Modeling and correcting method and system for static pointing error of horizontal telescope

Abstract

The invention belongs to the technical field of astronomical observation equipment, and particularly relates to a modeling and correcting method and system for static pointing errors of a horizontal telescope. The method comprises the following steps: S1, establishing a horizontal telescope static pointing model, and analyzing shafting error factors of the telescope; s2, deducing a telescope shafting static pointing error compensation model based on the static pointing model; s3, substituting experimental data, fitting the data by using a least square method, and determining each undetermined coefficient of the compensation model; and S4, correcting the static pointing error of the warp axis and the weft axis of the telescope by using the compensation model. The method has the characteristics that the observation precision can be improved, the calibration efficiency is improved, and the applicability is wide.

Description

Technical Field

[0001] This invention belongs to the field of astronomical observation equipment technology, specifically relating to a modeling and correction method and system for static pointing error of horizontal telescopes. Background Technology

[0002] Since the 1990s, countries have accelerated the development and launch of low-Earth orbit (LEO) satellites. Due to their low communication latency and relatively low launch costs, LEO satellites have become a key area of ​​development in modern satellite technology. Currently, there are over 4,000 LEO satellites globally, accounting for more than 80% of all satellites. In 2020 and 2021 alone, 1,122 and 1,664 LEO satellites were launched globally, respectively. This indicates that the number of LEO satellites on Earth will continue to grow rapidly over time. Rapidly detecting and accurately tracking LEO satellites has become a pressing technical challenge for countries in astronomical observation and space exploration.

[0003] Currently, the detection and tracking of ground-based targets mainly rely on radar technology and photoelectric telescope technology. Compared with radar technology, the detection capability of photoelectric telescopes is inversely proportional to the square of the effective range, offering higher detection efficiency and lower energy consumption in target detection and tracking. Based on their mechanical structures, photoelectric telescopes are mainly divided into three types: altazimuth, equatorial, and horizontal. Among them, horizontal telescopes have received widespread attention in recent years due to their absence of blind spots in the zenith region and their ability to cover any observation location within the latitude and longitude axes, particularly demonstrating significant advantages in missions involving precise tracking of low-Earth orbit satellites.

[0004] However, various errors inevitably occur during the manufacturing, installation, and use of horizontal telescopes. These errors cause the telescope's pointing direction to deviate from the theoretical target, thus reducing observation accuracy; these are collectively referred to as static pointing errors. In practical applications, axis error is the most common and impactful type of error. The mechanical structure of a horizontal telescope consists of a meridian axis and a parallel axis. Theoretically, these two axes should be perpendicular to each other and parallel to the ground plane, with the meridian axis pointing precisely in the north-south direction and the parallel axis pointing precisely in the east-west direction. However, due to the superposition of the aforementioned errors, the static pointing accuracy of horizontal telescopes often fails to meet the requirements of high-precision observations.

[0005] To address the above problems, this invention establishes a static pointing error compensation model based on the static pointing model of a horizontal telescope, taking into account various error factors such as axis system error, code disk error, and zero-point error. This model corrects the axis system error of a dual horizontal telescope, thereby improving the static pointing accuracy of the dual horizontal telescope. Summary of the Invention

[0006] The present invention aims to overcome the problem of static pointing error that easily occurs in the manufacturing, installation and use of existing horizontal telescopes, and provides a modeling and correction method and system for static pointing error of horizontal telescopes that can improve observation accuracy, improve calibration efficiency and has wide applicability.

[0007] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0008] The modeling and correction method for static pointing error of a horizontal telescope includes the following steps;

[0009] S1. Establish a static pointing model of a horizontal telescope and analyze the axis error factors of the telescope.

[0010] S2, Based on the static pointing model, derive the static pointing error compensation model of the telescope axis system;

[0011] S3, Substitute the experimental data, fit the data using the least squares method, and determine the undetermined coefficients of the compensation model;

[0012] S4 uses a compensation model to correct the static pointing errors of the telescope's meridian and parallel axes.

[0013] Preferably, step S1 includes the following steps:

[0014] S11, the mechanical structure of the horizontal telescope consists of a meridian axis and a parallel axis, and the corresponding static pointing model is established as follows:

[0015] (1);

[0016] (2);

[0017] in, Indicates the rotation angle of the warp axis. The angle of rotation of the latitude axis; For the warp rotation angle error, The latitudinal axis rotation error; a1, a2, a3, a4, a5, a5, a6, a7, b1, b2, b3, b4, and b5 are all parameters of the static pointing model of the horizontal telescope.

[0018] Preferably, in step S1, the telescope's axis error factors include:

[0019] Null position error: The error caused by the offset of the telescope's initial calibration point;

[0020] Code disk installation error: Geometric deviations that occur during the installation of the encoder or sensor;

[0021] Non-perpendicularity error of warp and weft axes: Error introduced by the warp and weft axes not being perfectly perpendicular during machining or assembly;

[0022] Perpendicularity error between the telescope's line of sight and the horizontal plane: the angular error between the telescope's line of sight and the horizontal plane.

[0023] Meridian alignment error: The error caused by the meridian not being perfectly aligned with the north-south direction;

[0024] Warp axis tilt error: Pointing deviation caused by warp axis tilt.

[0025] Preferably, step S2 includes the following steps:

[0026] S21. Establish a horizontal three-dimensional coordinate system. The horizontal three-dimensional coordinate system takes the installation position of the telescope as the origin and defines the directions of the three axes, which are perpendicular to the ground plane, to form a coordinate system based on the ground plane. In the coordinate system, the longitude axis of the horizontal telescope is parallel to the ground plane and points in the north-south direction, and the latitude axis is perpendicular to the longitude axis and points in the east-west direction.

[0027] S22, Analyzing formulas (1) and (2), the static pointing error compensation model for the shaft system is derived, as follows:

[0028] when At that time, the error compensation model for the horizontal telescope's warp axis system is expressed as:

[0029] (3);

[0030] (4);

[0031] Summarized as follows:

[0032] (5);

[0033] (6);

[0034] when At that time, the error compensation model for the latitudinal axis system of a horizontal telescope is expressed as:

[0035] (7);

[0036] (8);

[0037] Summarized as follows:

[0038] (9);

[0039] (10);

[0040] Where A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, and D3 are the undetermined coefficients after the integration of the error compensation model.

[0041] Preferably, step S3 includes the following steps:

[0042] S31, Obtain pointing error data through actual observation:

[0043] In the experiment, at least 50 stars distributed along the meridian and parallel axes from the HIP catalog were selected as observation targets, and the theoretical positions of each star were recorded. ) and actual observation location ( Using the deviation between the actual observed position and the theoretical position of a star as input data, the static pointing error of the axis system is calculated. :

[0044] (11)

[0045] S32, after obtaining the static pointing error of the shaft system Then, the static pointing error data is substituted into the model equations (5), (6), (9) and (10), and the error data is used as the input for least squares fitting.

[0046] S33, The error data is fitted using the least squares method:

[0047] By solving the linear equation system of formulas (5), (6), (9), and (10) or using a numerical optimization algorithm, the sum of squared errors is minimized, and the optimal values ​​of the undetermined coefficients A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, and D3 are obtained. Specifically,

[0048] For the warp axis, when B=0, the pointing error model ΔL (Equation 5) has the following sum of squared errors:

[0049]

[0050] By minimizing Solving for undetermined coefficients .

[0051] For the latitude axis, when B=0, the pointing error model ΔB (Equation 6) has the following sum of squared errors:

[0052]

[0053] By minimizing Solving for undetermined coefficients .

[0054] For the warp axis, when L=0, the pointing error model ΔL (Equation 9) has the following sum of squared errors:

[0055]

[0056] By minimizing Solving for undetermined coefficients .

[0057] For the latitude axis, when L=0, the pointing error model ΔB (Equation 10) has the following sum of squared errors:

[0058]

[0059] By minimizing Solving for undetermined coefficients In the above formulas, Under the condition B=0, the first Static pointing error at each observation point; Under the condition of L=0, the first Static pointing error at each observation point; This represents the number of valid observation data points under the corresponding conditions.

[0060] Preferably, step S4 includes the following steps:

[0061] S41, Settings , as well as These refer to the longitude axis (L), the latitude axis (B), and the overall static pointing accuracy of the system, which can be calculated using the standard deviation formula, as follows:

[0062] (12);

[0063] (13);

[0064] (14);

[0065] Where n is the number of stars in this observation experiment; For the first One observation point.

[0066] Using equations (12)-(14), the meridian pointing accuracy and the parallel pointing accuracy before and after the compensation model correction are calculated.

[0067] This invention also provides a modeling and correction system for the static pointing error of a horizontal telescope, including:

[0068] The model building module is used to build a static pointing model of a horizontal telescope and analyze the axis error factors of the telescope.

[0069] The model derivation module is used to derive the static pointing error compensation model of the telescope axis system based on the static pointing model.

[0070] The module for determining undetermined coefficients is used to input experimental data, fit the data using the least squares method, and determine the undetermined coefficients of the compensation model.

[0071] The correction module is used to correct the static pointing errors of the telescope's meridian and parallel axes using a compensation model.

[0072] Compared with the prior art, the beneficial effects of this invention are: (1) Improved observation accuracy: This invention significantly improves the pointing accuracy of the telescope's meridian and parallel axes through precise error modeling and compensation models, meeting the needs of high-precision astronomical observation and low-orbit satellite tracking tasks; (2) Improved calibration efficiency: Compared with traditional empirical formula correction and manual adjustment, this invention reduces the reliance on manual operation and improves calibration efficiency by combining observation data with mathematical models; (3) Wide applicability: This method is not only applicable to dual-horizontal telescopes, but can also be extended to the static pointing error correction of other photoelectric telescopes, and has strong engineering application value. Attached Figure Description

[0073] Figure 1 This is a flowchart illustrating a method for modeling and correcting the static pointing error of a horizontal telescope in this invention.

[0074] Figure 2 This is a schematic diagram of a static pointing model in the horizontal coordinate system of this invention;

[0075] Figure 3 A schematic diagram of the residuals of the meridian and parallel axes of a certain dual-horizontal telescope before correction, provided in an embodiment of the present invention;

[0076] Figure 4 This is a schematic diagram of the residuals of the meridian and parallel axes of a modified dual-horizontal telescope provided in an embodiment of the present invention. Detailed Implementation

[0077] To more clearly illustrate the embodiments of the present invention, specific implementation methods will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0078] like Figure 1As shown, this invention provides a method for modeling and correcting the static pointing error of a horizontal telescope. The method is based on a static pointing error compensation method using error modeling and parameter fitting. By comprehensively analyzing multiple error sources, a static pointing error model is established; combined with experimental observation data, the model parameters are fitted using the least squares method to derive an accurate compensation model; and the compensation model is simulated in actual observations, significantly improving the pointing accuracy of the telescope. The specific steps are as follows:

[0079] 1. Establish a static pointing model for a horizontal telescope and analyze the factors causing the telescope's axis error.

[0080] A horizontal telescope's mechanical structure consists of a meridian axis and a parallel axis. The meridian axis points north-south, and the parallel axis points east-west. Theoretically, these two axes should be perpendicular to each other and parallel to the ground plane. However, during actual manufacturing, installation, and placement, mechanical errors and environmental factors inevitably introduce various errors into the telescope. These errors cause the telescope's pointing direction to deviate from the theoretical value, thus affecting observation accuracy. These errors are collectively referred to as static pointing errors.

[0081] To comprehensively analyze the static pointing error of a horizontal telescope, this invention considers the following main sources of error:

[0082] (1) Zero position error: The error caused by the offset of the initial calibration point of the telescope.

[0083] (2) Code disk installation error: Geometric deviations generated during the installation of encoders or sensors.

[0084] (3) Error of warp and weft axes not being perpendicular: Error introduced by the warp and weft axes not being completely perpendicular during machining or assembly.

[0085] (4) Error of the line of sight not being perpendicular to the horizontal plane: the error of the angle between the telescope's line of sight and the horizontal plane.

[0086] (5) Meridian pointing error: The error caused by the meridian not being fully aligned with the north-south direction.

[0087] (6) Warp axis tilt error: Pointing deviation caused by the tilt of the warp axis.

[0088] To quantify and correct the aforementioned errors, this invention establishes a static pointing error model. The error model is derived for both the longitude and latitude axes, and its expressions are as follows:

[0089] (1);

[0090] (2);

[0091] in, Indicates the rotation angle of the warp axis. The angle of rotation of the latitude axis; For the warp rotation angle error, This represents the latitudinal axis rotation error; a1, a2, a3, a4, a5, a5, a6, a7, b1, b2, b3, b4, and b5 are all static pointing model parameters for a horizontal telescope. The specific definitions of the static pointing model parameters for a horizontal telescope are shown in Table 1 below.

[0092] Table 1 Physical meaning of parameters in the static pointing model of a horizontal telescope

[0093] 2. Based on the static pointing model, derive the static pointing error compensation model for the telescope axis system:

[0094] Based on the static pointing model of a horizontal telescope, a horizontal three-dimensional coordinate system is established. Considering the axis error factors of the horizontal telescope, a static pointing error compensation model is derived, such as... Figure 2 As shown. Figure 2 In the diagram, E, W, S, and N represent the four cardinal directions (north, south, east, and west); O represents the origin; L represents the meridian rotation angle; B represents the latitude rotation angle; Z represents the longitudinal axis; and T represents the observation point.

[0095] A horizontal three-dimensional coordinate system is established with the telescope's installation position as the origin. The directions of the three axes are defined perpendicular to the ground plane, forming a coordinate system based on the ground plane. In this coordinate system, the mechanical structure of the horizontal telescope consists of a longitude axis and a latitude axis. The longitude axis is parallel to the ground plane and points north-south, while the latitude axis is perpendicular to the longitude axis and points east-west.

[0096] When a horizontal telescope is pointed at a star on the meridian, the star's theoretical position should be on the circle formed by the meridian and the zenith. At this time, the latitudinal axis rotation angle... The observed actual position will deviate from the theoretical position due to shaft system errors. The deviation is caused by the static direction error of the shaft. Description. Similarly, when a horizontal telescope is pointed at a star on the latitudinal axis, the star's theoretical position lies on the circle formed by the latitudinal axis and the zenith, at which point the meridian angle... The deviation is statically directed from the latitude axis to the error. describe.

[0097] Analyzing equations (1) and (2), the static pointing error model of the shaft system is derived. When At that time, the error model of the horizontal telescope's warp axis system can be expressed as:

[0098] (3);

[0099] (4);

[0100] Summarized as follows:

[0101] (5);

[0102] (6);

[0103] when At that time, the error compensation model for the latitudinal axis system of a horizontal telescope can be expressed as:

[0104] (7);

[0105] (8);

[0106] Summarized as follows:

[0107] (9);

[0108] (10);

[0109] Where A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, and D3 are the undetermined coefficients after the integration of the error compensation model.

[0110] 3. Substitute the experimental data and use the least squares method to fit the data to determine the undetermined coefficients of the compensation model:

[0111] After establishing the static pointing error model, the model parameters were further fitted using actual observation data to determine the undetermined coefficients in the compensation model. In the experiment, 50 stars distributed along the meridian and parallel axes from the HIP star catalog were selected as observation targets, and the theoretical positions of each star were recorded. ) and actual observation location ( Using the deviation between the actual observed position and the theoretical position of the star as input data, the static pointing error of the axis is calculated. :

[0112] (11);

[0113] To fit the undetermined coefficients of the model, the least squares method was used to fit the above error data. The goal of the least squares method is to optimize the values ​​of the undetermined coefficients in the model by minimizing the sum of squared errors. The fitting results are shown in Table 2 below:

[0114] Table 2. Model coefficient fitting results.

[0115] The undetermined coefficients obtained through fitting can accurately describe the static pointing error distribution of the longitude and latitude axes, laying a data foundation for subsequent error correction.

[0116] 4. Correct the static pointing errors of the telescope's meridian and parallel axes using a compensation model:

[0117] Longitude L, latitude B, and overall static pointing accuracy of the system ( , as well as The standard deviation is calculated using the following formula:

[0118] (12);

[0119] (13);

[0120] (14);

[0121] Where n is the number of stars in this observation experiment; For the first One observation point.

[0122] Using equations (12)-(14), the meridian pointing accuracy and the parallel pointing accuracy before and after the compensation model correction are calculated.

[0123] The accuracy before and after pointing error correction was calculated using the standard deviation formula. The results are shown in Table 3 below:

[0124] Table 3. Correction Accuracy Data for Static Pointing Accuracy of a Certain Dual-Horizontal Telescope Axis System

[0125] Experimental results show that: before correction, the static pointing error of the meridian was 566.26 arcseconds, which was reduced to 4.08 arcseconds after correction; before correction, the static pointing error of the parallel was 629.49 arcseconds, which was reduced to 4.17 arcseconds after correction. To specifically characterize the correction effect, Figure 3 and Figure 4 The residuals of the meridian and parallel axes of a dual-horizontal telescope before and after the model correction of this invention are shown. The two figures visually demonstrate that the error distribution after correction converges significantly, and the observation points are closer to the theoretical values, indicating that the compensation model effectively improves the telescope's accuracy. Calculations using the standard deviation formula show that the static pointing error accuracy is significantly improved before and after correction, further verifying the feasibility and effectiveness of the error compensation model in practical applications.

[0126] In addition, the present invention also provides a modeling and correction system for the static pointing error of a horizontal telescope, including:

[0127] The model building module is used to build a static pointing model of a horizontal telescope and analyze the axis error factors of the telescope.

[0128] The model derivation module is used to derive the static pointing error compensation model of the telescope axis system based on the static pointing model.

[0129] The module for determining undetermined coefficients is used to input experimental data, fit the data using the least squares method, and determine the undetermined coefficients of the compensation model.

[0130] The correction module is used to correct the static pointing errors of the telescope's meridian and parallel axes using a compensation model.

[0131] This invention significantly improves the pointing accuracy of the telescope's meridian and parallel axes through precise error modeling and compensation, meeting the needs of high-precision astronomical observation and low-orbit satellite tracking missions. Compared with traditional empirical formula correction and manual adjustment, this invention reduces reliance on manual operation and improves calibration efficiency by combining observation data with mathematical models. The method of this invention is not only applicable to dual-horizontal telescopes, but can also be extended to the static pointing error correction of other photoelectric telescopes, and has strong engineering application value.

[0132] The above description is merely a detailed explanation of preferred embodiments and principles of the present invention. For those skilled in the art, there may be changes in specific implementation methods based on the ideas provided by the present invention, and these changes should also be considered within the scope of protection of the present invention.

Claims

1. A method for modeling and correcting the static pointing error of a horizontal telescope, characterized in that, Includes the following steps; S1. Establish a static pointing model of a horizontal telescope and analyze the axis error factors of the telescope. S2, Based on the static pointing model, derive the static pointing error compensation model of the telescope axis system; S3, Substitute the experimental data, fit the data using the least squares method, and determine the undetermined coefficients of the compensation model; S4 uses a compensation model to correct the static pointing errors of the telescope's meridian and parallel axes.

2. The method for modeling and correcting the static pointing error of a horizontal telescope according to claim 1, characterized in that, Step S1 includes the following steps: S11, the mechanical structure of the horizontal telescope consists of a meridian axis and a parallel axis, and the corresponding static pointing model is established as follows: （1）； （2）； in, Indicates the rotation angle of the warp axis. The angle of rotation of the latitude axis; For the warp rotation angle error, The latitudinal axis rotation error; a1, a2, a3, a4, a5, a5, a6, a7, b1, b2, b3, b4, and b5 are all parameters of the static pointing model of the horizontal telescope.

3. The method for modeling and correcting the static pointing error of a horizontal telescope according to claim 2, characterized in that, In step S1, the telescope's axis error factors include: Null position error: The error caused by the offset of the telescope's initial calibration point; Code disk installation error: Geometric deviations that occur during the installation of the encoder or sensor; Non-perpendicularity error of warp and weft axes: Error introduced by the warp and weft axes not being perfectly perpendicular during machining or assembly; Error of the line of sight not being perpendicular to the horizontal plane: the error in the angle between the telescope's line of sight and the horizontal plane; Meridian alignment error: The error caused by the meridian not being perfectly aligned with the north-south direction; Warp axis tilt error: Pointing deviation caused by warp axis tilt.

4. The method for modeling and correcting the static pointing error of a horizontal telescope according to claim 3, characterized in that, Step S2 includes the following steps: S21. Establish a horizontal three-dimensional coordinate system. The horizontal three-dimensional coordinate system takes the installation position of the telescope as the origin and defines the directions of the three axes, which are perpendicular to the ground plane, to form a coordinate system based on the ground plane. In the coordinate system, the longitude axis of the horizontal telescope is parallel to the ground plane and points in the north-south direction, and the latitude axis is perpendicular to the longitude axis and points in the east-west direction. S22, Analyzing formulas (1) and (2), the static pointing error compensation model for the shaft system is derived, as follows: when At that time, the error compensation model for the horizontal telescope's warp axis system is expressed as: （3）； （4）； Summarized as follows: （5）； （6）； when At that time, the error compensation model for the latitudinal axis system of a horizontal telescope is expressed as: （7）； （8）； Summarized as follows: （9） （10） Where A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, and D3 are the undetermined coefficients after the integration of the error compensation model.

5. The method for modeling and correcting the static pointing error of a horizontal telescope according to claim 4, characterized in that, Step S3 includes the following steps: S31, Obtain pointing error data through actual observation: In the experiment, at least 50 stars distributed along the meridian and parallel axes from the HIP catalog were selected as observation targets, and the theoretical positions of each star were recorded. ) and actual observation location ( Using the deviation between the actual observed position and the theoretical position of a star as input data, the static pointing error of the axis system is calculated. : （11） S32, after obtaining the static pointing error of the shaft system Then, the static pointing error data is substituted into the model equations (5), (6), (9) and (10), and the error data is used as the input for least squares fitting. S33, The error data is fitted using the least squares method: By solving the linear equation system of formulas (5), (6), (9) and (10) or by using a numerical optimization algorithm, the sum of squared errors is minimized to obtain the optimal values ​​of the undetermined coefficients A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, and D3.

6. The method for modeling and correcting the static pointing error of a horizontal telescope according to claim 5, characterized in that, Step S4 includes the following steps: S41, Settings , as well as These are the longitude axis L, the latitude axis B, and the overall static pointing accuracy of the system, calculated using the standard deviation formula, as follows: （12）； （13）； （14）； Where n is the number of stars in this observation experiment; For the first One observation point; Using equations (12)-(14), the meridian pointing accuracy and the parallel pointing accuracy before and after the compensation model correction are calculated.

7. A system for modeling and correcting static pointing error of a horizontal telescope, used to implement the method for modeling and correcting static pointing error of a horizontal telescope as described in any one of claims 1-6, characterized in that, The modeling and correction system for the static pointing error of the horizontal telescope includes: The model building module is used to build a static pointing model of a horizontal telescope and analyze the axis error factors of the telescope. The model derivation module is used to derive the static pointing error compensation model of the telescope axis system based on the static pointing model. The module for determining undetermined coefficients is used to input experimental data, fit the data using the least squares method, and determine the undetermined coefficients of the compensation model. The correction module is used to correct the static pointing errors of the telescope's meridian and parallel axes using a compensation model.

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