Azimuth-elevation radio telescope azimuth axis tilt pointing control method

Abstract

The application discloses an azimuth-elevation radio telescope azimuth axis tilt pointing control method and relates to the technical field of antenna servo control. Pointing observation data and model instruction data of a radio telescope are acquired, an ideal line-of-sight unit vector is constructed in a local east-north-zenith coordinate system, an azimuth axis tilt parameter is defined and an ordered three-dimensional rotation model of the azimuth axis tilt is constructed, an axis rotation is performed to obtain a tilted line-of-sight vector, a closed-form azimuth axis tilt residual error is calculated, a hybrid pointing model is obtained by embedding the closed-form azimuth axis tilt residual error into a low-order pointing model, a robust least square method is used to solve the hybrid pointing model to obtain the tilt parameter and the low-order term parameter, and the tilt parameter and the low-order term parameter are used to realize pointing control of the radio telescope. According to the application, the azimuth axis tilt error is embedded into the existing low-order pointing model in a closed-form geometric manner, so that more accurate characterization and compensation of the pointing error of the radio telescope are realized.

Description

Technical Field

[0001] This invention relates to the field of antenna servo control technology, and in particular to a method for controlling the tilt of the azimuth axis of an azimuth-elevation radio telescope. Background Technology

[0002] Existing azimuth-elevation radio telescopes typically employ low-order pointing models to uniformly model mechanical installation errors, encoder zero-point errors, non-orthogonality errors, deflection errors, and azimuth axis tilt errors. For azimuth axis tilt, a first-order linear approximation is commonly used in engineering. This involves introducing terms related to tan(EL) (Elevation, elevation angle / elevation angle) into the azimuth residual channel, and terms related to sin(AZ) (Azimuth, azimuth angle) and cos(AZ) into the elevation residual channel. This type of expression is simple in structure and easily compatible with existing pointing calculation programs, thus it is widely used in the routine calibration procedures of radio telescopes and related antenna systems. However, existing technologies have at least the following shortcomings: (1) The traditional azimuth axis tilt term is essentially a first-order linear approximation under small tilt angle conditions. This approximation is usually effective in the low and medium elevation angle region, but at high elevation angles, especially close to the zenith, the intrinsic azimuth coordinates themselves have coordinate singularities, which leads to a significant amplification effect of tan(EL) in the azimuth residual term, making the "approximation error" and "coordinate representation singularity" mixed together, making it difficult to directly determine whether it corresponds to a large pointing error on the real sky plane.

[0003] (2) Existing technologies typically handle azimuth tilt directly within the linear residual framework, without providing a closed finite rotational mapping that does not require small-angle truncation of the tilt angle from the perspective of local spatial geometric rotation. Therefore, in high elevation angle scenarios, although traditional models can still be used, their azimuth tilt terms do not possess strict closed geometric consistency. (3) Completely abandoning the existing low-order model and establishing a completely new model would lead to incompatibility with existing calibration software, historical parameter systems, and engineering application habits, increasing the cost of system modification.

[0004] In summary, the existing technology lacks an azimuth tilt modeling method that possesses both closed finite rotational geometric consistency and can be directly embedded into existing low-order pointing models and is applicable to engineering calibration processes. It needs to address the issues of the azimuth tilt term relying on a first-order linear approximation and insufficient geometric interpretation at high elevation angles, especially in the near-zenith region. Furthermore, in engineering, there is a need for a technical solution that only replaces the azimuth tilt sub-model while retaining the structural integrity of the remaining low-order terms, so that it can maintain compatibility with the traditional model parameter system and obtain a more reasonable geometric representation in the near-zenith region. Summary of the Invention

[0005] In view of this, the present invention provides an azimuth-elevation radio telescope azimuth axis tilt pointing control method, the purpose of which is to achieve compatibility with existing engineering calibration procedures, parameter calculation programs and control systems, reduce the interference of intrinsic azimuth coordinate singularities on error interpretation, and improve the physical consistency and engineering usability of radio telescope azimuth axis tilt term modeling.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for controlling the tilt of the azimuth axis of an azimuth-elevation radio telescope includes the following steps: S1 acquisition steps: Acquire the pointing observation data and model command data of the radio telescope; S2 construction steps: Construct an ideal line-of-sight unit vector in the local East-North-Zenith coordinate system based on the pointing observation data and model instruction data; S3 definition steps: Define the azimuth axis tilt parameters based on the ideal line-of-sight unit vector, and construct an ordered three-dimensional rotation model of the azimuth axis tilt based on the azimuth axis tilt parameters; S4 Rotation Steps: Rotate around the axis using an ordered 3D rotation model to obtain the tilted line-of-sight vector; S5 Embedding Steps: Calculate the closed azimuth axis tilt residual based on the line-of-sight vector, and embed the closed azimuth axis tilt residual into the low-order pointing model to obtain the hybrid pointing model; S6 Solution Steps: The robust least squares method is used to solve the hybrid pointing model to obtain the tilt parameters and low-order terms. The tilt parameters and low-order terms are used to model and compensate for the pointing error of the radio telescope.

[0007] In the above method, optionally, in S1, the pointing observation data includes: measured azimuth angle, measured elevation angle, azimuth deviation, elevation deviation, scan marker, and time information; the model command data includes: model azimuth angle and model elevation angle.

[0008] The above method can optionally point to observation data obtained by a single scan or cross scan of a radio telescope; The S1 acquisition step also includes: aggregating the original sub-scans according to the scan identifier to obtain the representative azimuth deviation and representative elevation deviation corresponding to one scan.

[0009] The above method, optionally, includes the following formula for calculating the ideal line-of-sight unit vector in the S2 construction step: s_c = [cosEL·sinAZ, cosEL·cosAZ, sinEL]^T In the formula, s_c represents the ideal line-of-sight unit vector, AZ represents the model azimuth angle obtained from the model command data, EL represents the model pitch angle obtained from the model command data, and T represents the matrix transpose.

[0010] The above method, optionally, the specific formula for calculating the line-of-sight vector in S4 is as follows: s = R_N(-α)·R_E(β)·s_c In the formula, s represents the line-of-sight vector, R_N(-α) represents the rotation of the ordered three-dimensional rotating model around the north axis of the local east-north-zenith coordinate system, R_E(β) represents the rotation of the ordered three-dimensional rotating model around the east axis of the local east-north-zenith coordinate system, s_c represents the ideal line-of-sight unit vector, and α and β are the azimuth axis tilt parameters, where α represents the amount of eastward tilt of the azimuth axis and β represents the amount of northward tilt of the azimuth axis.

[0011] The above method, optionally, includes the following specific steps in S5: calculating the closed azimuth axis tilt residual based on the line-of-sight vector: The three components E', N', and Z' of the line-of-sight vector are obtained based on the ordered three-dimensional rotation model. The closed azimuth axis tilt residuals are calculated based on the components E', N', and Z'.

[0012] The above method can optionally include closed azimuth axis tilt residuals and closed pitch residuals. The specific formula for calculating closed-loop azimuth residuals is as follows: ΔAZ_exact = wrap(AZ - AZ) In the formula, AZ Indicates the azimuth angle after tilting, AZ = atan2(E', N'), wrap indicates that the azimuth difference is normalized to the range of (-π, π] or (-180°, 180°]; the specific formula for calculating the closed pitch residual is: ΔEL_exact = EL - EL In the formula, EL EL indicates the pitch angle after tilting. = arcsin(clamp(Z',-1,1)), where clamp means to limit Z' to the range [-1,1] to avoid floating-point errors causing the arcsine function to go out of bounds.

[0013] Optionally, in the S5 embedding step of the above method, the specific calculation formula for the hybrid pointing model is as follows: ΔAZ = p1 + ΔAZ_exact(α,β) + p5·tanEL - p6 / cosEL ΔEL = p2 + ΔEL_exact(α,β) + p7·cosEL + p8 / tanEL In the formula, EL represents the model pitch angle obtained from the model command data, α and β are the azimuth axis tilt parameters, α represents the amount of eastward tilt of the azimuth axis, β represents the amount of northward tilt of the azimuth axis, and p1, p2, p5, p6, p7 and p8 are the low-order terms of the low-order pointing model.

[0014] Optionally, in the above method, the robust least squares method in S6 is the robust least squares estimation using the Huber loss function.

[0015] The above methods may also include: S7 Evaluation Steps: The pointing correction results of the radio telescope based on tilt parameters and low-order terms are evaluated using the sky-plane projection residuals.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention provides a method for controlling the azimuth axis tilt of an azimuth-elevation radio telescope, which has the following beneficial effects: (1) This invention replaces the traditional first-order linear approximation with ordered three-dimensional rotation in the local East-North-Zenith coordinate system, and directly establishes the closed finite rotational geometric mapping of the azimuth axis tilt term. Therefore, it has better geometric consistency and avoids the model approximation error caused by the first-order truncation of the tilt angle in the traditional method.

[0017] (2) Under small tilt conditions, this invention can naturally degenerate into existing AW / AN type expressions; in engineering parameter systems using the same positive sign convention as the embodiments of this invention, it can be equivalently converted to AW_eff=-α, AN_eff=β. If the telescope control system uses different azimuth positive directions or different AW / AN definitions, it should be converted according to the corresponding sign conventions. Therefore, this invention does not need to overturn existing low-order pointing models, but only needs to replace the azimuth axis tilt sub-item to be integrated into existing calibration software, historical data processing flow and engineering usage habits, and has strong compatibility.

[0018] (3) The present invention can be directly embedded into the standard robust least squares calibration process; the closed tilt term can be directly connected to the existing robust fitting process, and tilt parameters with the same magnitude and clear physical meaning as the traditional solution can be obtained. Therefore, it has good engineering implementation and promotion application value.

[0019] (4) This invention can be used not only for offline calibration analysis, but also for online updating of telescope control model parameters. It is beneficial to improve the pointing error characterization capability, model interpretation consistency and maintenance efficiency of large-aperture radio telescopes under high-frequency observation, narrow-beam observation and high elevation angle observation conditions. It has clear technical effects and application prospects. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a method for controlling the tilt of the azimuth axis of an azimuth-elevation radio telescope, as disclosed in this invention. Figure 2 This is a diagram illustrating the definition of the local ENZ coordinate system and the ideal line of sight as disclosed in an embodiment of the present invention. Figure 3 This is a schematic diagram of the positive directions of the azimuth axis tilt parameters α and β disclosed in the embodiments of the present invention; Figure 3 (a) shows the definition of the eastward tilt angle α and its positive direction. Figure 3 (b) is the definition of the northward tilt angle β and its positive direction; Figure 4 This is a schematic diagram illustrating the intrinsic orientation difference between the closed finite rotation mapping and the traditional first-order mapping on the all-sky grid disclosed in an embodiment of the present invention. Figure 5 This is a statistical diagram showing the difference between the closed finite rotational mapping disclosed in the embodiments of the present invention and the traditional first-order mapping as a function of elevation angle; Figure 6 This is a schematic diagram showing the variation of P95 residual difference with elevation angle under intrinsic coordinates as disclosed in an embodiment of the present invention; Figure 7 This is a schematic diagram showing the variation of the P95 residual difference with elevation angle under the sky plane projection disclosed in an embodiment of the present invention. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0024] This invention discloses a method for controlling the tilt of the azimuth axis of an azimuth-elevation radio telescope, comprising the following steps: S1 acquisition steps: Acquire the pointing observation data and model command data of the radio telescope; S2 construction steps: Construct an ideal line-of-sight unit vector in the local East-North-Zenith coordinate system based on the pointing observation data and model instruction data; S3 definition steps: Define the azimuth axis tilt parameters based on the ideal line-of-sight unit vector, and construct an ordered three-dimensional rotation model of the azimuth axis tilt based on the azimuth axis tilt parameters; S4 Rotation Steps: Rotate around the axis using an ordered 3D rotation model to obtain the tilted line-of-sight vector; S5 Embedding Steps: Calculate the closed azimuth axis tilt residual based on the line-of-sight vector, and embed the closed azimuth axis tilt residual into the low-order pointing model to obtain the hybrid pointing model; S6 Solution Steps: The robust least squares method is used to solve the hybrid pointing model to obtain the tilt parameters and low-order terms. The tilt parameters and low-order terms are used to model and compensate for the pointing error of the radio telescope.

[0025] The azimuth axis tilt pointing control of an azimuth-elevation radio telescope disclosed in this invention also includes outputting tilt parameters and low-order term parameters to the telescope pointing control system, offline calibration software, or parameter file to generate pointing correction parameters.

[0026] Optional, refer to Figure 1 In S1, the acquired pointing observation data includes: measured azimuth angle, measured elevation angle, azimuth deviation, elevation deviation, scan marker, and time information; the model command data includes: model azimuth angle and model elevation angle.

[0027] Optionally, the observation data is obtained by a single scan or cross scan of a radio telescope; the S1 acquisition step also includes: aggregating the original sub-scans according to the scan identifier to obtain the representative azimuth deviation and representative elevation deviation corresponding to a single scan.

[0028] Optionally, the formula for calculating the ideal line-of-sight unit vector in the S2 construction step is as follows: s_c = [cosEL·sinAZ, cosEL·cosAZ, sinEL]^T In the formula, s_c represents the ideal line-of-sight unit vector, AZ represents the model azimuth angle obtained from the model command data, EL represents the model pitch angle obtained from the model command data, and T represents the matrix transpose.

[0029] Specifically, refer to Figure 2 In S2, the local east-north-zenith coordinate system is denoted as the ENZ coordinate system, where E represents the eastward unit vector, N represents the northward unit vector, and Z represents the zenith direction unit vector; the ideal line-of-sight unit vector s_c is uniquely determined by the model azimuth angle AZ and the model pitch angle EL. The ENZ coordinate system is used to construct a closed azimuth axis tilt rotation mapping.

[0030] After obtaining the ideal line-of-sight unit vector, define the azimuth axis tilt parameter. For example... Figure 3 As shown, let α be the eastward tilt angle of the azimuth axis, and β be the northward tilt angle of the azimuth axis; where, Figure 3 In (a), α represents the amount of eastward tilt of the azimuth axis. Figure 3 In (b), β represents the amount of northward tilt of the azimuth axis, and α and β together characterize the tilt angle of the azimuth axis relative to the ideal local vertical.

[0031] Optionally, the specific formula for calculating the line-of-sight vector in S4 is as follows: s = R_N(-α)·R_E(β)·s_c In the formula, s represents the line-of-sight vector, R_N(-α) represents the rotation of the ordered three-dimensional rotating model around the north axis of the local east-north-zenith coordinate system, R_E(β) represents the rotation of the ordered three-dimensional rotating model around the east axis of the local east-north-zenith coordinate system, s_c represents the ideal line-of-sight unit vector, and α and β are the azimuth axis tilt parameters, where α represents the amount of eastward tilt of the azimuth axis and β represents the amount of northward tilt of the azimuth axis.

[0032] After constructing an ordered 3D rotation model with an azimuth axis tilt in step S3, in the rotation step S4, the ordered 3D rotation model first performs a rotation R_E(β) around the east axis, and then performs a rotation R_N(-α) around the north axis, thereby obtaining the tilted line-of-sight vector s. Through the above two ordered rotations, α and β are no longer truncated at small angles, but a closed geometric mapping is directly obtained.

[0033] Optionally, the calculation of the closed azimuth axis tilt residual based on the line-of-sight vector in S5 specifically includes: The three components E', N', and Z' of the line-of-sight vector are obtained based on the ordered three-dimensional rotation model. The closed azimuth axis tilt residuals are calculated based on the components E', N', and Z'.

[0034] Optionally, the closed azimuth axis tilt residual includes the closed azimuth residual and the closed pitch residual; The specific formula for calculating closed-loop azimuth residuals is as follows: ΔAZ_exact = wrap(AZ - AZ) In the formula, AZ Indicates the azimuth angle after tilting, AZ = atan2(E', N'), wrap indicates that the azimuth difference is normalized to the range of (-π, π] or (-180°, 180°]; the specific formula for calculating the closed pitch residual is: ΔEL_exact = EL - EL In the formula, EL EL indicates the pitch angle after tilting. = arcsin(clamp(Z',-1,1)), where clamp means to limit Z' to the range [-1,1] to avoid floating-point errors causing the arcsine function to go out of bounds.

[0035] Based on the ordered three-dimensional rotation model, the three components E', N', and Z' of the rotated line of sight vector are obtained, and then the accurate residual is obtained from the rotated line of sight vector.

[0036] Preferably, the calculation formulas for E', N', and Z' are as follows: E' = cosα·cosEL·sinAZ - sinα·(sinβ·cosEL·cosAZ + cosβ·sinEL) N' = cosβ·cosEL·cosAZ - sinβ·sinEL Z' = sinα·cosEL·sinAZ + cosα·(sinβ·cosEL·cosAZ + cosβ·sinEL) Optionally, in the S5 embedding step, the specific calculation formula for the hybrid pointing model is as follows: ΔAZ = p1 + ΔAZ_exact(α,β) + p5·tanEL - p6 / cosEL ΔEL = p2 + ΔEL_exact(α,β) + p7·cosEL + p8 / tanEL In the formula, EL represents the model pitch angle obtained from the model command data, α and β are the azimuth axis tilt parameters, α represents the amount of eastward tilt of the azimuth axis, β represents the amount of northward tilt of the azimuth axis, and p1, p2, p5, p6, p7 and p8 are the low-order terms of the low-order pointing model.

[0037] This invention embeds the closed azimuth axis tilt residual into an existing low-order pointing model to form a hybrid pointing model. It only replaces the azimuth axis tilt term in the traditional model, while retaining the zero-point term, deflection term, non-orthogonal term and other low-order terms unchanged, thereby obtaining the calculation formula of the above-mentioned hybrid pointing model.

[0038] Optionally, the robust least squares method in S6 is the robust least squares estimation using the Huber loss function.

[0039] Specifically, this invention solves the hybrid pointing model by employing robust least squares or other parameter estimation methods to obtain α, β, and other model parameters; and reduces the influence of outliers on the parameter solution by using robust least squares estimation with the Huber loss function; after obtaining the parameters, they are written back to the telescope pointing control system or used for offline calibration report generation.

[0040] In practice, the sign conventions for azimuth and elevation deviations are consistent with the definition of pointing residuals in the telescope control system; the observation deviations are fitted with the ΔAZ and ΔEL outputs of the hybrid pointing model according to the same sign. In actual calibration, the effective elevation angle range can be set according to the telescope's safety limits, obstruction conditions, and model numerical stability, avoiding the use of data near the horizon, near mechanical limits, or at singularities of EL=90° as ordinary calibration points.

[0041] Optional, such as Figure 1 As shown, the azimuth-elevation radio telescope azimuth axis tilt pointing control method disclosed in this invention further includes: S7 evaluation step: using the sky plane projection residual including cosEL·ΔAZ and ΔEL to evaluate the pointing correction effect of the radio telescope based on tilt parameters and low-order term parameters.

[0042] For high elevation angles, especially near the zenith, the sky plane projection residual is used to evaluate the correction effect. (Reference) Figure 4The horizontal axis represents the azimuth, and the vertical axis represents the elevation, with both axes in degrees (deg). It can be seen that the intrinsic azimuth difference between the closed finite rotation mapping and the traditional first-order mapping on the entire sky grid is mainly concentrated in the near-zenith region. Therefore, in the S7 evaluation step, this invention uses (cosEL·ΔAZ, ΔEL) as the evaluation quantity, without relying solely on the intrinsic azimuth residual ΔAZ, thereby distinguishing between the apparent azimuth magnification caused by coordinate singularity and the pointing error on the real sky plane.

[0043] Furthermore, when the tilt angle satisfies the small angle condition, the closed-form expression of this invention automatically degenerates to the traditional first-order form: ΔAZ ≈ -α·tanEL·cosAZ + β·tanEL·sinAZ ΔEL ≈ α·sinAZ + β·cosAZ Therefore, the correspondence with traditional parameters can be obtained: in an engineering parameter system that adopts the same notation convention as the embodiments of the present invention, it can be equivalently converted to AW_eff = -α, AN_eff = β; if the specific telescope control system adopts different azimuth positive directions or different AW / AN definitions, it should be converted according to the local notation convention.

[0044] By using the sky plane projection residual for evaluation, this invention achieves a more reasonable handling of the error interpretation problem in the high elevation angle, especially near the zenith region. Under representative small tilt angle conditions, the closed finite rotation mapping and the traditional first-order mapping mainly show differences in intrinsic azimuth coordinates at high elevation angles, while the corresponding sky plane projection remains small and bounded. This indicates that the large intrinsic azimuth difference near the zenith is mainly due to coordinate representation effects rather than unbounded physical pointing errors.

[0045] The following section uses the pointing calibration of an azimuth-elevation radio telescope as an example to provide a detailed description of the azimuth axis tilt pointing control method for an azimuth-elevation radio telescope disclosed in this invention.

[0046] First, pointing calibration observation data of the azimuth-elevation radio telescope are collected. Preferably, the observation method is cross-scanning, but it is not limited to this. For each scan, the corresponding model azimuth angle AZ, model elevation angle EL, azimuth measurement deviation, elevation measurement deviation, scan number, and time stamp are recorded. If a single scan contains multiple sub-scans, they can be aggregated according to the scan number, and the median is preferentially used to obtain the representative azimuth and elevation deviations of that scan to suppress the influence of local outliers.

[0047] Secondly, in the local east-north-zenith coordinate system, an ideal line-of-sight unit vector s_c is constructed based on the model azimuth AZ and model elevation EL corresponding to this scan. Here, AZ is the azimuth from north to east, and EL is the elevation angle. This vector represents the telescope's line-of-sight direction under ideal, tilt-free conditions.

[0048] Next, define the azimuth axis tilt parameters α and β. Here, α is the eastward tilt angle of the azimuth axis relative to the ideal vertical direction, and β is the northward tilt angle of the azimuth axis relative to the ideal vertical direction. Based on this definition, construct the ordered rotation relationship: s = R_N(-α)·R_E(β)·s_c. In this step, first rotate β around the eastward axis, then rotate -α around the northward axis. Through this ordered rotation, obtain the actual line-of-sight direction vector s considering the azimuth axis tilt.

[0049] Further expansion yields three components of the rotated line-of-sight vector s: E', N', and Z'. The specific calculation formulas are given in the previously disclosed embodiments. The tilted angle is then calculated as: AZ. and EL ; and thus we obtain the closed residuals: ΔAZ_exact, ΔEL_exact.

[0050] Subsequently, the aforementioned closed residuals are embedded into the existing low-order pointing model, replacing only the azimuth tilt term in the original model while keeping the structure of the remaining low-order terms unchanged, thus constructing a hybrid model.

[0051] Next, the observed azimuth and pitch deviations are used as observations, and the aforementioned hybrid model is used as the prediction model. A robust least squares method is employed to solve for all parameters. The Huber loss function is preferably used to reduce the impact of anomaly scans on the model parameters. After fitting, α, β, and the remaining parameters are output and saved as a new set of telescope pointing model parameters. If consistency with existing engineering parameter systems is required, the notation can be converted to AW_eff = -α and AN_eff = β when using the same notation as in the embodiments of this invention; for control systems using different AW / AN definitions, the conversion is performed according to local notation conventions.

[0052] The following analysis examines the differences between the closed finite rotation mapping used in this invention and the traditional first-order mapping from different perspectives. For example... Figure 5As shown, the horizontal axis represents the elevation angle, and the vertical axis represents the difference between the two mapping results, in arcseconds. Blue represents the statistical difference in azimuth direction ΔAZ, and orange represents the statistical difference in elevation direction ΔEL. The shaded area represents the 5%–95% distribution range, and the solid line represents RMS. It can be seen that in the low and medium elevation angle range, the two mappings are almost identical; when the elevation angle exceeds approximately 80°, the intrinsic azimuth difference ΔAZ begins to increase rapidly, while ΔEL remains very small. This indicates that the main difference between the two methods is concentrated in the near-zenith region and is mainly reflected in the coordinate amplification effect of the intrinsic azimuth in the alt–az coordinate system, rather than an equivalent order of magnitude error in the actual sky plane pointing.

[0053] On the other hand, refer to Figure 6 , Figure 6 This diagram illustrates the relationship between the P95 residual difference and elevation angle under intrinsic coordinates. The horizontal axis represents the elevation angle, and the vertical axis represents the 95th percentile of the absolute value of the difference between the two mappings, in arcseconds. The blue curve represents the P95 difference in the azimuth direction |ΔAZ|, and the orange curve represents the P95 difference in the pitch direction |ΔEL|. It can be seen that the difference between the two mappings is very small over most elevation angle ranges; when the elevation angle approaches 80° or higher, the intrinsic azimuth difference begins to increase rapidly and becomes significantly amplified near the zenith, while the pitch difference remains very small. This indicates that the main difference between the closed mapping and the traditional first-order mapping is concentrated in the intrinsic azimuth coordinates in the high elevation angle region, primarily reflecting the amplification effect caused by the singularity of the azimuth coordinates near the zenith.

[0054] Figure 7 This is a statistical graph showing the P95 difference between the closed finite rotational mapping and the traditional first-order mapping projected onto the sky plane as a function of elevation angle. The horizontal axis represents elevation angle, and the vertical axis represents the 95th percentile of the absolute difference, in arcseconds. The blue curve represents the P95 difference of the projected azimuth component |\cos ELΔAZ|, and the orange curve represents the P95 difference of the pitch component |ΔEL|. It can be seen that after projection onto \cos EL, the difference in azimuth direction is significantly reduced, remaining at a very small order of magnitude throughout the entire elevation angle range; even near the zenith, the difference between the two mappings on the sky plane is much smaller than the difference in the intrinsic azimuth angle. This indicates that the rapid increase in the intrinsic ΔAZ in the near-zenith region is mainly due to coordinate representation effects, rather than an equal amplification of the actual sky plane pointing error.

[0055] Therefore, it is clear from the above comparison that, in high elevation angles, especially near-zenith applications, this embodiment uses sky-plane projection residuals to evaluate the model's performance to avoid misjudgments caused by using intrinsic azimuth residuals alone. That is, using cosEL·ΔAZ and ΔEL as the main evaluation quantities is a more suitable choice. If cosEL·ΔAZ remains small and bounded, it indicates that the intrinsic azimuth difference is mainly caused by coordinate representation effects and should not be interpreted as an unbounded true pointing error. This evaluation method is more suitable for analyzing the near-zenith pointing performance of telescopes.

[0056] The technical advantages achieved in this embodiment are as follows: By replacing the traditional first-order tilt approximation with a closed finite rotational mapping, this invention improves the geometric consistency of the azimuth tilt term and enhances the physical rationality of the near-zenith region error interpretation without compromising the existing low-order model framework. This method can be deployed in offline calibration software or integrated into a telescope control computer, where the processor automatically executes program instructions to complete data reading, parameter fitting, model updating, and correction output.

[0057] Furthermore, the present invention also discloses an azimuth axis tilt pointing control device for an azimuth-elevation radio telescope, used to implement the azimuth axis tilt pointing control method for an azimuth-elevation radio telescope as described in any of the above embodiments. The device includes: a data acquisition module for reading scan data and model data; a vector generation module for constructing an ideal line-of-sight unit vector; a rotation solution module for performing ordered three-dimensional rotations and calculating E', N', and Z'; a residual calculation module for calculating closed residuals ΔAZ_exact and ΔEL_exact; a robust fitting module for combining with a low-order pointing model and solving for parameters; and a parameter output module for outputting correction parameters to the telescope control system, offline calibration software, or parameter files.

[0058] Furthermore, the present invention also discloses an electronic device, including a processor and a memory, wherein the memory stores a program that, when executed by the processor, implements the method described in any of the above embodiments; or a computer-readable storage medium storing a program that, when executed by the processor, implements a method for controlling the azimuth axis tilt of an azimuth-elevation radio telescope as described in any of the above embodiments.

[0059] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for controlling the tilt and pointing of the azimuth axis of an azimuth-elevation radio telescope, characterized in that, Includes the following steps: S1 acquisition steps: Acquire the pointing observation data and model command data of the radio telescope; S2 construction steps: Construct an ideal line-of-sight unit vector in the local East-North-Zenith coordinate system based on the pointing observation data and model instruction data; S3 definition steps: Define the azimuth axis tilt parameters based on the ideal line-of-sight unit vector, and construct an ordered three-dimensional rotation model of the azimuth axis tilt based on the azimuth axis tilt parameters; S4 Rotation Steps: Rotate around the axis using an ordered 3D rotation model to obtain the tilted line-of-sight vector; S5 Embedding Steps: Calculate the closed azimuth axis tilt residual based on the line-of-sight vector, and embed the closed azimuth axis tilt residual into the low-order pointing model to obtain the hybrid pointing model; S6 Solution Steps: The robust least squares method is used to solve the hybrid pointing model to obtain the tilt parameters and low-order terms. The tilt parameters and low-order terms are used to model and compensate for the pointing error of the radio telescope.

2. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, In S1, the pointing observation data includes: measured azimuth angle, measured elevation angle, azimuth deviation, elevation deviation, scan marker, and time information; the model command data includes: model azimuth angle and model elevation angle.

3. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 2, characterized in that, The observation data is obtained by the radio telescope through single or cross-scanning. The S1 acquisition step also includes: aggregating the original sub-scans according to the scan identifier to obtain the representative azimuth deviation and representative elevation deviation corresponding to one scan.

4. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, The specific formula for calculating the ideal line-of-sight unit vector in the S2 construction step is as follows: s_c = [cosEL·sinAZ, cosEL·cosAZ, sinEL]^T In the formula, s_c represents the ideal line-of-sight unit vector, AZ represents the model azimuth angle obtained from the model command data, EL represents the model pitch angle obtained from the model command data, and T represents the matrix transpose.

5. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, The specific formula for calculating the line-of-sight vector in S4 is as follows: s = R_N(-α)·R_E(β)·s_c In the formula, s represents the line-of-sight vector, R_N(-α) represents the rotation of the ordered three-dimensional rotating model around the north axis of the local east-north-zenith coordinate system, R_E(β) represents the rotation of the ordered three-dimensional rotating model around the east axis of the local east-north-zenith coordinate system, s_c represents the ideal line-of-sight unit vector, and α and β are the azimuth axis tilt parameters, where α represents the amount of eastward tilt of the azimuth axis and β represents the amount of northward tilt of the azimuth axis.

6. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, The calculation of the closed azimuth axis tilt residual based on the line-of-sight vector in S5 specifically includes: The three components E', N', and Z' of the line-of-sight vector are obtained based on the ordered three-dimensional rotation model. The closed azimuth axis tilt residuals are calculated based on the components E', N', and Z'.

7. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 6, characterized in that, Closed azimuth axis tilt residuals include closed azimuth residuals and closed pitch residuals; The specific formula for calculating closed-loop azimuth residuals is as follows: ΔAZ_exact = wrap(AZ - IT) In the formula, AZ Indicates the azimuth angle after tilting, AZ = atan2(E', N'), wrap indicates that the azimuth difference is normalized to the range of (-π, π] or (-180°, 180°]; the specific formula for calculating the closed pitch residual is: ΔEL_exact = EL - HE In the formula, EL EL indicates the pitch angle after tilting. = arcsin(clamp(Z',-1,1)), where clamp means to limit Z' to the range [-1,1] to avoid floating-point errors causing the arcsine function to go out of bounds.

8. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 7, characterized in that, In the S5 embedding step, the specific calculation formula for the hybrid pointing model is as follows: ΔAZ = p1 + ΔAZ_exact(α,β) + p5·tanEL - p6 / cosEL ΔEL = p2 + ΔEL_exact(α,β) + p7·cosEL + p8 / tanEL In the formula, EL represents the model pitch angle obtained from the model command data, α and β are the azimuth axis tilt parameters, α represents the amount of eastward tilt of the azimuth axis, β represents the amount of northward tilt of the azimuth axis, and p1, p2, p5, p6, p7 and p8 are the low-order terms of the low-order pointing model.

9. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, In S6, the robust least squares method is a robust least squares estimation using the Huber loss function.

10. The azimuth axis tilt pointing control method for an azimuth-elevation radio telescope according to claim 1, characterized in that, Also includes: S7 Evaluation Steps: The pointing correction results of the radio telescope based on tilt parameters and low-order terms are evaluated using the sky-plane projection residuals.

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