Activation array element rapid calculation method based on track plane projection

Abstract

The invention relates to the technical field of radio waves, in particular to an activated array element rapid calculation method based on track plane projection. Comprising the following steps: calculating a pair of orthogonal basis vectors of a plane where a rotation track is located by using azimuth and pitch angle information between a satellite and a measurement and control station at starting and ending moments of a visible segmental arc; and calculating nearest activation angles on the rotation tracks corresponding to different array elements under constraint conditions, and judging whether the array elements are activated or not according to the activation angles. Compared with a traditional calculation method based on time discrete sampling, according to the method, each array element only participates in calculation once, the calculation complexity is greatly reduced, and the real-time performance of calculation is guaranteed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radio wave technology, in particular to a kind of quick calculation method of active element based on trajectory plane projection. BACKGROUND

[0002] The full-space phased array TT&C system is emerging as the core force of the new generation of space TT&C, and its core advantage distinguishing from the traditional mechanical scanning system lies in the flexible control of the huge time domain and space domain resources. In time domain, the full-space phased array can cover the entire visible arc segment time window of the satellite "without interruption"; in space domain, the entire array contains thousands of independently controllable elements, forming a strong space diversity in space domain and different dynamic beams. To fully exert the great potential of the two-dimensional time-space resource coordination optimization, a key prerequisite is to accurately calculate the active element set required by the satellite in its visible arc segment.

[0003] In the traditional phased array system, the calculation of active elements usually relies on the real-time azimuth-elevation angle information of the satellite relative to the TT&C station. Specifically, the system first calculates the direction of the line connecting the satellite and the TT&C station at a certain time, and then determines the active elements as the elements on the array whose included angle with the direction is less than a preset threshold. When it is necessary to determine all possible active elements in the visible arc segment of the satellite, the conventional method is to discretely sample the visible arc segment, calculate the active element set corresponding to each sampling time, and finally take the union set of all sampling results as the final active element set.

[0004] This method usually faces the trade-off between computational complexity and computational accuracy. First, its computational accuracy is highly dependent on the number of sampling points. If the sampling points are dense, although all possible active elements in the satellite motion process can be covered, ensuring the accuracy of the calculation results, the computational burden will be significantly increased, especially in long arc segments or multi-satellite tasks, real-time performance is difficult to guarantee. On the contrary, if the sampling points are too few, although the calculation efficiency is improved, some key elements may be missed, leading to beam pointing error or incomplete signal coverage, affecting the TT&C performance. Let the number of discrete time sampling points be M, and the computational complexity of the traditional phased array active array calculation method is O(MN). SUMMARY

[0005] The present application discloses a kind of quick calculation method of active element based on trajectory plane projection, it is characterized in that, specific method is as follows:

[0006] Using the azimuth and elevation angle information between the satellite and the TT&C station at the start time and the end time of the visible arc segment, a pair of orthogonal basis vectors of the plane of the rotating trajectory is calculated;

[0007] The closest active angle on the rotating trajectory corresponding to different elements under the constraint condition is calculated;

[0008] The activation angle determines whether the corresponding array element is activated.

[0009] Furthermore, calculate a pair of orthogonal basis vectors in the plane containing the rotation trajectory, as follows:

[0010] The azimuth and elevation angles of the satellite relative to the telemetry and control station are obtained based on the start and end times of the visible arc.

[0011] Calculate the coordinate vectors of the azimuth and elevation angles at the start and end times of the visible arc in a rectangular coordinate system:

[0012]

[0013] Its rotation trajectory is vector d s Rotation towards d e The resulting curved trajectory;

[0014] Using the Gramm-Schmidt orthogonal method, calculate d m =d e -(d s ·d e )·d s "·" indicates calculating the dot product of two vectors, and "×" indicates calculating the cross product of two vectors.

[0015] d s With d m A pair of orthogonal bases forming the plane containing the rotation trajectory.

[0016] Furthermore, under constrained conditions, the nearest activation angle on the rotation trajectory corresponding to different array elements is calculated, specifically as follows:

[0017] Calculate the range of rotation angles corresponding to the visible arc segment, L = acos(d e ·d s );

[0018] For any array element, obtain its rectangular coordinate position as e = [x0, y0, z0], and calculate its position in d. s With d m The coordinates x = d on the plane s ·e, y=d m ·e;

[0019] Calculate the rotation angle α = atan(y / x) under unconstrained conditions. This angle represents the rotation angle of any array element in d. s With d m The projection vectors that constitute the plane and d s The size of the included angle;

[0020] The rotation angle is restricted to the rotation trajectory, specifically:

[0021]

[0022] The line connecting the "closest" point of the array element to its rotation trajectory under constrained conditions and the center of the phased array is obtained as follows:

[0023]

[0024] With e and The angle between them is used as the activation judgment angle, i.e., the activation angle.

[0025] Furthermore, the activation angle is used to determine whether the corresponding array element is activated. The specific method is as follows:

[0026] Determine e and If the included angle between them is less than a preset angle threshold Δ, then the array element is determined to be activated.

[0027] Conversely, it remains inactive.

[0028] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0029] Compared with traditional time-discrete sampling-based calculation methods, the proposed method involves each array element participating in the calculation only once, which greatly reduces the computational complexity and ensures the real-time performance of the calculation.

[0030] 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

[0031] The accompanying drawings of this invention are described below.

[0032] Figure 1 This is a schematic diagram of a phased array across the entire airspace.

[0033] Figure 2 The calculation results for the active array elements corresponding to satellite number sa411 within 50 seconds.

[0034] Figure 3 The calculation results for the active array elements corresponding to satellite number sa411 within 100 seconds.

[0035] Figure 4 The calculation results for the active array elements corresponding to satellite number sa411 within 300 seconds.

[0036] Figure 5The calculation results for the active array elements corresponding to satellite number se108 within 200 seconds.

[0037] Figure 6 This is a schematic diagram of the overall process. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0039] A fast calculation method for activation elements based on trajectory plane projection, such as... Figure 6 As shown, the specific steps are as follows:

[0040] S1. Obtain the azimuth and elevation angle information of the satellite relative to the telemetry and control station based on the start and end times of the visible arc segment.

[0041] S2. Calculate the coordinate vectors of the azimuth and elevation angles at the start and end times of the visible arc segment in a rectangular coordinate system:

[0042]

[0043] Correspondingly, its rotation trajectory is vector d. s Rotation towards d e The resulting curved trajectory. It is worth noting that the rotational trajectory mentioned in this invention is the trajectory scanned on a unit sphere, not the actual trajectory scanned on the phased array surface.

[0044] S3. Using the Gramm-Schmidt orthogonal method, calculate d. m =d e -(d s ·d e )·d s The dot (·) symbol indicates calculating the dot product of two vectors, and the cross (×) symbol indicates calculating the cross product of two vectors. In this case, d s With d m A pair of orthogonal bases forming the plane containing the rotation trajectory.

[0045] S4. Calculate the range of rotation angles corresponding to the visible arc segment: L = acos(d e ·d s ).

[0046] S5. For any array element, its rectangular coordinate position is obtained as e = [x0, y0, z0]. First, calculate its position in d. s With d m The coordinates x = d on the plane s ·e, y=d m ·e.

[0047] S6. Calculate the rotation angle α = atan(y / x) under unconstrained conditions. This angle represents the rotation angle of any array element in d. s With d m The projection vectors that constitute the plane and d s The size of the included angle.

[0048] S7. Since the rotation angle α may not be on the rotation trajectory, it is necessary to add constraints to restrict it to the rotation trajectory, specifically:

[0049]

[0050] Therefore, under constraints, we can obtain the line connecting the point closest to the rotation trajectory of this array element to the center of the phased array:

[0051]

[0052] S8, Determine whether e is... If the included angle between them is less than a preset angle threshold Δ, then the array element is determined to be activated. Conversely, it remains inactive.

[0053] simulation:

[0054] 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 2024-03-46:0:0 and ends at 2024-03-46:20:0. The tracking and control station is located at longitude 103°, latitude 31°. A full-space phased array is used. Figure 1 The array shown is a combination of spherical and cylindrical surfaces, 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 activated array elements, a binary vector a of length 26469 is first defined. st a st [i] = 1 indicates that the i-th element is active. The error ratio is defined as:

[0055]

[0056] The specific implementation steps of the present invention are illustrated by using the estimation calculation process of the satellite numbered "sa4111" within a 100-second visible arc.

[0057] Step 1: First, obtain the azimuth and elevation angles corresponding to the start and end times of the visible arc segment.

[0058] Step 2: Calculate d s and d e Vector, d s =[0.61-0.70.09],d e = [0.5-0.820.2568].

[0059] Step 3: Calculate d m = [-0.48 -0.27 0.835].

[0060] Step 4: Calculate L = 11.16.

[0061] Step 5: The existing normalized array element coordinates are e = [0 0.7071 0.7071], x = -0.4863, y = 0.3992.

[0062] Step 6: Calculate the rotation angle α = 140.6186.

[0063] Step 7: Calculation

[0064] Step 8: Since the activation conditions are not met, the system is determined to be inactive.

[0065] Figures 2 to 4 The calculation results of the active phased array elements for the low-Earth orbit satellite SA411 within 50 seconds, 100 seconds, and 300 seconds are presented, with the visible arc starting at 2024-03-46:09:20. As can be seen from the figures, the proposed algorithm can accurately calculate the set of active phased array elements within different time periods. With increasing time period length, the error ratio performance of the calculated active array element set by the proposed algorithm gradually decreases; however, within the tested range, the error ratio performance remains very good. The error ratios for 50 seconds, 100 seconds, and 300 seconds are 0, 0.0012, and 0.0673, respectively, all less than one percent.

[0066] To verify the effectiveness of the proposed algorithm, this invention further simulated the phased array activation calculation of satellite SE108 within 200 seconds, with the visible arc starting at 2024-03-46:12:40. Figure 5 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 0.0214, which remains at a very low level.

[0067] 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 protection scope of the claims of the present invention.

Claims

1. A fast calculation method for activation array elements based on trajectory plane projection, characterized in that, The specific method is as follows: Using the azimuth and elevation angle information between the satellite and the telemetry and control station at the start and end times of the visible arc segment, a pair of orthogonal basis vectors in the plane of the rotation trajectory are calculated; Calculate the nearest activation angle on the rotation trajectory corresponding to different array elements under constraints; The activation angle determines whether the corresponding array element is activated.

2. The fast calculation method for activation array elements based on trajectory plane projection as described in claim 1, characterized in that, Calculate a pair of orthogonal basis vectors in the plane containing the rotation trajectory, as follows: The azimuth and elevation angles of the satellite relative to the telemetry and control station are obtained based on the start and end times of the visible arc. Calculate the coordinate vectors of the azimuth and elevation angles at the start and end times of the visible arc in a rectangular coordinate system: Its rotation trajectory is vector d s Rotation towards d e The resulting curved trajectory; Using the Gramm-Schmidt orthogonal method, calculate d m =d e -(d s ·d e )·d s , "·" indicates calculating the dot product of two vectors, and "×" indicates calculating the cross product of two vectors; d s With d m A pair of orthogonal bases forming the plane containing the rotation trajectory.

3. The fast calculation method for activation array elements based on trajectory plane projection as described in claim 2, characterized in that, The method for calculating the nearest activation angle on the rotation trajectory corresponding to different array elements under constraints is as follows: Calculate the range of rotation angles corresponding to the visible arc segment, L = acos(d e ·d s ); For any array element, obtain its rectangular coordinate position as e = [x0, y0, z0], and calculate its position in d. s With d m The coordinates x = d on the plane s ·e, y=d m ·e; Calculate the rotation angle α = atan(y / x) under unconstrained conditions. This angle represents the rotation angle of any array element in d. s With d m The projection vectors that constitute the plane and d s The size of the included angle; The rotation angle is restricted to the rotation trajectory, specifically: The line connecting the point "closest" to the rotation trajectory of the array element under constraints and the center of the phased array is obtained as follows: With e and The angle between them is used as the activation judgment angle, i.e., the activation angle.

4. The fast calculation method for activation array elements based on trajectory plane projection as described in claim 3, characterized in that, The activation angle is used to determine whether the corresponding array element is activated. The specific method is as follows: Determine e and If the included angle between them is less than a preset angle threshold Δ, then the array element is determined to be activated. Conversely, it remains inactive.

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