Method for accurately calculating cross-border point for maritime rights protection

Abstract

The application discloses a method for accurately solving a cross-border point position for maritime rights protection, and belongs to the technical field of marine surveying and mapping. In view of the problem that traditional plotting methods result in distortion of geodesic line expression, and thus coordinates of a cross-border point position for maritime rights protection cannot be accurately solved, the application is based on the theory of geodesic subject forward and inverse solutions and conformal loxodrome forward and inverse solutions, takes an azimuth difference value as an iteration basis, extends the idea of bisection approximation interpolation to the intersection problem of geodesic lines and conformal loxodromes, and provides a method for accurately solving a cross-border point position on this basis.

Description

Technical Field

[0001] This invention belongs to the field of marine surveying and mapping technology, and relates to a method for accurately calculating the location of transgressed points for maritime rights protection. Background Technology

[0002] In the research of maritime delimitation techniques and methods, some representative domestic technical documents include: "Thoughts and Suggestions on my country's Maritime Delimitation Issues" (Li Linghua, 1998), "Research on Maritime Delimitation Techniques Cannot Be Ignored" (Li Linghua, 1998), "Research on Maritime Delimitation Techniques and Methods Between Countries" (Tan Shudong, 1997), "Delimitation Auxiliary Decision-Making System" (Shen Wenzhou, 2000), "Research on Maritime Delimitation Techniques and Methods" (Liang Deqing, 2000), "Several Key Issues in Implementing Precise Maritime Delimitation on an Ellipsoid" (Peng Rencan, 2001), "Research on Technological Methods for Delineating Maritime Boundaries" (Weng Min, 2000), and "Research on the Selection of Territorial Sea Base Points Based on Convex Shell Structure Technology" (Peng Rencan, 2002). Research papers include: “Research on Buffer Construction Technology Based on Earth Ellipsoid” (Peng Rencan 2005), “Research and Practice of GIS Technology for Marine Boundary Delineation” (Peng Rencan 2003), “Research and Implementation of Marine Boundary Delineation Technology Using High-Precision Distance Equal Scale Line Method” (Dong Jian 2009), “An Algorithm for Generating Centerlines Between Curves Based on the Intersection Model of Buffer Boundaries Approaching Each Other” (Dong Jian 2011), “Research on Marine Boundary Delineation Technology Method Based on GIS” (Zhang Jianhui 2013), “Marine Boundary Delineation Method Based on Earth Ellipsoid Model” (Zhang Jianhui 2013), “Research and Experiment of High-Precision Buffer Intersection Algorithm Approaching Each Other” (Ning Fanghui 2013), and “Development and Practice of Marine Boundary Delineation Technology” (Zhang Jianhui 2014).

[0003] Based on the aforementioned theories of maritime delimitation, domestic scholars have developed several specialized software programs for maritime delimitation. Among these, the more influential ones are the various maritime delimitation software systems independently developed by institutions such as the Institute of Marine Environment of the Naval Research Institute, the National Marine Information Center, and the Dalian Naval Academy. Some of these systems (such as the "Beibu Gulf Delimitation Decision Support System") have already been practically applied in the delimitation of the Beibu Gulf between my country and Vietnam. However, these software systems also have some obvious shortcomings. For example, some are based on map (nautical chart) projection planes, resulting in lower accuracy; some can only generate bilateral maritime boundaries such as equidistant lines / distance lines, but cannot generate various unilateral maritime boundaries parallel to the territorial sea baseline; some lack flexible interactive editing and modification functions, making it impossible to quickly adjust the delimitation scheme; and some are designed for specific maritime delimitation areas, making them difficult to apply universally. In addition, some institutions have explored and established some small-scale, single-function thematic databases of maritime rights information for my country's territorial waters, such as "Design and Implementation of the Maritime Rights Protection Information System" and "Establishment of the Maritime Delimitation Legal Theory and Territorial Sea Baseline Information System." Among them, the "Global Maritime Rights Boundary Dataset" produced by the Dalian Naval Academy is the most comprehensive and accurate, and it has designed a related boundary display and query system. However, because it does not take into account the problem of spatial curve intersection, these algorithms cannot be directly applied to the practical problem of finding the coordinates of the boundary crossing point. Summary of the Invention

[0004] To address the problem that traditional mapping methods result in distorted representation of geodesics, making it impossible to accurately determine the coordinates of points where maritime rights are violated, this invention proposes a method for accurately calculating the locations of points where maritime rights are violated.

[0005] The technical solution adopted in this invention is:

[0006] A method for accurately calculating the location of transgression points for maritime rights protection includes the following steps:

[0007] a) Inverse solution of azimuth angle of an equal-angled flight path

[0008] The azimuth of a certain segment of a conformal route is calculated using the inverse formulas (1) to (3) for the azimuth of a conformal route:

[0009]

[0010]

[0011]

[0012] Where, q A q B The latitudes of the starting point A and the ending point B of the isoangular flight path are equal. Let A and B be the geographical latitudes of the starting point and ending point of the isoangular flight path, respectively, and let e be the first eccentricity of the reference ellipsoid, and α be the eccentricity of the reference ellipsoid. AB For the azimuth angle of the conformal flight path, λ A , λ B These are the longitudes of the starting point A and the ending point B of the isoangular route, respectively.

[0013] b. Positive and negative solutions for the Earth theme

[0014] The length and azimuth of the geodetic line are calculated using the inverse solution of the Bessel geodetic theme. The forward solution of the geodetic theme is then performed using the nested coefficient method with the required azimuth and half the required geodetic line length as the step size. The latitude and longitude coordinates of the midpoint of this geodetic line segment are then calculated.

[0015] c. Angle Limit Judgment

[0016] The azimuth of the constant direction line from the midpoint of the geodetic line to a certain endpoint of the equal-angle route is obtained using the inverse formula of the azimuth of the equal-angle route. The difference between this azimuth and the azimuth of the equal-angle route obtained in step a is calculated. The difference is recorded and it is determined whether it is within the allowable range of angle tolerance. If the difference is within the allowable range of angle tolerance, the process is directly transferred to step e; otherwise, the process is transferred to step d.

[0017] d. Iterative method for solving interpolation points

[0018] Based on the relationship between the difference and zero, select one of the two ends of the geodetic line and the point approximately corresponding to the intersection point to form a new geodetic line segment. Proceed to step b to recalculate the latitude and longitude coordinates of the midpoint of the new geodetic line segment.

[0019] e. Output high-precision geographic coordinates of boundary crossing points

[0020] When the two azimuth error values ​​in step c are less than the angle limit, the midpoint of the geodetic line obtained after several iterations is infinitely close to the actual intersection point in space. Within the allowable range of the angle limit, the coordinates of the two points are considered to be equal.

[0021] f. Output result accuracy error analysis

[0022] By taking advantage of the fact that the distance between the midpoint of the obtained geodetic line and the actual intersection point is less than the distance from the midpoint of the geodetic line to the endpoint, a quantitative analysis model for the accuracy error of the results is established.

[0023] Since the method uses interpolation to obtain an approximate point, theoretically, when the angle limit error approaches infinity, the distance between the midpoint of the obtained geodetic line and the actual intersection point can be controlled to approach infinity, and the distance offset between the two points is positively correlated with the angle limit error.

[0024] The beneficial effects of this invention are as follows: Addressing the problem that traditional mapping methods lead to distorted representation of the geodetic line, making it impossible to accurately determine the coordinates of maritime rights-protection and boundary-crossing points, this invention, based on the theories of geodetic theme forward and inverse solutions and isometric route forward and inverse solutions, uses the azimuth difference as the iterative basis and extends the idea of ​​bisection method approximation interpolation to the problem of finding the intersection of the geodetic line and the isometric route. Furthermore, it provides my country's maritime forces with an accurate method for calculating the boundary-crossing points of foreign vessels. Attached Figure Description

[0025] Figure 1 This is a schematic diagram illustrating a method for accurately calculating the location of transgressions in maritime rights protection.

[0026] Figure 2 This is a schematic diagram illustrating the error analysis of a precise calculation method for transgression points in maritime rights protection. Detailed Implementation

[0027] The following description, in conjunction with the embodiments and accompanying drawings, further explains the specific implementation of the present invention, but is not intended to limit the present invention.

[0028] This invention is based on a spatial reference ellipsoid, and the territorial sea baseline is connected by geodesics, such as... Figure 1 The curve AB shown represents a planned route with a fixed heading angle, starting at point A and ending at point B. Curve CD represents the baseline of a certain territorial sea of ​​my country. Point P is the actual intersection of curves AB and CD. However, due to the combined effects of curvature and disturbance of the geodesic, accurately locating point P using the geodesic equation is extremely complex and impractical. Therefore, this invention utilizes geodesic interpolation to obtain approximate coordinates of point P that meet the accuracy requirements, replacing the actual intersection point P. The specific steps are as follows:

[0029] Step 1: Inverse solution of azimuth angles for conformal flight paths

[0030] Calculate the heading angle α of the constant-heading line AB using the inverse formula for the azimuth of a constant-heading route. AB .

[0031]

[0032]

[0033]

[0034] Where, q A q B The latitudes of the starting point A and the ending point B of the isoangular flight path are equal. Let A and B be the geographical latitudes of the starting point and ending point of the isoangular flight path, respectively, and let e be the first eccentricity of the reference ellipsoid, and α be the eccentricity of the reference ellipsoid. AB For the azimuth angle of the conformal flight path, λ A , λ BThese are the longitudes of the starting point A and the ending point B of the isoangular route, respectively.

[0035] Step 2, Earth Theme Forward and Inverse Solving

[0036] The length S of the geodesic segment CD is obtained by inverse kinematics of the geodesic theme. i (i represents the number of iterations, the same below), and with... Using the step size, the forward solution of the geodetic theme is calculated using the nested coefficient method, and P is obtained. i Point latitude and longitude coordinates.

[0037] Step 3, Angle Limit Judgment

[0038] Calculate P using the inverse kinematics formula for azimuth of a constant-angle flight path. i Azimuth B Then calculate its heading angle α with respect to the constant heading line AB. AB The difference between If Δα i If the angle error exceeds the limit σ (σ is adjusted according to accuracy requirements), proceed to step four; if Δα i If the angle difference is less than the limit σ, proceed to step five.

[0039] Step 4: Iteratively solve for the interpolation points.

[0040] judge With α AB The size relationship, if Then P i Assign the latitude and longitude of the point to the endpoint D of the geodetic line; if Then P i Assign the latitude and longitude coordinates of the point to the endpoint C of the geodetic line. At this point, the endpoint C or D of the geodetic line is assigned new latitude and longitude coordinate values, and proceed to step two.

[0041] Step 5: Output high-precision geographic coordinates of the boundary crossing points.

[0042] Output P i Point latitude and longitude coordinates, at this time the azimuth angle is considered With heading angle α AB They are equal under the required precision, therefore P i Point AB is the intersection of the isoangular route AB and the geodetic line CD.

[0043] Step 6: Output Result Accuracy Error Analysis

[0044] like Figure 2 As shown, after the first inverse solution of the earth theme, with The first interpolation using the step size yields point P1. It is easy to see the distance between P1 and the actual intersection point P. Less than the distance between P1 and the endpoint C of the earth wire At this time Interpolation step size Since they are equal, the inequality can be derived. After the second reinterpretation of the earth theme, with The second interpolation is performed to obtain point P2, and it is easy to know the distance between P2 and the actual intersection point P. Less than the distance between P2 and the interpolation point P1 At this time Interpolation step size Since they are equal, the inequality can be derived. And so on, after the i-th inverse solution of the earth theme, with Point P is obtained by performing the i-th interpolation with respect to the step size. i It is easy to know P i Distance between the actual intersection point P Smaller than interpolation step size Right now Due to S i It can be solved by inverse geodetic modeling. Under the condition that the angle limit is determined, the interpolation point P can be... i The distance offset from the actual intersection point P is calculated to ensure that the actual distance offset is not greater than the desired distance offset.

Claims

1. A method for accurately calculating the location of transgression points for maritime rights protection, characterized in that, Given that the isoangular flight path AB intersects the geodetic line CD at point P, use the following steps to find P that meets the accuracy requirements. i Point P is used to represent the actual intersection point: Step 1: Inverse solution of azimuth angles for conformal flight paths The azimuth angle α of the conformal route AB is calculated using the inverse formulas (1) to (3) for the azimuth angle of the conformal route. AB : Where, q A q B The latitudes of the starting point A and the ending point B of the isoangular flight path are equal. Let A and B be the geographical latitudes of the starting point and ending point of the isoangular flight path, respectively, and let e be the first eccentricity of the reference ellipsoid, and α be the eccentricity of the reference ellipsoid. AB For the azimuth angle of the conformal flight path, λ A , λ B These are the longitudes of the starting point A and the ending point B of the isoangular route, respectively. Step 2, Earth Theme Forward and Inverse Solving The length S of the geodesic segment CD is obtained by inverse kinematics of the geodesic theme. i and with Using the step size, the forward solution of the geodetic theme is calculated using the nested coefficient method, and P is obtained. i The latitude and longitude coordinates of the point; where i is the number of calculation iterations; Step 3, Angle Limit Judgment Calculate P using the inverse kinematics formula for azimuth of a constant-angle flight path. i Azimuth B Then calculate its azimuth angle α relative to the isoangular route AB. AB The difference between If Δα i If the angle difference is greater than the limit σ, proceed to step four; if Δα i If the angle is less than the limit σ, proceed to step five; Step 4: Iteratively solve for the interpolation points. judge With α AB The size relationship, if Then P i Assign the latitude and longitude of the point to the endpoint D of the geodetic line; if Then P i The latitude and longitude coordinates of the point are assigned to the endpoint C of the geodetic line. At this time, the endpoint C or D of the geodetic line is assigned new latitude and longitude coordinate values. Then, proceed to step two to recalculate the latitude and longitude coordinates of the midpoint of the new geodetic line segment. Step 5: Output high-precision geographic coordinates of the boundary crossing points. Output P i Point latitude and longitude coordinates, at this time the azimuth angle is considered With azimuth angle α AB They are equal under the required precision, therefore P i The point is the intersection of the isoangular route AB and the geodesic CD; Step 6: Output Result Accuracy Error Analysis After the first inverse interpretation of the earth theme, with The first interpolation using the step size yields point P1. It is easy to see the distance between P1 and the actual intersection point P. Less than the distance between P1 and the endpoint C of the earth wire At this time Interpolation step size Since they are equal, the inequality can be derived. After the second reinterpretation of the earth theme, with The second interpolation is performed to obtain point P2, and it is easy to know the distance between P2 and the actual intersection point P. Less than the distance between P2 and the interpolation point P1 At this time Interpolation step size Since they are equal, the inequality can be derived. And so on, after the i-th inverse solution of the earth theme, with Point P is obtained by performing the i-th interpolation with respect to the step size. i It is easy to know P i Distance between the actual intersection point P Smaller than interpolation step size Right now Due to S i The solution is obtained by inverse geodetic modeling, and under the condition that the angle limit is determined, the interpolation point P is calculated. i The distance offset from the actual intersection point P is calculated to ensure that the actual distance offset is not greater than the desired distance offset.

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