In-orbit optical axis rapid calibration method for a spaceborne laser communication terminal

Abstract

The present application relates to a kind of on-orbit optical axis fast calibration method of spaceborne laser communication terminal, to improve the pointing accuracy and stability of spaceborne laser communication system.The present application realizes the fast and accurate calibration of the optical axis of laser communication terminal by the comprehensive application of coordinate system conversion, error correction matrix, least square method optimization and golden section method etc.Technical means, the present application has comprehensively applied complex coordinate system conversion and error correction matrix, realizes the high-precision correction of theoretical pointing vector;Golden section method is used in combination with the optimization strategy of least square method, the convergence speed and accuracy of calibration process are improved;It has higher real-time and automation degree, can acquire and process relevant data in real time, realizes the real-time correction of optical axis pointing error;It has wide applicability and scalability, can be applied to other spacecraft systems needing high-precision pointing control.

Description

Technical Field

[0001] This invention belongs to the field of laser aerospace communication technology and can be applied to the correction of on-orbit pointing error in space laser communication. It overcomes the problems of large correction error and long on-orbit calibration time in traditional on-orbit calibration methods. Specifically, it is a rapid on-orbit optical axis calibration method for spaceborne laser communication terminals. Background Technology

[0002] With the continuous development of satellite communication technology, the application of inter-satellite services is becoming increasingly widespread, showing an exponential growth trend. Free-space optical communication has become the preferred method for long-distance inter-satellite communication due to its advantages such as high communication speed, low power consumption, and good confidentiality. Compared with traditional microwave communication, free-space optical communication uses laser as the information transmission carrier and has excellent directionality. Therefore, in order to ensure the stability and reliability of the communication link, the communication terminal needs to have high-precision pointing of the transmitted beam.

[0003] In recent years, the satellite internet field has developed rapidly. Given the limited frequency and orbital resources, both domestic and international companies have planned multiple mega-internet constellations. The US Starlink system plans to launch 42,000 satellites, and has already launched over 7,000, initially establishing a global satellite communication network. Europe's OneWeb has also launched over 600 satellites. my country has also planned multiple constellation projects, including the GW constellation, Hongyan constellation, Xingyun project, and Galaxy. Among these, the China Satellite Network Group, established in 2021, and the G60 Starlink system, launched in 2023, both plan to launch over 12,000 satellites. Inter-satellite laser communication technology features large communication capacity, miniaturization, and low power consumption. Point-to-point on-orbit laser communication is also maturing, providing a new solution for realizing satellite internet—namely, building a next-generation satellite optical network. From the current application perspective, inter-satellite laser communication networking is an inevitable trend. The next challenge is to improve the on-orbit robustness and service capabilities of laser communication links.

[0004] However, low-Earth orbit satellite constellations have limitations such as long communication distances, limited signal transmission power, fixed receiver sensor sensitivity, and limited receiver aperture, requiring beam divergence angles of tens of microradians. These small divergence angles make terminal acquisition difficult, necessitating precise alignment between the transmitting and target terminals. The laser communication terminal acquires the target star using a star sensor, allowing for on-orbit calibration of the transmitting optical axis's pointing deviation. Finally, the pointing error is reduced by correcting the terminal's mounting matrix.

[0005] Traditional pointing calibration methods employ a step-by-step search approach. This method not only suffers from large calibration errors and long cycles but also requires multiple iterations, proving inadequate for situations with significant error deviations. These problems severely restrict the efficiency of on-orbit link establishment and greatly impact the user experience. Therefore, achieving rapid and high-precision on-orbit calibration has become a major bottleneck in the development of current spaceborne laser communication terminal technology. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a rapid on-orbit optical axis calibration method for spaceborne laser communication terminals. This method employs convex optimization, is not limited by the search step size, and can achieve rapid and high-precision on-orbit calibration. This overcomes the problems of large correction errors and long on-orbit calibration time in traditional on-orbit calibration methods.

[0007] The technical solution of this invention is as follows:

[0008] A rapid on-orbit optical axis calibration method for a spaceborne laser communication terminal is disclosed. This method can be applied to correct on-orbit pointing errors in space laser communication, overcoming the problems of large correction errors and long on-orbit calibration times inherent in traditional on-orbit calibration methods, thereby improving the efficiency and success rate of space laser communication missions. The rapid on-orbit optical axis calibration method for a spaceborne laser communication terminal includes the following steps:

[0009] 1) Obtain the actual pointing vector based on the terminal azimuth and the motor angle value of the pitch axis;

[0010] 2) Calculate the theoretical pointing vector of the terminal based on the position vectors of the local satellite and the target satellite in the J2000.0 inertial coordinate system, the attitude matrix of the local satellite platform, and the theoretical installation matrix;

[0011] 3) Calculate the pointing errors of the laser communication terminal in terms of azimuth and elevation;

[0012] 4) The optimal installation angle correction matrix is ​​obtained by using the least squares optimization method to complete the rapid on-orbit optical axis pointing calibration.

[0013] In step 1), the actual pointing vector is obtained based on the terminal azimuth and the motor angle values ​​of the pitch axis.

[0014]

[0015] Among them, Az a El is the azimuth angle value in the coordinate system of the laser communication terminal. a This refers to the pitch angle value in the laser communication terminal coordinate system. Here, the X-axis of the terminal coordinate system is defined as the direction pointing from the azimuth and pitch of the ground-calibrated motor encoder disk, the Z-axis is vertically upward, and the Y-axis is determined by the right-hand rule direction defined by the Z-axis and X-axis.

[0016] Step 2) Based on the position vectors of the local satellite and the target satellite in the J2000.0 inertial coordinate system, the attitude matrix of the local satellite platform, and the theoretical installation matrix, the theoretical pointing vector of the terminal is calculated as follows:

[0017] 2.1 Position vector set V of the local and target satellites in the J2000.0 inertial coordinate system b and V t :

[0018]

[0019] 2.2 Based on the position vector set V of the local satellite and the target satellite in the J2000.0 inertial coordinate system b and V t Calculate the pointing vector set P of the target satellite relative to the local position:

[0020] P = V t -V b

[0021] 2.3 The attitude matrix of the local satellite platform is R J2000_to_satellite The attitude matrix is ​​the transformation matrix between the J2000.0 inertial coordinate system and the satellite body coordinate system, usually represented by Euler angles. Assuming the rotation angles around the X, Y, and Z axes are α, β, and γ respectively, the rotation matrix is...

[0022]

[0023] According to the rotation order "ZXY", the attitude matrix R of the local satellite platform is... J2000_to_satellite Represented as:

[0024]

[0025] 2.4 Theoretical Installation Matrix R satellite_to_terminal , is the transformation matrix from the satellite's own coordinate system to the laser communication terminal's coordinate system, including the transformation matrix R from the satellite's own coordinate system to the laser communication terminal's cube mirror (reference coordinate system). satellite_to_reference The transformation matrix R from the cubic mirror of the laser communication terminal to the terminal pointing coordinate system. reference_to_terminal And the installation error correction matrix R caused by thermal deformation, etc. rectification Among them, R reference_to_terminal The calibration method is to calculate the deviation between the motor encoder value and the motor zero position value of the reflected light from the terminal mirror and the cubic mirror into the same corner cone.

[0026] R satellite_to_terminal =R rectification *R reference_to_terminal *R satellite_to_reference

[0027]

[0028] Where α, β, and γ are the initial theoretical pointing vectors transformed into the corrected theoretical pointing vector R in the terminal coordinate system. satellite_to_terminal Rotation angles about the x, y, and z axes; rot(·) represents counterclockwise rotation about the axis. The correction matrix is ​​multiplied by the initial theoretical installation angle matrix to obtain the corrected theoretical installation angle matrix, thus completing the calibration.

[0029] 2.5 Based on the position vectors of the local satellite and the target satellite in the J2000.0 inertial coordinate system, the attitude matrix of the local satellite platform, and the theoretical installation matrix, the theoretical pointing vector set P of the laser communication terminal is calculated. cal for

[0030]

[0031] Among them, V x V y V z These are the x, y, and z coordinates of the theoretical pointing vector of the laser communication terminal in the J2000.0 inertial coordinate system.

[0032] 3. Step 3) Calculating the pointing errors of the laser communication terminal's azimuth and elevation is specifically as follows:

[0033] 3.1 The theoretical pointing vector set P of the laser communication terminal obtained in step 2.5 is... cal Substitute into the following formula to calculate the theoretical azimuth angle Az of the laser communication terminal. c And theoretical pitch angle El c

[0034]

[0035] 3.2 By using the theoretical azimuth angle Az of the laser communication terminal c and actual azimuth angle Az a The difference is used to obtain the azimuth pointing error e. Az The theoretical pitch angle El c And the actual pitch angle El a The difference is used to obtain the pitch angle pointing error e. El Thus, the deviations e of azimuth and pitch can be calculated. aft

[0036] e Az =Az c -Az a

[0037] e El =El c -El a

[0038]

[0039] Step 4) Use the optimization method based on the least squares method to obtain the optimal installation angle correction matrix, and complete the in-orbit rapid pointing calibration of the optical axis. In the calculation of the least squares method, the golden section method is used for iteration to find the optimal installation error correction matrix. This method has the advantages of a wide search range, being unrestricted by the search step size, small calibration error, and fast calibration speed. The specific steps are as follows:

[0040] The first step is to determine the initial interval. For the correction angles α, β, γ of the installation error correction matrix R rectification in Step 2.4, set the initial interval [a, b], where a is the upper boundary of the value range in degrees (°), b is the lower boundary of the value range in degrees (°), set the threshold epsilon, the boundary values are adjustable, and there is no need to set the step size.

[0041] The second step is to calculate two division points a1 and a2 within the interval [a, b] according to the golden section ratio (0.618 and 0.382)

[0042] a1 = b - 0.618 * (b - a)

[0043] a2 = a + 0.618 * (b - a)

[0044] The third step is to calculate the function values f(a1) and f(a2) at these two division points, so that the original interval is divided into three segments, where f(·) is to find the root mean square error e aft of the deviation of N azimuths and pitches, and N is the number of samples in the pointing vector set.

[0045] The fourth step is to utilize the unimodal property of the function according to the comparison result of the function values, remove the interval segments that do not contain the extreme point, and retain the interval segments that contain the extreme point.

[0046] The fifth step is to repeat the above steps on the retained interval, making the interval infinitely shrink until the threshold condition a N - a M < epsilon is satisfied. Among them, a N and a M are the interval ranges after the i-th iteration, so as to obtain an approximate solution of the optimal correction installation angle.

[0047] Compared with the prior art, the technical effects of the present invention:

[0048] 1) This invention compares the theoretical values ​​of azimuth and elevation pointing angles obtained from the theoretical values ​​of the installation matrix with measured data to correct the installation matrix parameters. By compensating for long-term on-orbit mechanical thermal deformation and ground assembly errors, the pointing angle of the laser communication terminal is corrected to ensure that the target satellite is within the effective field of view of the laser communication terminal and as close as possible to the center of the field of view. The optimal installation error correction matrix is ​​found using a convex optimization method, which differs from the traditional on-orbit calibration method's step-size search; instead, it uses a range search method, shortening the calibration time and improving calibration accuracy.

[0049] 2) It incorporates a complex transformation process involving the laser communication terminal coordinate system, the J2000.0 inertial coordinate system, the satellite body coordinate system, and the theoretical installation matrix. By calculating the positional relationship between the local satellite and the target satellite in the J2000.0 inertial coordinate system, and combining this with the attitude matrix of the local satellite platform, a precise transformation from the inertial coordinate system to the satellite body coordinate system, and then to the laser communication terminal coordinate system, is achieved. Simultaneously, an installation error correction matrix incorporating factors such as thermal deformation is introduced, enabling high-precision correction of the theoretical pointing vector and improving the accuracy of optical axis calibration.

[0050] 3) This invention achieves rapid on-orbit optical axis calibration by integrating complex coordinate system transformation and error correction processes. Compared to traditional calibration methods, this method offers higher real-time performance and automation. By acquiring the azimuth and pitch axis motor angles of the laser communication terminal in real time, as well as the position information of the local and target satellites, the deviation between the theoretical and actual pointing vectors can be quickly calculated, and the installation error correction matrix can be automatically adjusted to achieve real-time correction of the optical axis pointing error. This improvement in real-time performance and automation is of great significance for enhancing the stability and reliability of spaceborne laser communication systems. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the rapid on-orbit optical axis calibration method for a spaceborne laser communication terminal according to the present invention.

[0052] Figure 2 This defines the azimuth and elevation angles of the laser communication terminal in the J2000.0 inertial coordinate system for the rapid on-orbit optical axis calibration method of the spaceborne laser communication terminal of this invention. Detailed Implementation

[0053] The present invention will be further described below with reference to implementation examples and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention.

[0054] Please see Figure 1 , Figure 1 This is a flowchart illustrating the rapid on-orbit optical axis calibration method for a spaceborne laser communication terminal according to the present invention. As shown in the figure, the method includes the following steps:

[0055] Step 1. Obtaining the actual pointing vector:

[0056] Based on the azimuth and pitch axis motor angle values ​​of the laser communication terminal, the actual pointing vector of the terminal's optical axis in the current state is calculated using the following formula:

[0057]

[0058] In the formula, Az a El is the azimuth angle value in the coordinate system of the laser communication terminal. a It is the pitch angle value in the coordinate system of the laser communication terminal.

[0059] Define a terminal coordinate system to describe the terminal's azimuth, pitch, and optical axis orientation. In this coordinate system, the X-axis is the direction of the zero-position value of the motor encoder disk calibrated on the ground for azimuth and pitch. The Z-axis is vertically upward, opposite to the direction of Earth's gravity, representing the terminal's vertical direction. The Y-axis is determined by the Z-axis and X-axis through a right-hand rule.

[0060] Step 2. Calculation of the theoretical pointing vector:

[0061] Based on the position vectors of the local satellite and the target satellite in the J2000.0 inertial coordinate system, the attitude matrix of the local satellite platform, and the theoretical installation matrix, the theoretical pointing vector of the terminal is calculated.

[0062] 2.1 Calculate the position vector set V of the local and target stars in the J2000.0 inertial coordinate system. b and V t :

[0063]

[0064] 2.2 Calculate the pointing vector set P of the target satellite relative to the local position:

[0065] P = V t -V b

[0066] 2.3 The attitude matrix of the local satellite platform is R J2000_to_satellite The attitude matrix is ​​the transformation matrix between the J2000.0 inertial coordinate system and the satellite body coordinate system, usually represented by Euler angles. Assuming the rotation angles around the X, Y, and Z axes are α, β, and γ respectively, the rotation matrix is...

[0067]

[0068] According to the rotation order "ZXY", the attitude matrix R of the local satellite platform is... J2000_to_satellite Represented as:

[0069]

[0070] 2.4 Theoretical Installation Matrix R satellite_to_terminal , is the transformation matrix from the satellite's own coordinate system to the laser communication terminal's coordinate system, including the transformation matrix R from the satellite's own coordinate system to the laser communication terminal's cube mirror (reference coordinate system). satellite_to_reterence The transformation matrix R from the cubic mirror of the laser communication terminal to the terminal pointing coordinate system. reference_to_terminal And the installation error correction matrix R caused by thermal deformation, etc. rectification Among them, R reference_to_terminal The calibration method is to calculate the deviation between the motor encoder value and the motor zero position value of the reflected light from the terminal mirror and the cubic mirror into the same corner cone.

[0071] R satellite_to_terminal =R rectification *R reference_to_terminal *R satellite_to_reference

[0072]

[0073] Where α, β, and γ are the initial theoretical pointing vectors transformed into the corrected theoretical pointing vector R in the terminal coordinate system. satellite_t_oterminal Rotation angles about the x, y, and z axes; rot(·) represents counterclockwise rotation about the axis. The correction matrix is ​​multiplied by the initial theoretical installation angle matrix to obtain the corrected theoretical installation angle matrix, thus completing the calibration.

[0074] 2.5 Calculation of the theoretical pointing vector set P of the laser communication terminal cal :

[0075]

[0076] Among them, V x V y V z These are the x, y, and z coordinates of the theoretical pointing vector of the laser communication terminal in the J2000.0 inertial coordinate system.

[0077] Step 3. Calculate the pointing errors of the laser communication terminal in terms of azimuth and elevation;

[0078] 3.1 The theoretical pointing vector set P of the laser communication terminal obtained in step 2.5 is... cal Substitute into the following formula to calculate the theoretical azimuth angle Az of the laser communication terminal. c And theoretical pitch angle El c

[0079]

[0080] 3.2 By using the theoretical azimuth angle Az of the laser communication terminalc and actual azimuth angle Az a The difference is used to obtain the azimuth pointing error e. Az The theoretical pitch angle El c And the actual pitch angle El a The difference is used to obtain the pitch angle pointing error e. El Thus, the deviations e in azimuth and pitch are obtained. aft

[0081] e Az =Az c -Az a

[0082] e El =El c -El a

[0083]

[0084] Step 4. Use the least squares method to find the optimal installation angle correction matrix and complete the on-orbit optical axis rapid pointing calibration;

[0085] The least squares method employs the golden section method to iteratively find the optimal installation error correction matrix. This method has advantages such as a wide search range, no limitation on the search step size, small error after calibration, and fast calibration speed. The specific steps are as follows:

[0086] The first step is to determine the initial interval. For the installation error correction matrix R in step 2.4... rectification The correction angles α, β, and γ are set to an initial interval [a, b], where a is the upper boundary of the range in degrees (°) and b is the lower boundary of the range in degrees (°). The threshold epsilon is set, and the boundary values ​​are adjustable without setting a step size.

[0087] The second step is to calculate two dividing points a1 and a2 within the interval [a, b] according to the golden ratio (0.618 and 0.382).

[0088] a1 = b - 0.618 * (ba)

[0089] a² = a + 0.618 * (ba)

[0090] The third step is to calculate the function values ​​f(a1) and f(a2) at these two dividing points so that the original interval is divided into three segments, where f(·) is the deviation e for N azimuth and elevation. aft The root mean square error is N, where N is the number of samples in the pointing vector set.

[0091] The fourth step is to use the unimodal property of the function to remove the interval segments that do not contain extreme points and retain the interval segments that do contain extreme points based on the comparison results of the function values.

[0092] Fifth, repeat the above steps on the retained interval, making the interval infinitely smaller until the threshold condition a is met. N -a M <epsilon. Where, a N and a M Let be the interval range after the i-th iteration, thus obtaining an approximate solution for the optimal corrected installation angle.

[0093] This embodiment firstly, it comprehensively applies complex coordinate system transformations and error correction matrices to achieve high-precision correction of the theoretical pointing vector; secondly, it employs an optimization strategy combining the golden section method and the least squares method, improving the convergence speed and accuracy of the calibration process; thirdly, it has higher real-time performance and automation, capable of acquiring and processing relevant data in real time to achieve real-time correction of optical axis pointing errors; and fourthly, it has broad applicability and scalability, and can be applied to other spacecraft systems requiring high-precision pointing control. This invention provides an efficient and accurate on-orbit optical axis calibration method for spaceborne laser communication terminals, which is of great significance for improving the performance and stability of spaceborne laser communication systems.

Claims

1. A method for in-orbit optical axis fast calibration of a spaceborne laser communication terminal, characterized in that, The method includes the following steps: Step 1. Obtaining the actual pointing vector: Based on the azimuth axis motor angle value and the pitch axis motor angle value of the laser communication terminal, the actual pointing vector is calculated in the coordinate system of the laser communication terminal. The X-axis of the coordinate system of the laser communication terminal is defined as the pointing direction of the zero position value of the azimuth and pitch motor encoder disk calibrated on the ground, the Z-axis is vertically upward, and the Y-axis is determined by the right-hand system direction determined by the Z-axis and the X-axis. Step 2. Calculation of the theoretical pointing vector: Based on the position vectors of the local satellite and the target satellite in the J2000.0 inertial coordinate system, the attitude matrix of the local satellite platform, and the theoretical installation matrix, the theoretical pointing vector of the laser communication terminal is calculated, specifically including: 2.1) Obtain the position vector sets of the local satellite and the target satellite in the J2000.0 inertial coordinate system; 2.2) Calculate the pointing vector set of the target satellite relative to the local position based on the position vector set; 2.3) Based on the attitude matrix of the local satellite platform, convert the position vector in the J2000.0 inertial coordinate system into the position vector in the satellite body coordinate system; 2.4) converting the position vector in the satellite body coordinate system into a theoretical pointing vector in the laser communication terminal coordinate system by using a theoretical installation matrix; wherein the theoretical installation matrix comprises a conversion matrix from the satellite body system to the laser communication terminal cube mirror , a conversion matrix from the laser communication terminal cube mirror to the terminal pointing coordinate system , and a mounting error correction matrix caused by thermal deformation , and obtaining a correction matrix by calculating the deviation of the motor code disc value and the motor zero value of the reflected light of the terminal mirror and the cube mirror into the same angular cone, and multiplying the initial theoretical installation angle matrix to obtain a corrected theoretical installation angle matrix; The corrected theoretical installation angle matrix Obtained through the following methods: in, The initial theoretical pointing vector is transformed into the corrected theoretical pointing vector in the terminal coordinate system. Rotation angles about the x-axis, y-axis, and z-axis; The rotation is counterclockwise around the axis; by multiplying the obtained correction matrix with the initial theoretical installation angle matrix, the corrected theoretical installation angle matrix is ​​finally obtained, and the calibration is completed. Step 3. Calculate the pointing error between the actual pointing vector and the theoretical pointing vector of the laser communication terminal, specifically including: 3.1) Convert the calculated theoretical pointing vector into theoretical azimuth and theoretical elevation angles; 3.2) Compare the theoretical azimuth and theoretical elevation angles with the actual azimuth and actual elevation angles of the laser communication terminal, respectively, and calculate the azimuth pointing error and elevation pointing error; Step 4. Using the least squares optimization method, within the set initial range of correction angles, the optimal installation error correction matrix is ​​iteratively found using the golden section method to minimize the azimuth and pitch pointing errors, thus completing the rapid on-orbit optical axis pointing calibration. This specifically includes: 4.1) Set the initial range and threshold of the correction angle for the installation error correction matrix; 4.2) Within the initial interval, calculate two dividing points according to the golden ratio; 4.3) Calculate the function values ​​at these two dividing points, i.e., the root mean square error of the N azimuth and pitch deviations; 4.4) Based on the comparison results of function values, remove the interval segments that do not contain extreme points and retain the interval segments that do contain extreme points; 4.5) Repeat the above steps on the reserved interval until the threshold condition is met to obtain an approximate solution for the optimal corrected installation angle.

2. The method for rapid on-orbit optical axis calibration of a spaceborne laser communication terminal according to claim 1, characterized in that, In step 1, the actual pointing vector is obtained based on the terminal azimuth and the motor angle values ​​of the pitch axis. in, It is the azimuth angle value in the coordinate system of the laser communication terminal. It is the pitch angle value in the coordinate system of the laser communication terminal.

3. The method for rapid on-orbit optical axis calibration of a spaceborne laser communication terminal according to claim 1, characterized in that, Step 2. The attitude matrix of the Zhongben satellite platform is the transformation matrix of the J2000.0 inertial coordinate system relative to the satellite body coordinate system. It is represented by Euler angles and calculated based on the rotation angles around the X-axis, Y-axis and Z-axis.

4. The method for rapid on-orbit optical axis calibration of a spaceborne laser communication terminal according to claim 2, characterized in that, 3.1) converts the calculated theoretical pointing vector into a theoretical azimuth angle. and theoretical pitch angle The formula is as follows: In the formula, These are the x, y, and z coordinates of the theoretical pointing vector of the laser communication terminal in the J2000.0 inertial coordinate system.

5. The method for rapid on-orbit optical axis calibration of a spaceborne laser communication terminal according to claim 4, characterized in that, In step 3.2), the theoretical azimuth and theoretical elevation angles are compared with the actual azimuth and actual elevation angles of the laser communication terminal, respectively, to calculate the azimuth pointing error. and pitch angle pointing error The formula is as follows: In the formula, , For the theoretical and actual azimuth angles of the laser communication terminal, This refers to the deviation in azimuth and pitch.

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