Method for calculating north gradient of vertical component of disturbing gravity in sea area
By constructing a calculation model for the northward gradient of the vertical component of marine disturbance gravity, and utilizing physical geodetic boundary value theory and global gravity potential coefficient, the problem of position error accumulation in inertial navigation systems during long-term operation was solved, navigation accuracy was improved, and the effectiveness and accuracy of the calculation method were verified.
Patent Information
- Application Number
- CN202511318817.8
- 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
During long-term operation, inertial navigation systems accumulate position errors due to the inhomogeneity of the Earth's gravitational field. This leads to a severe degradation in navigation accuracy, especially in cross-regional, highly dynamic navigation scenarios. Under GNSS rejection conditions, the northward gradient of the vertical component of gravitational force due to ocean disturbance becomes a key element in decoupling the position error of the moving vehicle from the error of the vertical component of gravitational force due to ocean disturbance.
A method for calculating the northward gradient of the vertical component of gravitational force under marine disturbance is adopted. Using the physical geodetic boundary value theory and the fully normalized global gravity potential coefficient, a calculation model for the northward gradient of the vertical component of gravitational force under marine disturbance is constructed. Based on the highest order and order of spherical harmonic expansion, the northward gradient of the vertical component of gravitational force under marine disturbance is calculated.
The method improves the navigation accuracy of inertial navigation systems under position error constraints of moving vehicles. Verification experiments show the effectiveness and accuracy of the calculation method, which can well express the high-frequency characteristics of the marine gravity field. The small standard deviation of the difference values indicates the high accuracy of the calculation method.
Smart Images
Figure CN121475192A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of marine gravity technology, and in particular, it is a method for calculating the northward gradient of the vertical component of gravitational force during marine disturbance. Background Technology
[0002] All objects on Earth and their states of motion are affected by Earth's gravity, and its non-uniformity is one of the decisive factors in the performance of precision navigation systems. Inertial navigation systems calculate motion states by using the specific force signals output by integrating accelerometers and gyroscopes, and their theoretical basis is built upon a homogeneous Earth model within the framework of classical Newtonian mechanics. However, due to the irregularity of the Earth's shape and the non-uniformity of its internal mass distribution, the actual Earth's gravitational field exhibits significant spatial anisotropy. This inherent characteristic leads to an exponential increase in accumulated errors in traditional inertial navigation systems over long periods of operation. Especially in cross-regional, high-dynamic navigation scenarios, the coupling effect of position errors and gravitational field disturbances severely degrades navigation accuracy. The vertical component of oceanic perturbation gravity can characterize the characteristics of oceanic gravitational field disturbances; therefore, developing navigation-aided methods based on the vertical component of oceanic perturbation gravity in inertial navigation systems is one of the effective ways to improve navigation accuracy. With the increasing demands for autonomous navigation from deep-sea exploration, polar scientific expeditions, and long-endurance underwater vehicles, inertial navigation systems (INS) are placing higher requirements on the accuracy of the vertical component of the perturbation gravitational force at the location of the moving vehicle. Under GNSS rejection conditions, the INS cannot be calibrated for extended periods, and the moving vehicle itself has significant positional errors. In this case, the magnitude of the error in the vertical component of the perturbation gravitational force is directly determined by the gradient of the vertical component in the horizontal direction. Therefore, the northward gradient of the vertical component of the perturbation gravitational force becomes a key element in decoupling the positional error of the moving vehicle from the error in the vertical component of the perturbation gravitational force. Summary of the Invention
[0003] The purpose of this invention is to address the navigation-aided navigation requirements of inertial navigation systems under positional error constraints of moving vehicles in the sea area. This invention proposes a method for calculating the northward gradient of the vertical component ...
[0004] The technical problem solved by this invention is achieved through the following technical solution: A method for calculating the northward gradient of the vertical component of gravitational force in marine disturbances is proposed. This method utilizes the physical geodetic boundary value theory and, based on the fully normalized global gravity potential coefficient, constructs a calculation model for the northward gradient of the vertical component of gravitational force in marine disturbances, thereby realizing the calculation of the northward gradient of the vertical component of gravitational force in marine disturbances.
[0005] Furthermore, the calculation model for the northward gradient of the vertical component of the gravitational force of ocean disturbance is as follows:
[0006] In the formula The northward gradient of the vertical component of the gravitational force of ocean disturbance. The vertical component of gravitational force due to ocean disturbance. The gravitational constant of Earth, For a point on a sphere, the geocentric radius is... The major radius of the Earth's ellipsoid. It is the highest order of spherical harmonic expansion. and It refers to the order and suborder of global gravitational potential. and It is the latitude and longitude of the sea surface point. and For a fully normalized global gravitational potential coefficient, For fully normalized association Legendre functions.
[0007] The advantages and positive effects of this invention are: This invention addresses the navigational needs of inertial navigation systems constrained by positional errors of moving vehicles in marine environments by proposing a method for calculating the northward gradient of the vertical component of marine perturbation gravity. Utilizing physical geodetic boundary value theory and based on fully normalized global gravitational potential coefficients, a calculation model for the northward gradient of the vertical component of marine perturbation gravity is constructed, enabling the calculation of this gradient. This invention aims to improve the navigational accuracy of inertial navigation systems constrained by positional errors of moving vehicles by enhancing the navigation capability of the vertical component of perturbation gravity. Furthermore, the effectiveness of this invention is verified through experiments calculating the northward gradient of the vertical component of perturbation gravity based on a global gravitational potential spherical harmonic model. Attached Figure Description
[0008] Figure 1 A schematic diagram of the standard value of the northward gradient of the vertical component of the gravitational disturbance in the test sea area according to an embodiment of the present invention; Figure 2 A schematic diagram illustrating the calculation of the northward gradient of the vertical component of gravitational disturbance in the test sea area according to an embodiment of the present invention; Figure 3 A schematic diagram illustrating the difference between the standard value and the calculated value of the northward gradient of the vertical component of the disturbance gravity in the test sea area according to an embodiment of the present invention. Detailed Implementation
[0009] The present invention will now be described in further detail.
[0010] A method for calculating the northward gradient of the vertical component of gravitational force in marine disturbances is proposed. This method utilizes the physical geodetic boundary value theory and, based on the fully normalized global gravity potential coefficient, constructs a calculation model for the northward gradient of the vertical component of gravitational force in marine disturbances, thereby realizing the calculation of the northward gradient of the vertical component of gravitational force in marine disturbances.
[0011] The calculation model for the northward gradient of the vertical component of gravitational force during ocean disturbance is as follows:
[0012] In the formula The northward gradient of the vertical component of the gravitational force of ocean disturbance. The vertical component of gravitational force due to ocean disturbance. The gravitational constant of Earth, For a point on a sphere, the geocentric radius is... The major radius of the Earth's ellipsoid. It is the highest order of spherical harmonic expansion. and It refers to the order and suborder of global gravitational potential. and It is the latitude and longitude of the sea surface point. and For a fully normalized global gravitational potential coefficient, For fully normalized association Legendre functions.
[0013] Based on the above-mentioned method for calculating the northward gradient of the vertical component of marine disturbance gravity, this invention designed an experiment to calculate the northward gradient of the vertical component of disturbance gravity based on a global gravity potential model, verifying the effectiveness of this invention.
[0014] The EGM2008 model was selected as the global gravity potential baseline model. The northward gradient of the vertical component of the perturbation gravitational force in a specific sea area was calculated based on the potential coefficients of the EGM2008 gravity field model. The calculation range was: latitude 13°~14°, longitude 112°~113°; grid spacing was 1 minute. For comparative analysis, the vertical component of the perturbation gravitational force in this sea area was also calculated based on the potential coefficients of the EGM2008 gravity field model. The northward difference component of the vertical component of the perturbation gravitational force was used as the standard value of the northward gradient of the vertical component of the perturbation gravitational force in the sea area. It is necessary to point out that the northward difference component of the perturbation gravitational vertical component includes not only the northward gradient of the perturbation gravitational vertical component, but also higher-order terms such as the second-order and third-order gradients of the perturbation gravitational vertical component. In the domain of ocean gravity potential field, since the first-order gradient of the gravity field element is dominant, the consistency of the trends of the northward difference component and the northward gradient of the perturbation gravitational vertical component proves the correctness of the algorithm of this invention. Therefore, the effectiveness of this invention can be evaluated by the statistics of the difference between the standard value and the calculated value of the northward gradient of the perturbation gravitational vertical component in the sea area. Table 1 gives the statistics of the standard value, calculated value, and difference between the northward gradient of the perturbation gravitational vertical component in the experimental sea area. Figure 1 A schematic diagram of the contour lines of the standard value of the northward gradient of the vertical component of the disturbance gravity in the test sea area is given. Figure 2 A schematic diagram of the contour lines for the calculated northward gradient of the vertical component of the disturbance gravity in the test sea area is provided. Figure 3 A schematic diagram of contour lines showing the difference between the standard and calculated values of the northward gradient of the vertical component of the disturbance gravity in the experimental sea area is presented.
[0015] Table 1. Correlation statistics of the northward gradient of the vertical component of the disturbance gravity in the test sea area / Unit: Eotvos
[0016] From Table 1, Figure 1 , Figure 2 and Figure 3 It can be seen that the amplitude of the calculated northward gradient of the vertical component of the perturbation gravity in the experimental sea area reaches 90.29 Eotvos, and the standard deviation is 14.66 Eotvos, which shows that the northward gradient of the vertical component of the perturbation gravity in the sea area can well express the high-frequency characteristics of the sea area's gravity field. The overall trend of the calculated value of the northward gradient of the vertical component of the perturbation gravity in the sea area is consistent with the standard value, and the standard deviation of the difference between the two is only 2.19 Eotvos, indicating that the calculation method of the northward gradient of the vertical component of the perturbation gravity in the sea area proposed in this invention has a good level of accuracy, proving that the technical solution given in this invention is feasible and has high application value.
[0017] It should be emphasized that the embodiments described in this invention are illustrative rather than limiting. Therefore, this invention includes, but is not limited to, the embodiments described in the specific implementation. Any other implementations derived by those skilled in the art based on the technical solutions of this invention are also within the scope of protection of this invention.
Claims
1. A method for calculating the northward gradient of the vertical component of gravitational force during ocean disturbance, characterized in that: Using the physical geodetic boundary value theory and based on the fully normalized global gravity potential coefficient, a calculation model for the northward gradient of the vertical component of marine disturbance gravity is constructed to realize the calculation of the northward gradient of the vertical component of marine disturbance gravity.
2. The method for calculating the northward gradient of the vertical component of gravitational force during ocean disturbance according to claim 1, characterized in that... The calculation model for the northward gradient of the vertical component of the gravitational force of the marine disturbance is as follows: ； In the formula The northward gradient of the vertical component of the gravitational force of ocean disturbance. The vertical component of gravitational force due to ocean disturbance. The gravitational constant of Earth, For a point on a sphere, the geocentric radius is... The major radius of the Earth's ellipsoid. It is the highest order of spherical harmonic expansion. and It refers to the order and suborder of global gravitational potential. and It is the latitude and longitude of the sea surface point. and For a fully normalized global gravitational potential coefficient, For fully normalized association Legendre functions.