Gravity satellite constellation design method for eliminating sea tide mixing

Abstract

The invention discloses a gravity satellite constellation design method for eliminating sea tide mixing, and relates to the technical field of satellite gravity. Comprising the following steps: calculating an ascending node angular distance difference of each sea tide component; determining the satellite orbital plane number, the orbital height, the orbital inclination angle and the inversion period of the gravity satellite constellation; determining a sea tide frequency mixing control strategy; and determining an optimal satellite constellation design scheme according to the sea tide mixing elimination strategy. According to the invention, a sea tide mixing control strategy is formulated according to the sea tide mixing characteristic of each sea tide component, and a practical method is provided for eliminating the influence of sea tide mixing on the inversion gravity field by using satellite constellation design.

Description

Technical Field

[0001] The present invention belongs to the field of satellite gravity technology, and in particular relates to a gravity satellite constellation design method for eliminating ocean tide aliasing. Background Art

[0002] Undersampling of ocean tide signals by gravity satellite missions and inaccurate ocean tide models used to deduct ocean tide signals during gravity inversion result in ocean tide aliasing errors in the inverted gravity field model. Ocean tide aliasing errors are a key source of error that limits the accuracy of satellite gravity measurement inversions. Eliminating aliasing errors from as many ocean tide components as possible and controlling the impact of ocean tide aliasing on satellite gravity field inversions within a range compatible with existing observation technology are urgent challenges in the field of satellite gravity. For a specific satellite mission, once the satellite orbit is determined, the ocean tide aliasing characteristics are also fixed. Therefore, whether the elimination of the effects of ocean tide aliasing can be considered during the satellite mission design phase is crucial for the subsequent high-precision gravity field inversion. However, there is currently no gravity satellite constellation design method specifically designed to eliminate ocean tide aliasing. Summary of the Invention

[0003] The purpose of the present invention is to provide a gravity satellite constellation design method that eliminates ocean tidal aliasing. By rationally designing the orbital parameters of the satellite constellation, the ocean tidal aliasing error is fundamentally eliminated or reduced, thereby improving the accuracy and reliability of gravity satellite measurements of the Earth's gravity field.

[0004] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0005] The present invention provides a method for designing a gravity satellite constellation to eliminate tidal aliasing, comprising the following steps:

[0006] S1. Calculate the angular distance difference of the ascending node of each tidal component to eliminate the aliasing effect;

[0007] S2. Determine the number of satellite orbit planes, orbit altitude range, orbit inclination range, inversion period and corresponding ocean tide mixing frequency of the gravity satellite constellation;

[0008] S3, determine the ocean tidal mixing control strategy, including classifying the elimination mode of ocean tidal components;

[0009] S4. Determine the optimal satellite constellation design scheme based on the ocean tidal frequency mixing elimination strategy.

[0010] As a preferred technical solution of the present invention, step S1 includes:

[0011] S11. Calculate the longitude phase change of each tidal component: where f t is the frequency of the tidal component, T sd is the length of the sidereal day;

[0012] S12. Calculate the angular distance difference of the ascending node based on the longitude phase change of each tidal component

[0013] As a preferred technical solution of the present invention, step S2 specifically includes:

[0014] S21. Determine the number of satellite orbital planes of the gravity satellite constellation;

[0015] S22. Determine the orbital altitude range and orbital inclination range of the satellite in each orbital plane;

[0016] S23. Determine the inversion period T to be used for the satellite constellation mission r ;

[0017] S24, calculating the ocean tidal mixing frequency based on the satellite's orbital altitude range, orbital inclination range, and inversion period; S24 specifically includes:

[0018] S241, calculate the first mixing frequency of the ocean tide component according to the satellite's orbital altitude range and orbital inclination range

[0019]

[0020] Where f is the frequency of the ocean tide signal, is the precession rate of the orbital plane relative to the Earth, and N is any integer that can minimize the equation;

[0021] S242, calculating the second mixing frequency according to the first mixing frequency and the pseudo-inversion period

[0022]

[0023] in, is the first mixing frequency, T r is the inversion period, and N is any integer that can minimize the formula.

[0024] As a preferred technical solution of the present invention, step S3 specifically includes:

[0025] S31. Determine the range of tidal components that need to be considered;

[0026] S32. Determine which tidal components can eliminate aliasing effects through constellation design based on the ascending node angular distance difference of the tidal components, the number of orbital planes, and the tidal aliasing frequency, i.e., determine the orbital plane elimination components.

[0027] S33. Determine the data processing and elimination mixing mode of the remaining ocean tide components, and determine the average component within the solution and the numerical estimation component respectively. Among them, the ocean tide component with a mixing frequency lower than the inversion period is defined as the average component within the solution; the ocean tide component with a mixing frequency higher than one inversion period but lower than the satellite design life is defined as the numerical estimation component.

[0028] As a preferred technical solution of the present invention, step S4 specifically includes:

[0029] S41. Narrowing the orbital altitude and orbital inclination search range of the satellite mission based on the ocean tide mixing control strategy;

[0030] S42. Determine the optimal orbital parameters of each orbital surface using an optimization algorithm within the narrowed range.

[0031] As a preferred technical solution of the present invention, step S42 specifically includes:

[0032] The optimization algorithm is used to determine the optimal orbital altitude and orbital inclination of the satellite on each orbital plane within the narrowed orbital parameter range. The data model of the optimization algorithm is:

[0033]

[0034] in is the mean orbital precession, G is the gravitational constant, M e is the mass of the Earth, a=h+R e is the height of the satellite from the center of the earth, R e is the average radius of the earth, h is the satellite orbit height, i is the orbit inclination, is the orbit repetition period, β and α are two positive integers and are mutually prime, ω e is the average angular velocity of the Earth, J2 is the harmonic coefficient of the Earth's gravity field;

[0035] By analogy, determining the orbital parameters of satellites in all orbital planes is the optimal gravity satellite constellation design scheme that optimally considers eliminating ocean tidal aliasing.

[0036] As a preferred technical solution of the present invention, the optimization algorithm in step S42 takes the orbit height h and the orbit inclination i as variables, and takes β and α as two positive integers that are mutually prime and α=max(T r ) as the constraint condition, taking the minimum β / α as the objective function, the optimal orbital parameters are determined through the search strategy, and then the orbital parameters of all orbital satellites are determined to obtain the optimal satellite constellation design scheme.

[0037] As a preferred technical solution of the present invention, the above.

[0038] The present invention has the following beneficial effects:

[0039] The present invention can determine the aliasing elimination modes of different ocean tidal components during the satellite constellation design stage. By distinguishing between orbital plane elimination components, intra-solution average components, and numerical estimation components, the ocean tidal aliasing error can be effectively controlled, providing a practical method for eliminating ocean tidal aliasing errors using satellite constellation design.

[0040] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0044] See also Figure 1 As shown, the present invention is a method for designing a gravity satellite constellation to eliminate ocean tidal aliasing, which specifically includes the following steps:

[0045] S1. Calculate the angular distance difference of the ascending node of each tidal component to eliminate the aliasing effect;

[0046] S11. Calculate the longitude phase change of the tidal component: where f t is the frequency of the tidal component (a known value for each tidal component), T sd is the length of the sidereal day;

[0047] S12. Calculate the angular distance difference of the ascending node based on the longitude phase change of each tidal component

[0048] S2 determines the number of satellite orbit planes, orbit altitude range, orbit inclination range, inversion period, and corresponding ocean tide mixing frequency of the gravity satellite constellation, specifically including the following steps:

[0049] S21 determines the number of satellite orbital planes of the gravity satellite constellation.

[0050] S22 determines the orbital altitude range and orbital inclination range of the satellites contained in each orbital plane.

[0051] The inversion period T to be adopted by the S23 satellite constellation mission r .

[0052] S24 calculates the ocean tidal mixing frequency based on satellite orbit parameters and inversion period, which is divided into the following two steps:

[0053] S241 calculates the first mixing frequency of the ocean tide component based on the satellite orbit altitude range and orbit inclination range

[0054]

[0055] Where f is the frequency of the ocean tide signal, is the precession rate of the orbital plane relative to the Earth, and N is any integer that can minimize the equation.

[0056] S242 calculates the second mixing frequency based on the first mixing frequency and the pseudo-inversion period

[0057]

[0058] in, is the first mixing frequency, T r is the inversion period, and N is any integer that can minimize the formula.

[0059] S3 determines the ocean tidal mixing control strategy, which specifically includes:

[0060] S31 determines the range of tidal components that need to be considered, which can be selected based on the accuracy requirements of gravity field inversion and the observation accuracy of key payloads, such as selecting 8 main tidal components or expanding to other tidal components;

[0061] S32 determines the mixing effect elimination mode of different tidal components under consideration, specifically including:

[0062] According to the angular distance difference of the ascending node of the ocean tide component, the number of orbital planes and the ocean tide mixing frequency, it is determined which ocean tide components can eliminate the mixing effect through constellation design, that is, the orbital plane elimination component is determined;

[0063] Compare the calculated mixing frequencies with known tidal component frequencies to analyze which tidal component mixing frequencies can be controlled or eliminated through orbit design and sampling strategies. If the mixing frequencies of certain tidal components have specific integer multiple relationships or resonant relationships with the satellite orbit sampling frequency, orbital plane precession frequency, etc., this may lead to enhanced mixing effects, which need to be avoided by adjusting orbital parameters or increasing the number of orbital planes. On the other hand, those tidal components whose tidal mixing frequencies can be averaged or offset during orbital operation and sampling can be identified as possible orbital plane elimination components.

[0064] S33 determines the data processing mode for eliminating aliasing of the remaining tidal components, that is, determining the average component within the solution and the numerical estimation component respectively, wherein the tidal component with a aliasing frequency lower than the inversion period is defined as the average component within the solution;

[0065] The ocean tide components with mixing frequencies higher than one inversion period but lower than the satellite design life are defined as numerical estimation components.

[0066] The above three mixing elimination modes are specifically implemented as follows:

[0067] (1) Orbital plane cancellation: By designing the satellite orbital plane position, the mixing signals of the ocean tide component are in opposite phase (the phase difference is 180 degrees). At this time, the mixing signals can cancel each other out during the joint solution.

[0068] (2) Intra-solution averaging means that when the ocean tidal mixing period is smaller than the inversion period, most of the energy of the ocean tidal mixing signal can be averaged out during the inversion process, thereby achieving the purpose of eliminating the ocean tidal mixing effect;

[0069] (3) Numerical estimation refers to eliminating the influence of tidal aliasing by synchronously estimating the tidal correction parameters during the gravity field inversion process or by estimating the tidal correction using the residual time series after the gravity field inversion.

[0070] S4 determines the optimal satellite constellation design based on the ocean tidal frequency aliasing elimination strategy, specifically including:

[0071] S41 narrows the orbital altitude and inclination search range of the satellite mission based on the ocean tidal mixing control strategy. Specifically:

[0072] The orbital height and orbital inclination range of the S411 orbital plane to eliminate the tidal component is composed of the orbital height and orbital inclination corresponding to the tidal mixing period less than 1 year, denoted as h1 and I1;

[0073] The tidal component of S412 using the solution average mode must be selected to satisfy the orbit height and orbit inclination corresponding to the tidal mixing period that is less than the inversion period, denoted as h2 and I2;

[0074] The numerically estimated ocean tide component of S413 must ensure that its ocean tide mixing signal and the main geophysical signal of gravity mission concern meet the Rayleigh condition for signal separation, so as to determine its corresponding orbital altitude and orbital inclination. Specifically, the following are involved:

[0075] S4131 calculates the Rayleigh period set based on the principle of separating ocean tidal mixing signals and time-varying signals; the Rayleigh period T Ray The calculation is as follows:

[0076] T Ray_ij |f ai -f sj |≥1

[0077] Where: f ai is the ith ocean tide mixing frequency, f sj is the j-th signal frequency, i, j = 1...Na, 1...Ms.

[0078] S4132 narrows the satellite orbit parameter search range based on the satellite mission planned life Lt and Rayleigh period set. The specific steps are as follows:

[0079] S41321 When the Rayleigh period is greater than the satellite lifespan, mark the Rayleigh period and put it into a new set T Ray_del That is, when T Ray_ij >Lt, T Ray_ij ∈T Ray_del .

[0080] S41322 will be T Ray_del Find the ocean tidal mixing frequencies corresponding to all subscripts i in the set, and find the corresponding orbital altitudes and orbital inclinations and mark them;

[0081] S41323 removes the orbital height and orbital inclination marked in S323 from the original orbital height and orbital inclination variation range, and records them as h3 and I3.

[0082] The orbit height hs and orbit inclination Is of the reduced range of S414 are the intersection of different tide components to achieve their respective elimination modes, that is,

[0083] hs=h1∩h2∩h3

[0084] Is=I1∩I2∩I3

[0085] S42 determines the optimal satellite constellation design within a narrowed orbital parameter search range.

[0086] The optimal orbital height and inclination of each orbital plane are determined using an optimization algorithm within a reduced orbital parameter range.

[0087] The data model of its optimization algorithm is

[0088]

[0089] in is the mean orbital precession, G is the gravitational constant, M e is the mass of the Earth, a=h+R e is the height of the satellite from the center of the earth, R e is the average radius of the earth, h is the satellite orbit height, i is the orbit inclination, is the orbit repetition period, β and α are two positive integers and are mutually prime, ω e is the average angular velocity of the Earth, and J2 is the harmonic coefficient of the Earth's gravity field.

[0090] The above mathematical model is used to construct an optimization algorithm, whose variables are orbit height h and orbit inclination i, and the constraints are that β and α are two positive integers and are mutually prime, and α=max(T r ), the objective function is to minimize β / α. The search strategy can be exhaustive method.

[0091] The specific operation is to use the satellite height h and orbit inclination i to form a two-dimensional discrete variable with a certain step size, and use numerical simulation to calculate the orbit repetition period β / α according to the above mathematical model, and select α=max(T r ) corresponds to the orbital repetition period, and under the premise that the satellite mission data is evenly distributed within the inversion period, the minimum value of β / α is calculated and obtained, and the corresponding orbital altitude and orbital inclination are the optimal orbital parameters.

[0092] By analogy, determining the orbital parameters of satellites in all orbital planes is the optimal gravity satellite constellation design scheme that optimally considers eliminating ocean tidal aliasing.

[0093] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0094] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for designing a gravity satellite constellation to eliminate ocean tidal aliasing, characterized in that: The following steps are involved: S1. Calculate the angular distance difference of the ascending node of each tidal component to eliminate the aliasing effect; S2. Determine the number of satellite orbit planes, orbit altitude range, orbit inclination range, inversion period and corresponding ocean tide mixing frequency of the gravity satellite constellation; S3, determine the ocean tidal mixing control strategy, including classifying the elimination mode of ocean tidal components; S4. Determine the optimal satellite constellation design scheme based on the ocean tidal frequency mixing elimination strategy.

2. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: The step S1 comprises: S11. Calculate the longitude phase change of each tidal component: where f t is the frequency of the tidal component, T sd is the length of the sidereal day; S12. Calculate the angular distance difference of the ascending node based on the longitude phase change of each tidal component 3. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: The step S2 specifically includes: S21. Determine the number of satellite orbital planes of the gravity satellite constellation; S22. Determine the orbital altitude range and orbital inclination range of the satellite in each orbital plane; S23. Determine the inversion period T to be used for the satellite constellation mission r ; S24, calculating the ocean tidal mixing frequency based on the satellite's orbital altitude range, orbital inclination range, and inversion period; S24 specifically includes: S241, calculate the first mixing frequency of the ocean tide component according to the satellite's orbital altitude range and orbital inclination range Where f is the frequency of the ocean tide signal, is the precession rate of the orbital plane relative to the Earth, and N is any integer that can minimize the equation; S242, calculating the second mixing frequency according to the first mixing frequency and the pseudo-inversion period in, is the first mixing frequency, T r is the inversion period, and N is any integer that can minimize the formula.

4. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: The step S3 specifically includes: S31. Determine the range of tidal components that need to be considered; S32. Determine which tidal components can eliminate aliasing effects through constellation design based on the ascending node angular distance difference of the tidal components, the number of orbital planes, and the tidal aliasing frequency, i.e., determine the orbital plane elimination components. S33. Determine the data processing and elimination mixing mode of the remaining ocean tide components, and determine the average component within the solution and the numerical estimation component respectively. Among them, the ocean tide component with a mixing frequency lower than the inversion period is defined as the average component within the solution; the ocean tide component with a mixing frequency higher than one inversion period but lower than the satellite design life is defined as the numerical estimation component.

5. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: The step S4 specifically includes: S41. Narrowing the orbital altitude and orbital inclination search range of the satellite mission based on the ocean tide mixing control strategy; S42. Determine the optimal orbital parameters of each orbital surface using an optimization algorithm within the narrowed range.

6. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: The step S42 specifically includes: The optimization algorithm is used to determine the optimal orbital altitude and orbital inclination of the satellite on each orbital plane within the narrowed orbital parameter range. The data model of the optimization algorithm is: in is the mean orbital precession, G is the gravitational constant, M e is the mass of the Earth, a=h+R e is the height of the satellite from the center of the earth, R e is the average radius of the earth, h is the satellite orbit height, i is the orbit inclination, is the orbit repetition period, β and α are two positive integers and are mutually prime, ω e is the average angular velocity of the Earth, J2 is the harmonic coefficient of the Earth's gravity field; By analogy, determining the orbital parameters of satellites in all orbital planes is the optimal gravity satellite constellation design scheme that optimally considers eliminating ocean tidal aliasing.

7. The method for designing a gravity satellite constellation to eliminate ocean tidal aliasing according to claim 1, characterized in that: In step S42, the optimization algorithm uses the orbit height h and the orbit inclination i as variables, and takes β and α as two positive integers that are mutually prime and α=max(T r ) as the constraint condition, taking the minimum β / α as the objective function, the optimal orbital parameters are determined through the search strategy, and then the orbital parameters of all orbital satellites are determined to obtain the optimal satellite constellation design scheme.

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