A method for designing the orbit of a gravity satellite considering the tide mixing frequency

Abstract

The present invention discloses a method for designing a gravity satellite orbit considering ocean tide mixing, which relates to the technical field of satellite gravity. The method includes the following steps: determining a set of time-varying signal periods, a satellite orbit search range, and a set of gravity field inversion periods according to the mission objectives of the gravity satellite mission; calculating the ocean tide mixing periods caused by different orbital elements and different inversion periods within the search range of the satellite orbital elements; and searching for the optimal satellite orbit parameters according to the separation principle of ocean tide mixing signals and time-varying signals. The present invention utilizes the non-linear relationship among the satellite orbital elements, the ocean tide mixing period, and the time-varying signal period, and uses an optimization algorithm to determine the gravity satellite orbit parameters considering ocean tide mixing, providing a practical method for minimizing the influence of ocean tide mixing through orbit design to the greatest extent.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite gravity, and particularly relates to a method for designing a gravity satellite orbit considering ocean tide mixing frequencies. Background Art

[0002] During the gravity satellite observation and gravity field inversion processes, undersampling of the ocean tide signal occurs, causing high-frequency ocean tide signals to mix into low-frequency gravity field time-varying signals, resulting in ocean tide mixing. The ocean tide mixing error severely restricts the inversion accuracy of satellite gravity measurements. Since a specific satellite orbit causes a specific ocean tide mixing frequency, making it impossible to separate the ocean tide mixing error from the time-varying signal error, using post-processing methods to eliminate the ocean tide mixing error has limited improvement on the inverted gravity field. Therefore, in order to effectively improve the gravity field inversion accuracy, it is necessary to screen the satellite orbit from the beginning of the satellite mission design to avoid the problem that the ocean tide mixing error is difficult to eliminate afterwards. Summary of the Invention

[0003] The purpose of the present invention is to design a satellite orbit that can effectively separate time-varying signals and ocean tide mixing errors according to the satellite gravity observation target, and provide an orbit design method considering ocean tide mixing for gravity satellite mission design.

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

[0005] The present invention is a method for designing a gravity satellite orbit considering ocean tide mixing, including the following steps:

[0006] S1: Task objective decomposition and parameter determination, decompose the gravity satellite task objective, and determine the time-varying signal period set, satellite orbit search range, and gravity field inversion period set;

[0007] S2: Ocean tide mixing frequency calculation, calculate the ocean tide mixing frequencies caused by different orbital elements and different inversion periods within the satellite orbit element search range;

[0008] S3: Screening and determining the optimal satellite orbit parameters, determine the optimal orbit parameters through an optimal algorithm according to the principle of separating ocean tide mixing signals and time-varying signals.

[0009] As a preferred technical solution of the present invention, the S1 specifically includes the following steps:

[0010] S1.1: Task objective decomposition: Decompose the gravity satellite task objective, and determine the time-varying signal to be observed, satellite orbit type, and time resolution of the gravity model product to be generated;

[0011] S1.2: Determination of the time-varying signal frequency set: Determine the time-varying signal frequency set f s , the number of its elements is M;

[0012] S1.3: Determination of the search range of satellite orbital elements: According to the satellite orbit type, determine the search range of satellite orbital elements, including the range of orbital altitude variation and the range of orbital inclination variation;

[0013] S1.4: Determination of the gravity field inversion period set: According to the time resolution of the gravity model product to be generated, determine the gravity satellite inversion period set T r , and the number of its elements is L.

[0014] As a preferred technical solution of the present invention, the S2 specifically includes the following steps:

[0015] S2.1: Calculate the first mixing frequency set f according to the orbital elements and the frequency of the ocean tide component a1 ;

[0016] S2.2: Calculate the second mixing frequency set f according to the first mixing frequency and the inversion period a2 ;

[0017] S2.3: Combine the first mixing frequency set and the second mixing frequency set to form the ocean tide mixing frequency set f a , and the number of its elements is Na.

[0018] As a preferred technical solution of the present invention, in the S2.1, the calculation formula of the first mixing frequency set is

[0019]

[0020] where f tide 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 make this formula take the minimum value.

[0021] As a preferred technical solution of the present invention, in the S2.2, the calculation formula of the second mixing frequency set is

[0022]

[0023] where f a1 is the first mixing frequency, T r is the inversion period, and N is any integer that can make this formula take the minimum value.

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

[0025] S3.1: Calculate the Rayleigh period set according to the ocean tide mixing signal and the time-varying signal separation principle;

[0026] S3.2: Narrow the search range of satellite orbit parameters based on the satellite mission planned lifetime Lt and Rayleigh period set;

[0027] S3.3: Determine the optimal satellite orbit parameters through an optimization algorithm within the reduced satellite orbit parameter search range.

[0028] As a preferred technical solution of the present invention, the Rayleigh period is calculated as follows:

[0029] T Ray_ij |f ai -f sj |≥1

[0030] Where: f ai is the ith ocean tidal mixing frequency, f sj is the jth signal frequency.

[0031] As a preferred technical solution of the present invention, S3.2 specifically includes the following steps:

[0032] S3.21 When the Rayleigh period is greater than the planned mission life of the satellite Lt, 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 ;

[0033] S3.22 T Ray_del Find the tidal mixing frequencies corresponding to all the subscripts i in the set, and find the corresponding orbital heights and orbital inclinations and mark them;

[0034] S3.23 removes the marked orbital altitude and orbital inclination from the original orbital altitude and orbital inclination variation range to obtain a reduced orbital parameter variation range.

[0035] As a preferred technical solution of the present invention, the mathematical model of the optimization algorithm in S3.3 is:

[0036]

[0037] The present invention has the following beneficial effects:

[0038] The present invention decomposes the objectives of the satellite mission, determines the period set of the time-varying signal to be observed, the satellite orbit search range and the time-varying resolution of the gravity model product to be generated, and then determines the ocean tide mixing frequency. According to the mixing frequency and the time-varying signal and the planned life of the satellite, the satellite orbit search range is narrowed and the optimal orbit parameters are determined. The time-varying signal and the ocean tide mixing error are effectively separated, and a practical method is provided for the orbit design of the gravity satellite mission taking into account the ocean tide mixing.

[0039] Of course, it is not necessary for any product implementing the present invention to achieve all the above-mentioned advantages simultaneously. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0041] Figure 1 Flowchart of a method for designing a gravity satellite orbit considering tidal mixing. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0043] A specific embodiment of the present invention is as follows:

[0044] As Figure 1 shown, to implement a method for designing a gravity satellite orbit considering tidal mixing, it includes

[0045] S1 Determine the time-varying signal period set, satellite orbit search range, and gravity field inversion period set according to the task objectives of the gravity satellite mission, specifically including the following steps:

[0046] S1.1 Decompose the objectives of the gravity satellite mission, including the time-varying signals to be observed, the type of satellite orbit, and the time resolution of the gravity model products to be generated;

[0047] S1.2 Determine the time-varying signal frequency set f s , the number of its elements is M;

[0048] S1.3 Determine the satellite orbit element search range according to the type of satellite orbit, including the range of orbital altitude change and the range of orbital inclination change;

[0049] S1.4 Determine the gravity satellite inversion period set T r , the number of its elements is L.

[0050] S2 Calculate the tidal mixing periods caused by different orbit elements and different inversion periods within the satellite orbit element search range, specifically including the following steps:

[0051] S2.1 Calculate the first mixing frequency set f according to the orbital elements and the tidal component frequencies a1

[0052]

[0053] where f tide is the frequency of the tidal signal, is the precession rate of the orbital plane relative to the Earth, and N is any integer that minimizes this expression;

[0054] S2.2 Calculate the second mixing frequency set f according to the first mixing frequency and the inversion period a2 ,

[0055]

[0056] where f a1 is the first mixing frequency, T r is the inversion period, and N is any integer that minimizes this expression.

[0057] S2.3 Combine the first mixing frequency set and the second mixing frequency set to form the tidal mixing frequency set f a , the number of its elements is Na.

[0058] S3 Search for the optimal satellite orbit parameters according to the tidal mixing signal and the time-varying signal separation principle, specifically including:

[0059] S3.1 Calculate the Rayleigh period set according to the tidal mixing signal and the time-varying signal separation principle; the Rayleigh period T Ray is calculated as follows:

[0060] T Ray_ij |f ai -f sj |≥1

[0061] where: f ai is the i-th tidal mixing frequency, f sj is the j-th time-varying signal frequency, i, j = 1...Na, 1...M.

[0062] S3.2 Narrow the satellite orbit parameter search range according to the satellite mission planned lifetime Lt and the Rayleigh period set. The specific steps are as follows:

[0063] S3.21 When the Rayleigh period is greater than the satellite mission planned lifetime Lt, mark this 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 .

[0064] S3.22 Find the tidal mixing frequencies corresponding to all subscripts i in the T Ray_del set, find the corresponding orbital altitude and orbital inclination and make marks;

[0065] S3.23 Exclude the marked orbital altitude and orbital inclination in S3.23 from the original range of orbital altitude and orbital inclination changes to obtain a reduced range of orbital parameter changes.

[0066] S3.3 Determine the optimal satellite orbital parameters through an optimization algorithm within the reduced range of satellite orbital parameters. Its mathematical model is

[0067]

[0068] where is the mean precession of the orbit, 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 mean radius of the Earth, h is the satellite orbital altitude, i is the orbital inclination, is the orbital repeat period, β, α are two positive integers and are relatively prime, ω e is the mean angular velocity of the Earth, and J2 is the zonal harmonic coefficient of the Earth's gravitational field.

[0069] Construct an optimization algorithm using the above mathematical model, with its variables being the orbital altitude h and the orbital inclination i, and the constraint conditions being that β, α are two positive integers and are relatively prime, and α = max(T r ), and the objective function is to be minimized. The search strategy can use the exhaustive method. The specific operation is to form two-dimensional discrete variables with the satellite altitude h and the orbital inclination i at a certain step size, and use numerical simulation to calculate the orbital repeat period according to the above mathematical model screen out the orbital repeat period corresponding to α = max(T r ), calculate and obtain the minimum value, and the corresponding orbital altitude and orbital inclination are the optimal orbital parameters.

[0070] In the description of this specification, the descriptions referring to terms such as "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0071] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A gravity satellite orbit design method considering tide mixing frequencies, characterized in that, It includes the following steps: S1: Task objective decomposition and parameter determination. Decompose the objectives of the gravity satellite mission, and determine the time-varying signal period set, the satellite orbit search range, and the gravity field inversion period set. S2: Calculation of ocean tide mixing frequencies. Calculate the ocean tide mixing frequencies caused by different orbital elements and different inversion periods within the satellite orbit element search range. S3: Screening and determination of optimal satellite orbit parameters. According to the principle of separating ocean tide mixing signals and time-varying signals, determine the optimal orbit parameters through an optimal algorithm. The specific steps of S3 include the following: S3.1: Calculate the Rayleigh period set according to the principle of separating ocean tide mixing signals and time-varying signals. The Rayleigh period calculation in S3.1 is as follows T Ray_ij |f ai -f sj |≥1 Where: f ai is the i-th ocean tide mixing frequency, and f sj is the j-th signal frequency; S3.2: Narrow the satellite orbit parameter search range according to the planned mission lifetime Lt of the satellite and the Rayleigh period set. S3.21 When the Rayleigh period is greater than the satellite mission planned lifetime Lt, mark this 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 ; S3.22 Find the tidal mixing frequencies corresponding to all subscripts i in the T Ray_del set, and find the corresponding orbital altitude and orbital inclination and make marks; S3.23 Exclude the marked orbital altitude and orbital inclination from the original orbital altitude and orbital inclination variation ranges to obtain the narrowed orbital parameter variation range. S3.3: Determine the optimal satellite orbit parameters through an optimization algorithm within the narrowed satellite orbit parameter search range. The mathematical model of the optimization algorithm in S3.3 is: Among them is the orbital mean 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 mean radius of the Earth, h is the satellite orbit height, i is the orbital inclination, is the orbital repeat period, β, α are two positive integers and relatively prime, ω e is the mean angular velocity of the Earth, J2 is the zonal harmonic coefficient of the Earth's gravity field.

2. The method for designing a gravity satellite orbit considering ocean tide mixing frequencies according to claim 1, characterized in that, The specific steps of S1 include the following: S1.1: Task objective decomposition. Decompose the objectives of the gravity satellite mission, and determine the time-varying signals to be observed, the satellite orbit type, and the time resolution of the gravity model products to be generated. S1.2: Determination of the time-varying signal frequency set: Determine the time-varying signal frequency set \(f\) according to the time-varying signal to be observed s , the number of its elements is \(M\); S1.3: Determination of satellite orbit element search range. According to the satellite orbit type, determine the satellite orbit element search range, including the orbital altitude variation range and the orbital inclination variation range. S1.4: Determination of the gravity field inversion period set: Determine the gravity satellite inversion period set \(T\) according to the time resolution of the gravity model product to be generated. r The number of its elements is \(L\).

3. A method for designing a gravity satellite orbit considering tide mixing frequencies according to claim 2, characterized in that, The specific steps of S2 include the following: S2.1: Calculate the first mixing frequency set f according to the orbital elements and the tidal component frequencies a1 ; S2.2: Calculate the second mixing frequency set f according to the first mixing frequency and the inversion period a2 ; S2.3: Combine the first mixing frequency set and the second mixing frequency set to form the ocean tide mixing frequency set f a , and the number of its elements is Na.

4. A method for designing a gravity satellite orbit considering ocean tide mixing frequencies according to claim 3, characterized in that In S2.1, the calculation formula for the first mixing frequency set is where f tide is the frequency of the ocean tide signal, is the precession rate of the orbital plane relative to the Earth, and N is an arbitrary integer that minimizes this expression.

5. A method for designing a gravity satellite orbit considering ocean tide mixing frequencies according to claim 4, characterized in that, In S2.2, the calculation formula for the second mixing frequency set is where f a1 is the first mixing frequency, T r is the inversion period, and N is any integer that minimizes this expression.

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