Method for calculating east gradient of prime component of plumb line deviation in sea area
By calculating the eastward gradient of the ramus-groove components of the vertical deviation in the sea area, and utilizing physical geodesy and a global gravity potential coefficient model, the position error problem of the inertial navigation system under GNSS rejection conditions was solved, thus improving navigation accuracy.
Patent Information
- Application Number
- CN202511318815.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-16
- Publication Date
- 2026-02-06
AI Technical Summary
Under GNSS rejection conditions, the inertial navigation system, due to prolonged lack of calibration, results in significant positional errors of the moving vehicle. This is particularly pronounced in cross-regional, highly dynamic navigation scenarios where navigation accuracy is severely degraded. The error in the ramus component of the vertical deviation in the sea area directly affects navigation accuracy.
The calculation method of the eastward gradient of the mafic and genus components of the marine vertical deviation is adopted. By using the physical geodetic boundary value theory and the fully normalized global gravity potential coefficient, a calculation model of the eastward gradient of the mafic and genus components of the marine vertical deviation is constructed to improve the compensation capability of the inertial navigation system.
By accurately calculating the eastward gradient of the mafic-groove components of the vertical deviation in the sea area, the navigation accuracy of the inertial navigation system was improved, the position error was reduced, and the effectiveness and accuracy of the calculation method were verified.
Smart Images
Figure CN121475191A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of marine gravity, and particularly relates to a method for calculating eastward gradient of vertical deflection of an ocean. BACKGROUND
[0002] All objects and their motion states on the earth are affected by the gravity of the earth, and the non-uniformity thereof is one of decisive factors for performance of a precise navigation system. An inertial navigation system realizes motion state calculation by integrating specific force signals output by an accelerometer and a gyroscope, and a theoretical basis thereof is established on a homogeneous earth model under a classical Newtonian mechanics framework. However, due to irregularity of the shape of the earth and non-uniformity of internal mass distribution, the actual gravity field of the earth has significant spatial variability, and this inherent characteristic causes accumulated errors of the traditional inertial navigation system to exponentially increase in a long-time running process, especially in a cross-regional high dynamic navigation scene, and a coupling effect of position errors and gravity field disturbances seriously degrades navigation accuracy. The vertical deflection of the ocean can represent the disturbance characteristic of the gravity field of the ocean, and developing vertical deflection compensation of the inertial navigation system is one of effective ways to improve navigation accuracy. With the increasing demand for autonomous navigation of deep sea exploration, polar scientific research and underwater long-time submersible, the vertical deflection compensation scheme of the inertial navigation system puts forward higher requirements for the accuracy level of the vertical deflection of the ocean at the position of the moving carrier. Under the condition of GNSS denial, the inertial navigation system cannot be calibrated for a long time, and the moving carrier itself has a large position error, and at this time, the error size of the vertical deflection of the ocean is directly determined by the gradient of the vertical deflection of the ocean in the horizontal direction, and the eastward gradient of the vertical deflection of the ocean becomes a key element for decoupling the position error of the moving carrier and the error of the vertical deflection of the ocean. SUMMARY
[0003] The application aims at the compensation demand of the vertical deflection of the inertial navigation system under the position error constraint of the moving carrier of the ocean, and proposes a method for calculating the eastward gradient of the vertical deflection of the ocean, so as to improve the compensation ability of the vertical deflection of the inertial navigation system under the position error constraint of the moving carrier of the ocean and improve the navigation accuracy of the inertial navigation system.
[0004] The application solves the technical problem by adopting the following technical scheme: The method for calculating the eastward gradient of the vertical deflection of the ocean comprises the following steps: using physical geodesy boundary value theory, constructing a calculation model of the eastward gradient of the vertical deflection of the ocean based on completely normalized global gravity potential coefficients, and realizing calculation of the eastward gradient of the vertical deflection of the ocean.
[0005] The calculation model of the eastward gradient of the vertical deflection of the ocean is as follows:
[0006] wherein is the eastward gradient of the vertical deviation component of the sea area, , is the vertical deviation component of the sea area, is the gravitational constant of the earth, is the geocentric radius of the spherical point, is the long radius of the earth ellipsoid, is the highest order of the spherical harmonic expansion, and are the order and the degree of the global gravity potential, and are the colatitude and the longitude of the sea surface point, and are the completely normalized global gravity potential coefficients, is the completely normalized associated Legendre function.
[0007] The advantages and positive effects of the present application are: The present application proposes a method for calculating the eastward gradient of the vertical deviation component of the sea area aiming at the demand for vertical deviation compensation of the inertial navigation system under the constraint of the position error of the moving carrier. The eastward gradient calculation model of the vertical deviation component of the sea area is constructed based on the completely normalized global gravity potential coefficients by using the physical geodesy boundary value theory, so as to realize the eastward gradient calculation of the vertical deviation component of the sea area. The present application aims to improve the vertical deviation compensation ability of the inertial navigation system under the constraint of the position error of the moving carrier and improve the navigation precision of the inertial navigation system. At the same time, the present application verifies the effectiveness of the present application by carrying out the eastward gradient calculation test of the vertical deviation component of the sea area based on the global gravity potential spherical harmonic model. BRIEF DESCRIPTION OF DRAWINGS
[0008] Figure 1 The present application is a test sea area vertical deviation component eastward gradient standard value contour diagram; Figure 2 The present application is a test sea area vertical deviation component eastward gradient standard value contour diagram; Figure 3 The present application is a test sea area vertical deviation component eastward gradient standard value contour diagram. DETAILED DESCRIPTION
[0009] The present application is further described below.
[0010] A method for calculating the eastward gradient of the vertical deviation component of the sea area, comprising the following steps: Step 1, using physical geodesy boundary value theory, based on the fully normalized global gravity potential coefficients, the construction of sea vertical deviation of the east gradient of the east component of the calculation model, to realize the sea vertical deviation of the east gradient of the east component of the calculation.
[0011] And step 1 to calculate the specific implementation method of the east gradient of the east component of the sea vertical deviation is:
[0012] In the formula is the east gradient of the east component of the sea vertical deviation, , is the east component of the sea vertical deviation, is the earth's gravitational constant, is the geocentric radius of the spherical point, is the long radius of the earth ellipsoid, is the highest order of spherical harmonic expansion, and is the order and the secondary of the global gravity potential, and is the residual latitude and longitude of the sea surface point, and is the fully normalized global gravity potential coefficient, is the fully normalized associated Legendre function.
[0013] According to the above-mentioned one kind of sea vertical deviation of the east gradient of the east component of the calculation method, the application designs the global gravity potential model based on the east gradient of the east component of the vertical deviation calculation test, and verifies the effectiveness of the application.
[0014] EGM2008 is selected as a global gravity potential base model, and the east gradient of the vertical deflection component of the meridian plane in a certain sea area is calculated based on the gravity field model coefficient of EGM2008. The calculation range is latitude 13°-14°, longitude 112°-113°, and the grid spacing is 1 minute. In order to make a comparative analysis, the vertical deflection component of the meridian plane in the sea area is also calculated based on the gravity field model coefficient of EGM2008, and the east difference component of the vertical deflection component of the meridian plane is used as the standard value of the east gradient of the vertical deflection component of the meridian plane in the sea area. It is necessary to point out here that, in addition to the east gradient of the vertical deflection component of the meridian plane, the east difference component of the vertical deflection component of the meridian plane also includes the east second-order gradient and the east third-order gradient of the vertical deflection component of the meridian plane; in the field of marine gravity potential field, the first-order gradient of the gravity field element is dominant, and the consistency of the trend of the east difference component of the vertical deflection component of the meridian plane and the east gradient of the vertical deflection component of the meridian plane can prove the correctness of the algorithm; therefore, the effectiveness of the present application can be evaluated by the statistical quantity of the difference between the standard value and the calculated value of the east gradient of the vertical deflection component of the meridian plane in the sea area. Table 1 gives the statistical quantity of the difference between the standard value and the calculated value of the east gradient of the vertical deflection component of the meridian plane in the test sea area. Figure 1 The standard value of the east gradient of the vertical deflection component of the meridian plane in the test sea area is given in the contour diagram, Figure 2 The calculated value of the east gradient of the vertical deflection component of the meridian plane in the test sea area is given in the contour diagram, Figure 3 The difference between the standard value and the calculated value of the east gradient of the vertical deflection component of the meridian plane in the test sea area is given in the contour diagram.
[0015] Table 1 Related statistical quantities of the east gradient of the vertical deflection component of the meridian plane in the test sea area / Unit Eotvos
[0016] From Table 1, Figure 1 and Figure 2 It can be seen that the amplitude of the calculated value of the east gradient of the vertical deflection component of the meridian plane in the test sea area reaches 25.25 Eotvos, and the standard deviation is 3.67 Eotvos, which reflects that the east gradient of the vertical deflection component of the meridian plane in the sea area can better express the high-frequency characteristics of the sea area gravity field; the overall trend of the calculated value and the standard value of the east gradient of the vertical deflection component of the meridian plane in the test sea area is consistent, and the standard deviation of the difference between the two is only 0.61 Eotvos, indicating that the calculation method of the east gradient of the vertical deflection component of the meridian plane in the sea area proposed by the present application has a good precision level, proving that the technical solution given by the present application is feasible and has high application value.
[0017] It should be emphasized that the embodiments described in the present application are illustrative rather than limiting, and therefore the present application includes but is not limited to the embodiments described in the specific embodiments, and any other embodiments derived from the technical solution of the present application by those skilled in the art also belong to the scope of protection of the present application.
Claims
1. A method for calculating the eastward gradient of the meridian component of the vertical deviation in a sea area, characterized in that: By using physical geodesy boundary value theory, based on the fully normalized global gravity potential coefficients, the east gradient calculation model of the sea vertical deviation normal component is constructed, and the east gradient calculation of the sea vertical deviation normal component is realized.
2. The method of claim 1, wherein the method is characterized by The east gradient calculation model of the sea vertical deviation normal component is: ； where is the eastward gradient of the normal component of the sea surface vertical deflection, , is the normal component of the sea surface vertical deflection, is the gravitational constant of the Earth, is the geocentric radius vector of a spherical point, is the semi-major axis of the Earth's ellipsoid, is the highest order of the spherical harmonic expansion, and are the order and degree of the global gravitational potential, and are the colatitude and longitude of a sea surface point, and are the fully normalized global gravitational potential coefficients, are the fully normalized associated Legendre functions.