Error optimization method and device for joint attitude angle of reflector antenna

Abstract

The application discloses a method and device for error optimization of joint attitude angle of a reflector antenna, and relates to the technical field of intelligent control. The method comprises the following steps: acquiring real and estimated moments of the reflector antenna, and determining a moment deviation; acquiring a Gaussian variational distribution of the deviation; combining training data containing angular velocity, angular acceleration and angular displacement with the deviation to obtain a posterior distribution; maximizing a lower bound function of the variational distribution by adjusting the mean and covariance of the variational distribution, so that the posterior distribution and the probability difference based on the variational distribution are minimized; and taking the mean of the posterior distribution at this time as a moment deviation compensation term to optimize the joint attitude angle error. The method optimizes the parameters of the probability distribution through variational inference, realizes accurate error correction by using the compensation term, and effectively improves the control accuracy and system robustness of the joint attitude angle of the reflector antenna.

Description

Technical Field

[0001] This application relates to the field of intelligent control technology, and in particular to a method and apparatus for optimizing the joint attitude angle of a reflector antenna. Background Technology

[0002] Reflector antennas are key equipment in satellite communications, radio astronomy, and deep space exploration. Their servo systems need to achieve high-precision pointing and tracking in complex dynamic environments (such as wind loads, sudden temperature changes, and multi-axis coupling effects). As application scenarios increasingly demand higher tracking accuracy and anti-interference capabilities, traditional control methods face significant challenges in dealing with system parameter uncertainties, unmodeled dynamics, and external disturbances.

[0003] Currently, existing methods struggle to balance high-precision tracking, strong robustness, and millisecond-level real-time computing efficiency in complex environments, thus limiting the performance of reflector antennas in high-end application scenarios.

[0004] Therefore, it cannot meet the high-precision tracking requirements of the reflector antenna servo system under extreme conditions, and it cannot optimize the error of the reflector antenna joint attitude angle. Summary of the Invention

[0005] This application provides a method and apparatus for optimizing the joint attitude angle of a reflector antenna, which can meet the high-precision tracking requirements of the reflector antenna servo system under extreme conditions and achieve error optimization of the joint attitude angle of the reflector antenna.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] In a first aspect, this application provides a method for optimizing the joint attitude angle error of a reflector antenna, including:

[0008] Obtain the actual reflector antenna torque and estimate the reflector antenna torque;

[0009] The deviation of the estimated reflector antenna torque is determined based on the actual reflector antenna torque and the estimated reflector antenna torque.

[0010] Obtain the variational distribution of the estimated reflector antenna moment deviation, wherein the variational distribution is a Gaussian distribution;

[0011] The posterior distribution of the estimated reflector antenna moment is obtained based on the training data and the deviation of the estimated reflector antenna moment. The training data includes angular velocity, angular acceleration, and angular displacement.

[0012] By continuously adjusting the mean and covariance of the variational distribution, the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0013] The mean of the posterior distribution corresponding to the minimum value is determined as the compensation term for the torque deviation, and the error of the joint attitude angle is optimized using the compensation term.

[0014] Optionally, the probability based on the variational distribution can be determined in the following way:

[0015] Based on the conditional distribution of the predicted implicit function at a given induction point, the conditional distribution of the training implicit function at a given induction point, and the variational distribution of the induction point value, determine the probability based on the variational distribution.

[0016] Optionally, the mean of the probability based on the variational distribution can be determined in the following way:

[0017] The mean of the probability based on the variational distribution is determined by the mean of the variational distribution, the kernel function matrix between the induced point and the test point, and the inverse of the kernel matrix of the induced point itself.

[0018] Optionally, the posterior distribution can be determined in the following way:

[0019] The posterior distribution is determined based on the conditional distribution of the predicted implicit function given the induced point, the conditional distribution of the training implicit function given the induced point, and the distribution of the induced point derived from the observation data.

[0020] Optionally, by continuously adjusting the mean and covariance of the variational distribution, the difference between the posterior distribution and the probability based on the variational distribution is minimized, including:

[0021] By continuously adjusting the mean and covariance of the variational distribution, the variational lower bound function is maximized, thereby minimizing the difference between the posterior distribution and the probability based on the variational distribution.

[0022] Optionally, the maximizing variational lower bound function can be determined in the following way:

[0023] Based on the approximation error of the covariance matrix and the normal distribution of the observed data, the maximum variational lower bound function is determined.

[0024] Optionally, the variational lower bound function can be maximized by continuously adjusting the mean and covariance of the variational distribution, including:

[0025] Solve for the gradients of the variational lower bound function with respect to the mean and covariance of the variational distribution to obtain the adjustment direction. That is, the gradient of the mean of the variational distribution reflects the amount of correction of the deviation between the mean and the training data, and the gradient of the covariance of the variational distribution reflects the amount of correction of the covariance for the uncertainty estimate.

[0026] The mean and covariance of the variational distribution are updated gradually along the gradient direction. The variational lower bound function is recalculated after each adjustment until the change in the variational lower bound function is less than the preset threshold or the maximum number of iterations is reached.

[0027] The mean and covariance of the variational distribution obtained from the last adjustment are used as the optimal variational parameters, at which point the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0028] Secondly, this application provides an error optimization device for the joint attitude angle of a reflector antenna, comprising:

[0029] The acquisition module is used to acquire the actual reflector antenna torque and the estimated reflector antenna torque; and to acquire the variational distribution of the deviation of the estimated reflector antenna torque, wherein the variational distribution is a Gaussian distribution.

[0030] The determination module is used to determine the deviation of the estimated reflector antenna torque based on the actual reflector antenna torque and the estimated reflector antenna torque; and to obtain the posterior distribution of the estimated reflector antenna torque based on the training data of the estimated reflector antenna torque and the deviation of the estimated reflector antenna torque, wherein the training data includes angular velocity, angular acceleration and angular displacement;

[0031] The optimization module is used to minimize the difference between the posterior distribution and the probability based on the variational distribution by continuously adjusting the mean and covariance of the variational distribution; the mean of the posterior distribution corresponding to the minimum value is determined as the compensation term for the torque deviation, and the error of the joint attitude angle is optimized by using the compensation term.

[0032] Thirdly, this application provides a computing device, including a memory and a processor;

[0033] The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0034] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0035] As can be seen from the above technical solution, this application has at least the following beneficial effects:

[0036] In this application, the method optimizes the torque deviation compensation term through variational inference, which can accurately capture nonlinear errors and unmodeled dynamics in the reflector antenna dynamic model, significantly improving the control accuracy of joint attitude angles; it dynamically adjusts the sliding mode gain based on the variational distribution covariance matrix to achieve adaptive compensation for model uncertainties, improving system robustness when the system faces strong wind interference or parameter mutations; and it utilizes a sparse variational Gaussian process to optimize computational efficiency, reducing the computational cost of traditional Gaussian processes. Complexity reduced to This method meets the real-time control requirements of reflector antennas. The optimization algorithm only needs to adjust two core parameters, mean and covariance, and converges quickly to the optimal solution through the gradient ascent method. It is usually stable within 50-100 iterations, reducing the difficulty of engineering implementation. This method can be embedded into traditional controllers as a feedforward compensation module without significantly modifying the original control architecture. Through kernel function design, it can naturally incorporate prior knowledge of different physical fields, making it suitable for handling complex working conditions such as temperature fluctuations and wind disturbances in high-altitude areas.

[0037] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0038] Figure 1 A flowchart illustrating an error optimization method for the joint attitude angle of a reflector antenna provided in this application embodiment;

[0039] Figure 2 A schematic diagram of an error optimization device for the joint attitude angle of a reflector antenna provided in an embodiment of this application;

[0040] Figure 3 This is a schematic diagram of a computing device provided in an embodiment of this application. Detailed Implementation

[0041] The terms "first," "second," and "third," etc., used in this application specification and accompanying drawings are used to distinguish different objects, not to limit a specific order.

[0042] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0043] To ensure clarity and conciseness in the description of the following embodiments, a brief introduction to the related technologies is given first:

[0044] A reflector antenna is an antenna that receives or transmits signals by reflecting electromagnetic waves. It is widely used in fields such as radio astronomy and satellite communications. Its servo system requires high-precision control of joint movements to achieve target tracking.

[0045] The angular positions of the moving joints (such as azimuth and elevation axes) of the reflector antenna are the control target. The problem is to improve the control accuracy of the joint attitude angles and solve the tracking errors caused by interference such as strong winds and temperature changes.

[0046] Defined as the expected value of angular displacement ( ) and actual value ( The difference between () The deviation between the actual position of the antenna and the target position is reflected and is an evaluation index of control performance.

[0047] In the field of reflector antenna control, the true reflector antenna torque refers to the physical torque that actually acts on the antenna joint, while the estimated reflector antenna torque is an approximation based on a simplified nominal model.

[0048] Variational distributions are tools used in Bayesian inference to approximate complex posterior distributions; in this application, it is assumed that their mean is... Covariance is The Gaussian distribution, by introducing the technique of induced points, transforms the high-dimensional integral problem into a low-dimensional optimization problem. The posterior distribution is a probabilistic description of the torque deviation after fusing observation data (such as angular velocity, angular acceleration, and angular displacement).

[0049] Existing reflector antenna control methods struggle to simultaneously meet the requirements of high-precision tracking and real-time performance, and are prone to significant joint attitude angle errors under complex operating conditions (such as strong winds and temperature variations). Antenna dynamics models incorporate factors that are difficult to accurately model, such as nonlinear friction and time-varying wind loads, leading to discrepancies between estimated and actual torques.

[0050] The computational cost of traditional Gaussian process inference increases cubically with the amount of data, making it unsuitable for millisecond-level control cycles. Controllers with fixed parameters struggle to cope with environmental disturbances and system parameter drift; for example, sudden changes in wind speed can cause a surge in tracking errors. Traditional methods cannot effectively characterize the probability distribution of model errors, hindering adaptive adjustments to the control strategy.

[0051] In view of this, embodiments of this application provide an error optimization method for the joint attitude angle of a reflector antenna, which can be executed by a processing device. The processing device can be a terminal or a server. Terminals include, but are not limited to, smartphones, tablets, laptops, personal digital assistants, or smart wearable devices. The server can be a cloud server, such as a central server in a central cloud computing cluster or an edge server in an edge cloud computing cluster. Alternatively, the server can be a server in a local data center. A local data center refers to a data center directly controlled by the user.

[0052] In the field of high-precision control of reflector antennas, traditional methods suffer from significant joint attitude angle tracking errors due to the difficulty in accurately modeling complex dynamic characteristics (such as nonlinear friction and time-varying wind loads) and processing massive amounts of data in real time, especially under extreme conditions. This application constructs an adaptive compensation mechanism through a sparse variational Gaussian process (SVGP) to achieve quantitative characterization and dynamic compensation of model uncertainties. Specifically, it uses a variational distribution to approximate the posterior probability of the torque deviation and optimizes the variational parameters (mean...) Covariance Minimize the difference from the true posterior, and dynamically adjust the control gain based on the covariance to form a closed-loop architecture of probabilistic modeling, real-time optimization, and robust control.

[0053] The method first obtains the actual reflector antenna torque and the estimated reflector antenna torque; then, it determines the deviation of the estimated reflector antenna torque based on the actual and estimated reflector antenna torques; finally, it obtains the variational distribution of the deviation of the estimated reflector antenna torque, wherein the variational distribution has a mean of... The covariance is The Gaussian distribution is used; the posterior distribution of the estimated reflector antenna torque is obtained based on the training data and the deviation of the estimated reflector antenna torque, wherein the training data includes angular velocity, angular acceleration, and angular displacement; finally, by continuously adjusting the mean and covariance of the variational distribution, the minimum value of the posterior distribution and the probability based on the variational distribution is obtained; the mean of the posterior distribution corresponding to the minimum value is determined as the compensation term for the torque deviation, and the error of the joint attitude angle is optimized using the compensation term.

[0054] This method optimizes the torque deviation compensation term through variational inference, accurately capturing nonlinear errors and unmodeled dynamics in the reflector antenna dynamic model, significantly improving the control accuracy of joint attitude angles. Based on the variational distribution covariance matrix, it dynamically adjusts the sliding mode gain to achieve adaptive compensation for model uncertainties, enhancing system robustness when facing strong wind interference or parameter mutations. Furthermore, it utilizes a sparse variational Gaussian process to optimize computational efficiency, reducing the computational cost of traditional Gaussian processes. Complexity reduced to This method meets the real-time control requirements of reflector antennas; the optimization algorithm only needs to adjust two parameters, mean and covariance, and converges quickly to the optimal solution through the gradient ascent method, usually stabilizing within 50-100 iterations, reducing the difficulty of engineering implementation; this method can be embedded as a feedforward compensation module into traditional controllers without significantly modifying the original control architecture; through kernel function design, it can naturally incorporate prior knowledge of different physical fields, and is suitable for handling complex working conditions such as temperature fluctuations and wind disturbances in high-altitude areas.

[0055] To make the technical solution of this application clearer and easier to understand, the following describes, in conjunction with the accompanying drawings, an error optimization method for the joint attitude angle of a reflector antenna provided in an embodiment of this application. For example... Figure 1 As shown in the figure, this is a flowchart of an error optimization method for the joint attitude angle of a reflector antenna provided in an embodiment of this application.

[0056] S201, The processing equipment obtains the actual reflector antenna torque and estimates the reflector antenna torque.

[0057] The processing equipment first directly collects or indirectly calculates the actual reflector antenna torque through a sensor system (such as torque sensors, encoders, etc.). The actual torque is the physical torque experienced by each joint of the antenna during actual operation. Its magnitude is determined by the antenna's dynamic characteristics (such as inertia, friction, and gravity) and external environmental disturbances (such as wind load and temperature changes). It can be calculated using the complete dynamic equation of the reflector antenna, expressed as:

[0058]

[0059] in, Represents the actual torque. Represents the inertia matrix. Represents the matrices of centrifugal force and Coriolis force. Represents the friction term. Represents the gravity term. Represents the uncertainties in the model. Angular acceleration, Angular velocity, This represents angular displacement.

[0060] Simultaneously, the processing device calculates and estimates the reflector antenna moment based on a simplified nominal model. The nominal model is an approximation of the actual dynamic model, and the estimated parameters (such as...) are obtained through identification methods. , , The structure is constructed using the following expression:

[0061]

[0062] in, Indicates the estimated torque. Represents the estimated inertia matrix. This represents the estimated centrifugal force and Coriolis force matrices. This represents the estimated friction term. This represents the estimated gravity term. The nominal model ignores some complex dynamics (such as subtle frictional characteristics and sudden wind loads), therefore there is a discrepancy between the estimated torque and the actual torque.

[0063] S202. The processing equipment determines the deviation of the estimated reflector antenna torque based on the actual reflector antenna torque and the estimated reflector antenna torque.

[0064] Based on the actual reflector antenna moment and the estimated reflector antenna moment, the processing equipment can further calculate the moment deviation, expressed as:

[0065]

[0066] in, Indicates torque deviation. Indicates the inertia matrix deviation. This indicates the deviation of the centrifugal force and Coriolis force matrix. Indicates the deviation of the friction term. This indicates the deviation of the gravity term.

[0067] This deviation reflects the error caused by model simplification and unmodeled dynamics, and serves as the basis for subsequent error compensation through sparse variational Gaussian process (SVGP) fitting.

[0068] S203. The processing device obtains the variational distribution of the estimated reflector antenna torque deviation, and the variational distribution is a Gaussian distribution.

[0069] The variational distribution of the estimated reflector antenna moment deviation is assumed to have a mean of Covariance is The Gaussian distribution is expressed as:

[0070] in, for variational distribution, These are the function values ​​corresponding to the induced points selected from the training data (representing key features of torque deviation); Represents a normal distribution, with mean... It is the optimal estimate of the induced point function value, reflecting the central tendency of the torque deviation; covariance It is a measure of the uncertainty of the induced point function value, reflecting the correlation between different induced points and the range of prediction error; These are variational parameters and need to be solved using optimization algorithms.

[0071] S204. The processing device obtains the posterior distribution of the estimated reflector antenna torque based on the training data and the deviation of the estimated reflector antenna torque. The training data includes angular velocity, angular acceleration, and angular displacement.

[0072] Angular velocity, angular acceleration, and angular displacement in the training data are key input variables influencing torque deviation. For example, as angular velocity increases, the friction torque deviation may increase non-linearly; changes in angular displacement will cause changes in the gravity term deviation. The processing device correlates these inputs with the corresponding torque deviations (…). Pairing them up to form a training set ( =[ ]), Indicates the first One sample.

[0073] The posterior distribution is a probabilistic description of the variation of the estimated reflector antenna torque deviation with input variables (angular velocity, angular acceleration, angular displacement), given training data and observed torque deviation values. Its mathematical form is:

[0074]

[0075] in, To provide a given test input Observational data Training input At that time, the test output The probability distribution, Given training output and predict input At that time, the test output The conditional probability distribution; Given training input and observation data At that time, training output The posterior distribution, This represents the test input data. This indicates the implicit function being tested, i.e., the test output data. Represents observation data, This represents the training input data. This represents the training implicit function, i.e., the training output data.

[0076] For the input in the above formula The hidden, predicted posterior distribution can be represented as:

[0077]

[0078] in, for Remove input The implicit expression, similarly, and They are respectively and Remove input Implicit expressions.

[0079] In the training set A set of induced points were randomly selected. The input corresponding to the induced point is , This indicates the number of induced points.

[0080] Based on this, the predicted posterior distribution can be expressed as:

[0081]

[0082] in, Denotes the posterior distribution. Representative based on observation data Derivation of the distribution of the induced points, Indicates a given training hidden function and induction point time Conditional distribution, Indicates a given training hidden function and induction point The conditional distribution at that time.

[0083] It is a parameter A sufficient statistic, given Under the conditions, and It is completely independent, that is The above formula can be simplified to determining the posterior distribution based on the conditional distribution of the predicted latent function given the induction point, the conditional distribution of the trained latent function given the induction point, and the distribution of the induction point derived from the observation data. The expression is as follows:

[0084]

[0085] in, Denotes the posterior distribution. Indicates a given induction point The predictive implicit function of time Conditional distribution, Indicates a given induction point Training hidden function value at time Conditional distribution, Representative based on observation data Derive the distribution of the induced points.

[0086] In practice, find the way to It is usually difficult to find a sufficient statistic as a condition. As An approximation, therefore, based on the conditional distribution of the predicted implicit function given the inducing point, the conditional distribution of the trained implicit function given the inducing point, and the variational distribution of the inducing point value, the probability based on the variational distribution is determined, expressed as:

[0087]

[0088] in, Represents the probability based on the variational distribution. Indicates a given induction point The predictive implicit function of time Conditional distribution, Indicates a given induction point Training hidden function at time Conditional distribution, Indicates the value of the induced point The variational distribution of .

[0089] The mean is Covariance is Since the distribution is Gaussian, the probability prediction distribution based on the variational distribution is:

[0090]

[0091] in, Represents the probability based on the variational distribution. This represents the mean of the probability based on the variational distribution. This represents the covariance of the probability based on the variational distribution.

[0092] Based on the mean of the variational distribution, the kernel function matrix between the induced point and the test point, and the inverse of the kernel matrix of the induced point itself, the mean of the probability based on the variational distribution is determined, and the calculation expression is as follows:

[0093]

[0094] in, This represents the mean of the probability based on the variational distribution. This represents the mean of the variational distribution. This represents the kernel function matrix between the induced points and the test points. express The inverse of the kernel matrix of each induced point.

[0095] The expression for the covariance of the probability based on the variational distribution is:

[0096]

[0097] in, The covariance represents the probability based on the variational distribution. This represents the kernel function constant value of the test point itself. This represents the kernel function matrix between the induced points and the test points. express The inverse of the kernel matrix of each induced point. Represents variational distribution The covariance matrix.

[0098] The mapping relationship between input variables and torque deviation is quantified by means and variance. The mean reflects the most likely value of the deviation, and the variance reflects the uncertainty of the prediction (such as error fluctuations caused by environmental disturbances).

[0099] S205. By continuously adjusting the mean and covariance of the variational distribution, the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0100] By continuously adjusting the mean of the variational distribution Covariance Maximize the variational lower bound function to minimize the difference between the posterior distribution and the probability based on the variational distribution.

[0101] Based on the approximation error of the covariance matrix and the normal distribution of the observed data, the maximum variational lower bound function ELBO is determined, and its calculation expression is as follows:

[0102]

[0103] in, Denotes the variational lower bound function. The observed data follows a normal distribution. The Nystrom approximation for the covariance matrix of the training points. This represents the approximate error of the covariance matrix. express The identity matrix, This represents the observation data given the training set. The standard deviation of the observed noise, Represents a matrix Seeking traces.

[0104] The expression is:

[0105]

[0106] in, Represents the matrix of induced point pairs The Nystrom approximation, The kernel function matrix represents the relationship between training points and induced points. express The inverse of the kernel matrix of each induced point. yes The transpose of .

[0107] The expression is:

[0108]

[0109] in, This represents the approximate error of the covariance matrix. This represents the kernel function matrix of the training point itself.

[0110] Solve for the gradients of ELBO with respect to the mean and covariance of the variational distribution to obtain the adjustment direction. That is, the gradient of the mean of the variational distribution reflects the amount of correction of the deviation between the mean and the training data, and the gradient of the covariance of the variational distribution reflects the amount of correction of the covariance for the uncertainty estimate.

[0111] The ELBO gradient with respect to the mean of the variational distribution, that is, the gradient with respect to... Differentiation yields:

[0112]

[0113] in, This represents the gradient of ELBO with respect to the mean of the variational distribution. The standard deviation of the observed noise, express The identity matrix, This represents the observation data given the training set. The Nystrom approximation for the covariance matrix of the training points. This represents the kernel function matrix between training points and induced points. This represents the mean of the variational distribution.

[0114] This gradient reflects the direction of the residual between the mean prediction and the actual torque deviation, driving... Adjust in a direction that reduces prediction error.

[0115] The ELBO gradient with respect to the covariance of the variational distribution, that is, the gradient with respect to the variational distribution. Differentiation yields:

[0116]

[0117] in, This represents the gradient of ELBO with respect to the variational distribution covariance.

[0118] This gradient reflects the bias of the covariance matrix towards the uncertainty estimate, driving the adjustment. To match the true distribution characteristics of the data.

[0119] The mean and covariance of the variational distribution are updated gradually along the gradient direction. After each adjustment, the ELBO is recalculated until the change in ELBO is less than the preset threshold or the maximum number of iterations is reached.

[0120] When updating parameters along the gradient direction, the adjustment magnitude needs to be controlled by the learning rate (step size):

[0121] mean Update:

[0122]

[0123] in, This represents the updated mean. This represents the mean before the update. Set a learning rate (e.g., 0.01) to ensure that each adjustment is moderate and avoid ELBO oscillations caused by excessively large step sizes.

[0124] covariance Update:

[0125]

[0126] in, This represents the updated covariance. This represents the covariance before the update, while ensuring that... The positive definiteness of .

[0127] The significance of incremental updates lies in the fact that torque deviation data contains noise and nonlinearity. Small-step adjustments allow the parameters to gradually approach the optimal value in a complex distribution, avoiding model instability caused by a large-scale adjustment at once.

[0128] Each update and Afterwards, the ELBO value needs to be recalculated. The purpose of recalculation is to evaluate whether the current parameters make the model better: if the ELBO increases, it means that the adjustment is effective (the probability based on the variational distribution is closer to the predicted posterior distribution); if it decreases, it may be that the step size is too large or the gradient calculation is incorrect, and subsequent correction is required.

[0129] The mean and covariance of the variational distribution obtained from the last adjustment are used as the optimal variational parameters, at which point the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0130] When the iteration terminates (the change in ELBO is less than the threshold or the maximum number of iterations is reached), the mean of the variational distribution obtained from the last adjustment is... Covariance It was determined to be the optimal parameter.

[0131] S206. The mean of the posterior distribution corresponding to the minimum value is determined as the compensation term for the torque deviation, and the error of the joint attitude angle is optimized by using the compensation term.

[0132] When the difference between the posterior distribution and the probability based on the variational distribution reaches its minimum (i.e., ELBO convergence), the mean of the posterior distribution is the torque deviation. The optimal estimate of the torque deviation is obtained by considering historical error patterns in the training data, input characteristics of the current operating condition (angular velocity, angular acceleration, angular displacement), and the probabilistic characteristics of model uncertainty. Essentially, it is the best-fit value for the torque deviation under a "data-driven + physical constraint" framework. For example, under strong wind interference, the antenna joint experiences a 0.1 ohm increase due to additional wind load. The mean of the posterior distribution of the torque deviation will be accurately output as 0.1 by learning the correlation between wind speed and torque deviation in historical data. As a compensation benchmark.

[0133] The compensation term (the mean of the posterior distribution) is directly added to the equivalent control input to form the corrected control quantity:

[0134]

[0135] in, Indicates the estimated torque. For the desired angular acceleration, For the desired angular velocity, This represents the estimation of the inertia matrix. This represents the estimated centrifugal force and Coriolis force matrices. This indicates an estimate of the friction term. This indicates an estimate of the gravity term. Let represent the mean of the posterior distribution. For torque deviation, For test data, This is the training dataset.

[0136] This operation is equivalent to predicting and offsetting torque deviations in advance in the control commands, making the actual torque output by the actuator closer to the real requirements, and reducing attitude angle errors from the source.

[0137] Based on the above description, this application has the following beneficial effects:

[0138] This method optimizes the torque deviation compensation term through variational inference, accurately capturing nonlinear errors and unmodeled dynamics in the reflector antenna dynamic model, significantly improving the control accuracy of joint attitude angles. Based on the variational distribution covariance matrix, it dynamically adjusts the sliding mode gain to achieve adaptive compensation for model uncertainties, enhancing system robustness when facing strong wind interference or parameter mutations. Furthermore, it utilizes a sparse variational Gaussian process to optimize computational efficiency, reducing the computational cost of traditional Gaussian processes. Complexity reduced to This method meets the real-time control requirements of reflector antennas. The optimization algorithm only needs to adjust two core parameters, mean and covariance, and converges quickly to the optimal solution through the gradient ascent method. It is usually stable within 50-100 iterations, reducing the difficulty of engineering implementation. This method can be embedded into traditional controllers as a feedforward compensation module without significantly modifying the original control architecture. Through kernel function design, it can naturally incorporate prior knowledge of different physical fields, making it suitable for handling complex working conditions such as temperature fluctuations and wind disturbances in high-altitude areas.

[0139] The above text combined Figure 1 The method for optimizing the joint attitude angle of the reflector antenna provided in this application embodiment has been described in detail. The apparatus and device provided in this application embodiment will be described below with reference to the accompanying drawings.

[0140] like Figure 2 As shown in the figure, this is a schematic diagram of an error optimization device for the joint attitude angle of a reflector antenna provided in an embodiment of this application. The device includes:

[0141] The acquisition module 301 is used to acquire the actual reflector antenna torque and the estimated reflector antenna torque; and to acquire the variational distribution of the deviation of the estimated reflector antenna torque, wherein the variational distribution is a Gaussian distribution.

[0142] The determination module 302 is used to determine the deviation of the estimated reflector antenna torque based on the actual reflector antenna torque and the estimated reflector antenna torque; and to obtain the posterior distribution of the estimated reflector antenna torque based on the training data of the estimated reflector antenna torque and the deviation of the estimated reflector antenna torque, wherein the training data includes angular velocity, angular acceleration and angular displacement;

[0143] The optimization module 303 is used to minimize the difference between the posterior distribution and the probability based on the variational distribution by continuously adjusting the mean and covariance of the variational distribution.

[0144] The mean of the posterior distribution corresponding to the minimum value is determined as the compensation term for the torque deviation, and the error of the joint attitude angle is optimized using the compensation term.

[0145] Optionally, the determining module 302 is specifically used to determine the probability based on the variational distribution, according to the conditional distribution of the predicted implicit function when given the induction point, the conditional distribution of the trained implicit function when given the induction point, and the variational distribution of the induction point value.

[0146] Optionally, module 302 is specifically used to determine the mean of the probability based on the variational distribution, the kernel function matrix between the induced point and the test point, and the inverse of the kernel matrix of the induced point itself.

[0147] Optionally, module 302 is specifically used to determine the posterior distribution based on the conditional distribution of the predicted implicit function given the induced point, the conditional distribution of the trained implicit function given the induced point, and the distribution of the induced point derived from the observation data.

[0148] Optionally, the optimization module 303 is specifically used to maximize the variational lower bound function by continuously adjusting the mean and covariance of the variational distribution, so that the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0149] Optionally, module 302 is specifically used to determine the maximum variational lower bound function based on the approximation error of the covariance matrix and the normal distribution of the observed data.

[0150] Optionally, the optimization module 303 is specifically used to solve the gradients of ELBO with respect to the mean and covariance of the variational distribution to obtain the adjustment direction. That is, the gradient of the mean of the variational distribution reflects the amount of correction of the deviation between the mean and the training data, and the gradient of the covariance of the variational distribution reflects the amount of correction of the covariance for the uncertainty estimation.

[0151] The mean and covariance of the variational distribution are updated gradually along the gradient direction. After each adjustment, the ELBO is recalculated until the change in ELBO is less than the preset threshold or the maximum number of iterations is reached.

[0152] The mean and covariance of the variational distribution obtained from the last adjustment are used as the optimal variational parameters, at which point the difference between the posterior distribution and the probability based on the variational distribution is minimized.

[0153] The error optimization device for the joint attitude angle of the reflector antenna according to the embodiments of this application can correspond to the execution of the method described in the embodiments of this application, and the other operations and / or functions of each module / unit of the error optimization device for the joint attitude angle of the reflector antenna are respectively for implementing Figure 1 For the sake of brevity, the corresponding processes of each method in the illustrated embodiments will not be described in detail here.

[0154] This application also provides a computing device. For example... Figure 3As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 700 includes a bus 701, a processor 702, a communication interface 703, and a memory 704. The processor 702, the memory 704, and the communication interface 703 communicate with each other via the bus 701.

[0155] The 701 bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 3 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0156] The processor 702 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0157] The communication interface 703 is used for communication with external devices.

[0158] Memory 704 may include volatile memory, such as random access memory (RAM). Memory 704 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0159] The memory 704 stores executable code, and the processor 702 executes the executable code to perform the aforementioned error optimization method for the joint attitude angle of the reflector antenna.

[0160] Specifically, in achieving Figure 2 In the case of the illustrated embodiment, and Figure 2 When the modules or units of the error optimization device for the joint attitude angle of the reflector antenna described in the embodiment are implemented by software, the execution... Figure 2The software or program code required for the functions of each module / unit can be partially or entirely stored in the memory 704. The processor 702 executes the program code corresponding to each unit stored in the memory 704, and executes the aforementioned error optimization method for the joint attitude angle of the reflector antenna.

[0161] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to execute the aforementioned error optimization method for the joint attitude angle of the reflector antenna.

[0162] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0163] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0164] When the computer program product is executed by a computer, the computer executes any of the aforementioned methods for optimizing the joint attitude angles of the reflector antenna. The computer program product can be a software installation package; when any of the aforementioned methods for optimizing the joint attitude angles of the reflector antenna is required, the computer program product can be downloaded and executed on the computer.

[0165] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0166] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A method of error optimization of joint attitude angles of a reflector antenna, characterized in that, The method comprises: acquiring a real reflector antenna moment and an estimated reflector antenna moment; determining an estimated reflector antenna moment deviation according to the real reflector antenna moment and the estimated reflector antenna moment; acquiring a variational distribution of the estimated reflector antenna moment deviation, the variational distribution being a Gaussian distribution; obtaining a posterior distribution of the estimated reflector antenna moment according to training data of the estimated reflector antenna moment and the estimated reflector antenna moment deviation, the training data comprising angular velocity, angular acceleration and angular displacement; minimizing a difference between the posterior distribution and a probability based on the variational distribution by continuously adjusting a mean and a covariance of the variational distribution; determining a mean of the posterior distribution corresponding to a minimum value as a compensation term of the moment deviation, and optimizing an error of a joint attitude angle by using the compensation term.

2. The method of claim 1, wherein, The probability based on the variational distribution can be determined in the following manner: determining the probability based on the variational distribution according to a conditional distribution of a predicted latent function at a given inducing point, a conditional distribution of a training latent function at the given inducing point and a variational distribution of an inducing point value.

3. The method of claim 1, wherein, The mean of the probability based on the variational distribution can be determined in the following manner: determining the mean of the probability based on the variational distribution according to the mean of the variational distribution, a kernel function matrix between the inducing point and a test point and an inverse of a kernel matrix of the inducing point itself.

4. The method of claim 1, wherein, The posterior distribution can be determined in the following manner: determining the posterior distribution according to the conditional distribution of the predicted latent function at the given inducing point, the conditional distribution of the training latent function at the given inducing point and a distribution of the inducing point derived based on observation data.

5. The method of claim 1, wherein, The minimizing the difference between the posterior distribution and the probability based on the variational distribution by continuously adjusting the mean and the covariance of the variational distribution comprises: maximizing a variational lower bound function by continuously adjusting the mean and the covariance of the variational distribution, so as to minimize the difference between the posterior distribution and the probability based on the variational distribution.

6. The method of claim 5, wherein, The maximizing the variational lower bound function can be determined in the following manner: determining the maximizing the variational lower bound function according to an approximation error of a covariance matrix and a normal distribution of the observation data.

7. The method of claim 5, wherein, The maximizing the variational lower bound function by continuously adjusting the mean and the covariance of the variational distribution comprises: respectively solving gradients of the variational lower bound function with respect to the mean and the covariance of the variational distribution to obtain an adjustment direction, that is, a gradient of the mean of the variational distribution reflects a deviation correction amount of the mean and the training data, and a gradient of the covariance of the variational distribution reflects a correction amount of the covariance to uncertainty estimation; gradually updating the mean and the covariance of the variational distribution along the gradient direction, and recalculating the variational lower bound function after each adjustment until a variation amount of the variational lower bound function is less than a preset threshold or a maximum iteration number is reached; taking the mean and the covariance of the variational distribution obtained after the last adjustment as optimal variational parameters, at which time the difference between the posterior distribution and the probability based on the variational distribution is minimum.

8. An error optimization device for joint attitude angles of a reflector antenna, characterized by The device comprises: an acquisition module configured to acquire a real reflector antenna moment and an estimated reflector antenna moment, and acquire a variational distribution of an estimated reflector antenna moment deviation, the variational distribution being a Gaussian distribution; The determining module is configured to determine an estimated reflector antenna moment deviation according to the real reflector antenna moment and the estimated reflector antenna moment, and obtain a posterior distribution of the estimated reflector antenna moment according to training data of the estimated reflector antenna moment and the estimated reflector antenna moment deviation, wherein the training data comprises angular velocity, angular acceleration and angular displacement; The optimization module is configured to minimize a difference between the posterior distribution and a probability based on a variational distribution by continuously adjusting a mean and a covariance of the variational distribution, and determine a mean of the posterior distribution corresponding to a minimum value as a compensation term of the moment deviation, and optimize an error of the joint posture angle by using the compensation term.

9. A computing device, comprising: comprise a memory and a processor; The memory stores one or more computer programs comprising instructions, and when the instructions are executed by the processor, the computing device performs the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium is used to store a computer program for executing the method according to any one of claims 1 to 7.

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