A design method for Earth-Moon space navigation constellation based on special long-period orbits

Abstract

The present invention discloses a method for designing an Earth-Moon space navigation constellation based on a special long-period orbit, comprising the following steps: step 1, designing Halo orbits of Earth-Moon L1 and L2 libration points in a dynamic model of a circular restricted three-body problem; step 2, designing a special long-period orbit using the invariant manifold of the Halo orbit, on which a spacecraft performs periodic motion; step 3, forming a navigation satellite constellation by deploying multiple navigation satellites on the special long-period orbit according to configuration parameters; step 4, setting a series of sample points in an ecliptic plane for simulating and analyzing the navigation performance of the constellation; at the sample points, first obtaining visible satellites according to a coverage judgment condition; then performing a star selection operation according to an optimal GDOP method, i.e., selecting a four-satellite combination with the smallest GDOP value for positioning; and calculating the minimum GDOP of each sample point at each time during the simulation process; and step 5, establishing a navigation constellation optimization model under constraint conditions, using the configuration parameters in step 3 as input, optimizing each configuration parameter of the constellation using an optimization algorithm to minimize the optimization index, and using the optimized parameters as the configuration parameters for the navigation constellation design. The present invention can solve the problem that existing navigation systems cannot meet the demand for high-precision navigation and positioning in the entire Earth-Moon space.

Description

Technical Field

[0001] The present invention relates to the field of cis-lunar space satellite navigation technology, and in particular to a method for designing a cis-lunar space navigation constellation based on a special long-period orbit. Background Art

[0002] Cislunar space refers to the space between Earth and the Moon, consisting of near-Earth space, lunar space, and the Cislunar transfer space. Because human spaceflight activities in near-Earth space, within geosynchronous orbit (GEO), have become routine, near-Earth space is typically excluded from discussions of Cislunar space. All Cislunar space missions rely on navigation systems. With the increasing frequency and deepening of lunar exploration and deep space exploration, the scope of satellite navigation systems will expand from Earth and near-Earth space to Cislunar space. Future manned lunar landings and the construction of lunar bases require continuous, redundant Cislunar communications, even enabling real-time positioning capabilities similar to GPS. Therefore, a new Cislunar space navigation system is needed to support future Cislunar space activities.

[0003] Currently, lunar probes, both domestic and international, primarily utilize ground-based measurement techniques for orbit determination, including ground-based radio ranging, velocity measurement, and interferometry. However, obtaining high-precision orbits using ground-based orbit determination systems requires long periods of continuous tracking, especially during the Earth-Moon transfer orbit. Furthermore, the farther the probe is from Earth, the poorer the ground-based measurement geometry. This limits the accuracy and applicability of lunar probe orbit determination using ground-based measurement techniques. Using space-based navigation systems can effectively reduce the requirements for station geometry, equipment performance, and operating arcs required by ground-based systems. Furthermore, they can provide backup and data processing with ground-based systems, further improving navigation reliability and accuracy. Due to the limitations of existing navigation satellites, high-precision navigation support for deep space probes, such as the Moon, is currently unavailable. Lunar space probes using only GNSS technology suffer from weak signals, a small number of visible satellites, and a poor DOP (Dilution of Precision).

[0004] Therefore, it is necessary to build a cis-lunar space navigation constellation to meet the high-precision navigation and positioning needs of multiple users in the entire cis-lunar space, and provide high-precision navigation services for future cis-lunar space missions. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for designing a navigation constellation in Earth-Moon space based on a special long-period orbit, which can solve the problem that the existing navigation system cannot meet the high-precision navigation and positioning requirements of the entire Earth-Moon space.

[0006] To solve the above technical problems, the present invention provides a method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit, comprising the following steps:

[0007] Step 1: Design the Halo orbits of the Earth-Moon L1 and L2 libration points in the dynamic model of the circular restricted three-body problem;

[0008] Step 2: Use the invariant manifold of the Halo orbit to design a special long-period orbit, on which the spacecraft performs periodic motion;

[0009] Step 3: Deploy multiple navigation satellites on special long-period orbits according to configuration parameters to form a navigation satellite constellation;

[0010] Step 4: Set a series of sample points within the ecliptic plane to simulate and analyze the navigation performance of the constellation. At the sample points, first obtain visible satellites based on the coverage judgment conditions, and then perform a satellite selection operation based on the optimal GDOP method. That is, the four-satellite combination with the smallest GDOP value is selected for positioning. During the simulation process, calculate the minimum GDOP value of each sample point at each time.

[0011] Step 5: Establish a navigation constellation optimization model under constraints. Using the configuration parameters in step 3 as input, use the optimization algorithm to optimize the various configuration parameters of the constellation to minimize the optimization index. The optimized parameters are used as the configuration parameters for the navigation constellation design.

[0012] Preferably, in step 1, the Halo orbit refers to a periodic orbit that moves around a specific collinear libration point in a circular restricted three-body system consisting of the Earth, the Moon, and the spacecraft.

[0013] Preferably, in step 2, the invariant manifold refers to a set of stable orbits existing near the Halo orbit in dynamics theory, including unstable manifolds and stable manifolds.

[0014] Preferably, in step 3, the configuration parameters include one or more of the following: the number of orbits used by the constellation, the number of satellites on each orbit, and the time phase difference between satellites on the same orbit.

[0015] Preferably, in step 4, GDOP refers to the geometric dilution of precision, which is calculated as follows: Assume that the positions of the four observable satellites are X i =[x i ,y i ,z i ], i=1,2,3,4 The position of user receiver is X p =[x p ,y p ,z p ];

[0016] The distance between the user and the four satellites is

[0017] The measurement error equation is V = HX - L; where X = [δx, δy, δz, δt] T is a vector composed of position error and clock error, L is a constant vector, V is the observation error vector, H is the measurement matrix,

[0018] The weight inverse matrix Q of the parameter vector X xx for

[0019] Then the geometric dilution of precision is

[0020] Preferably, in step 5, the optimization algorithm includes genetic algorithm, particle swarm optimization algorithm, NSGA-II algorithm, and simulated annealing algorithm.

[0021] Preferably, in step 5, the optimization index is:

[0022] J=max{GDOP1(1),GDOP1(2),GDOP1(3),…,GDOP i (j),…}

[0023] Among them, GDOP i (j) represents the optimal GDOP of the i-th sample point at the j-th time, i, j are integers and satisfy 1≤i≤N, 1≤j≤T, N is the total number of sample points, and T is the total number of simulation moments.

[0024] The beneficial effects of the present invention are as follows: (1) The special long-period orbit designed in the present invention has a larger range of motion in the Earth-Moon space, and the navigation satellites deployed on the orbit have a larger coverage range; (2) The constellation design scheme proposed in the present invention provides a more comprehensive constellation navigation performance analysis method and constellation configuration parameter optimization method; (3) The navigation constellation designed by the present invention uses a four-star geometric positioning method to provide navigation services, which has the advantages of strong real-time positioning, high accuracy, and no restriction on the number of users. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the method of the present invention.

[0026] Figure 2 Schematic diagram of the Halo orbit of points L1 and L2 of the present invention.

[0027] Figure 3 This is a schematic diagram of the present invention designing a special long-period orbit using the invariant manifold of the L1 point Halo orbit.

[0028] Figure 4This is a schematic diagram of the special long-period orbit designed by the present invention using the Halo orbit invariant manifold of points L1 and L2.

[0029] Figure 5 This is a schematic diagram of the principle of the navigation satellite being observable to the user according to the present invention.

[0030] Figure 6 This is a schematic diagram of the principle of the four-star time difference positioning of the present invention.

[0031] Figure 7 This is a schematic diagram of the Earth-Moon space navigation constellation finally obtained by the present invention. DETAILED DESCRIPTION

[0032] like Figure 1 As shown, a method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit includes the following steps:

[0033] Step S1: Design the Halo orbits of the Earth-Moon L1 and L2 libration points in the circular restricted three-body problem model, such as Figure 2 As shown;

[0034] Step S2: Design a special long-period orbit based on the invariant manifold of the Halo orbit, where the special long-period orbit corresponding to the Halo orbit of point L1 is as follows: Figure 3 As shown, the special long-period orbit designed using the invariant manifold of the Halo orbits of points L1 and L2 is as follows Figure 4 As shown;

[0035] Step S3: deploying multiple navigation satellites on a special long-period orbit according to configuration parameters to form a navigation satellite constellation;

[0036] Step S4: Set a series of sample points within the ecliptic plane to analyze the navigation performance of the constellation. The user selects stars based on the coverage judgment criteria and the optimal geometric dilution of precision (GDOP) method, and uses the four-star time difference positioning principle for positioning. During the simulation process, the minimum GDOP of each sample point at each time is calculated.

[0037] Step S5: Establish a constrained navigation constellation optimization model. Using the configuration parameters from step S3 as input, simulate the initial navigation constellation. Obtain the minimum GDOP for each sample point at each moment during the simulation. Finally, output the maximum GDOP value, which is the optimization index J. Use an optimization algorithm to optimize the constellation's configuration parameters until they meet the design requirements. These optimized parameters are then used as the configuration parameters for the navigation constellation design.

[0038] Among them, the optimization indicators are:

[0039] J=max{GDOP1(1),GDOP1(2),GDOP1(3),…,GDOPi (j),…}

[0040] Among them, GDOP i (j) represents the optimal GDOP of the i-th sample point at the j-th moment. The smaller the GDOP value, the better.

[0041] According to the size of the quantitative index J, the advantages and disadvantages of the geometric structure of the constellation with different constellation configuration parameters can be judged, and then the optimization algorithm can be used to optimize the constellation configuration parameters to improve the navigation performance of the constellation.

[0042] The configuration parameters described in step S3 include one or more of the following:

[0043] (1) The number of orbits used by the constellation;

[0044] (2) The number of satellites in each special long-period orbit;

[0045] (3) The time phase difference between satellites in the same orbit.

[0046] The observable state in step S4 means that the communication between the user and the navigation satellite is not interrupted by the obstruction of the earth and the moon. If the position relationship between a navigation satellite S and the user P is as follows: Figure 5 As shown in the figure, when the user is outside the shaded area in the figure, the navigation satellite can be observed.

[0047] The geometric dilution of precision GDOP is calculated by the following steps:

[0048] Assume that the positions of the four observable satellites are X i =[x i ,y i ,z i ], i=1,2,3,4 The position of user receiver is X p =[x p ,y p ,z p ],like Figure 6 shown.

[0049] The distance between the user and the four satellites is

[0050] The measurement error equation is V = HX-L;

[0051] where X = [δx, δy, δz, δt] T is a vector composed of position error and clock error, L is a constant vector, V is the observation error vector, and H is the measurement matrix. It is calculated according to the following formula

[0052] The weight inverse matrix Q of the parameter vector X xx for

[0053] Then the geometric dilution of precision is

[0054] The optimization algorithms described in step S5 include genetic algorithm, particle swarm optimization algorithm, NSGA-II algorithm, and simulated annealing algorithm.

[0055] The navigation constellation obtained after optimization is as follows Figure 7 As shown, the navigation constellation can cover the entire cislunar space and provide real-time high-precision navigation services for space missions in the cislunar space.

Claims

1. A method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit, characterized in that: The steps include: Step 1: Design the Halo orbits of the Earth-Moon L1 and L2 libration points in the dynamic model of the circular restricted three-body problem; Step 2: Use the invariant manifold of the Halo orbit to design a special long-period orbit, on which the spacecraft performs periodic motion; Step 3: Deploy multiple navigation satellites on special long-period orbits according to configuration parameters to form a navigation satellite constellation; Step 4: Set a series of sample points in the ecliptic plane to simulate and analyze the navigation performance of the constellation. At the sample points, first obtain the visible satellites according to the coverage judgment conditions, and then select the satellites according to the optimal GDOP method, that is, select the four-star combination with the smallest GDOP value for positioning. During the simulation process, calculate the minimum GDOP value of each sample point at each time; GDOP refers to the geometric dilution of precision, and its specific calculation method is: Assume that the positions of the four observable satellites are X i =[x i ,y i ,z i ], i=1,2,3,4 The position of user receiver is X p =[x p ,y p ,z p ]; The distance between the user and the four satellites is The measurement error equation is V = HX - L; where X = [δx, δy, δz, δt] T is a vector composed of position error and clock error, L is a constant vector, V is the observation error vector, H is the measurement matrix, The weight inverse matrix Q of the parameter vector X xx for Then the geometric dilution of precision is Step 5: Establish a navigation constellation optimization model under constraints. Using the configuration parameters in step 3 as input, use the optimization algorithm to optimize the various configuration parameters of the constellation to minimize the optimization index. The optimized parameters are used as the configuration parameters for the navigation constellation design.

2. The method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit according to claim 1, wherein: In step 1, the Halo orbit refers to a periodic orbit around a specific collinear libration point in a circular restricted three-body system consisting of the Earth, the Moon, and the spacecraft.

3. The method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit according to claim 1, wherein: In step 2, the invariant manifold refers to a set of stable orbits near the Halo orbit in dynamical theory, including unstable manifolds and stable manifolds.

4. The method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit according to claim 1, wherein: In step 3, the configuration parameters include one or more of the following: the number of orbits used by the constellation, the number of satellites on each orbit, and the time phase difference between satellites on the same orbit.

5. The method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit as claimed in claim 1, wherein: In step 5, the optimization algorithms include genetic algorithm, particle swarm optimization algorithm, NSGA-II algorithm, and simulated annealing algorithm.

6. The method for designing a terrestrial-lunar space navigation constellation based on a special long-period orbit as claimed in claim 1, wherein: In step 5, the optimization index is: J=max{GDOP1(1),GDOP1(2),GDOP1(3),...,GDOP i (j),...} Among them, GDOP i (j) represents the optimal GDOP of the i-th sample point at the j-th time, i, j are integers and satisfy 1≤i≤N, 1≤j≤T, N is the total number of sample points, and T is the total number of simulation moments.

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