A method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation

Abstract

The present invention discloses a method for correcting the non-linear pointing error of a telescope based on kernel weight function estimation. The specific steps are as follows: First, track and observe multiple stars on a moving platform. Through the observation data and the pointing error correction method, calculate the azimuth angle and elevation angle of each star in the inertial navigation system, and calculate the residual non-linear azimuth pointing error and elevation pointing error of the telescope for each star after correction by the pointing error correction method. Then, establish a kernel weight function estimation model for the non-linear azimuth pointing error and elevation pointing error of the target, and use the generalized cross-validation method to determine the window width parameter required for kernel weight function estimation. Finally, according to the position information of the target, on the basis of correcting the linear pointing error by the pointing error correction method, use the established kernel weight function estimation model to estimate the non-linear azimuth pointing error and elevation pointing error of the target, and then obtain the further corrected guiding value to guide the telescope to point at the target quickly and with high precision. The correction accuracy of the present invention is high.

Description

Technical Field

[0001] The present invention relates to the technical field of telescope pointing correction under a moving platform, and specifically relates to a method for correcting the non-linear pointing error of a telescope based on kernel weight function estimation. Background Art

[0002] Telescopes play a very important role in fields such as optical communication and astronomical observation. For a telescope to meet the usage requirements, it must have high-precision acquisition, tracking, and aiming functions. Among them, acquisition is the prerequisite for tracking and aiming. To achieve fast and high-probability target acquisition, the telescope must have high-precision pointing. Therefore, high-precision pointing has become the key to whether the telescope can work properly.

[0003] Currently, ground-based and moving platform-based are the two main working environments of telescopes. The source of the pointing error of ground-based telescopes is mainly the geometric error of the telescope system itself. The geometric error is linear and can be well corrected through the rack model. However, for moving platform-based telescopes, in addition to the linear geometric error, there is also a considerable part of non-linear error. The sources of these non-linear errors are unknown and the action mechanism is not clear, making it difficult to establish a parameterized mathematical model for correction. To ensure the pointing accuracy of the telescope on the moving platform, it is necessary to correct the non-linear part of the pointing error, which has become the key to improving the pointing accuracy of the telescope on the moving platform. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for correcting the non-linear pointing error of a telescope based on kernel weight function estimation, which is used to achieve fast and high-precision pointing of a moving platform telescope.

[0005] The technical solution adopted by the present invention is as follows: A method for correcting the non-linear pointing error of a telescope based on kernel weight function estimation, which has the following steps:

[0006] Step (1): Use the telescope installed on the moving platform to observe n stars, record the azimuth angle A of each star in the horizon coordinate system ei , elevation angle E ei , and record the measured azimuth angle A of the telescope for the star i , elevation angle E i , as well as the three attitude angles of the moving platform measured by the attitude sensor, namely the heading angle H i , elevation angle P i and roll angle R i , i = 1, 2 ··· n.

[0007] Step (2): Obtain the remaining azimuth pointing error ΔA of the telescope for each star after correction through the recorded information and the pointing error correction method obtained by derivation using D-H matrix modeling / the pointing error correction method in Chinese Patent Application CN202110646764.8 i and the remaining elevation pointing error ΔE i , ΔA i and ΔE i are actually the non-linear parts of the pointing error.

[0008] Step (3): Convert the azimuth angle and elevation angle of each star in the horizon system to the azimuth angle A gi and elevation angle E gi in the inertial navigation system through the three attitude angles.

[0009] Step (4): Based on the remaining non-linear azimuth pointing error ΔA i and elevation pointing error ΔE i as well as the azimuth angle A gi and elevation angle E gi of each star in the inertial navigation system, establish a kernel weight function estimation model for the non-linear azimuth pointing error ΔA c and elevation pointing error ΔE c of the target.

[0010] Step (5): Determine the window widths h A and h E using the generalized cross-validation method.

[0011] Step (6): Obtain the azimuth angle A t , elevation angle E t of the target in the horizon system, and the attitude angles (H t , P t , R t ) of the moving platform measured by the attitude sensor. According to the pointing error correction method obtained by derivation using D-H matrix modeling / the pointing error correction method in Chinese Patent Application CN202110646764.8, obtain the theoretical azimuth angle A c and elevation angle E c of the target relative to the telescope after correction.

[0012] Step (7): Convert the azimuth angle and elevation angle of the target in the horizon system to the azimuth angle A α and elevation angle E α in the inertial navigation system.

[0013] Step (8): Estimate the non-linear azimuth pointing error ΔA c and elevation pointing error ΔE c of the target using the established kernel weight function estimation model.

[0014] Step (9), use A c +ΔA c , E c +ΔE c to obtain the guiding value Guide the moving platform telescope to quickly and accurately point to the target. The guiding value is the angle that the azimuth axis and elevation axis of the telescope need to rotate to point to the target.

[0015] Furthermore, in step (1), select the stars evenly distributed within the hemisphere above the observation station as the observed stars, and the telescope needs to observe in different postures, ensuring that the sampling points are closely distributed in the polar coordinate system of the inertial navigation.

[0016] Furthermore, in step (2), first calculate the theoretical azimuth angle A oi and elevation angle E oi of each star relative to the telescope after correction by the pointing error correction method, and then calculate the corresponding residual non-linear azimuth pointing error ΔA i and elevation pointing error ΔE i .

[0017] Furthermore, in step (3), first calculate the unit direction vector (x gi , y gi , z gi ) T of each star in the inertial navigation system, and then calculate the azimuth angle A gi and elevation angle E gi of each star in the inertial navigation system. Step (7) is the same.

[0018] Furthermore, in step (4), taking the example of establishing the kernel weight function estimation model of the non-linear azimuth pointing error ΔA c of the target, assuming that the azimuth angle A α and elevation angle E α of the target in the inertial navigation system are known. First, calculate the azimuth angle distance d Ai and elevation angle distance d Ei between the target and n stars in the inertial navigation system, then calculate the angular Euclidean distance d i between the target and n stars in the inertial navigation system. Then, according to the kernel function K(·), define the corresponding kernel weight function Finally, use the kernel weight function and the non-linear azimuth pointing error ΔA i of each star to estimate the non-linear azimuth pointing error ΔA c of the target, and select the Gaussian function as the kernel function K(·). The kernel weight function estimation method for the non-linear elevation pointing error ΔE c of the target is the same as that of ΔA cThe estimation method is the same.

[0019] Further, in step (5), taking the estimation of the non-linear azimuth pointing error as an example, the non-linear azimuth pointing errors ΔA of the n stars are estimated successively by the kernel weight function estimation method i , and the estimation equation is written in matrix form, then the residual sum of squares RSS(h) of the kernel weight function estimation is calculated, and then the generalized cross-validation value GCV(h) is calculated. Finally, a suitable window width h A is selected to minimize the generalized cross-validation value GCV(h). h A is the window width for estimating the non-linear azimuth pointing error by the kernel weight function. Similarly, the window width h for estimating the non-linear pitch pointing error by the kernel weight function can be obtained E .

[0020] Further, in step (7), first calculate the unit direction vector of the target in the inertial navigation system, and then calculate the azimuth angle A α and the pitch angle E α of the target in the inertial navigation system. This calculation method is the same as that in step (3).

[0021] Further, in step (8), through the window widths h A and h E , as well as the residual non-linear azimuth pointing errors ΔA i and pitch pointing errors ΔE i of each star, and the angular Euclidean distance d i between the target and the n stars, calculate the non-linear azimuth pointing error ΔA c and pitch pointing error ΔE c of the target.

[0022] The advantages of the present invention compared with the prior art are as follows:

[0023] (1) On the basis of correcting the linear pointing error by the pointing error correction method of the present invention, the non-linear pointing error of the telescope on the moving platform can be corrected, so as to further improve the pointing accuracy.

[0024] (2) The kernel weight function estimation method adopted by the present invention is a non-parametric estimation method, which avoids the complex physical modeling process and makes the correction of the non-linear pointing error simple and easy to implement.

[0025] (3) The method of the present invention can make the pointing correction process fully automated, realizing the fast and high-precision pointing of the telescope on the moving platform. Brief Description of the Drawings

[0026] Figure 1 is a processing flow chart of a method for correcting the non-linear pointing error of a telescope based on kernel weight function estimation according to the present invention. Detailed implementation manners

[0027] The following will make a detailed description of the specific implementation manners of the present invention with reference to the accompanying drawings.

[0028] The specific process of a telescope non - linear pointing error correction method based on kernel weight function estimation according to the present invention is as shown in the accompanying Figure 1 drawing, and the specific steps are as follows:

[0029] (1) Use the telescope installed on the moving platform to observe n stars, record the azimuth angle A ei and elevation angle E ei of each star in the horizon system, and record the measured azimuth angle A i and elevation angle E i of the telescope with respect to the stars, as well as the three attitude angles of the moving platform measured by the attitude sensor, namely the heading angle H i and elevation angle P i and roll angle R i , where i = 1, 2 ··· n.

[0030] (2) Through the recorded information and the pointing error correction method in the Chinese patent application for invention CN202110646764.8, obtain the residual azimuth pointing error ΔA i and residual elevation pointing error ΔE i after correction. ΔA i and ΔE i are actually the non - linear parts of the pointing error. The specific method is as follows:

[0031] Assume that the function expression of the pointing error correction method in Chinese patent CN202110646764.8 is f(·), then the theoretical azimuth angle A oi and elevation angle E oi of each star relative to the telescope after correction are:

[0032] (A oi , E oi ) = f(A ei , E ei , H i , P i , R i ) (1)

[0033] The corresponding residual non - linear azimuth pointing error ΔA i and elevation pointing error ΔE i are:

[0034]

[0035] (3) Through the three attitude angles, convert the azimuth angle and pitch angle of each star in the horizon system into the azimuth angle A gi and pitch angle E gi . The specific method is as follows:

[0036]

[0037] where (x gi , y gi , z gi ) T is the unit direction vector of each star in the inertial navigation system.

[0038] Then the azimuth angle A gi and pitch angle E gi of each star in the inertial navigation system are:

[0039]

[0040] (4) According to the residual non-linear azimuth pointing error ΔA i and pitch pointing error ΔE i as well as the azimuth angle A gi and pitch angle E gi of each star in the inertial navigation system, establish a kernel weight function estimation model for the non-linear azimuth pointing error ΔA c and pitch pointing error ΔE c of the target. Taking the establishment of the kernel weight function estimation model for the non-linear azimuth pointing error ΔA c of the target as an example, the specific method is as follows:

[0041] Assume that the azimuth angle A α and pitch angle E α of the target in the inertial navigation system are known. First, calculate the azimuth angle distance d Ai and pitch angle distance d Ei between the target and n stars in the inertial navigation system:

[0042] d Ai = min(|A α - A gi |, 2π - |A α - A gi |), d Ei = |E α - E gi |, i = 1, 2…n (5)

[0043] Then calculate the angular Euclidean distance d i between the target and n stars in the inertial navigation system:

[0044]

[0045] Then, according to the kernel function K(·), the corresponding kernel weight function is defined as follows:

[0046]

[0047] where the window width h is the smoothing parameter of the kernel weight function.

[0048] The non - linear azimuth pointing error ΔA of the finally estimated target c is as follows:

[0049]

[0050] Select the Gaussian function as the kernel function K(·):

[0051]

[0052] The non - linear elevation pointing error ΔE of the target c has the same estimation method of the kernel weight function as that of ΔA c .

[0053] (5) Determine the window width h A and h E using the generalized cross - validation method. Taking the estimation of the non - linear azimuth pointing error as an example, the specific method is as follows:

[0054] Estimate the non - linear azimuth pointing error ΔA of the above - mentioned n stars in turn using the kernel weight function estimation method i . The estimated value of each star is as follows:

[0055]

[0056] where d ij is the angular Euclidean distance between the i - th star and the j - th star in the inertial navigation system, and is calculated by formula (5 - 6).

[0057] Write equation (10) in matrix form:

[0058]

[0059] where

[0060]

[0061] Calculate the residual sum of squares RSS(h) of the kernel weight function estimation:

[0062]

[0063] Calculate the generalized cross - validation GCV(h):

[0064]

[0065] Select an appropriate window width to minimize the value of the Generalized Cross Validation (GCV)(h), that is, the window width h for estimating the non-linear azimuth pointing error using the kernel weight function A is:

[0066]

[0067] Similarly, the window width h for estimating the non-linear pitch pointing error using the kernel weight function can be obtained E .

[0068] (6) Obtain the azimuth angle A of the target in the horizon coordinate system t , pitch angle E t , and the attitude angles (H t , P t , R t ) of the moving platform measured by the attitude sensor. According to the pointing error correction method in the Chinese invention patent application CN202110646764.8, the corrected theoretical azimuth angle A c and pitch angle E c of the target relative to the telescope are obtained. The calculation method is the same as formula (1).

[0069] (7) Convert the azimuth angle and pitch angle of the target in the horizon coordinate system to the azimuth angle A α and pitch angle E α in the inertial navigation coordinate system. The calculation method is the same as in step (3).

[0070] (8) Estimate the non-linear azimuth pointing error ΔA c and pitch pointing error ΔE c of the target using the established kernel weight function estimation model. The specific method is:

[0071] Through the window widths h A and h E , as well as the residual non-linear azimuth pointing error ΔA i and pitch pointing error ΔE i of each star, and the angular Euclidean distance d i between the target and n stars, calculate the non-linear azimuth pointing error ΔA c and pitch pointing error ΔE c of the target. The calculation method is the same as formula (8).

[0072] (9) Use A c +ΔA c , E c +ΔE c to obtain the guiding value Guide the moving platform telescope to quickly and accurately point to the target. The guiding value is the angle that the azimuth axis and elevation axis of the telescope need to rotate to point to the target.

[0073] The method of the present invention can correct the non-linear pointing error of the telescope on the moving platform, with high correction accuracy. Moreover, the correction method avoids the complex physical modeling process, is easy to implement, has stable performance, and can achieve the quick and high-precision pointing of the telescope on the moving platform.

[0074] As mentioned above, it is only the specific implementation manner in the present invention, but the protection scope of the present invention is not limited thereto. Any transformation or replacement that can be understood and conceived by those familiar with the technology within the technical scope disclosed by the present invention should be covered within the scope of the present invention. The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

Claims

1. A method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation, characterized in that: The method has the following steps: Step (1): Observe n stars with a telescope installed on a moving platform, and record the azimuth angles of the stars in the horizon coordinate system , elevation angles , and record the measured azimuth angles , elevation angles of the telescope with respect to the stars, as well as the three attitude angles of the moving platform measured by an attitude sensor, namely the heading angle H i , elevation angle P i and roll angle R i , where i = 1, 2 ··· n; Step (2): Obtain the remaining azimuth pointing errors and elevation pointing errors of the telescope for each star after correction through the above-recorded information and the pointing error correction method derived by modeling with the D-H matrix and the remaining elevation pointing errors , and which are actually the non-linear parts of the pointing errors; Step (3), convert the azimuth angle and elevation angle of each star in the horizon coordinate system into the azimuth angle in the inertial navigation coordinate system through the three attitude angles and elevation angle ; Step (4), based on the azimuth pointing residual error and the pitch pointing residual error as well as the azimuth angles of the respective stars in the inertial navigation system and the pitch angles , establish a kernel weight function estimation model for the nonlinear azimuth pointing error and the pitch pointing error of the target; Assume the azimuth angle of the target in the inertial navigation system and pitch angle are known. First, calculate the azimuth angle distance d Ai and pitch angle distance d Ei between the target and n stars in the inertial navigation system as follows: ， ， (5) Calculate the angular Euclidean distance d between the target and n stars in the inertial navigation system again i : (6) Then, according to the kernel function , define the corresponding kernel weight function as follows: (7) Among them, the window width h is the smoothing parameter of the kernel weight function; Final estimated non-linear azimuth pointing error of the target is as follows: (8) Select the Gaussian function as the kernel function : (9) Nonlinear pitch pointing error of the target The kernel weight function estimation method of is the same as the estimation method of Step (5), determining the window width using the generalized cross-validation method and ; Step (6), obtain the azimuth angle of the target in the horizon coordinate system , elevation angle , and the attitude angle of the moving platform measured by the attitude sensor . According to the pointing error correction method derived by modeling based on the D-H matrix, obtain the corrected theoretical azimuth angle and elevation angle of the target relative to the telescope; Step (7), convert the azimuth angle and elevation angle of the target in the horizon coordinate system into the azimuth angle and elevation angle ; Step (8), estimating the non-linear azimuth pointing error and pitch pointing error of the target using the established kernel weight function estimation model and pitch pointing error ; Step (9), use to obtain a guiding value , and guide the moving platform telescope to quickly and accurately point to the target. The guiding value is the angle that the azimuth axis and elevation axis of the telescope need to rotate to point to the target.

2. The method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (1), stars evenly distributed within the hemisphere above the observation station are selected as the observed stars, and the telescope needs to perform observations in different postures, ensuring that the sampling points are closely distributed in the polar coordinate system of the inertial navigation.

3. The method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (2), first calculate the theoretical azimuth angles of the respective stars relative to the telescope after correction by the pointing error correction method and elevation angles , and then calculate the corresponding azimuth pointing residual error and elevation pointing residual error .

4. The method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (3), first calculate the unit direction vectors of each star in the inertial navigation system , and then calculate the azimuth angles of each star in the inertial navigation system and pitch angles .

5. The method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (4), the nonlinear azimuth pointing error of the target is established The kernel weight function estimation model assumes that the azimuth of the target in the inertial navigation system is and pitch angle It is known that we first calculate the azimuth distance d between the target and n stars in the inertial navigation system. Ai and pitch angle distance d Ei , and then calculate the angular Euclidean distance d between the target and n stars in the inertial navigation system i , and then according to the kernel function , define the corresponding kernel weight function , and finally use the kernel weight function and the residual error of the azimuth pointing of each star Estimating the nonlinear heading error of a target , select Gaussian function as kernel function , the nonlinear pitch pointing error of the target The kernel weight function estimation method and The estimation method is the same.

6. The method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (5), taking the estimation of the non-linear azimuth pointing error as an example, the azimuth pointing residual errors of the n stars are first estimated one by one using the kernel weight function estimation method , and the estimation equation is written in matrix form. Then, the residual sum of squares RSS(h) of the kernel weight function estimation is calculated, and the generalized cross-validation value GCV(h) is calculated. Finally, a suitable window width h A is selected to minimize the generalized cross-validation value GCV(h). h A is the window width for estimating the non-linear azimuth pointing error using the kernel weight function. Similarly, the window width for estimating the non-linear pitch pointing error using the kernel weight function is obtained .

7. A method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (7), first calculate the unit direction vector of the target in the inertial navigation system, and then calculate the azimuth angle of the target in the inertial navigation system and the pitch angle .

8. A method for correcting the non - linear pointing error of a telescope based on kernel weight function estimation according to claim 1, characterized in that: In step (8), through the window width and , as well as the azimuth pointing residual error of each star and the pitch pointing residual error , and the angular Euclidean distance d i between the target and n stars, calculate the non-linear azimuth pointing error and the pitch pointing error of the target.

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