A fast calculation method of active elements based on trajectory included angle solution

Abstract

The present application relates to the technical field of radio waves, and particularly relates to a kind of active element fast calculation method based on trajectory included angle solution.The present application is close to constant or linear growth lower computational complexity, and the precision of discrete sampling method is realized, and the complete active array in the whole visible arc segment is directly output, and the computational complexity is significantly reduced.

Description

Technical Field

[0001] This invention relates to the field of radio wave technology, and in particular to a fast calculation method for activated array elements based on trajectory angle calculation. Background Technology

[0002] For the future of aerospace telemetry, tracking, and command (TT&C), particularly in serving the increasingly large low-Earth orbit satellite constellation systems, all-space phased array technology demonstrates unparalleled advantages. A single ground TT&C station equipped with an all-space phased array can continuously and agilely track and control multiple satellites (or other spacecraft) flying within its line of sight (limited by the Earth's curvature). This capability is a key cornerstone for improving TT&C efficiency, ensuring operational safety, optimizing ground station layout, and reducing system construction and maintenance costs for large satellite constellations operating at high frequency and with multiple targets.

[0003] One of the core advantages of this technology is its ability to dynamically adjust the "active array surface." Traditional methods determine activation based on the angle between the line of sight (line of sight) connecting the spacecraft and the ground control station and the array normal: array elements whose angle with the array element normal is less than a certain threshold (e.g., 20 degrees) are considered active. This method is conceptually clear, computationally direct, and feasible and efficient for calculating the required active array surface (i.e., the subset of array elements needed for instantaneous beam pointing) for a single satellite at a specific moment. However, space missions often require the control system to provide continuous service throughout the satellite's entire visible arc. Planning the "active array surface" within the visible arc needs to cover all potentially usable array elements over the entire time period. Currently, engineering practice commonly uses a discrete-time sampling approach: the satellite's visible arc is divided into a series of discrete moments, and the corresponding active array surface is calculated independently at each sampling time point. Finally, the union of the obtained active array surfaces is used as the final active array surface estimate covering the entire visible arc.

[0004] Clearly, while this discrete sampling method is logically simple, its computational accuracy depends entirely on the sampling density (time step). To capture subtle changes in activated elements during rapid satellite movement and beam pointing variations (especially during perigee or high-dynamic maneuvers), a relatively small sampling interval is theoretically required to ensure that the final union covers all possible activated elements within the entire visible arc without omission. However, the practical contradiction lies in the fact that excessively high sampling accuracy leads to a dramatic increase in the number of discrete points, resulting in an explosive increase in the number of calculations required for the instantaneous activated array. For advanced phased arrays composed of thousands or even tens of thousands of elements, calculating the instantaneous activated array itself carries a significant computational load. When multiplied by a large number of sampling points, the overall computational complexity becomes unacceptable, failing to meet the requirements of real-time planning or large-scale automated constellation scheduling. Its theoretical computational complexity is O(MN), where M represents the number of sampling points and N represents the number of elements in the phased array. Summary of the Invention

[0005] This invention discloses a method for calculating activation array elements based on trajectory angle calculation, characterized by the following specific method: Preprocessing by slicing the visible arc segments of the satellite's future trajectory; Discrete-time sampling is performed based on the visible arc segments after slicing; Calculate the azimuth and elevation angle information of the connection between the satellite and the ground control station at the sampling time; Convert azimuth and elevation information into three-dimensional rectangular coordinate information; Based on the fitted slices using three-dimensional rectangular coordinate information, the satellite coordinates within the arc segment relative to time can be observed. Relationship; For any array element, calculate the minimum included angle of its rotation trajectory within the visible arc segment of the slice; Compare the minimum included angle with the threshold. If the minimum included angle is less than the threshold, the array element is in an active state; otherwise, the array element is in an inactive state.

[0006] Furthermore, the time slice length for slice preprocessing is determined using the following method: The solution for the appropriate time slice length is modeled as a multi-objective optimization problem, with the specific formula as follows:

[0007] In the formula, This indicates that the time slice length is At that time, the first The first task and the first Accuracy of task conflict calculation; Indicated by The candidate values ​​for a series of time slices obtained by the step size. Indicates the duration of the visible arc segment; Indicates in Given a time slice of length, calculate the computational complexity function corresponding to conflicts between tasks. By using multi-objective weighting techniques, the problem is transformed into the following single-objective optimization problem:

[0008] In the formula, These are the weighting coefficients used to balance the two objectives; By setting the weight ratio of the two objectives, reinforcement learning techniques are used to obtain optimal solutions of different qualities, i.e., the time slice length.

[0009] Furthermore, when performing discrete-time sampling based on the visible arc segments after slicing, if the satellite flight trajectory is stable, the number of sampling points is reduced; if the satellite flight is in a highly dynamic maneuvering state, the number of sampling points is increased. The sampling time is recorded as .

[0010] Furthermore, the azimuth and elevation information is converted into three-dimensional rectangular coordinate information, and the specific method is as follows: Calculate the azimuth and elevation angle information of the line connecting the satellite and the ground control station at each sampling time, store it in an angle matrix, and record it as follows. ; Will The azimuth and elevation information corresponding to the array is converted into three-dimensional rectangular coordinates. The specific conversion formula is as follows:

[0011]

[0012]

[0013] Furthermore, by fitting slices based on three-dimensional rectangular coordinate information, the satellite coordinates within the visible arc segment compared to time are... The relationship is explained in the following specific methods: use , Within the visible arc segment of the fitted slice, the satellite Axis coordinates relative to time The relationship between them yields the corresponding functional expression, as follows:

[0014]

[0015]

[0016] Using cubic polynomials , , A high-precision fit was performed, which is represented as:

[0017] Furthermore, for any array element, the minimum included angle of its rotation trajectory within the visible arc segment of the slice is calculated using the following method: Assume its normalized coordinates in three-dimensional space are The angle between it and the satellite's rotation trajectory within the visible arc can be expressed as:

[0018] Since the cosine function is decreasing between 0 and 180 degrees, and the minimum angle corresponds to the maximum value in the above formula, solving for the minimum angle between the array element and the rotation trajectory is equivalent to solving the following optimization problem:

[0019]

[0020] The objective function is a nonlinear function and a univariate function. An optimization algorithm is used to solve it, and the optimal solution is denoted as... The formula for calculating the minimum included angle is:

[0021] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects: 1. This application achieves accuracy comparable to discrete sampling methods with a low computational complexity that is close to constant or linearly increasing, and directly outputs the complete active array within the entire visible arc segment, significantly reducing computational complexity.

[0022] 2. This application optimizes the length of slice preprocessing, thereby reducing the invalid activation time of array elements and improving the efficiency of array element utilization while ensuring computational complexity.

[0023] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0024] The accompanying drawings of this invention are described below.

[0025] Figure 1 Satellite SA4111 activates array calculation for 50 seconds of visible arc. Figure 2 Satellite SA4111 activates array calculation for 100 seconds of visible arc; Figure 3 Satellite SA4111's visible arc segment is activated for array calculations for 200 seconds; Figure 4 Satellite SE108's visible arc segment is activated for array calculations for 200 seconds; Figure 5 This is a schematic diagram of the overall process. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0027] A method for calculating activation array elements based on trajectory angle calculation, such as Figure 5 As shown, the specific steps are as follows: S1. Perform slice preprocessing on the visible arc segments of the satellite's future trajectory.

[0028] In step S1, to minimize the idle time reserved for phased array elements within the visible arc of the satellite (i.e., the difference between the reserved time and the actual time used), the time slice length needs to be set to an appropriate value before calculating the activation elements. If the time slice is too long, the satellite mission processing granularity is too large, resulting in more redundant elements and a higher false alarm rate for activation surface collision detection between satellite missions. If the time slice is too small, although activation surface collision detection between satellite missions is more accurate, the computational complexity increases rapidly. To determine a suitable time slice length, the following optimization steps are adopted: S11. The solution for the appropriate time slice length is modeled as a multi-objective optimization problem, and the multi-objective optimization model formula is as follows:

[0029] in This indicates that the time slice length is At that time, the first The first task and the first Accuracy of calculating individual task conflicts. Indicated by The candidate values ​​for a series of time slices obtained by the step size. Indicates the duration of the visible arc segment. Indicates in Given a time slice of a certain length, calculate the computational complexity function corresponding to conflicts between tasks.

[0030] S12. Using multi-objective weighting techniques, the above problem can be further transformed into the following single-objective optimization problem. By setting the weight ratio of the two objectives, reinforcement learning techniques can be used to obtain optimal solutions of different qualities, and finally, a more ideal time slice length can be selected. The formula for the single-objective optimization model is as follows:

[0031] In the formula, These are the weighting coefficients used to balance the two objectives.

[0032] S2. Perform discrete-time sampling based on the visible arc segments after slicing.

[0033] In step S2, the duration of the time slice needs to be calculated. Perform moderate discrete-time sampling. If the satellite's flight trajectory is relatively stable, a smaller number of sampling points can be used, such as 5. If the satellite performs highly dynamic maneuvers, a larger number of sampling points is required, such as 20. Each sampling time It is evident that the start and end times of an arc segment generally need to be included within the sampling points.

[0034] S3. Calculate the azimuth and elevation angle information of the satellite and the ground control station at the sampling time, and store them in an angle matrix. .

[0035] S4. Obtained from step S3 The azimuth and elevation information corresponding to the array is converted into three-dimensional rectangular coordinate information using the following formula: , , .

[0036] S5, Utilization , Within the fitted visible arc segment, the satellite Axis coordinates relative to time The relationship is used to obtain the corresponding functional expression. Similarly, Functional relationship between axis coordinates and time , Using a cubic polynomial to... , , A high-precision fit was performed. Therefore, its trajectory within the visible arc segment can be parameterized as follows: .

[0037] S6. For any array element, assume its normalized coordinates in three-dimensional space are... The angle between it and the satellite's rotation trajectory within the visible arc can be expressed as:

[0038] Since the cosine function is decreasing between 0 and 180 degrees, the minimum angle corresponds to the maximum value in the above formula. Therefore, solving for the angle between this array element and the nearest point of the rotation trajectory can be equivalent to solving the following optimization problem:

[0039]

[0040] The objective function of the above problem is a nonlinear function, but since it is only a univariate function, it can be solved efficiently using existing optimization algorithms. This embodiment uses the fminbnb function from the Matlab optimization toolbox.

[0041] The optimal solution to the above optimization problem is denoted as: The minimum included angle can be calculated using the following formula, i.e. .

[0042] S7, if If the condition is met, the array element is in an active state; otherwise, the array element is in an inactive state.

[0043] It is important to note that although discrete-time sampling is used in this embodiment, the sampling point information is only used for satellite trajectory fitting within the time slice. Each array element actually participates in step S7 only once, which significantly reduces computational complexity compared to traditional activation array calculation methods based on discrete-time sampling.

[0044] Simulation experiment: To verify the effectiveness of the fast calculation method proposed in this invention, the following content provides a specific example of phased array activation element calculation in a satellite telemetry and control scenario.

[0045] The STK software was used to generate GPS satellite orbit information and Starlink low-Earth orbit satellite orbit information. Based on the generated satellite information, a set of visible arc segments and a set of satellite missions were created. The set of visible arc segments includes: satellite number, visible arc segment number, start time, end time, and duration of the visible arc segment. The set of missions includes: mission number, satellite ID, mission execution duration, and mission execution status. The scheduling cycle starts at 6:0:00 on March 4, 2024, and ends at 6:20:00 on March 4, 2024. The tracking station is located at longitude 103°, latitude 31°. A full-space phased array is used. Figure 1 The array shown is a spherical and cylindrical array with 26469 array elements. For the Starlink low-Earth orbit satellite mission set, the phased array activation angle is set to 20 degrees. To statistically analyze the differences between the proposed algorithm and traditional algorithms in calculating the activation elements, a binary vector of length 26469 is first defined. , Indicates the first Each array element is in an active state. The error ratio is defined as follows:

[0046] This embodiment takes the trajectory fitting of a 100-second visible arc segment of satellite number "se108" as an example. The specific steps are as follows: First, a time slice is obtained as the time processing range for solving the active array elements. In this embodiment, the visible arc of the satellite is 10 minutes, and the time slice size is determined to be 100 seconds. During the calculation, the scale used is... The reinforcement learning method used is deep Q-learning, specifically the DQN algorithm. The time slice candidate set is... The final calculated time slice length is 100 seconds. For a given time slice, discrete-time sampling is performed every 10 seconds to obtain the azimuth and elevation angle information, which is stored in the `angle` array. The contents of the `angle` array are as follows: angle=[ 148.0570 5.6320 147.4610 6.4300 146.8240 7.2580 146.1400 8.1170 145.4040 9.0120 144.6120 9.9450 143.7560 10.9190 142.8280 11.9380 141.8200 13.0050 140.7210 14.1250 139.5190 15.3020 ]; Convert to rectangular coordinates and normalize to obtain the corresponding rectangular coordinate values, as follows: [ -0.8440 0.5270 0.0980 -0.8380 0.5340 0.1120 -0.8300 0.5430 0.1260 -0.8220 0.5520 0.1410 -0.8130 0.5610 0.1570 -0.8030 0.5700 0.1730 -0.7920 0.5810 0.1890 -0.7800 0.5910 0.2070 -0.7660 0.6020 0.2250 -0.7510 0.6140 0.2440 -0.7340 0.6260 0.2640 ] right By fitting the formula to the axis coordinates, we can obtain...

[0047]

[0048]

[0049] For a certain array element, its rectangular coordinates are e=[0 100 100]. Solving the corresponding optimization problem, we can find that the cosine value of the nearest point on the trajectory is 0.6294, which is less than the cosine value corresponding to 20 degrees. Therefore, this point is determined to be inactive.

[0050] Figures 1 to 3 The calculation results of the active phased array elements for the low-Earth orbit satellite (SA411) at 50 seconds, 100 seconds, and 200 seconds are presented, with the visible arc starting at 6:09:20 on March 4, 2024. As can be seen from the figures, the proposed algorithm can accurately calculate the set of active phased array elements at different time intervals. With increasing time interval length, the error ratio performance of the calculated active array element set gradually decreases; however, within the tested range, the error ratio performance remains very good. The error ratios for 50 seconds, 100 seconds, and 200 seconds are 0, 0, and 0.0112, respectively.

[0051] To verify the effectiveness of the proposed algorithm, this application further simulated the phased array activation calculation of satellite SE108 within 200 seconds, with the visible arc starting at 6:12:40 on March 4, 2024. Figure 4 As shown, within a 200-second time period, the proposed algorithm can still accurately calculate the set of active array elements of the phased array within that time period, with an error ratio of 0.0179, which remains at a very low level.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating activation array elements based on trajectory angle calculation, characterized in that, The specific method is as follows: Preprocessing by slicing the visible arc segments of the satellite's future trajectory; Discrete-time sampling is performed based on the visible arc segments after slicing; Calculate the azimuth and elevation angle information of the connection between the satellite and the ground control station at the sampling time; Convert azimuth and elevation information into three-dimensional rectangular coordinate information; Based on the fitted slices using three-dimensional rectangular coordinate information, the satellite coordinates within the arc segment relative to time can be observed. Relationship; For any array element, calculate the minimum included angle of its rotation trajectory within the visible arc segment of the slice; Compare the minimum included angle with the threshold. If the minimum included angle is less than the threshold, the array element is in an active state; otherwise, the array element is in an inactive state. The specific method for determining the slice preprocessing time and slice length is as follows: The solution for the appropriate time slice length is modeled as a multi-objective optimization problem, with the specific formula as follows: In the formula, This indicates that the time slice length is At that time, the first The first task and the first Accuracy of task conflict calculation; Indicated by The candidate values ​​for a series of time slices obtained by the step size. Indicates the duration of the visible arc segment; Indicates in Given a time slice of length, calculate the computational complexity function corresponding to conflicts between tasks. By using multi-objective weighting techniques, the multi-objective problem is transformed into the following single-objective optimization problem: In the formula, These are the weighting coefficients used to balance the two objectives; By setting the weight ratio of the two objectives, reinforcement learning techniques are used to obtain optimal solutions of different qualities, i.e., the time slice length.

2. The activation element calculation method based on trajectory angle calculation as described in claim 1, characterized in that, When performing discrete-time sampling based on the visible arc segments after slicing, if the satellite flight trajectory is stable, the number of sampling points should be reduced; if the satellite flight is in a highly dynamic maneuvering state, the number of sampling points should be increased. The sampling time is recorded as .

3. The activation element calculation method based on trajectory angle calculation as described in claim 1, characterized in that, The azimuth and elevation information is converted into three-dimensional Cartesian coordinate information using the following method: Calculate the azimuth and elevation angle information of the line connecting the satellite and the ground control station at each sampling time, store it in an angle matrix, and record it as follows. ; Will The azimuth and elevation information corresponding to the array is converted into three-dimensional rectangular coordinates. The specific conversion formula is as follows: 。 4. The activation element calculation method based on trajectory angle calculation as described in claim 3, characterized in that, Based on the fitted slices using three-dimensional rectangular coordinate information, the satellite coordinates within the arc segment relative to time can be observed. The relationship is explained in the following specific methods: use , Within the visible arc segment of the fitted slice, the satellite Axis coordinates relative to time The relationship between them yields the corresponding functional expression, as follows: Using cubic polynomials , , A high-precision fit was performed, which is represented as: 。 5. The activation element calculation method based on trajectory angle calculation as described in claim 4, characterized in that, For any array element, calculate the minimum angle of its rotation trajectory within the visible arc segment of the slice. The specific method is as follows: Assume its normalized coordinates in three-dimensional space are The angle between it and the satellite's rotation trajectory within the visible arc can be expressed as: Since the cosine function is decreasing between 0 and 180 degrees, and the minimum angle corresponds to the maximum value in the above formula, solving for the minimum angle between the array element and the rotation trajectory is equivalent to solving the following optimization problem: The objective function is a nonlinear function and a univariate function. An optimization algorithm is used to solve it, and the optimal solution is denoted as... The formula for calculating the minimum included angle is: 。

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