Measurement and control link multiple access method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a measurement and control link multiple access method and device based on a high-dimensional discrete space, electronic equipment and a storage medium. The method comprises the following steps: constructing the high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space comprises space resources of at least one of a time domain, a frequency domain and a code domain; in a high-dimensional discrete space, constructing a non-stipulated coordinate system matched with the control scene requirement by taking the initial stipulated coordinate system as a reference; constructing a dual mapping relation matrix according to a non-stipulated coordinate system of the initial stipulated coordinate system, and updating the dual mapping relation matrix based on the measured data; and accessing at least one satellite or spacecraft to the ground station based on the updated dual mapping relation matrix and the constellation measurement and control link, thereby realizing effective expansion of the measurement and control link multiple access technology, and improving the measurement and control link multiple access efficiency based on the available discrete space of the multi-dimensional joint variable.

Description

Technical Field

[0001] The present invention relates to the field of aircraft measurement and control technology, and in particular to a measurement and control link multiple access method, device, electronic equipment and storage medium based on high-dimensional discrete space. Background Art

[0002] With the continuous expansion of the Starlink system and the continuous improvement of its networking application efficiency, the field of satellite communication constellations has once again attracted the attention of academia and industry. How to efficiently control in-orbit spacecraft based on existing aerospace measurement and control means has become a real problem that needs to be solved urgently.

[0003] In tasks such as large-scale constellation control and on-orbit operation and control of space station complexes, neighborhood multi-target measurement and control links cannot achieve beam isolation in space and overlap with each other. The use of a single dimension such as pure frequency division or pure code division does not meet the requirements of multi-user link use, reducing the efficiency of multiple access to the measurement and control link. Summary of the Invention

[0004] The embodiments of the present invention provide a method, device, electronic device and storage medium for multiple access of a measurement and control link based on a high-dimensional discrete space, which can solve the problem that the use of a single dimension such as pure frequency division or pure code division in related technologies does not meet the requirements of multi-user link usage, and improve the efficiency of multiple access of the measurement and control link.

[0005] In one aspect, an embodiment of the present invention discloses a method for multiple access of a measurement and control link based on a high-dimensional discrete space, the method comprising:

[0006] Constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain;

[0007] In the high-dimensional discrete space, based on the initial specification coordinate system, a non-specification coordinate system adapted to the control scenario requirements is constructed; the initial specification coordinate system is a standardized virtual base class coordinate system; the non-specification coordinate system is a non-standardized coordinate system that matches the initial specification coordinate system;

[0008] Constructing a dual mapping relationship matrix according to the non-reduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the non-reduced coordinate system and the initial reduced coordinate system;

[0009] Based on the updated dual mapping relationship matrix, at least one satellite or spacecraft is connected to the ground station based on the constellation tracking and control link.

[0010] Optionally, constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system includes:

[0011] Determining a combination matrix based on a set of discrete points corresponding to at least one satellite or spacecraft in the orthogonal vector coordinate system; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain;

[0012] A high-dimensional discrete space is constructed according to the combined matrix.

[0013] Optionally, constructing a non-reduced coordinate system adapted to the control scenario requirements on the high-dimensional discrete space with the initial reduced coordinate system as a reference includes:

[0014] In the high-dimensional discrete space, a three-dimensional space under a first constraint condition is determined according to a combination matrix; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain;

[0015] In the three-dimensional space, based on the principle of forward derivation and taking the initial specification coordinate system as the benchmark, the control scenario requirements are determined;

[0016] Based on the control scenario requirements, a non-standardized coordinate system adapted to the control scenario requirements is constructed.

[0017] Optionally, constructing a non-reduced coordinate system adapted to the control scenario requirement based on the control scenario requirement includes:

[0018] In the case where the control scenario is long-term control of a space station complex, the initial reduced coordinate system is sliced ​​with the time domain X-axis as the normal direction to construct an O-YZ reduced coordinate system adapted to the long-term control mission of the space station complex; the O-YZ reduced coordinate system is used to represent the two-dimensional discrete space composed of the frequency domain and the code domain;

[0019] Based on the O-YZ standardized coordinate system, a non-standardized coordinate system is constructed that is compatible with the long-term control requirements of the space station assembly.

[0020] Optionally, constructing a non-reduced coordinate system adapted to the control scenario requirement based on the control scenario requirement includes:

[0021] When the control scenario is large-scale low-orbit constellation control, constructing an O-XYZ reduced coordinate system adapted to the large-scale low-orbit constellation control scenario; the O-XYZ reduced coordinate system is used to represent a three-dimensional discrete space consisting of a time domain, a frequency domain, and a code domain;

[0022] Based on the O-XYZ standardized coordinate system, a non-standardized coordinate system adapted to the control requirements of large-scale low-orbit constellations is constructed.

[0023] Optionally, constructing a non-reduced coordinate system adapted to the control scenario requirement based on the control scenario requirement includes:

[0024] When the control scenario is the measurement and control of multiple satellites into orbit with one rocket, the initial reduced coordinate system is sliced ​​with the Z axis of the code domain as the normal direction to construct an O-XY reduced coordinate system adapted to the measurement and control task of the multiple satellites into orbit with one rocket; the O-XY reduced coordinate system is used to represent the two-dimensional discrete space composed of the time domain and the frequency domain;

[0025] Based on the O-XY conventional coordinate system, a non-conventional coordinate system adapted to the measurement and control requirements of the multi-satellite-in-orbit launch phase is constructed.

[0026] Optionally, constructing a dual mapping relationship matrix according to the unreduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data, includes:

[0027] Performing dimensionality reduction processing on the non-reduced coordinate system according to prior information corresponding to the non-reduced coordinate system and the task;

[0028] Determine the non-standardized threshold boundary cone surface without link interference based on Monte Carlo simulation of finite element analysis or actual link testing;

[0029] Mapping the unreduced coordinate system into a reduced coordinate system;

[0030] Determine the reduced coordinate system and dual mapping relationship matrix that are suitable for the current task;

[0031] The dual mapping relationship matrix is ​​continuously updated iteratively using statistical learning methods and measured data.

[0032] In another aspect, an embodiment of the present invention discloses a multiple access device for a measurement and control link based on a high-dimensional discrete space, the device comprising:

[0033] A construction module, configured to construct a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain;

[0034] A construction module is used to construct an unreduced coordinate system adapted to the control scenario requirements on the high-dimensional discrete space based on the initial reduced coordinate system; the initial reduced coordinate system is a standardized virtual base class coordinate system; the unreduced coordinate system is a non-standardized coordinate system that matches the initial reduced coordinate system; and a dual mapping relationship matrix is ​​constructed based on the unreduced coordinate system of the initial reduced coordinate system;

[0035] An updating module, configured to update the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system;

[0036] An access module is used to connect at least one satellite or spacecraft to a ground station based on the updated dual mapping relationship matrix and the constellation measurement and control link.

[0037] Optionally, the building block includes:

[0038] a determination module, configured to determine a combination matrix based on a set of discrete points corresponding to at least one satellite or spacecraft in the orthogonal vector coordinate system; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain;

[0039] A construction submodule is used to construct a high-dimensional discrete space according to the combination matrix.

[0040] Optionally, the construction module includes:

[0041] A first determination submodule is configured to determine a three-dimensional space under a first constraint condition in the high-dimensional discrete space based on a combination matrix; the combination matrix is ​​configured to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain; and in the three-dimensional space, based on a forward derivation principle and with an initial reduced coordinate system as a reference, determine control scenario requirements;

[0042] The first construction submodule is used to construct a non-reduced coordinate system adapted to the control scenario requirements based on the control scenario requirements.

[0043] Optionally, the construction module further includes:

[0044] The first slicing module is used to slice the initial reduced coordinate system with the time domain X-axis as the normal direction when the control scenario is long-term control of the space station assembly;

[0045] The second construction submodule is used to construct an O-YZ protocol coordinate system that is compatible with the long-term control mission of the space station assembly; the O-YZ protocol coordinate system is used to represent the two-dimensional discrete space composed of the frequency domain and the code domain; based on the O-YZ protocol coordinate system, a non-reduced coordinate system that is compatible with the long-term control requirements of the space station assembly is constructed.

[0046] Optionally, the construction module further includes:

[0047] The third construction submodule is configured to construct an O-XYZ reduced coordinate system compatible with the large-scale LEO constellation control scenario, when the control scenario is large-scale LEO constellation control. The O-XYZ reduced coordinate system is used to represent the three-dimensional discrete space composed of the time domain, frequency domain, and code domain. Based on the O-XYZ reduced coordinate system, an unreduced coordinate system compatible with the requirements of large-scale LEO constellation control is constructed.

[0048] Optionally, the construction module further includes:

[0049] The second slicing module is configured to slice the initial reduced coordinate system with the code domain Z axis as the normal direction when the control scenario is the measurement and control of multiple satellites into orbit with one rocket;

[0050] The third construction submodule is used to construct an O-XY reduced coordinate system that is compatible with the measurement and control mission of the multi-satellite launch into orbit phase; the O-XY reduced coordinate system is used to represent the two-dimensional discrete space composed of the time domain and the frequency domain; based on the O-XY reduced coordinate system, a non-reduced coordinate system that is compatible with the measurement and control requirements of the multi-satellite launch into orbit phase is constructed.

[0051] Optionally, the update module includes:

[0052] A dimensionality reduction module, configured to perform dimensionality reduction processing on the non-reduced coordinate system according to the prior information corresponding to the non-reduced coordinate system and the task;

[0053] A second determination submodule is configured to determine a non-standardized threshold boundary cone surface without link interference based on a Monte Carlo simulation of finite element analysis or an actual link test;

[0054] A mapping module, configured to map the non-reduced coordinate system into a reduced coordinate system;

[0055] The second determination submodule is further used to determine a reduced coordinate system and a dual mapping relationship matrix adapted to the current task;

[0056] The updating submodule is used to continuously iteratively update the dual mapping relationship matrix using statistical learning methods and measured data.

[0057] On the other hand, an embodiment of the present invention further discloses an electronic device, which includes a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus; the memory is used to store executable instructions, and the executable instructions enable the processor to execute the aforementioned measurement and control link multiple access method based on high-dimensional discrete space.

[0058] An embodiment of the present invention further discloses a readable storage medium. When the instructions in the readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the aforementioned measurement and control link multiple access method based on high-dimensional discrete space.

[0059] The embodiments of the present invention include the following advantages:

[0060] An embodiment of the present invention provides a method for multiple access of a measurement and control link based on a high-dimensional discrete space. The method includes: constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes spatial resources in at least one of a time domain, a frequency domain, and a code domain; constructing an unreduced coordinate system adapted to the control scenario requirements in the high-dimensional discrete space with the initial reduced coordinate system as a reference; the initial reduced coordinate system is a standardized virtual base class coordinate system; the unreduced coordinate system is a coordinate system that matches the initial reduced coordinate system; constructing a dual mapping relationship matrix based on the unreduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system; based on the updated dual mapping relationship matrix, connecting at least one satellite or spacecraft to a ground station based on a constellation measurement and control link, thereby achieving effective expansion of measurement and control link multiple access technology in tasks such as large-scale constellation control and on-orbit operation and control of space station assemblies, and improving the efficiency of measurement and control link multiple access based on the available discrete space of multi-dimensional joint variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments of the present invention. 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 paying any creative labor.

[0062] Figure 1 This is a flowchart of an embodiment of a method for multiple access of a measurement and control link based on a high-dimensional discrete space according to the present invention;

[0063] Figure 2 It is a schematic diagram of a three-dimensional discrete variable reduced coordinate system of the present invention;

[0064] Figure 3 This is a flow chart of a method for constructing a high-dimensional discrete space based on the forward derivation principle of the present invention;

[0065] Figure 4 This is an example diagram of multiple access to a constellation tracking and control link according to the present invention;

[0066] Figure 5 This is a simulation result diagram of bit error rate with different interference-to-signal ratio at the same frequency according to the present invention;

[0067] Figure 6 This is a simulation result diagram of bit error rate at different frequency offsets when the interference-to-signal ratio is 30dB according to the present invention;

[0068] Figure 7 This is a simulation result diagram of bit error rate at different frequency offsets when the interference-to-signal ratio is 25dB according to the present invention;

[0069] Figure 8 This is a structural block diagram of an embodiment of a measurement and control link multiple access device based on high-dimensional discrete space of the present invention;

[0070] Figure 9 This is a structural block diagram of an electronic device provided by an example of the present invention. DETAILED DESCRIPTION

[0071] The following will provide a clear and complete description of 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 them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0072] The terms "first", "second", etc. in the specification and claims of the present invention are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present invention can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first", "second", etc. are generally of one type, and the number of objects is not limited. For example, the first object can be one or more. In addition, the term "and / or" in the specification and claims is used to describe the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. In the embodiments of the present invention, the term "multiple" refers to two or more, and its quantifiers are similar.

[0073] Method Example

[0074] Reference Figure 1 , shows a flowchart of an embodiment of a method for multiple access of a measurement and control link based on a high-dimensional discrete space of the present invention. The method may specifically include the following steps:

[0075] S101. Constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain;

[0076] S102. In the high-dimensional discrete space, based on the initial specification coordinate system, construct a non-reduction coordinate system that is adapted to the control scenario requirements; the initial specification coordinate system is a standardized virtual base class coordinate system; the non-reduction coordinate system is a coordinate system that matches the initial specification coordinate system;

[0077] S103, constructing a dual mapping relationship matrix based on the unreduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system;

[0078] S104: Based on the updated dual mapping relationship matrix, at least one satellite or spacecraft is connected to the ground station based on the constellation tracking and control link.

[0079] A high-dimensional discrete space is constructed based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain.

[0080] The initial orthogonal vector coordinate system refers to a coordinate frame constructed based on three dimensions in generalized space.

[0081] The process of constructing a high-dimensional discrete space based on orthogonal vectors in space (time domain), frequency (frequency domain), and pseudocode (code domain) is essentially a process of mathematical abstraction and structured integration of orthogonal resources of different dimensions. First, the physical meaning and mathematical representation of the orthogonal vectors in each dimension must be clarified: the spatial dimension corresponds to different positions or beam directions of the antenna array, the frequency dimension represents the frequency values ​​of different carriers or subchannels, and the pseudocode dimension represents mutually orthogonal spreading codes or address codes (such as Walsh codes in Code Division Multiple Access (CDMA)). These vectors are orthogonal within their respective dimensions, meaning their inner products are zero, ensuring the independence of resources within a single dimension. Subsequently, through mathematical operations such as tensor products or Cartesian products, the orthogonal vectors of each dimension are combined into a joint vector in the high-dimensional space. For example, a two-dimensional joint vector can be represented as the product of a space vector and a frequency vector. A three-dimensional joint vector further incorporates the pseudocode vector to form a three-dimensional orthogonal basis of "space-frequency-pseudocode." Each high-dimensional vector corresponds to a unique resource unit and can be used to identify a specific user or channel in a communication system.

[0082] This construction process must adhere to two core principles: orthogonality preservation and discretization. Orthogonality preservation ensures that resources of different dimensions remain independent in the joint space, avoiding interference. For example, in a Multiple-Input Multiple-Output Orthogonal Frequency-Division Multiplexing (MIMO-OFDM) system, different antennas in the spatial dimension, different subcarriers in the frequency dimension, and different spreading codes in the pseudo-code dimension are jointly orthogonalized. This allows each user's three-dimensional "space-frequency-pseudo-code" vectors to be orthogonal in the high-dimensional space, thereby enabling parallel transmission and accurate separation of multi-user signals. Discretization divides continuous physical resources (such as continuous frequency bands) into discrete orthogonal units, facilitating digital signal processing and resource allocation. For example, the frequency axis is discretized into N orthogonal subcarriers, the spatial direction is discretized into M beams, and the pseudo-code set is discretized into K orthogonal code groups, ultimately constructing a discrete vector space of dimensions M×N×K.

[0083] A high-dimensional discrete space is a multidimensional structured mathematical space constructed by integrating discrete vectors in multiple orthogonal dimensions, such as space, frequency, pseudocode, and time. In this space, vectors in each dimension (such as beam pointing in space, subcarriers in frequency, and spread spectrum sequences in pseudocode) are orthogonal (the inner product is zero), ensuring the independence of resources within a single dimension. Through mathematical operations such as tensor products or Cartesian products, vectors of each dimension are combined into a high-dimensional joint vector, such as a three-dimensional "space-frequency-pseudocode" vector. Each vector corresponds to a unique resource unit, which can accurately identify users, channels, or signal characteristics in the communication system, providing a mathematical basis for the orderly allocation and management of multi-dimensional resources.

[0084] The core feature of this space is the combination of orthogonality and discretization: orthogonality ensures that resources of different dimensions do not interfere with each other in the joint space. For example, in the MIMO-OFDM system, the spatial vectors of the antenna array, the frequency vectors of the subcarriers, and the pseudo-code vectors of the spread spectrum code are orthogonal to each other, allowing multi-user signals to be transmitted in parallel; discretization converts continuous physical quantities (such as frequency bands and spatial angles) into a finite number of discrete units, which facilitates digital signal processing.

[0085] In high-dimensional discrete space, based on the initial specification coordinate system, a non-reduction coordinate system adapted to the control scenario requirements is constructed; the initial specification coordinate system is a standardized virtual base class coordinate system; the non-reduction coordinate system is a coordinate system that matches the initial specification coordinate system;

[0086] Among them, the initial reduced coordinate system is a reference coordinate system used to describe the structure of space-time in theoretical physics or cosmology research. Its construction is based on the original agreement and mathematical idealization of physical laws. In theoretical frameworks such as general relativity, it is usually set as a "disturbance-free" or "uniform and isotropic" reference system to characterize the initial state of the universe or a simplified physical model. For example, in the standard model of cosmology, the initial reduced coordinate system can correspond to the cosmic microwave background radiation rest system, in which the cosmological principle (the universe is uniform and isotropic on a large scale) is strictly satisfied, the spatial coordinate grid is aligned with the Hubble flow of the universe's expansion, and the time coordinate corresponds to the original time of the universe (the time experienced by a co-moving observer). This coordinate system removes the influence of local motion and gravitational perturbations through mathematical coordinate selection (such as co-moving coordinates), making it easier to study the overall evolution laws of the universe, such as the expansion rate and the statistical characteristics of matter distribution.

[0087] The core characteristics of the initial reduced coordinate system are its "conventionality" and "theoretical instrumentality". It does not directly correspond to the physical observation coordinate system in reality, but is an ideal model introduced to simplify theoretical analysis. For example, when dealing with gravitational field equations, by selecting specific coordinate conditions (such as harmonic coordinate conditions, Einstein-de Sitter coordinates), the space-time metric can be decomposed into the background metric and the perturbation term, where the background metric corresponds to the space-time structure under the initial reduced coordinate system. This decomposition method is widely used in cosmic perturbation theory and gravitational wave research, helping researchers to separate background evolution from small-scale physical effects. It should be noted that the specific form of the initial reduced coordinate system depends on the assumptions of the theoretical model. Different coordinate conventions may be used in different research scenarios, but their essence is to construct a benchmark framework that is convenient for theoretical derivation through mathematical conventions, providing a simplified logical starting point for understanding the complex physical phenomena of the real universe.

[0088] In computer science or theoretical modeling, using the initial reduced coordinate system as a benchmark refers to transforming this abstract physical concept into a virtual base class in object-oriented programming. This virtual class serves as an abstract template, defining the core properties of the initial reduced coordinate system (such as the spacetime metric, coordinate transformation rules, and uniform isotropy constraints) and methods (such as coordinate conversion functions and perturbation superposition algorithms), but without providing specific implementation details. For example, a virtual class might declare an abstract method "CalculateMetric()" for calculating the spacetime metric, but the specific implementation must be completed by subclasses (such as the co-moving coordinate system subclass in cosmological models or the background coordinate system subclass in gravitational field perturbation models). This design allows different physical models to inherit the basic framework of the initial reduced coordinate system while adding differentiated logic based on specific scenarios (such as an expanding universe or curved spacetime), embodying the object-oriented design principle of "unified interface, customized implementation."

[0089] Treating the initial reduced coordinate system as a virtual class essentially uses programming abstraction to capture its theoretical properties—an idealized model that doesn't directly correspond to real-world observations but provides a foundational framework for theoretical derivations. The virtual nature of the virtual class mirrors the conventional nature of the initial reduced coordinate system: the former provides an abstract interface that can't be instantiated at the code level, while the latter provides an idealized reference system that can't be directly observed at the physical level. For example, in a program simulating cosmic evolution, the PrimordialGaugeCoordinateSystem virtual class defines the basic properties of co-moving coordinates, while the ExpandingUniverseCoordinate subclass inherits from it and implements a scale factor function that evolves with cosmic time. In this way, the virtual class serves as a bridge between physical theory and computational modeling, preserving the theoretical rigor of the initial reduced coordinate system while providing a scalable programming paradigm for numerical simulations of complex physical scenarios.

[0090] For example, using the initial specification coordinate system as a virtual class to construct a specification coordinate system for a specific application scenario can be regarded as the first level of concrete extension of abstract theory in object-oriented modeling. The initial virtual class defines core abstract interfaces such as spacetime homogeneity and isotropy, coordinate transformation rules, etc. (such as GetCosmicTime() to obtain the original time of the universe, TransformToComoving() to convert to co-moving coordinates), and the specific specification coordinate system as its subclass needs to fill in details according to specific scenarios. For example, in cosmological research, Subclasses of the (FLRW) reduced coordinate system can inherit from the initial virtual class to implement the "CalculateFLRWMetric()" method for calculating the spacetime metric based on the cosmological constant and matter density parameters, and define the conversion relationship between co-moving coordinates and physical coordinates. This base class design ensures that reduced coordinate systems in different scenarios (such as flat space and closed space models) share a unified interface contract, while supporting their respective physical logic through polymorphism, providing a standardized foundational framework for the subsequent derivation of non-reduced coordinate systems.

[0091] Derivation of unreduced coordinate systems from the reduced coordinate system essentially breaks ideal assumptions and introduces realistic physical factors through mechanisms such as "perturbation superposition" or "constraint relaxation." For example, based on the FLRW reduced coordinate system base class, the PerturbedCosmicCoordinate unreduced subclass can inherit its comoving coordinate framework while adding the perturbation function "AddDensityPerturbation()" to describe density fluctuations and the method "ComputeGravitationalPotential()" to calculate the gravitational potential. In this case, the spacetime metric of the unreduced coordinate system is represented as a superposition of the base class background metric and the perturbation term. The coordinate grid is allowed to be locally distorted by the distribution of matter, and the time coordinate no longer strictly corresponds to the global proper time. This hierarchical modeling approach not only retains the mathematical rigor of the initial theory (by constraining basic physical laws through base classes), but also enables the characterization of non-uniform and dynamic scenarios (such as gravitational perturbations during galaxy formation) through subclass extension, enabling the model to smoothly transition from an idealized, conventional space to a non-conventional space close to actual measurements, providing a hierarchical modeling tool for applications such as cosmological simulations and gravitational wave data analysis.

[0092] Different non-standard coordinate systems can be adapted to meet the requirements of different control scenarios.

[0093] A dual mapping relationship matrix is ​​constructed according to the non-reduced coordinate system of the initial reduced coordinate system, and the dual mapping relationship matrix is ​​updated based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the non-reduced coordinate system and the initial reduced coordinate system.

[0094] A non-reduced coordinate system is a type of coordinate system that does not rely on idealized theoretical assumptions and directly reflects the true state or observational characteristics of a physical system. Unlike the initial reduced coordinate system (such as the uniform and isotropic co-moving coordinate system), it allows for the existence of inhomogeneities, anisotropies or gravitational perturbations in spacetime, and is closer to the complex physical structure of the real world. For example, in a strong gravitational field (such as near a black hole), the non-reduced coordinate system needs to adapt to the severe curvature of spacetime, its coordinate grid no longer follows a uniform distribution, and the time coordinate will also be localized due to differences in gravitational potential; in cosmological perturbation scenarios, it can directly include the spacetime distortion caused by fluctuations in matter density, and the metric is manifested as a superposition of background evolution and local perturbations, rather than stripping off interference terms through mathematical conventions. This type of coordinate system is based on actual observational data or the boundary conditions of a specific problem. It does not pursue theoretical simplification, but is committed to truly depicting the details of physical phenomena.

[0095] In the field of aircraft measurement and control technology, the dual mapping relationship matrix is ​​a mathematical tool used to characterize the dual correlation characteristics between input and output, and between signals and parameters in the measurement and control system. Physical quantities in the measurement and control process (such as angles, distances, speeds, and other measurement values) and target state parameters (such as position, attitude, and trajectory) are bidirectionally mapped and modeled in matrix form, clearly showing the linear or nonlinear conversion relationship between the two. This matrix is ​​often constructed based on the system geometry, signal propagation characteristics, and measurement principles, and can be used to analyze the observation capability, error transfer characteristics, and optimize the measurement layout of the measurement and control system.

[0096] In the field of spacecraft measurement and control technology, a non-standard coordinate system framework (i.e., a non-standard coordinate system) is selected or designed to meet specific measurement and control mission requirements (such as low-Earth orbit tracking, deep space probe navigation, multi-platform collaborative measurement and control, etc.), and a bidirectional mapping matrix model between the measurement signal and the target state parameters in this coordinate system is established. Non-standard coordinate systems are usually customized based on the particularity of the scene, such as a local coordinate system with the measurement and control station as the origin, a body coordinate system that moves with the spacecraft, or an orbital coordinate system defined for specific orbital characteristics. This adaptation process needs to combine the geometric relationships in the scene, the characteristics of the measurement method (such as radar angle measurement / ranging, optical imaging), and the computational efficiency requirements, so that the coordinate axis definition and origin position of the coordinate system are highly consistent with the measurement and control mission, thereby simplifying the subsequent mathematical modeling and data processing process.

[0097] The core of constructing the dual mapping relationship matrix is ​​to establish a mapping bridge between the measurement space and the state space in the non-reduced coordinate system. Specifically, it is necessary to describe the mathematical relationship between the measurement value (such as azimuth, pitch angle, slant range) and the target state parameter (such as three-dimensional position, velocity vector) in the non-reduced coordinate system through coordinate transformation theory (such as rotation matrix, translation vector, homogeneous transformation, etc.), and characterize this two-way conversion relationship in the form of a matrix. For example, in the ground-based radar measurement and control scenario, if the polar coordinate system with the radar station as the origin is used as the non-reduced coordinate system, the measurement values ​​in the polar coordinates (distance r, azimuth θ, pitch angle) need to be converted into the state space of the non-reduced coordinate system. ) is converted to a position vector in a Cartesian coordinate system through a coordinate transformation matrix. Simultaneously, a Jacobian matrix is ​​established from the state parameters (such as Cartesian coordinates x, y, z and their derivatives) to the measured values, forming a dual mapping relationship. This matrix may contain nonlinear terms (such as trigonometric functions) and requires linearization or iterative algorithms for efficient solution.

[0098] Through the flexible design of non-reduced coordinate systems, the limitations of standard coordinate systems in specific scenarios (such as coordinate transformation redundancy and geometric singularities) can be circumvented, allowing the dual mapping relationship to more directly reflect the physical process of measurement and control. For example, in the measurement and control of the re-entry phase of a spacecraft, the use of a body-attached coordinate system to construct a matrix can more accurately describe the relationship between the target attitude angle and the radar scattering signal; in the triangulation of deep space probes, a non-reduced coordinate system based on the line of sight of relay satellites can simplify the solution model of multi-station time difference measurement. In addition, this matrix can also be used to analyze the system observability and error covariance propagation characteristics in the non-reduced coordinate system, providing a theoretical basis for the configuration of measurement and control resources (such as station location and sensor orientation) and the design of filtering algorithms, ultimately improving the accuracy and reliability of spacecraft state estimation.

[0099] The bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system refers to the mutual mapping of coordinate values ​​between the two coordinate systems through a set of certain mathematical transformations. It can not only convert the coordinate quantities in the unreduced coordinate system into the expression form of the initial reduced coordinate system, but also reversely deduce and realize the inverse transformation.

[0100] For example, the mathematical essence of the bidirectional transformation relationship is an isomorphic mapping of the coordinate space, which must satisfy the reversibility and uniqueness of the transformation. In specific implementation, the forward transformation (unreduced -> initial) usually corrects the origin deviation by the translation vector, and then uses the rotation matrix (such as the Euler angle, the direction cosine matrix of the quaternion conversion) to complete the posture alignment of the coordinate axis; the inverse transformation (initial -> unreduced) is the inverse process of the forward transformation, which is achieved by transposing the rotation matrix and reversing the translation vector. For example, when converting the measurement values ​​(distance r, azimuth angle θ, pitch angle φ) in the radar station polar coordinate system (unreduced) to the geocentric fixed coordinate system (initial), it is necessary to first complete the translation through the radar station coordinates (X0, Y0, Z0), and then use the azimuth and pitch angles to construct a rotation matrix, and finally obtain the Cartesian coordinates (X, Y, Z) of the target in the initial coordinate system; conversely, if the coordinates of the target in the initial coordinate system are known, its expression in the radar station polar coordinate system can be solved by inverse rotation and inverse translation. The accuracy of bidirectional transformation directly affects the consistency of measurement and control data and the accuracy of system fusion, and is the key basis for realizing collaborative measurement and control of multiple coordinate systems.

[0101] Based on the updated dual mapping relationship matrix, at least one satellite or spacecraft is connected to the ground station based on the constellation tracking and control link.

[0102] The constellation tracking and control link refers to the communication link system used to track, measure, control, and transmit data to each satellite in the satellite constellation. It is a key infrastructure to ensure the normal operation of the constellation and the completion of various missions.

[0103] For example, constellation tracking and control links primarily include links between ground tracking and control stations and satellites, as well as intersatellite links (ISLs) between satellites. Ground tracking and control stations use radio signals in specific frequency bands, such as the S-band and X-band, to send remote control commands to satellites, enabling control of satellite attitude adjustment, orbit control, payload operations, and other functions. They also receive telemetry data transmitted from satellites, including satellite operating status parameters, environmental parameters, and payload data, to monitor satellite operations in real time. ISLs are communication links established between satellites, employing Ka-band, laser, and other communication methods. These links enable information exchange, data transmission, and collaborative operations between satellites, such as intersatellite ranging, intersatellite communication, and data sharing. This allows the entire constellation to function as an integrated whole, enhancing its autonomy and collaborative capabilities.

[0104] The updating process of the dual mapping relationship matrix is ​​the key link to ensure the dynamic matching of the matrix model with the actual measurement and control scenario. Its core is to correct the matrix according to real-time measurement data, system parameter changes or error feedback.

[0105] For example, the update processing of the dual mapping relationship matrix can be realized based on real-time measurement data. When the measurement and control system obtains new measurement data (such as new radar angle / range measurement values, optical image feature point coordinates), the matrix parameters can be iteratively corrected through the least squares method or Kalman filtering algorithm.

[0106] A ground station is the core terrestrial facility of aerospace measurement, control, and communication systems. It refers to a dedicated location or combination of equipment located on Earth's surface for tracking, measuring, controlling, and exchanging data with spacecraft (such as satellites, spacecraft, and probes). It is typically equipped with a highly sensitive antenna system (such as a parabolic antenna), radio frequency transceiver equipment (responsible for signal modulation, demodulation, and power amplification), a data processing system (for telemetry data decoding, telecontrol command encoding, and orbit calculation), and communication network equipment (for collaborative operation with other ground stations or measurement and control centers). Ground stations establish a communication link with spacecraft via radio waves and perform several critical tasks: They receive telemetry data (such as equipment status, environmental parameters, and scientific exploration data) transmitted by spacecraft for real-time monitoring of their operational status; they also send telecontrol commands to spacecraft for tasks such as orbit adjustment, attitude control, and payload operations. Furthermore, they can determine the spacecraft's position and motion parameters through ranging and velocity measurements. According to mission requirements, ground stations can be divided into fixed (such as deep space tracking and control stations), mobile (such as vehicle-mounted and ship-mounted stations) and portable types. Their global or regional layout is the basis for ensuring the full life cycle management of spacecraft.

[0107] At least one satellite or spacecraft refers to a man-made aircraft that performs specific missions in outer space beyond the atmosphere and is the core vehicle for human space activities. Satellites are the most common type, typically orbiting the Earth or other celestial bodies. They can be categorized by purpose as scientific satellites (such as the Insight-HXMT satellite for astronomical observation), application satellites (such as communications satellites, navigation satellites, and meteorological satellites), and technology test satellites (used to verify new technologies). For example, communications satellites relay radio signals to enable global communications, while navigation satellites provide positioning and navigation services to users on the ground, in the air, and at sea through multi-satellite networks. Spacecraft are a broader category, encompassing not only satellites but also manned spacecraft (such as the Shenzhou spacecraft), space stations (such as the Chinese space station), and probes (such as the Tianwen-1 Mars rover). They are typically equipped with propulsion systems (for orbital maneuvers), attitude control systems (for maintaining flight direction), power systems (such as solar panels), payload systems (equipment that performs specific tasks, such as remote sensing cameras and particle detectors), and communication systems (for interacting with ground stations or other spacecraft). The design of spacecraft needs to adapt to the extreme space environment (such as high vacuum, strong radiation, and drastic temperature differences), and with the support of ground measurement and control systems, complete the entire process from launch into orbit, on-orbit operation to mission completion. It is an important tool for human beings to explore the universe and develop space resources.

[0108] In an optional embodiment of the present invention, constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system may specifically include the following steps:

[0109] S1011. Determine a combination matrix based on a set of discrete points corresponding to at least one satellite or spacecraft in an orthogonal vector coordinate system; the combination matrix is ​​used to represent a combination of multiple space resources corresponding to the time domain, the frequency domain, and the code domain;

[0110] S1012. Construct a high-dimensional discrete space based on the combination matrix.

[0111] A combination matrix is ​​determined based on a set of discrete points corresponding to at least one satellite or spacecraft in an orthogonal vector coordinate system; the combination matrix is ​​used to represent the combination of multiple space resources corresponding to the time domain, frequency domain, and code domain.

[0112] A discrete point set is a digital representation of a spacecraft's spatial motion. These discrete points not only contain position information but can also be used to derive other key parameters (such as orbital radius, flight direction, acceleration, etc.) through vector operations. For example, the coordinate difference between adjacent discrete points can be used to calculate the spacecraft's average velocity, and orbital trends can be extrapolated by fitting multiple sets of discrete points. In space tracking and control, this type of discrete point set is the foundation for orbit determination and prediction. Ground stations acquire discrete observation data from spacecraft through radar or optical observations, fit orbital parameters (such as Kepler orbital elements) using algorithms such as least squares, and then predict their future positions using mechanical models. Furthermore, in spacecraft collaborative missions (such as satellite constellation networking), multi-target discrete point sets can be used to analyze the stability of formation configurations or design efficient communication and collaboration strategies by optimizing the distribution of discrete points. The precision and sampling density of the discrete point set directly impact the accuracy of spacecraft state estimation and are the key link between theoretical orbital models and actual engineering observations.

[0113] The combination matrix is ​​used to represent the combination of multiple spatial resources corresponding to the time domain, frequency domain and code domain.

[0114] Construct high-dimensional discrete space based on combination matrix.

[0115] For example, in traditional TT&C link multiple access design, the scatter set method is mainly used. If a combination matrix is ​​used to describe (0: non-orthogonal; 1: orthogonal), there are a total of 8 combinations, as shown in Table 1.

[0116] Table 1

[0117]

[0118] To further enhance the multi-access capacity of the measurement and control link, this invention expands from a collection of scattered points to a multidimensional discrete space, coupling and analyzing different variables to fully exploit the available discrete space of multidimensional joint variables. Without loss of generality, using three-dimensional coordinates as an example, the following coordinate system can be used after normalization. The computational complexity of continuous variable space is enormous and incompatible with discrete gear shifting designs in engineering.

[0119] In an optional embodiment of the present invention, constructing an unreduced coordinate system adapted to the control scenario requirements on the high-dimensional joint discrete vector space with the initial reduced coordinate system as a reference may specifically include the following steps:

[0120] S1021. Determine, in the high-dimensional joint discrete vector space, a three-dimensional space under the first constraint condition according to a combination matrix; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain;

[0121] S1022. In three-dimensional space, based on the principle of forward derivation and taking the initial specification coordinate system as the benchmark, determine the control scenario requirements;

[0122] S1023. Construct a non-standardized coordinate system that is compatible with the control scenario requirements based on the control scenario requirements.

[0123] In the high-dimensional joint discrete vector space, a three-dimensional space under the first constraint condition is determined according to a combination matrix; the combination matrix is ​​used to represent the combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain.

[0124] The three-dimensional space under the first constraint condition can be used to expand the original seven multiple access schemes (the other seven vertices of the cube except the origin O(0, 0, 0) in the figure) into a constrained multiple access scheme under the condition of three-dimensional discrete variables.

[0125] Assume that the multiple access scheme is a three-dimensional vector Then the constraints are

[0126] It is thus obtained that the feasible solution of the constrained multiple access scheme is the entire cubic space outside (including) the cone surface in the figure.

[0127] Reference Figure 2 , shows a schematic diagram of a three-dimensional discrete variable reduction coordinate system of the present invention. As shown in the figure, the XYZ coordinate system represents X space (time domain), Y frequency (frequency domain), and Z codeword (code domain).

[0128] In three-dimensional space, based on the principle of forward derivation and taking the initial specification coordinate system as the benchmark, the control scenario requirements are determined.

[0129] The principle of forward derivation is widely used in scientific research, engineering technology, data modeling, and other fields. In theoretical research, it can be used to construct the logical framework of a discipline—for example, in physics, the complete theoretical system of classical mechanics was derived from Newton's three laws of motion. In the data field, it manifests itself as starting from raw data and generating derived indicators or predictive models through forward processing processes such as statistical analysis and algorithmic calculations (for example, deriving a consumer preference index from user behavior data).

[0130] For example, the principle of forward derivation is a methodology for forward deduction and expansion based on the original properties or initial conditions of things through logical reasoning, causal relationships or mathematical rules. Its core idea is to start from known basic elements (such as axioms, theorems, initial data, etc.), and gradually derive new conclusions, states or structures according to established rules or laws. For example, in the field of mathematics, starting from basic axioms and definitions, proving new theorems through deductive reasoning is a typical application of forward derivation; in engineering design, based on user needs and technical specifications, gradually refining from conceptual design to detailed structural drawings is also a manifestation of the principle of forward derivation. This principle emphasizes the directionality and logic of the deduction process, and requires that each step of derivation be based on clear premises and rules to avoid subjective conjecture or leaping inferences.

[0131] The control scenario requirements may include scenario requirements corresponding to various large-scale constellation control tasks, which may include: pre-relay return link, or ground-based full-airspace multi-beam, or ground-based joint measurement and control, etc.

[0132] Based on the requirements of the control scenario, a non-standard coordinate system is constructed to adapt to the requirements of the control scenario.

[0133] For example, taking large-scale constellation control tasks as an example, the ground-to-space interface indicators of each batch of satellites in the same cluster are basically the same (same code, fixed bandwidth, fine-tunable frequency, closed-loop control based on the angle between ground beams), and the ground station uses full-space multi-beam technology, with different beams pointing to different satellites in the cluster. Under this condition, Figure 1 In the three-dimensional coordinate system shown, z = 0. Feasible solutions are located in all squares outside (and including) the blue curve in the XY plane. The boundary feasible solution lies on the blue curve. After satellites enter orbit, as the inter-satellite distance increases and the inter-beam angle continues to increase, the value of x approaches 1 and the value of y approaches 0, and the area where the frequency bands between satellites can overlap continues to increase.

[0134] The present invention designs a high-dimensional discrete space construction method based on the forward derivation principle, taking the initial reduced coordinate system as the virtual class, and gradually deriving the adapted non-reduced coordinate system in combination with the given measurement and control application scenario. Figure 3 , showing a flow chart of a high-dimensional discrete space construction method based on the forward derivation principle of the present invention.

[0135] 1. Scenario 1: Long-term control of the space station complex

[0136] The space station complex consists of three main modules: the Tianhe core module, the Wentian laboratory module, and the Mengtian laboratory module, as well as on-orbit rendezvous and docking vehicles such as the Shenzhou manned spacecraft and the Tianzhou cargo spacecraft. Each module has its own measurement and control link access application scenario. Because the distances between modules do not exceed a few hundred meters, from the perspective of ground stations or relay satellites, these modules can be viewed as a single point in space, making them indistinguishable using spatial division multiple access.

[0137] In the case of multiple cabins sharing a common orbit, the present invention slices the initial protocol coordinate system (virtual class) with the spatial X-axis as the normal direction, constructs an O-YZ protocol coordinate system (base class 1) adapted to the long-term control mission of the space station assembly, and then constructs a non-protocol coordinate system cluster in combination with specific application scenarios, such as the non-protocol coordinate system for the return link before relay (derivative class 1-1), and adopts two-dimensional discrete space (frequency division + code division) to realize multiple access to the multi-cabin measurement and control link.

[0138] Scenario 2: Large-scale low-orbit constellation management and control

[0139] With the emergence of various constellation systems, the number of satellites in orbit has increased sharply. The number of satellites visible at the same time above the same tracking and control station will reach dozens or even hundreds, posing unprecedented challenges to the multi-target parallel tracking and control capabilities of the tracking and control equipment.

[0140] In the case that space division, frequency division and code division resources are limited, considering that there is a certain angle between satellite nodes of different constellation systems in the field of view of the measurement and control equipment, the present invention constructs an O-XYZ protocol coordinate system (base class 2) adapted to the large-scale low-orbit constellation control scenario based on the initial protocol coordinate system (virtual class), such as the ground-based full-space multi-beam non-reduced coordinate system (derivative class 2-1), and adopts three-dimensional discrete space (space division + frequency division + code division) to realize multi-satellite measurement and control link multiple access.

[0141] Scenario 3: Tracking and Control of Multiple Satellites into Orbit with One Launch

[0142] With the continued rise of commercial spaceflight, a number of commercial satellite companies have emerged in China, driving increasing demand for launch capacity. Launch vehicles often employ a multi-satellite launch strategy, carrying multiple satellites into orbit. Due to the limited number of available codewords or regulatory constraints, and the fact that satellites from the same batch often orbit in coplanar or non-coplanar orbits with significant spatial separation, these satellites may be assigned the same code group, making them indistinguishable using code division multiple access (CDMA).

[0143] In the case of multiple satellites with the same code, the present invention slices the initial standardized coordinate system (virtual class) with the codeword Z axis as the normal direction, constructs an O-XY standardized coordinate system (base class 3) adapted to the measurement and control mission of multiple satellites into orbit with one rocket, and then constructs a non-standard coordinate system cluster based on specific application scenarios, such as the non-standard coordinate system for joint ground-to-space measurement and control (derivative class 3-1), and adopts two-dimensional discrete space (space division + frequency division) to realize multiple access to the measurement and control link of the orbit segment.

[0144] In an optional embodiment of the present invention, constructing a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements may specifically include the following steps:

[0145] S10231. When the control scenario is long-term control of the space station complex, slice the initial reduced coordinate system with the time domain X-axis as the normal direction to construct an O-YZ reduced coordinate system that is compatible with the long-term control mission of the space station complex; the O-YZ reduced coordinate system is used to represent the two-dimensional discrete space composed of the frequency domain and the code domain.

[0146] S10232. Based on the O-YZ standard coordinate system, construct a non-standard coordinate system that is compatible with the long-term control requirements of the space station complex.

[0147] Among them, the long-term management and control of the space station complex refers to the continuous and systematic management and control of the entire space station composed of multiple modules and spacecraft, covering multiple aspects from the system operation of the space station, resource allocation to the life and work arrangements of the astronauts. In terms of system operation, it is necessary to ensure the stable operation of various systems such as energy, thermal control, and information. For example, the use of energy after the three modules are connected to the grid should be reasonably allocated, and the heat dissipation capacity should be allocated according to the needs of different modules to ensure the accuracy and timeliness of information transmission. For resource allocation, it is necessary to optimize and safeguard limited space, equipment and supplies on orbit, such as the reasonable allocation of sleeping areas, kitchens, and sanitary areas for astronauts. At the same time, it is also necessary to manage and coordinate the work plans of the astronauts, coordinate the task arrangements of different crews, avoid work conflicts, and ensure the orderly handover of work between crews.

[0148] In the initial reduced coordinate system (such as a three-dimensional Cartesian coordinate system), "taking the time domain X-axis as the normal" means defining the time dimension (X-axis) as the normal direction of the slice plane, that is, the slice plane is perpendicular to the X-axis. In this case, each slice corresponds to a fixed value on the X-axis (such as time point t = t0), and the coordinates within the slice plane are composed of other dimensions (such as the Y and Z axes). For example, if the initial coordinate system is a four-dimensional space-time coordinate system (X is time, Y, Z, and W are spatial dimensions), the slice with the X-axis as the normal direction is the three-dimensional space section at a fixed time point (YZW space at t = t0). This treatment converts the dynamic problem into a static cross-section analysis by "freezing" the time domain variables, making it easier to study the spatial distribution or state characteristics of the system at a specific moment.

[0149] The core purpose of normal slicing of the initial reduced coordinate system is to separate the variables in the time domain and the space domain, and to achieve dimensionality reduction analysis of multidimensional data. For example, in signal processing, if the X-axis represents time, the Y-axis represents signal amplitude, and the Z-axis represents frequency, then slicing can extract the signal spectrum at a certain moment (YZ plane) for analyzing transient frequency characteristics; in fluid mechanics simulations, slicing can display the velocity distribution of the flow field at a certain moment (such as the vector field in the YZ plane), assisting in the observation of transient structures such as vortices and shock waves. In addition, through continuous slicing (such as obtaining multiple X-axis slices in time series), the evolution of the system over time can also be reconstructed, similar to the relationship between a single frame and continuous playback of a movie film. This method is widely used in fields such as radar echo analysis, medical imaging (such as time series slicing of CT scans), and aerospace dynamics orbital status monitoring. It simplifies the analysis difficulty of complex systems by "dividing time and governing".

[0150] The space station complex consists of three main modules: the Tianhe core module, the Wentian laboratory module, and the Mengtian laboratory module, as well as on-orbit rendezvous and docking vehicles such as the Shenzhou manned spacecraft and the Tianzhou cargo spacecraft. Each module has its own measurement and control link access application scenario. Because the distances between modules do not exceed a few hundred meters, from the perspective of ground stations or relay satellites, these modules can be viewed as a single point in space, making them indistinguishable using spatial division multiple access.

[0151] In the case of multiple cabins sharing a common orbit, the present invention slices the initial protocol coordinate system (virtual class) with the spatial X-axis as the normal direction, constructs an O-YZ protocol coordinate system (base class 1) adapted to the long-term control mission of the space station assembly, and then constructs a non-protocol coordinate system cluster in combination with specific application scenarios, such as the non-protocol coordinate system for the return link before relay (derivative class 1-1), and adopts two-dimensional discrete space (frequency division + code division) to realize multiple access to the multi-cabin measurement and control link.

[0152] In an optional embodiment of the present invention, constructing a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements may specifically include the following steps:

[0153] S10233. When the control scenario is large-scale low-orbit constellation control, construct an O-XYZ reduced coordinate system adapted to the large-scale low-orbit constellation control scenario; the O-XYZ reduced coordinate system is used to represent a three-dimensional discrete space consisting of a time domain, a frequency domain, and a code domain;

[0154] S10234. Based on the O-XYZ standard coordinate system, construct a non-standard coordinate system that is compatible with the control requirements of large-scale low-orbit constellations.

[0155] With the emergence of various constellation systems, the number of satellites in orbit has increased sharply. The number of satellites visible at the same time above the same tracking and control station will reach dozens or even hundreds, posing unprecedented challenges to the multi-target parallel tracking and control capabilities of the tracking and control equipment.

[0156] In the case that space division, frequency division and code division resources are limited, considering that there is a certain angle between satellite nodes of different constellation systems in the field of view of the measurement and control equipment, the present invention constructs an O-XYZ protocol coordinate system (base class 2) adapted to the large-scale low-orbit constellation control scenario based on the initial protocol coordinate system (virtual class), such as the ground-based full-space multi-beam non-reduced coordinate system (derivative class 2-1), and adopts three-dimensional discrete space (space division + frequency division + code division) to realize multi-satellite measurement and control link multiple access.

[0157] In an optional embodiment of the present invention, constructing a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements may specifically include the following steps:

[0158] S10235. When the control scenario is the measurement and control of multiple satellites into orbit on a single rocket, slice the initial reduced coordinate system with the Z axis of the code domain as the normal direction to construct an O-XY reduced coordinate system suitable for the measurement and control mission of the multiple satellites into orbit on a single rocket; the O-XY reduced coordinate system is used to represent the two-dimensional discrete space composed of the time domain and the frequency domain.

[0159] S10236. Based on the O-XY standard coordinate system, construct a non-standard coordinate system that is compatible with the measurement and control requirements of the multi-satellite-in-orbit launch phase.

[0160] With the continued rise of commercial spaceflight, a number of commercial satellite companies have emerged in China, driving increasing demand for launch capacity. Launch vehicles often employ a multi-satellite launch strategy, carrying multiple satellites into orbit. Due to the limited number of available codewords or regulatory constraints, and the fact that satellites from the same batch often orbit in coplanar or non-coplanar orbits with significant spatial separation, these satellites may be assigned the same code group, making them indistinguishable using code division multiple access (CDMA).

[0161] In the case of multiple satellites with the same code, the present invention slices the initial standardized coordinate system (virtual class) with the codeword Z axis as the normal direction, constructs an O-XY standardized coordinate system (base class 3) adapted to the measurement and control mission of multiple satellites into orbit with one rocket, and then constructs a non-standard coordinate system cluster based on specific application scenarios, such as the non-standard coordinate system for joint ground-to-space measurement and control (derivative class 3-1), and adopts two-dimensional discrete space (space division + frequency division) to realize multiple access to the measurement and control link of the orbit segment.

[0162] In an optional embodiment of the present invention, constructing a dual mapping relationship matrix based on the unreduced coordinate system of the initial reduced coordinate system and updating the dual mapping relationship matrix based on measured data may specifically include the following steps:

[0163] S1031. Perform dimensionality reduction processing on the non-reduced coordinate system according to the prior information corresponding to the non-reduced coordinate system and the task;

[0164] S1032. Determine a non-conventional threshold boundary cone surface without link interference based on a Monte Carlo simulation of finite element analysis or an actual link test;

[0165] S1033, mapping the non-reduced coordinate system to the reduced coordinate system;

[0166] S1034. Determine a reduced coordinate system and a dual mapping relationship matrix suitable for the current task;

[0167] S1035. Utilize statistical learning methods and measured data to continuously iteratively update the dual mapping relationship matrix.

[0168] Based on the construction method of high-dimensional discrete space, an initial reduced coordinate system and derived non-reduced coordinate systems at each level adapted to specific application scenarios are formed. Furthermore, based on the dual mapping principle, a high-dimensional discrete space evolution strategy constructs a dual mapping relationship matrix for the non-reduced coordinate system adapted to a given measurement and control application scenario. This dual mapping relationship matrix is ​​continuously iteratively updated through statistical learning of measured data.

[0169] The mapping relationship matrix is ​​related to the space-ground interface indicators of each space mission. It is necessary to construct the dual space of the three-dimensional discrete variable specification coordinate system to solve the actual engineering problem. The specific process is as follows:

[0170] Step 1: Construct a three-dimensional discrete variable unreduced coordinate system, with each dimension measured using physical dimensions. Dimensionality reduction can be performed on the coordinate system based on prior engineering information.

[0171] Step 2: Explore the non-standardized threshold boundary cone with no link interference through Monte Carlo simulation based on finite element analysis or actual link testing.

[0172] Step 3: Map the three-dimensional discrete variable non-reduced coordinate system to the reduced coordinate system. Each dimension is dimensionless and has a value range of . The mapping constraint is that the modulus of each point on the reduced threshold boundary cone is 1.

[0173] Step 4: Iterative evolution: select the reduced coordinate system and dual mapping relationship matrix that best suits the current task, combine actual link data and performance evaluation results, and use statistical learning methods to continuously iteratively update the dual mapping relationship matrix.

[0174] For example, the constellation tracking link multiple access example is as follows, referring to Figure 4 , shows an example diagram of multiple access to a constellation tracking and control link of the present invention, and an example diagram of multiple access to a constellation tracking and control link is shown in FIG. Figure 4As shown in the figure, combined with the high-dimensional discrete space derivative framework, it is necessary to adopt a ground-based full-space multi-beam non-reduced coordinate system (derivative type 2-1) and use three-dimensional discrete space (space division (time division) + frequency division + code division) to achieve multi-satellite tracking and control link multiple access, where:

[0175] 1) Satellite 1 and satellite 2 cannot be distinguished through space division multiple access. Since the signal from satellite 1 may be much stronger than the reception threshold of satellite 2, it is necessary to introduce frequency division multiple access in a two-dimensional discrete space (pseudo-code + space).

[0176] 2) Satellite 1 and Satellite 3 can be distinguished through spatial division multiple access;

[0177] 3) Satellite 2 and Satellite 3 can be distinguished by space division multiple access.

[0178] The present invention belongs to the field of aircraft measurement and control, and mainly includes the following: First, a high-dimensional joint discrete vector space is constructed based on orthogonal vectors such as space, frequency, and pseudocode, which realizes the effective expansion of the measurement and control link multiple access technology from a scattered point set to a multi-dimensional discrete space; second, a high-dimensional discrete space construction method based on the forward derivation principle is designed, with the original reduced coordinate system as the virtual class, and the adaptive non-reduced coordinate system is gradually derived in combination with a given measurement and control application scenario; third, a high-dimensional discrete space evolution strategy based on the dual mapping principle is designed, and the dual mapping relationship matrix is ​​constructed for the adaptive non-reduced coordinate system of a given measurement and control application scenario, and the dual mapping relationship matrix is ​​continuously iterated and updated through statistical learning of measured data. At the same time, the present invention also designs a constellation measurement and control link multiple access system based on a three-dimensional discrete space in combination with a large-scale constellation control application scenario example, and evaluates the multiple access strategy. The present invention realizes the effective expansion of the measurement and control link multiple access technology, and improves the efficiency of the measurement and control link multiple access based on the available discrete space of the multi-dimensional joint variable.

[0179] In space tracking and control, ground stations need to communicate with multiple satellites or spacecraft simultaneously, making time division multiple access (TDMA) impractical. Current space tracking and control links typically employ three types of multiple access technologies: space division, frequency division, or code division (CDG) to achieve simultaneous tracking and control of multiple spacecraft. Space Division Multiple Access (SDMA) leverages the spatial dimension to distinguish different users or signals, meaning different spacecraft are located in different antenna beams. Frequency Division Multiple Access (FDMA) divides the available spectrum into multiple non-overlapping sub-bands, each assigned to a different user or device, effectively allocating different frequency bands to different spacecraft. Code Division Multiple Access (CDMA) uses different pseudo-random codes (PN codes) to distinguish different users or devices, effectively assigning different PN codes to different spacecraft.

[0180] One objective of the present invention is to construct a high-dimensional joint discrete vector space based on orthogonal vectors such as space, frequency, and pseudocode, thereby effectively extending measurement and control link multiple access technology from a scattered set of points to a multidimensional discrete space. The orthogonal vectors in the high-dimensional joint discrete vector space include, but are not limited to, space, frequency, pseudocode, and time.

[0181] Furthermore, in conjunction with a given multi-target measurement and control application scenario, the second purpose of the present invention is to design a high-dimensional discrete space construction method based on the forward derivation principle, using the original reduced coordinate system as a virtual class to construct a reduced coordinate system adapted to the specific application scenario, and using this as a base class to derive an adapted non-reduced coordinate system. Multi-target measurement and control application scenarios include, but are not limited to, large-scale constellation control and on-orbit operation and control of space station complexes. Application scenarios include, but are not limited to, large-scale low-orbit constellation control, long-term control of space station complexes, and measurement and control of multiple satellites into orbit with one rocket.

[0182] Furthermore, a third objective of the present invention is to design a high-dimensional discrete space evolution strategy based on the dual mapping principle. This strategy constructs a dual mapping relationship matrix for a given measurement and control application scenario using an adaptive, unreduced coordinate system. This matrix is ​​then continuously and iteratively updated through statistical learning from measured data. Measured data includes, but is not limited to, mission data obtained through actual mission links, such as equipment release, wireless joint testing, and on-orbit management. Statistical learning methods include, but are not limited to, manual interpretation, expert systems, and machine learning.

[0183] Based on a large-scale constellation control application scenario, this paper designs a constellation tracking and control link multiple access system based on three-dimensional discrete space and evaluates the multiple access strategy. Discrete spaces include, but are not limited to, one-dimensional, two-dimensional, and three-dimensional, and coordinate systems include, but are not limited to, "space," "frequency," "pseudocode," "space-frequency," "space-pseudocode," "frequency-pseudocode," and "space-frequency-pseudocode."

[0184] The present invention can support the effective expansion of measurement and control link multiple access technology from a low-dimensional scattered point set to a high-dimensional discrete space, and can be extended to fields such as space-based measurement and control, providing a solution for efficient measurement and control of massive space targets.

[0185] The following joint simulation analysis is conducted on the interference signal power (spatial domain) and signal frequency interval (frequency domain) under the same code group to study the relationship between the interference signal power and the signal frequency interval, providing support for the formulation of high-dimensional discrete space strategies.

[0186] 1. Simulation conditions

[0187] Build a simulation environment. The simulation conditions are as follows:

[0188] (1) Using the Bernoulli binary generator as the original data source, the Gold sequence generator is used to generate the task spread spectrum signal. The data rate is set to 48 kbps, the spread spectrum code is set to 1023 long balanced Gold code, and the pseudo code rate is set to 10.23 MHz.

[0189] (2) The spread spectrum signal is added with Gaussian white noise (AWGN) through the additive white Gaussian noise (AWGN) channel simulation module to simulate various signal-to-noise ratios;

[0190] (3) Use another Bernoulli binary generator and Gold sequence generator to generate interference spread spectrum signal, the data rate is set to 48kbps, the spread spectrum code is set to 1023 long balanced Gold code, and the pseudo code rate is set to 10.23MHz;

[0191] (4) The interference spread spectrum signal is mixed with the carrier of the sine wave generator to simulate different frequency intervals;

[0192] (5) The generated interference signal is power-converted through a gain module to simulate different interference signal powers;

[0193] (6) After the task spread spectrum signal and the interference spread spectrum signal are superimposed, the demodulated data is restored through despreading and demodulation, and is sent to the bit error rate statistics module together with the original data for bit error rate statistics.

[0194] 2. Simulation results

[0195] Based on the above simulation conditions, simulation analysis was carried out in combination with different application scenarios.

[0196] (1) Same frequency, different interference-to-signal ratio

[0197] Under the conditions of the same frequency and different interference-to-signal ratio, that is, the two-dimensional discrete coordinate system (pseudo code + space), the multiple access interference simulation results are as follows Figure 5 The figure shows the simulation result of bit error rate of the same frequency with different interference signal ratios of the present invention. Table 2 shows the comparison data of the simulation result of bit error rate of the same frequency with different interference signal ratios.

[0198] Table 2 Simulation results of bit error rate with different interference-to-signal ratios at the same frequency

[0199] Interference-to-signal ratio (dB) ≤18 19 20 21 22 Bit Error Rate 0 1.35E-05 2.11E-04 0.0024 0.1888

[0200] The simulation results above show that when the interference-to-signal ratio (ISR) is below 18dB, co-channel MAI has no impact on the received bit error rate (BER). However, as the ISR increases, the BER deteriorates dramatically. Given that the simulations do not account for tracking errors in the receiver's carrier, pseudo-code, and data loops, the actual MAI mitigation capability deteriorates further.

[0201] (2) Different frequencies and different interference-to-signal ratios

[0202] The following simulation shows how frequency offset improves bit error rate performance under different interference-to-signal ratios, using a three-dimensional discrete coordinate system (pseudocode + space + frequency). The multiple access interference simulation results are shown below.

[0203] a. When the interference-to-signal ratio is 30dB, the bit error rates corresponding to different frequency offsets are as follows Figure 6 The figure shows the simulation result of bit error rate at different frequency offsets when the interference-to-signal ratio is 30dB. Table 3 shows the comparison data of the simulation result of bit error rate at different frequency offsets when the interference-to-signal ratio is 30dB.

[0204] Table 3 Simulation results of bit error rate at different frequency offsets when the interference-to-signal ratio is 30dB

[0205]

[0206] b. When the interference-to-signal ratio is 25dB, the bit error rates corresponding to different frequency offsets are as follows Figure 7 The figure shows the simulation results of bit error rate at different frequency offsets when the interference-to-signal ratio is 25dB. Table 4 shows the comparison data of the simulation results of bit error rate at different frequency offsets when the interference-to-signal ratio is 25dB.

[0207] Table 4 Simulation results of bit error rate at different frequency offsets when the interference-to-signal ratio is 25dB

[0208]

[0209] c. When the interference-to-signal ratio is 20 dB, the bit error rates corresponding to different frequency offsets are shown in Table 5. Table 5 shows the comparison data of the simulation results of the bit error rates of different frequency offsets when the interference-to-signal ratio is 20 dB.

[0210] Table 5 Simulation results of bit error rate at different frequency offsets when the interference-to-signal ratio is 20dB

[0211]

[0212] From the above simulation results, we can see that:

[0213] 1) Introducing a third dimension, frequency offset (frequency division), in the two-dimensional discrete space (pseudo-code + space) significantly improves multiple access capacity, remedying the problem that the previous "pseudo-code + space" two-dimensional discrete space multiple access system could not operate with an interference-to-signal ratio above 18dB;

[0214] 2) As the interference-to-signal ratio increases (the effectiveness of the second dimension of spatial division decreases), the frequency offset required to achieve error-free bit detection also increases accordingly (increasing the need for the newly introduced third dimension of frequency division). Specifically, when the interference-to-signal ratio is 20dB, only a 1MHz offset is required. When the interference-to-signal ratio is 25dB, the offset is reduced to 6MHz. When the interference-to-signal ratio is 30dB, at least a 10MHz offset is required.

[0215] In summary, an embodiment of the present invention provides a method for multiple access of a measurement and control link based on a high-dimensional discrete space, the method comprising: constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain; in the high-dimensional discrete space, based on the initial reduced coordinate system, constructing an unreduced coordinate system adapted to the control scenario requirements; the initial reduced coordinate system is a standardized virtual base class coordinate system; the unreduced coordinate system is a coordinate system that matches the initial reduced coordinate system; constructing a dual mapping relationship matrix based on the unreduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system; based on the updated dual mapping relationship matrix, at least one satellite or spacecraft is connected to a ground station based on the constellation measurement and control link, thereby realizing the effective expansion of the measurement and control link multiple access technology in tasks such as large-scale constellation control and on-orbit operation and control of space station assemblies, and improving the efficiency of the measurement and control link multiple access based on the available discrete space of multi-dimensional joint variables.

[0216] It should be noted that for the sake of simplicity, the method embodiments are described as a series of actions. However, those skilled in the art should be aware that the embodiments of the present invention are not limited by the order of the actions described, because according to the embodiments of the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all preferred embodiments, and the actions involved are not necessarily required for the embodiments of the present invention.

[0217] Device embodiment

[0218] Reference Figure 8 , shows a structural block diagram of a multi-access device for measurement and control links based on high-dimensional discrete space of the present invention, the device specifically may include:

[0219] A construction module 501 is configured to construct a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain;

[0220] A construction module 502 is configured to construct, in the high-dimensional discrete space, an unreduced coordinate system adapted to the control scenario requirements based on the initial reduced coordinate system; the initial reduced coordinate system is a standardized virtual base class coordinate system; the unreduced coordinate system is a non-standardized coordinate system that matches the initial reduced coordinate system; and a dual mapping relationship matrix is ​​constructed based on the unreduced coordinate system of the initial reduced coordinate system.

[0221] An updating module 503 is configured to update the dual mapping relationship matrix based on the measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system;

[0222] The access module 504 is configured to access at least one satellite or spacecraft to the ground station based on the updated dual mapping relationship matrix and the constellation tracking and control link.

[0223] Optionally, the building block includes:

[0224] a determination module, configured to determine a combination matrix based on a set of discrete points corresponding to at least one satellite or spacecraft in the orthogonal vector coordinate system; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain;

[0225] A construction submodule is used to construct a high-dimensional discrete space according to the combination matrix.

[0226] Optionally, the construction module includes:

[0227] A first determination submodule is configured to determine a three-dimensional space under a first constraint condition in the high-dimensional discrete space based on a combination matrix; the combination matrix is ​​configured to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain; and in the three-dimensional space, based on a forward derivation principle and with an initial reduced coordinate system as a reference, determine control scenario requirements;

[0228] The first construction submodule is used to construct a non-reduced coordinate system adapted to the control scenario requirements based on the control scenario requirements.

[0229] Optionally, the construction module further includes:

[0230] The first slicing module is used to slice the initial reduced coordinate system with the time domain X-axis as the normal direction when the control scenario is long-term control of the space station assembly;

[0231] The second construction submodule is used to construct an O-YZ protocol coordinate system that is compatible with the long-term control mission of the space station assembly; the O-YZ protocol coordinate system is used to represent the two-dimensional discrete space composed of the frequency domain and the code domain; based on the O-YZ protocol coordinate system, a non-reduced coordinate system that is compatible with the long-term control requirements of the space station assembly is constructed.

[0232] Optionally, the construction module further includes:

[0233] The third construction submodule is configured to construct an O-XYZ reduced coordinate system compatible with the large-scale LEO constellation control scenario, when the control scenario is large-scale LEO constellation control. The O-XYZ reduced coordinate system is used to represent the three-dimensional discrete space composed of the time domain, frequency domain, and code domain. Based on the O-XYZ reduced coordinate system, an unreduced coordinate system compatible with the requirements of large-scale LEO constellation control is constructed.

[0234] Optionally, the construction module further includes:

[0235] The second slicing module is configured to slice the initial reduced coordinate system with the code domain Z axis as the normal direction when the control scenario is the measurement and control of multiple satellites into orbit with one rocket;

[0236] The third construction submodule is used to construct an O-XY reduced coordinate system that is compatible with the measurement and control mission of the multi-satellite launch into orbit phase; the O-XY reduced coordinate system is used to represent the two-dimensional discrete space composed of the time domain and the frequency domain; based on the O-XY reduced coordinate system, a non-reduced coordinate system that is compatible with the measurement and control requirements of the multi-satellite launch into orbit phase is constructed.

[0237] Optionally, the update module includes:

[0238] A dimensionality reduction module, configured to perform dimensionality reduction processing on the non-reduced coordinate system according to the prior information corresponding to the non-reduced coordinate system and the task;

[0239] A second determination submodule is configured to determine a non-standardized threshold boundary cone surface without link interference based on a Monte Carlo simulation of finite element analysis or an actual link test;

[0240] A mapping module, configured to map the non-reduced coordinate system into a reduced coordinate system;

[0241] The second determination submodule is further used to determine a reduced coordinate system and a dual mapping relationship matrix adapted to the current task;

[0242] The updating submodule is used to continuously iteratively update the dual mapping relationship matrix using statistical learning methods and measured data.

[0243] In summary, an embodiment of the present invention provides a multi-access device for a measurement and control link based on a high-dimensional discrete space. The multi-access device for a measurement and control link based on a high-dimensional discrete space includes: a construction module for constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain; a construction module for constructing a non-reduced coordinate system adapted to the control scenario requirements on the high-dimensional discrete space with the initial reduced coordinate system as a reference; the initial reduced coordinate system is a standardized virtual base class coordinate system; the non-reduced coordinate system is a coordinate system that matches the initial reduced coordinate system; according to The unreduced coordinate system of the initial reduced coordinate system constructs a dual mapping relationship matrix; the update module is used to update the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system; the access module is used to connect at least one satellite or spacecraft to the ground station based on the constellation measurement and control link based on the updated dual mapping relationship matrix, and then in tasks such as large-scale constellation control and on-orbit operation and control of space station complexes, fully explore the available discrete space of multi-dimensional joint variables, thereby improving the efficiency of multiple access of the measurement and control link based on the high-dimensional discrete space.

[0244] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0245] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0246] Regarding the processor in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method and will not be elaborated here.

[0247] Reference Figure 9 , is a structural block diagram of an electronic device for multiple access of a measurement and control link based on a high-dimensional discrete space, provided by an embodiment of the present invention. Figure 9 As shown, the electronic device includes: a processor, a memory, a communication interface and a communication bus, and the processor, the memory and the communication interface communicate with each other through the communication bus; the memory is used to store executable instructions, and the executable instructions enable the processor to execute the measurement and control link multiple access method based on high-dimensional discrete space of the aforementioned embodiment.

[0248] The processor may be a CPU, a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable device, a transistor logic device, a hardware component, or any combination thereof. The processor may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, and the like.

[0249] The communication bus may include a path for transmitting information between the memory and the communication interface. The communication bus may be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus. The communication bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9 The fact that only one line is used does not mean that there is only one bus or one type of bus.

[0250] The memory may be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM), a magnetic tape, a floppy disk, an optical data storage device, etc.

[0251] The embodiment of the present invention further provides a non-transitory computer-readable storage medium, which, when the instructions in the storage medium are executed by a processor of an electronic device (server or terminal), enables the processor to execute Figure 1 The multiple access method of measurement and control link based on high-dimensional discrete space is shown.

[0252] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0253] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, apparatus, or computer program products. Thus, embodiments of the present invention may take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0254] The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of the methods, terminal devices (systems) and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing terminal device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0255] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing terminal device to operate in a predictable manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0256] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0257] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they become aware of the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0258] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or terminal device that includes the element.

[0259] The above is a detailed introduction to the measurement and control link multiple access method, device, electronic device and storage medium based on high-dimensional discrete space provided by the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for general technical personnel in this field, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A multiple access method for measurement and control links based on high-dimensional discrete space, characterized in that: The method comprises: Constructing a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain; In the high-dimensional discrete space, based on the initial specification coordinate system, a non-specification coordinate system adapted to the control scenario requirements is constructed; the initial specification coordinate system is a standardized virtual base class coordinate system; the non-specification coordinate system is a non-standardized coordinate system that matches the initial specification coordinate system; Constructing a dual mapping relationship matrix according to the non-reduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the non-reduced coordinate system and the initial reduced coordinate system; Based on the updated dual mapping relationship matrix, at least one satellite or spacecraft is connected to the ground station based on the constellation tracking and control link.

2. The method according to claim 1, characterized in that The construction of a high-dimensional discrete space based on an initial orthogonal vector coordinate system includes: Determining a combination matrix based on a set of discrete points corresponding to at least one satellite or spacecraft in the orthogonal vector coordinate system; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain; A high-dimensional discrete space is constructed according to the combined matrix.

3. The method according to claim 1, characterized in that In the high-dimensional discrete space, based on the initial reduced coordinate system, a non-reduced coordinate system adapted to the control scenario requirements is constructed, including: In the high-dimensional discrete space, a three-dimensional space under a first constraint condition is determined according to a combination matrix; the combination matrix is ​​used to represent a combination of multiple spatial resources corresponding to the time domain, the frequency domain, and the code domain; In the three-dimensional space, based on the principle of forward derivation and taking the initial specification coordinate system as the benchmark, the control scenario requirements are determined; Based on the control scenario requirements, a non-standardized coordinate system adapted to the control scenario requirements is constructed.

4. The method according to claim 1, wherein The constructing of a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements includes: In the case where the control scenario is long-term control of a space station complex, the initial reduced coordinate system is sliced ​​with the time domain X-axis as the normal direction to construct an O-YZ reduced coordinate system adapted to the long-term control mission of the space station complex; the O-YZ reduced coordinate system is used to represent the two-dimensional discrete space composed of the frequency domain and the code domain; Based on the O-YZ standardized coordinate system, a non-standardized coordinate system is constructed that is compatible with the long-term control requirements of the space station assembly.

5. The method according to claim 1, wherein The constructing of a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements includes: When the control scenario is large-scale low-orbit constellation control, constructing an O-XYZ reduced coordinate system adapted to the large-scale low-orbit constellation control scenario; the O-XYZ reduced coordinate system is used to represent a three-dimensional discrete space consisting of a time domain, a frequency domain, and a code domain; Based on the O-XYZ standardized coordinate system, a non-standardized coordinate system adapted to the control requirements of large-scale low-orbit constellations is constructed.

6. The method according to claim 1, characterized in that The constructing of a non-standardized coordinate system adapted to the control scenario requirements based on the control scenario requirements includes: When the control scenario is the measurement and control of multiple satellites into orbit with one rocket, the initial reduced coordinate system is sliced ​​with the Z axis of the code domain as the normal direction to construct an O-XY reduced coordinate system adapted to the measurement and control task of the multiple satellites into orbit with one rocket; the O-XY reduced coordinate system is used to represent the two-dimensional discrete space composed of the time domain and the frequency domain; Based on the O-XY conventional coordinate system, a non-conventional coordinate system adapted to the measurement and control requirements of the multi-satellite-in-orbit launch phase is constructed.

7. The method according to claim 1, characterized in that The constructing a dual mapping relationship matrix according to the unreduced coordinate system of the initial reduced coordinate system, and updating the dual mapping relationship matrix based on measured data, includes: Performing dimensionality reduction processing on the non-reduced coordinate system according to prior information corresponding to the non-reduced coordinate system and the task; Determine the non-standardized threshold boundary cone surface without link interference based on Monte Carlo simulation of finite element analysis or actual link testing; Mapping the unreduced coordinate system into a reduced coordinate system; Determine the reduced coordinate system and dual mapping relationship matrix that are suitable for the current task; The dual mapping relationship matrix is ​​continuously updated iteratively using statistical learning methods and measured data.

8. A multi-access device for measurement and control links based on high-dimensional discrete space, characterized in that: The device comprises: A construction module, configured to construct a high-dimensional discrete space based on an initial orthogonal vector coordinate system; the high-dimensional discrete space includes at least one spatial resource in the time domain, the frequency domain, and the code domain; A construction module is used to construct an unreduced coordinate system adapted to the control scenario requirements on the high-dimensional discrete space based on the initial reduced coordinate system; the initial reduced coordinate system is a standardized virtual base class coordinate system; the unreduced coordinate system is a non-standardized coordinate system that matches the initial reduced coordinate system; and a dual mapping relationship matrix is ​​constructed based on the unreduced coordinate system of the initial reduced coordinate system; An updating module, configured to update the dual mapping relationship matrix based on measured data; the dual mapping relationship matrix is ​​used to establish a bidirectional transformation relationship between the unreduced coordinate system and the initial reduced coordinate system; An access module is used to connect at least one satellite or spacecraft to a ground station based on the updated dual mapping relationship matrix and the constellation measurement and control link.

9. An electronic device, characterized in that: The electronic device includes a processor, a memory, a communication interface and a communication bus, and the processor, the memory and the communication interface communicate with each other via the communication bus; The memory is used to store executable instructions, and the executable instructions enable the processor to execute the measurement and control link multiple access method based on high-dimensional discrete space according to any one of claims 1 to 7.

10. A readable storage medium, characterized in that: When the instructions in the readable storage medium are executed by a processor of an electronic device, the processor is enabled to execute the measurement and control link multiple access method based on high-dimensional discrete space as described in any one of claims 1 to 7.

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