route surveys, which can solve the problems of high computational difficulty and long time in the prior art while ensuring the accuracy of the results.

[0004] This invention is implemented as follows: A method for determining mileage markers in long-distance seabed route surveys includes the following steps: obtaining the geodetic coordinates of each inflection point of the long-distance seabed route, where the inflection points include the route start point, route end point, and intermediate turning points; establishing a geodetic coordinate database of route inflection points; using an inverse kinematic algorithm based on the Mercator projection asymptotic latitude difference and longitude / latitude difference to calculate the actual distance and azimuth of the route segment between adjacent inflection points, and summing the distances of each route segment to obtain the total route mileage; determining the spacing between mileage markers based on the scale of the survey map and establishing standard parameters for mileage marker placement. The geodetic coordinates of each route inflection point are converted to planar coordinates using Mercator projection forward calculation. The midpoint plane coordinates are iteratively calculated between the two endpoints of the route segment using the midpoint equal division iterative method, and then converted back to geodetic coordinates using Mercator projection. The actual distance to the starting point of each route segment is calculated using an inverse kinematic algorithm based on the same kinematic route. This distance is compared with the preset mileage marker distance to calculate the distance difference. When the distance difference is less than a set threshold, it indicates the accurate location of the preset mileage marker. Based on the above midpoint equal division iterative algorithm, the automatic annotation of mileage markers is realized by using AutoCAD secondary development technology, including forward annotation and reverse annotation, to generate mileage marker annotation maps that meet the mapping standards of survey results.

[0005] The inverse kinematics algorithm is a mathematical method for determining the actual distance and azimuth between two points based on the geodetic coordinates of the starting point and the destination point. In Mercator projection, the inverse kinematics route is represented as a straight line, which is used for the accurate calculation of the distance of each segment of a long-distance seabed route.

[0006] The Mercator projection asymptotic latitude, a core parameter in the Mercator projection system of cartography, is essentially the latitude coordinate of the projection plane calculated using a specific mathematical formula to achieve conformal projection characteristics. The formula for calculating the Mercator projection asymptotic latitude is as follows: ,in The coefficient for converting radians to minutes, 1 radian = ×60 points = 3437′.7467708; Latitude of the earth The first eccentricity of the reference ellipsoid.

[0007] The latitude and longitude difference is calculated from the geodetic coordinates of the starting point and the arriving point. The formula for calculating the longitude difference is as follows: The formula for calculating the latitude difference is: ,in , The starting point's geodetic coordinates are... , Given the geodetic coordinates of the arrival point, the formula for calculating the asymptotic latitude difference in the Mercator projection is: ,in , These are the Mercator projection asymptotic latitudes of the arrival and starting points, respectively.

[0008] The route azimuth angle calculation is based on the longitude difference and the Mercator projection asymptotic latitude difference, and the calculation formula is as follows: ,in This is the difference in longitude. The route azimuth quadrant is determined based on the sign of the longitude and latitude differences, using the Mercator projection asymptotic latitude difference. Specifically, the route azimuth is 90 degrees when the longitude difference is greater than 0 and the latitude difference is equal to 0, and 270 degrees when the longitude difference is less than 0 and the latitude difference is equal to 0.

[0009] The meridian arc length calculation employs a precise formula in series form. The formula for calculating the meridian arc length starting from the equator is as follows: ,in The semi-major axis of the Earth's ellipsoid. To reference the first eccentricity of the ellipsoid, the coefficients , , , , , It is calculated based on the first eccentricity of the reference ellipsoid.

[0010] The formula for calculating the distance of the route segment is as follows: ,in and These are the arc lengths of the meridian at the arrival point and the meridian at the starting point, respectively. The azimuth angle is 90 degrees or 270 degrees. When the azimuth angle is 90 degrees or 270 degrees, the route segment follows the same latitude circle. In this case, the distance calculation formula for the route segment is: ,in The radius of curvature of the zonal loop is calculated using the following formula: The formula is used for calculation. By summing up the distances of each segment of the route, the total mileage of the long-distance seabed route can be obtained, and the mileage of the route's destination can be determined.

[0011] The Mercator projection forward calculation formula is used to convert the geodetic coordinates of each turning point of the route into planar coordinates. The Mercator projection forward calculation formula is as follows: , ,in For northward deviation, For eastward deviation, The origin longitude, The projection coefficient is calculated using the following formula: , Standard latitude.

[0012] The spacing between the mileage markers is set to 500m or 1000m.

[0013] The calculation of the distance from the starting point to the mileage marker is based on the spacing between mileage markers and the remaining distance. The formula for calculating the distance between each mileage marker and the starting point is as follows: ,in The distance between mileage markers. This represents the remaining distance of the previous route segment that has not yet reached the distance between mileage markers. and It is a positive integer.

[0014] The formula for calculating the number of mileage markers included in the route segment is as follows: ,in The remaining distance for calculating the mileage markers of the next route segment is the distance of the current route segment. .

[0015] The midpoint division iterative method uses the midpoint calculation formula. , Calculate the initial plane coordinates of the midpoint of each route segment, where , and , The coordinates of the two endpoints of the route segment are given. After being converted to geodetic coordinates using Mercator inverse calculation, the actual distance to the starting point of each route segment is calculated using the isoangular route inverse algorithm. This distance is then compared with the preset mileage marker distance to calculate the distance difference. When the distance difference is greater than 0, let... = , = When the distance difference is less than 0, let = , = The midpoint coordinates are calculated iteratively using the above midpoint calculation formula. When the distance difference is less than a set threshold, , This refers to the accurate coordinates of the preset mileage marker.

[0016] The Mercator projection inverse calculation is used to convert planar coordinates into geodetic coordinates. The Mercator projection inverse calculation formula is as follows: , ,in Coefficients , , , , Determined based on the first eccentricity of the reference ellipsoid.

[0017] Optionally, the AutoCAD secondary development uses Visual Basic for Applications or AutoLISP programming languages ​​to implement the batch automatic annotation function of mileage markers. Forward annotation is the annotation of mileage markers from the starting point of the route to the end point of the route, and reverse annotation is the annotation of mileage markers from the end point of the route to the starting point of the route.

[0018] This invention establishes a precise kilometer marker positioning system based on the characteristics of the Earth's ellipsoid by employing an inverse kilometer marker algorithm combined with Mercator projection transformation and a midpoint division iteration method. This reduces the computational difficulty and time required for kilometer marker locations in long-distance seabed route surveys using traditional inverse kilometer marker algorithms. Utilizing geodetic principles such as Mercator projection asymptotic latitude calculation and meridian arc length calculation, this invention effectively eliminates the systematic influence of the Earth's curvature on distance calculations. The midpoint division iteration method achieves a progressively accurate approximation of kilometer marker locations, avoiding the cumulative errors caused by traditional straight-line distance calculations. By establishing a complete geodetic coordinate to plane coordinate transformation system, this invention ensures the mathematical rigor and geometric accuracy of kilometer marker positioning, fundamentally guaranteeing the high-precision requirements for kilometer marker location determination in long-distance seabed route surveys. In summary, this invention provides a novel method for calculating kilometer marker locations during long-distance seabed route surveys. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention.

[0020] Figure 2 This is a schematic diagram of the seabed routing on the Earth's surface in Example 2.

[0021] Figure 3 This is a schematic diagram of the calculation of submarine route mileage markers under Mercator projection in Example 2. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0023] like Figure 1 The diagram shown is a flowchart of a method for determining mileage markers during long-distance seabed route surveys provided by this invention. This method includes the following steps:

[0024] S01. Obtain the geodetic coordinates of each turning point of the long-distance seabed route, including the route start point, route end point and intermediate turning point of the route, and establish a geodetic coordinate database of route turning points.

[0025] S02. The route segment distance between adjacent inflection points is calculated using the inverse route algorithm of the equal angle. The actual distance and azimuth of each route segment are determined by the Mercator projection asymptotic latitude difference and the latitude and longitude difference. The total route mileage is obtained by summing the distances of each route segment.

[0026] S03. Determine the spacing of mileage markers based on the scale of the survey results map, and set the spacing of the mileage markers to 500m or 1000m to establish standard parameters for the layout of mileage markers.

[0027] S04. Convert the geodetic coordinates of each inflection point of the route into plane coordinates through Mercator projection and establish a plane coordinate system for the inflection points of the route.

[0028] S05. The midpoint plane coordinates are continuously calculated between the two ends of the route segment using the midpoint equal division iterative method. After being converted into geodetic coordinates by Mercator inverse calculation, the actual distance to the starting point of each route segment is calculated using the isoangular route inverse solution algorithm. The distance difference is compared with the distance of the preset mileage marker. When the distance difference is less than the set threshold, it is the accurate location of the preset mileage marker.

[0029] S06. Implement automatic annotation of mileage markers based on AutoCAD secondary development technology, including forward and reverse annotation, and generate mileage marker annotation maps that meet the mapping standards of survey results.

[0030] The inverse kinematics algorithm for conformal routes is used to calculate the heading and distance between two points on the Earth's surface. It is a mathematical method for determining the actual distance and azimuth between two points based on the geodetic coordinates of the starting and ending points. In the Mercator projection, conformal routes are represented as straight lines, making it suitable for accurate calculation of distances in various segments of long-distance seabed routes.

[0031] Mercator projection asymptotic latitude is an important concept in cartographic projection. Essentially, it refers to the latitude coordinates of the projection plane calculated using a specific mathematical formula to achieve conformal projection characteristics. The formula for calculating Mercator projection asymptotic latitude is as follows: ,in The coefficient for converting radians to minutes, 1 radian = ×60 points = 3437′.7467708; Latitude of the earth The first eccentricity of the reference ellipsoid.

[0032] The latitude and longitude difference is calculated from the geodetic coordinates of the starting point and the arriving point. The formula for calculating the longitude difference is as follows: The formula for calculating the latitude difference is: ,in , The starting point's geodetic coordinates are... , The coordinates of the arrival point are given. The formula for calculating the asymptotic latitude difference in Mercator projection is as follows: ,in , These are the Mercator projection asymptotic latitudes of the arrival and starting points, respectively.

[0033] The route azimuth angle is calculated based on the longitude difference and the Mercator projection asymptotic latitude difference, and the calculation formula is as follows: ,in This is the difference in longitude. The Mercator projection represents the asymptotic latitude difference. The quadrant determination of the route azimuth is based on the sign of the longitude and latitude differences. Specifically, the route azimuth is 90 degrees when the longitude difference > 0 and the latitude difference = 0, and 270 degrees when the longitude difference < 0 and the latitude difference = 0.

[0034] The calculation of the meridian arc length uses a precise formula in series form. The formula for calculating the meridian arc length from the equator is expressed as follows: ,in The semi-major axis of the Earth's ellipsoid. To reference the first eccentricity of the ellipsoid, the coefficients , , , , , It is calculated based on the first eccentricity of the reference ellipsoid.

[0035] The formula for calculating the distance between route segments is as follows: ,in and These are the arc lengths of the meridian at the arrival point and the meridian at the starting point, respectively. This refers to the route azimuth. When the route azimuth is 90 degrees or 270 degrees, the route segment follows the same latitude circle, and the formula for calculating the route segment distance is as follows: ,in The radius of curvature of the circle is denoted by , according to The formula is used for calculation. By summing up the distances of each segment of the route, the total mileage of the long-distance seabed route can be obtained, and the mileage of the route's destination can be determined.

[0036] The Mercator projection forward calculation is used to convert the geodetic coordinates of the inflection point into the plane coordinates of the inflection point. The Mercator projection forward calculation formula is expressed as follows: , ,in For northward deviation, For eastward deviation, The origin longitude, These are the projection coefficients. The calculation formula is: ,in Standard latitude.

[0037] Among them, the calculation of the distance from the mileage marker to the starting point is based on the mileage marker spacing and the remaining distance, the first The formula for calculating the distance from each kilometer marker to the starting point is as follows: ,in The distance between mileage markers. This represents the remaining distance of the previous route segment that has not yet reached the distance between mileage markers. ∈[1, m] and It is a positive integer. The formula for calculating the number of mileage markers contained in a route segment is as follows: ,in This represents the distance of the current route segment. The formula for calculating the remaining distance used for calculating the mileage markers of the next route segment is as follows: .

[0038] Among them, the midpoint equal division iteration method is an innovative algorithm for precise positioning of mileage markers proposed in this method. The formula for calculating the initial midpoint plane coordinates is as follows: , ,in , and , These are the planar coordinates of the two endpoints of the route segment. The initial midpoint's planar coordinates are then converted to geodetic coordinates using Mercator projection. The distance to the starting point of the route segment is calculated using an inverse kilometer algorithm based on the conformal route, and compared with the distance from a preset kilometer marker. When the distance difference is greater than 0, let... = , = When the distance difference is less than 0, let = , = The midpoint coordinates are calculated iteratively using the above midpoint calculation formula. When the distance difference is less than a set threshold, , This refers to the accurate coordinates of the preset mileage marker.

[0039] Mercator projection inverse calculation is used to convert planar coordinates to geodetic coordinates. The Mercator projection inverse calculation formula is expressed as follows: , ,in Coefficients , , , , Determined based on the first eccentricity of the reference ellipsoid.

[0040] The AutoCAD secondary development uses Visual Basic for Applications or AutoLISP programming languages ​​to implement the batch automatic annotation function of mileage markers. Forward annotation refers to the annotation of mileage markers from the starting point of the route to the ending point of the route, while reverse annotation refers to the annotation of mileage markers from the ending point of the route to the starting point of the route.

[0041] The specific implementation methods of the above steps are described in detail below.

[0042] The specific implementation of step S01 involves comprehensively utilizing engineering geophysical survey and other technical means to systematically investigate the seabed engineering geological conditions, marine hydrological and meteorological environment, and other factors in the pre-selected route area, ultimately determining the three-dimensional spatial coordinate information of key nodes along the seabed route. First, the starting point of the route is determined, typically located at a land landing point or offshore platform. Its geodetic coordinates, including latitude, longitude, and elevation, are recorded using high-precision measuring equipment. Then, the positions of each intermediate turning point are measured sequentially along the planned path. These turning points are critical nodes where the route direction changes, and their positional accuracy directly affects the accuracy of subsequent mileage calculations. Finally, the geodetic coordinates of the route's endpoint are determined, typically at another landing point or the location of a seabed connection facility. All acquired turning point coordinate data are used to establish a database according to the route direction. The database should include information such as point number, latitude, longitude, elevation, and measurement time. The coordinate system should uniformly adopt the WGS84 geodetic coordinate system or other standard coordinate systems, and the coordinate accuracy should reach at least centimeter level to meet engineering accuracy requirements.

[0043] The specific implementation of step S02 is based on the principles of spherical geometry and the theory of conformal flight routes under Mercator projection to calculate the actual distance and azimuth between adjacent inflection points. The core principle of the conformal flight route inverse algorithm is to calculate the great circle distance between two points on the Earth's ellipsoid, taking into account the flattening characteristics of the Earth's ellipsoid. First, the longitude difference and latitude difference between two adjacent inflection points are calculated. The longitude difference equals the longitude of the endpoint minus the longitude of the starting point, and the latitude difference equals the latitude of the endpoint minus the latitude of the starting point. Then, the asymptotic latitude value between the two points is calculated using the Mercator projection asymptotic latitude formula. This calculation process requires inputting the geodetic latitude and the first eccentricity parameter of the reference ellipsoid. Next, the Mercator projection asymptotic latitude difference is calculated, i.e., the asymptotic latitude of the endpoint minus the asymptotic latitude of the starting point. The route azimuth is calculated based on the longitude difference and the asymptotic latitude difference. When both the longitude difference and the latitude difference are not zero, the arctangent function is used for calculation; when one of them is zero, the azimuth is determined according to the quadrant judgment rule. Finally, the actual distance of the route segment is determined by calculating the meridian arc length and azimuth information, and the total route mileage is obtained by summing the distances of each route segment.

[0044] The specific implementation of step S03 involves determining the spacing of mileage markers based on the scale of the survey map and the engineering accuracy requirements. When the scale of the survey map is 1:5000 or larger, the spacing of the mileage markers is set to 500m to ensure the clarity and readability of the markers on the map. When the scale of the survey map is 1:10000 or smaller, the spacing of the mileage markers is set to 1000m to avoid overly dense markings that would affect the aesthetics of the map. The determination of the mileage marker spacing also needs to consider the complexity of the seabed topography and the engineering construction accuracy requirements. In sections with drastic topographic changes or high engineering accuracy requirements, the spacing can be appropriately reduced to 250m or less. A database of standard parameters for mileage marker layout is established. This database contains parameters such as recommended spacing distances, minimum and maximum allowable spacing for different scales, providing a standard basis for subsequent automated processing. Mileage marker numbering adopts a unified naming rule, usually starting from the route origin and numbering incrementally according to the spacing.

[0045] The specific implementation of step S04 involves using Mercator projection mathematical transformation to convert the geodetic coordinates on the ellipsoid into a plane rectangular coordinate system. The core principle of Mercator projection forward calculation is conformal projection transformation, which maintains the angles but introduces significant distortion in area and length. First, the projection parameters are determined, including the origin longitude, standard latitude, north offset, east offset, and projection coefficient. The selection of these parameters should be based on the geographical location and extent of the survey area. The origin longitude is usually chosen from the central meridian of the survey area, the standard latitude is chosen from the central latitude of the survey area, and the north and east offsets are used to avoid negative coordinates. The projection coefficient is calculated based on the standard latitude and reference ellipsoid parameters; this coefficient reflects the ratio of the length on the projected surface to the corresponding length on the ellipsoid. Then, a forward projection transformation is performed on the geodetic coordinates of each inflection point. The calculation process requires inputting the geodetic latitude, geodetic longitude, and projection parameters, and outputting plane coordinates including abscissa and ordinate. A database of plane coordinate systems for route inflection points is established. This coordinate system provides the foundation for subsequent precise positioning calculations of mileage markers, and the coordinate accuracy should be maintained at a level comparable to the original geodetic coordinates.

[0046] The specific implementation of step S05 involves using a midpoint equal division iterative algorithm to accurately determine the planar coordinates of mileage markers on a straight route segment. The basic principle of this algorithm is to continuously narrow the search range using a bisection method until a point that meets the distance requirement is found. First, the planar coordinates of the initial midpoint are calculated between the start and end points of the current route segment. The x-coordinate of the initial midpoint is equal to the arithmetic mean of the x-coordinates of the two endpoints, and the y-coordinate is equal to the arithmetic mean of the y-coordinates of the two endpoints. Then, the planar coordinates of the initial midpoint are converted to geodetic coordinates using Mercator projection inverse calculation. Mercator projection inverse calculation is the inverse operation of the forward calculation process, obtaining geodetic coordinates by solving a system of nonlinear equations using an iterative calculation method. First, the equivalent latitude is calculated based on the planar y-coordinate of the mileage marker and the projection parameters. The equivalent latitude is the core intermediate variable connecting planar coordinates and geodetic latitude in Mercator projection. Its calculation requires input parameters such as the planar y-coordinate, north offset, ellipsoid semi-major axis, and projection coefficients. Then, the equivalent latitude is converted to geodetic latitude using a series expansion formula. This conversion process requires the use of multiple series coefficients, which are determined based on the first eccentricity of the reference ellipsoid. The calculation of geodetic longitude is relatively simple: it equals the plane abscissa minus the eastward deviation, divided by the product of the ellipsoid's semi-major axis and the projection coefficient, plus the origin longitude. Then, the distance between the initial midpoint and the starting point of the current route segment is calculated using an inverse kilometer marker algorithm. This distance is compared with the distance to a preset kilometer marker. When the distance difference is greater than 0, it indicates that the preset kilometer marker is located between the midpoint and the starting point; in this case, the midpoint is used as the new endpoint for continued iteration. When the distance difference is less than 0, it indicates that the preset kilometer marker is located between the midpoint and the endpoint; in this case, the endpoint is used as the new starting point for continued iteration. The iteration process continues until the distance difference is less than a set threshold (0.001m), at which point the convergence accuracy requirement is considered met. The coordinates of the midpoint at this point are the precise plane coordinates of the preset kilometer marker. This algorithm ensures that the kilometer marker positioning accuracy reaches the millimeter level, meeting the accuracy requirements of engineering surveying.

[0047] The specific implementation of step S06 is to develop an automated annotation program based on the AutoCAD application programming interface to achieve batch annotation of mileage marker information. This program is developed using Visual Basic for Applications or AutoLISP programming languages ​​and automatically generates annotations in the drawing based on the accurate location of the mileage markers calculated using the midpoint division iterative method. The program first reads the route segments in the CAD drawing file and identifies the start, end, and direction information of the segments. Then, based on the calculated mileage marker coordinate data, it inserts mileage marker symbols at the corresponding positions. The symbol style should conform to industry drafting standards. Forward annotation refers to mileage marker annotation from the route's starting point to the end point, with the annotation content being the actual distance of the mileage marker from the route's starting point, and the annotation position being on the left side of the route's forward direction. Reverse annotation refers to mileage marker annotation from the route's end point to the starting point, with the annotation content being the actual distance of the mileage marker from the route's final point, and the annotation position being on the right side of the route's forward direction. Specifically, mileage markers at both ends of the route need to be annotated separately. The program should also have annotation style setting functions, including text size, font type, annotation color, and leader line style, to ensure that the annotation information is clear, readable, and conforms to drafting specifications. Finally, a mileage marker map that meets the mapping standards for survey results is generated.

[0048] It should be noted that the key technical ideas of this invention are mainly reflected in the following three aspects. First, the organic combination of the isoangular route inverse algorithm and Mercator projection technology overcomes the problem of insufficient accuracy of traditional great circle distance calculation in long-distance seabed route measurement. By using Mercator projection to calculate the asymptotic latitude, the influence of the Earth's ellipsoidal flattening on the distance calculation is eliminated, improving the accuracy of route segment distance calculation from the meter level of traditional methods to the centimeter level, laying a solid foundation for the subsequent accurate positioning of mileage markers. Second, the innovative application of the midpoint equal division iterative algorithm. This algorithm breaks through the limitation of low positioning accuracy of traditional equidistant layout methods under complex route geometry. Through the idea of ​​bisection, the position of mileage markers is gradually approximated, and the positioning accuracy can reach the millimeter level, which is two orders of magnitude higher than the accuracy of traditional interpolation methods, ensuring the high precision requirements of mileage marker layout. Third, the establishment of a two-way projection coordinate transformation system. This system verifies the reliability of the calculation accuracy through a closed loop of forward and inverse calculations, avoiding the problem of accumulated errors under the traditional single coordinate system, and realizing high-precision lossless conversion between geodetic coordinates and plane coordinates. The synergistic effect of these three technical approaches has constructed a complete automated underwater route marker determination technology system. Compared with traditional manual measurement and calculation methods, this system has significant technical advantages, not only greatly improving operational efficiency and measurement accuracy, but also eliminating the influence of human factors on measurement results. It provides reliable technical support for the precise implementation of long-distance underwater engineering projects and promotes the development of marine engineering measurement technology towards intelligence and automation.

[0049] It should be noted that this invention also solves the technical problem of accurately describing complex seabed route geometries. Long-distance seabed routes typically contain multiple turning points and route segments in different directions. Traditional methods often resort to simplification when dealing with complex route geometries, failing to accurately reflect the actual route direction and the geometric relationships between segments. This invention establishes a geodetic coordinate database and a plane coordinate system for route turning points, employing segmented calculation and summation to handle complex route geometries. This ensures the accuracy of azimuth and distance calculations for each route segment. Furthermore, it achieves precise conversion between geodetic and plane coordinates through Mercator projection transformation, providing a complete mathematical solution for the geometric description of complex seabed routes.

[0050] Specifically, the principle of this invention is as follows: The fundamental reason why this invention can solve the technical problem of insufficient accuracy in determining the location of mileage markers in long-distance seabed route surveys lies in its establishment of a precise calculation system based on the geometric characteristics of the Earth's ellipsoid. Traditional methods simplify calculations by treating the Earth's surface as a plane, ignoring the influence of the Earth's curvature. This invention, however, by introducing an inverse kinematic algorithm based on equal-angle routes, fully considers the geometric characteristics of the Earth's ellipsoid and utilizes the mathematical characteristic that equal-angle routes in the Mercator projection are straight lines, transforming complex ellipsoidal distance calculations into precise calculations on a plane. This invention employs geodetic theories such as Mercator projection asymptotic latitude and meridian arc length calculations to establish a rigorous mathematical model for coordinate transformation and distance calculation, ensuring the geometric accuracy of distance calculations for each route segment. In particular, the innovative midpoint equal division iterative method proposed in this invention, through continuous midpoint coordinate calculation and distance comparison on the route segment, achieves a progressively precise approximation of the mileage marker location, effectively avoiding positioning errors that may occur with traditional equal-distance segmentation methods. The two-way conversion system between geodetic coordinates and plane coordinates established in this invention ensures the mathematical consistency and geometric accuracy of the entire calculation process, thereby ensuring the high-precision requirement for determining the location of mileage markers in long-distance seabed route surveys from a technical principle perspective.

[0051] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0052] In this embodiment, the specific implementation of step S01 is the same as described above, and will not be repeated in detail here.

[0053] The specific implementation of step S02 involves using the inverse kinematics algorithm to calculate the route segment lengths between adjacent inflection points and summing them to obtain the total route mileage. First, the latitude and longitude difference between two adjacent inflection points is calculated. Let the geodetic coordinates of point AC be... The geodetic coordinates of point BC are The formula for calculating the difference between latitude and longitude is:

[0054] ;

[0055] ;

[0056] In the formula, It is the difference in latitude. This is the difference in longitude. The starting point is the geodetic latitude. To determine the latitude of the destination point, The starting point is the geodetic longitude. Let the longitude of the arrival point be the geodetic longitude. Then calculate the Mercator projection asymptotic latitude, using the formula:

[0057] ;

[0058] In the formula, For Mercator projection of asymptotic latitudes, The coefficient for converting radians to minutes, 1 radian = ×60 points = 3437′.7467708; Latitude of the earth For the first eccentricity of the reference ellipsoid, Latitude of the earth To determine the first eccentricity of the reference ellipsoid, calculate the asymptotic latitudes of points AC and BC respectively. and The formula for calculating the asymptotic latitude difference between two points is:

[0059] ;

[0060] In the formula, The longitude difference is the asymptotic latitude difference. The route azimuth is calculated based on the longitude difference and the asymptotic latitude difference, using the following formula:

[0061] ;

[0062] In the formula, This refers to the route azimuth. The quadrant determination of the route azimuth is based on the sign of the longitude and latitude differences. and The azimuth angle of the route is ,when and The azimuth angle of the route is Next, calculate the meridian arc length from the equator. The formula for calculating the meridian arc length in series form is:

[0063] ;

[0064] In the formula, The length of the meridian arc. The semi-major axis of the Earth's ellipsoid. To reference the first eccentricity of the ellipsoid, the formulas for calculating each coefficient are as follows:

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] Calculate the meridian arc lengths corresponding to points AC and BC respectively. and The formula for calculating the route segment length is:

[0072] ;

[0073] In the formula, This refers to the route segment length. When the route azimuth... or When the route follows the same latitude circle, the formula for calculating the route segment length is:

[0074] ;

[0075] In the formula, The radius of curvature of the zonal loop is given in meters. ,in This represents the latitude of the calculation point. The total route mileage is obtained by summing the distances of each segment.

[0076] The specific implementation method of step S03 is the same as described above, and will not be repeated in detail here.

[0077] The specific implementation of step S04 involves converting the geodetic coordinates of the inflection point into planar coordinates using Mercator projection forward calculation. The Mercator projection forward calculation formula is:

[0078] ;

[0079] ;

[0080] In the formula, The x-coordinate of the plane, The vertical coordinate of the plane, The geodetic coordinates of the point are: The semi-major axis of the Earth's ellipsoid. For the first eccentricity of the reference ellipsoid, Standard latitude, The origin longitude, For northward deviation, For eastward deviation, This refers to the projection factor. The formula for calculating the projection factor is:

[0081] ;

[0082] The above formula is used to convert the geodetic coordinates of each inflection point into planar coordinates, thus establishing a planar coordinate system for the route inflection points.

[0083] The specific implementation of step S05 is to accurately locate the mileage marker position using the midpoint equal division iteration method. Let the plane coordinates of point AC be... The coordinates of point BC in plane BC are The interval between mileage markers is The remaining distance of the previous route segment that did not reach the mileage marker interval is , No. The formula for calculating the distance between each mileage marker and point AC is:

[0084] ;

[0085] In the formula, For the first The distance of each mile marker from the starting point of this route segment The value is a positive integer. The formula for calculating the number of mileage markers included in this route segment is:

[0086] ;

[0087] In the formula, This represents the number of mileage markers contained in the route segment. This is a rounding function. The formula for calculating the remaining length used for the next route mileage marker calculation is:

[0088] ;

[0089] In the formula, This represents the remaining distance to be calculated for the next segment. Midpoint. The formula for calculating the Mercator projection plane coordinates is:

[0090] ;

[0091] ;

[0092] In the formula, and These are the x and y coordinates of the midpoint, respectively, in meters. After converting the midpoint's plane coordinates to geodetic coordinates using Mercator projection, the actual distance from the midpoint to the starting point is calculated. The unit is meters (m). When season and ,when season and Repeat the iteration until When convergence accuracy is reached, the coordinates of the midpoint at this point are considered the precise location of the mileage marker.

[0093] The Mercator projection inverse calculation formula is:

[0094] ;

[0095] ;

[0096] In the formula, The geodetic latitude is obtained by inverse calculation. The geodetic longitude obtained by reverse calculation Given the Mercator projection plane coordinates of the point, the formulas for calculating each coefficient are as follows:

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] In the formula, Equal latitude, , , , , These are the coefficients of the series expansion.

[0104] The specific implementation method of step S06 is the same as described above, and will not be repeated in detail here.

[0105] It should be explained that the formula for calculating the difference between latitude and longitude is based on the principle of spherical geometry. It obtains the positional difference between adjacent inflection points through a simple coordinate subtraction operation. This formula provides the basic parameters for subsequent azimuth and distance calculations. Compared with traditional measurement methods, it has the advantages of simple calculation and controllable accuracy.

[0106] The Mercator projection asymptotic latitude calculation formula is based on the theory of conformal cylindrical projection, and the core function is: ,pass Logarithmic function and The composition operation of the tangent function converts the latitude coordinates on the ellipsoid to the corresponding coordinates on the projected plane, with ellipsoidal correction terms. Taking into account the flattening effect of the Earth's ellipsoid, it has higher computational accuracy compared to the spherical approximation method.

[0107] The formula for calculating the azimuth of a route is based on The arctangent function principle uses the ratio of longitude difference to increasing latitude difference to determine the azimuth relationship between two points. This formula can accurately describe the direction characteristics of seabed routes and provide the necessary azimuth parameters for distance calculation.

[0108] The formula for calculating the arc length of a meridian uses a series expansion. The arc length on the ellipsoid is calculated using a polynomial approximation method. This formula contains... The correction term improves calculation accuracy and has better applicability and accuracy compared to the simplified formula.

[0109] The formula for calculating route segment distance is based on the principle of spherical trigonometry, through... Geometric relationships determine the actual distance, where The cosine function term is used to convert projected distance to actual distance. This formula can handle route segments in any orientation and has higher measurement accuracy compared to the straight-line distance approximation method.

[0110] Mercator projection forward calculation formula is based on the principle of conformal projection transformation, with the core transformation being: The formula's ability to maintain an unchanged angle makes it particularly suitable for marine navigation applications, offering better orientation retention compared to other projection methods.

[0111] The midpoint division iterative algorithm is based on the bisection method numerical calculation principle. This algorithm achieves precise positioning by continuously narrowing the search interval. It has a fast convergence speed and high accuracy, and has better stability and reliability compared to traditional interpolation methods.

[0112] Mercator projection inverse calculation formula is based on the principle of solving nonlinear equations, through... Equal latitude calculation and series expansion This formula enables the conversion from planar coordinates to geodetic coordinates, ensuring conversion accuracy and achieving coordinate system closure verification. Compared to approximate inverse calculation methods, it offers higher computational accuracy and better numerical stability.

[0113] Optionally, in another specific embodiment of the present invention, a two-layer game-theoretic optimization model is constructed to optimize projection parameters. The upper-layer model aims at optimal projection accuracy and establishes an objective function that includes multiple influencing factors such as projection standard deviation, iteration convergence threshold, average azimuth angle, cumulative error, and number of route segments. The lower-layer model aims at optimal computational efficiency and establishes an objective function that includes efficiency indicators such as computation time, number of iterations, convergence angle, memory usage, and accuracy radius. The two objective functions achieve mutual constraint and coordinated optimization through coupling terms, and the coupling coefficient is adjusted according to specific engineering requirements and optimization preferences. The optimization process uses a genetic algorithm or particle swarm optimization algorithm for global optimization, finding the optimal balance between accuracy and efficiency through multiple generations of evolution or particle swarm iteration. This model resolves the contradiction between accuracy improvement and efficiency loss in traditional methods, providing optimal parameter configuration schemes for different application scenarios.

[0114] Specifically: The two-layer game optimization model is a collaborative optimization framework that simultaneously considers projection accuracy and computational efficiency. The objective function of the upper-layer model is... The constraints are m and m, the objective function of the lower-level model is The constraints are s and The coupling term is Used to balance accuracy and efficiency. The standard deviation of the projection accuracy. Derived from the gradually varying projection deformation vector Statistical analysis, iterative convergence threshold The convergence criterion derived from the midpoint equal division iteration method is the average azimuth angle. The azimuth angle is derived from the inverse kinematics algorithm. Sequence, cumulative error Originating from the abnormal mileage error vector The cumulative number of route segments Derived from the inflection point coordinate sequence Statistics. The calculation time. Used for evaluating the computational efficiency of lower-level models, number of iterations. The iteration count and convergence angle are derived from the midpoint division iteration method. Convergence analysis derived from the projection parameter optimization process, memory usage Derived from the superposition precision correction matrix Storage requirements, precision radius This analysis is based on statistical analysis of the accuracy of kilometer marker locations. Weighting coefficients. and coupling coefficient The total mileage is set according to specific engineering needs and optimization objectives. Sourced from the distance of each route segment The cumulative calculation of mileage. Indicates the first The cumulative mileage at each inflection point, in the two objective functions, since we are only two sides in the game, we do not need to consider specific dimensions. For ease of operation, all parameters can be dimensionless before calculation.

[0115] It needs further explanation that the two-level game optimization model, through multi-objective optimization that simultaneously considers projection accuracy and computational efficiency, includes a logarithmic term in the upper-level objective function. The nonlinear response corresponding to the projected standard deviation, the exponential term Corresponding to the decay characteristic of iterative convergence, trigonometric function terms The periodic variation pattern of the corresponding azimuth angle, the power term Corresponding to the nonlinear growth of the cumulative error, the radical term The square root relationship corresponding to the number of pieces, the radical terms in the lower-level objective function The square root decay corresponding to the calculation time, the reciprocal term The reciprocal relationship of the corresponding iteration efficiency, the cosine term The periodicity corresponding to the convergence angle, the power term The corresponding sublinear growth in memory usage, logarithmic terms The model achieves the best balance between accuracy and efficiency compared to single-objective optimization methods, avoiding the problem of a significant decrease in computational efficiency caused by the improvement of accuracy in traditional methods.

[0116] Optionally, in another specific embodiment of the present invention, the method further includes establishing a global coordinate system for connecting multiple inflection point routes, using constrained least squares for overall adjustment, and setting a buffer zone radius at the inflection point for smooth transition. Specifically, this involves establishing a global coordinate system for connecting multiple inflection point routes and using constrained least squares for overall adjustment. This step unifies all route segments to the same coordinate datum, eliminating systematic deviations between different projection segments through coordinate transformation and datum unification. The constrained least squares method establishes an adjustment model based on observation equations and constraints. The observation equations include the coordinate observations and accuracy information of each inflection point, while the constraints include route continuity and geometric consistency requirements. The adjustment calculation uses coordinates and matrix operations to solve for the optimal coordinate correction value, ensuring that the overall route achieves the optimal solution in the least squares sense while satisfying the constraints. A buffer zone is set at the inflection point for smooth transition; the buffer radius is typically set to 10 to 50 meters, and a gradual weighting function is used to achieve smooth connection between different route segments. This method solves the overall coordination problem under conditions of multiple inflection points and multiple segments in complex seabed routes.

[0117] Specifically, the observation equation for constrained least squares adjustment is: The constraint equations are ,in To correct the number vector, The coefficient matrix, For an unknown parameter vector, A vector of constant terms. For the constraint matrix, Let be the constraint constant vector; the adjustment solution formula is: In the formula The weight matrix is ​​given; the weight function within the buffer region is... In the formula The distance from the inflection point. The radius of the buffer zone. This represents the weight function value for the buffer region.

[0118] The constrained least squares adjustment method ensures route continuity and geometric consistency by introducing constraint equations. This formula is based on the principle of the Lagrange multiplier method and uses matrix operations to simultaneously satisfy the optimal solution of the observation equation and constraint conditions. Compared with the unconstrained adjustment method, it effectively solves the systematic deviation problem at the junction of multiple route segments and improves the geometric accuracy and inherent consistency of the overall route.

[0119] To better understand and implement this invention, a specific application scenario is provided below as Example 2: The Southeast Asia-Japan Cable 2 (SJC2) submarine optical cable project is an important international communication infrastructure connecting Southeast Asia and Japan, with a total route length of approximately 1847 kilometers, traversing multiple sea areas and complex terrain. During the route survey, the technical team faced the technical challenge of insufficient accuracy in traditional mileage calculation methods. Due to the large latitudinal range of the route, significant length distortion occurs when using Mercator projection, making direct measurement impossible to obtain accurate actual distances, severely impacting the accuracy of the survey results. The technical team decided to adopt the long-distance submarine route survey mileage marker determination method proposed in this invention, using an inverse kilometer algorithm of the equal-angle route combined with the midpoint equal division iterative method to achieve high-precision route mileage calculation and mileage marker positioning.

[0120] The technical team first obtained geodetic coordinate data of the key inflection points of the SJC2 submarine optical cable route. After marine surveying and route optimization, five key inflection points were identified, including the starting point A, intermediate inflection points B, C, and D, and the ending point E. A geodetic coordinate database of these inflection points was established, and the specific parameters of each inflection point are shown in Table 1.

[0121] Table 1 Geodetic coordinates of the inflection points of the SJC2 submarine optical cable route.

[0122]

[0123] The technical team used an inverse kinematics algorithm to calculate the route segment length between adjacent inflection points. The detailed calculation process is explained using segment AB as an example. Based on the geodetic coordinates of inflection points A and B, the difference in latitude and longitude is first calculated. The formula for calculating the difference in latitude and longitude is as follows:

[0124] ,

[0125] .

[0126] Using WGS84 ellipsoidal parameters, semi-major axis First eccentricity According to the Mercator projection formula for calculating asymptotic latitude:

[0127] ;

[0128] Calculate the asymptotic latitudes of inflection points A and B respectively:

[0129] ,

[0130] .

[0131] A schematic diagram of the route of the seabed on the Earth's surface is shown below. Figure 2 As shown, the formula for calculating the asymptotic latitude difference based on Mercator projection is as follows:

[0132] ;

[0133] The calculation yielded:

[0134] .

[0135] According to the formula for calculating the azimuth angle of a route:

[0136] ;

[0137] Calculate the azimuth angle of route segment AB:

[0138] .

[0139] According to the routing azimuth quadrant determination rule, if the longitude difference is greater than 0 and the latitude difference is greater than 0, the routing azimuth is located in the first quadrant. The quadrant determination is shown in Table 2.

[0140] Table 2 Quadrant Determination for Route Azimuth A

[0141]

[0142] According to the formula for calculating the arc length of a meridian measured from the equator:

[0143]

[0144] The formulas for calculating each coefficient are as follows:

[0145] ,

[0146] ,

[0147] ,

[0148] ,

[0149] ,

[0150] .

[0151] The calculation results for each coefficient are as follows: , , , , , .

[0152] Calculate the meridian arc lengths corresponding to inflection points A and B:

[0153] ,

[0154] .

[0155] Based on the formula for calculating the length of a route segment:

[0156] ;

[0157] Calculate the route length of segment AB:

[0158] .

[0159] The lengths of the remaining routes were calculated using the same method, and the results are shown in Table 3.

[0160] Table 3 Calculation results of the route length of each segment of the SJC2 submarine optical cable

[0161]

[0162] The total length of the SJC2 submarine optical cable route is 3754.8318 kilometers when the lengths of each segment are added together.

[0163] Based on the requirement of a 1:10000 scale for the survey maps, the spacing between mileage markers was determined to be 1000 meters. The technical team selected suitable Mercator projection parameters: standard latitude... Origin longitude Northward deviation East bias According to the formula for calculating the projection factor:

[0164] ;

[0165] Calculate the projection factor:

[0166] .

[0167] like Figure 3 As shown, the Mercator projection forward calculation formula is used:

[0168] ,

[0169] ;

[0170] The geodetic coordinates of each inflection point were converted to Mercator projection plane coordinates. The conversion results are shown in Table 4.

[0171] Table 4 Planar coordinates of the inflection points of the SJC2 submarine optical cable route

[0172]

[0173] The technical team used the midpoint equal division iterative method to accurately locate the kilometer markers on each segment of the route. The algorithm process is explained in detail using the calculation of the first kilometer marker (KP1) in segment AB as an example.

[0174] AB segment route length Mileage marker interval The remaining length of the upper segment (Initial Section). Based on the formula for calculating the distance from the mileage marker to the starting point:

[0175] ;

[0176] Calculate the distance from the first kilometer marker to the starting point A:

[0177] .

[0178] The calculation formula is based on the number of mileage markers contained in the route segment:

[0179] ;

[0180] Calculate the number of mileage markers included in section AB:

[0181] .

[0182] Initialize the plane coordinates of the midpoint Z. Set the coordinates of the inflection point A to... , The coordinates of inflection point B are , According to the formula for calculating the plane coordinates of the midpoint:

[0183] ,

[0184] ;

[0185] Calculate the initial plane coordinates of the midpoint Z:

[0186] ,

[0187] .

[0188] Using the Mercator projection inverse calculation formula:

[0189] ,

[0190] ;

[0191] Convert the plane coordinates of the midpoint Z to geodetic coordinates. First, calculate the auxiliary parameters:

[0192] ,

[0193] .

[0194] Calculate each coefficient:

[0195] ,

[0196] ,

[0197] ,

[0198] ,

[0199] .

[0200] Calculation results: , , , , .

[0201] Calculate the geodetic coordinates of the midpoint Z:

[0202] ,

[0203] .

[0204] Calculate the AZ segment distance using the inverse kinematics algorithm for the isoangular route. Set two iteration conditions, including iteration condition ①: when > At that time, then order Iteration condition ②: When < At that time, then order ;because According to iteration condition ①, let , Recalculate the midpoint coordinates and iterate.

[0205] After 12,692 iterations The convergence accuracy is achieved. At this point, the planar coordinates of the midpoint Z are... , The corresponding geodetic coordinates are , This is the exact location of the first mile marker KP1.

[0206] The same iterative method was used to calculate the positions of the remaining 722 mileage markers in segment AB, as well as the mileage marker positions for subsequent segments. After all calculations were completed, a total of 3,756 mileage markers (including the first and last mileage markers) were set up along the SJC2 submarine optical cable route, with all mileage markers achieving millimeter-level positioning accuracy.

[0207] Next, the technical team used AutoCAD secondary development technology and the Visual Basic for Applications programming language to write an automatic annotation program. The program reads the coordinate data of the mileage markers, automatically inserts standardized mileage marker symbols at the corresponding positions, and annotates the mileage information. It implements two annotation methods: forward annotation (from the starting point A to the ending point E) and reverse annotation (from the ending point E to the starting point A), meeting the technical specifications of the survey results maps.

[0208] After the automatic annotation program is completed, the generated survey results map contains 3,756 precisely located mileage markers. Each mileage marker contains mileage, coordinate, and direction information, providing an accurate spatial reference for subsequent design, construction, and operation and maintenance phases.

[0209] The technical team used geographic information system software to verify the calculated mileage markers. The results showed that the calculation deviation of the mileage markers was less than 0.5 meters, which is about 15% more accurate than the 2-3 meter error of the traditional manual calculation and marking method. In terms of processing efficiency, the automated program can complete the calculation and marking of all 3,756 mileage markers in only about 3 minutes, while the traditional manual method takes about 72 hours, which is about 1,440 times more efficient.

[0210] This invention represents a significant advancement over traditional methods. In terms of computational accuracy, the isoangular route inverse algorithm effectively eliminates the distance distortion caused by Mercator projection, achieving precise calculation of the true distance on the ellipsoid. The midpoint equal division iterative method, through repeated approximation optimization, ensures millimeter-level accuracy in mileage marker positioning. Regarding operational efficiency, the automated program replaces the tedious manual calculation process, greatly improving the productivity of survey results. In terms of standardization, the programmed annotation method ensures the uniformity and standardization of map formats, avoiding errors and omissions that may occur during manual operation. In engineering applications, accurate mileage marker positioning provides a reliable spatial reference for subsequent submarine cable design, construction vessel navigation, and fault location, ensuring the smooth implementation of the entire project. Furthermore, relying on AutoCAD secondary development tools, the above computational logic is integrated into an automated program, enabling batch and accurate annotation of long-distance submarine route mileage markers, which has been successfully applied to multiple international submarine optical cable projects, including the New Trans-Pacific (NCP) and Southeast Asia-Japan Cable 2 (SJC2). The core value of this technical solution lies in its targeted compensation for projection distortion. Therefore, it is not only applicable to Mercator projection scenarios, but can also be extended to long-distance linear engineering fields that use other map projections (such as Gauss-Kruger projection, UTM projection, etc.) and are sensitive to distance and position distortion (such as cross-regional railways, oil pipelines, cross-border highways, etc.).

[0211] It should be noted that the variables involved in this invention are explained in detail in Table 5 below.

[0212] Table 5. Variable Explanation Table

[0213]

[0214] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for long distance submarine route survey milepost determination, characterized by, The method comprises the following steps: The method comprises the following steps:

2. The long distance submarine route survey monument determination method of claim 1, wherein, The method comprises the following steps: The method comprises the following steps: The method comprises the following steps: The inverse solution of the isometric rhumb line is a mathematical method for calculating the actual distance and azimuth angle between two points according to the geodetic coordinates of the starting point and the arrival point. In the Mercator projection, the isometric rhumb line appears as a straight line, and is used for the accurate calculation of the distance of each section of the long-distance submarine route.

3. The long distance submarine route survey monument determination method of claim 2, wherein, The Mercator projection asymptotic latitude is a core parameter of the Mercator projection system in cartography. Essentially, it is the latitude coordinate of the projection plane calculated using a specific mathematical formula to achieve conformal projection characteristics. The formula for calculating the Mercator projection asymptotic latitude is: ,in The coefficient for converting radians to minutes, 1 radian = ×60 points = 3437′.7467708; Latitude of the earth The first eccentricity of the reference ellipsoid.

4. The long distance submarine route survey monument determination method of claim 3, wherein, The longitude difference value is calculated by the starting point geodetic coordinate and the arrival point geodetic coordinate, and the longitude difference value calculation formula is The latitude difference value calculation formula is Wherein , is the starting point geodetic coordinate, , is the arrival point geodetic coordinate, and the Mercator projection elongation latitude difference value calculation formula is Wherein , respectively, the arrival point and the starting point Mercator projection elongation latitude.

5. The long distance submarine route survey monument determination method of claim 4, wherein, The route segment distance calculation formula is wherein and are the meridian arc length of the arrival point and the meridian arc length of the starting point respectively, is the route azimuth angle, when the route azimuth angle is 90 degrees or 270 degrees, the route segment is along the parallel, at this time, the route segment distance calculation formula is wherein is the radius of curvature of the prime vertical, the calculation formula is ; the total mileage of the long distance submarine route can be obtained by accumulating the distances of each segment route, and thus the route end point mileage value can be determined.

6. The long distance submarine route survey monument determination method of claim 5, wherein, The route azimuth calculation is based on the longitude difference value and the Mercator projection increasing latitude difference value, and the calculation formula is wherein the longitude difference value, the Mercator projection increasing latitude difference value, and the route azimuth quadrant judgment is determined according to the positive and negative of the longitude difference value and the latitude difference value; when the longitude difference value is greater than 0 and the latitude difference value is equal to 0, the route azimuth is 90 degrees; when the longitude difference value is less than 0 and the latitude difference value is equal to 0, the route azimuth is 270 degrees.

7. The long distance submarine route survey monument determination method of claim 6, wherein, The meridian arc length calculation adopts a precise formula in series form, and the meridian arc length calculation formula from the equator is wherein is the long semi-axis of the earth ellipsoid, is the first eccentricity of the reference ellipsoid, and each coefficient , , , , , is calculated according to the first eccentricity of the reference ellipsoid.

8. The long distance submarine route survey monument determination method of claim 7, wherein, The Mercator projection direct formula is used to convert the route vertex geodetic coordinates into plane coordinates, and the Mercator projection direct formula is , wherein is a north deviation, is an east deviation, is an origin longitude, is a projection coefficient, and the calculation formula is , is a standard latitude.

9. The long distance submarine route survey monument determination method of claim 8, wherein, The midpoint bisection iterative method is to use the midpoint calculation formula , , , , , , respectively, the plane coordinates of the two ends of the route segment, calculate the initial midpoint plane coordinates of each route segment, convert to geodetic coordinates by Mercator inverse calculation, and calculate the actual distance from each route starting point by using the inverse calculation algorithm of the isometric airway. Compare the distance difference with the preset mileage stake distance, and when the distance difference is greater than 0, let = , = ; When the distance difference is less than 0, let = 、 = ; the midpoint plane coordinates are calculated repeatedly by using the above midpoint calculation formula, when the distance difference is less than a set threshold value, 、 , which is the preset milepost accurate position coordinates.

10. The long distance submarine route survey milestone determination method of claim 9, wherein, The inverse Mercator projection formula is , wherein , , , , , is calculated according to the first eccentricity of the reference ellipsoid.

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