Radio telescope pointing error correction method based on parameter optimization
Through step-by-step regression and MCMC methods, the radio telescope pointing error model is optimized, redundant terms are eliminated and parameter uncertainty is quantified, and the problems of multicollinearity and non-convergence of parameters in traditional methods are solved, high-precision and stable pointing error correction are achieved, and the quality of observation data is improved.
Patent Information
- Application Number
- CN202510412803.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-03
- Publication Date
- 2025-07-11
AI Technical Summary
There are multicollinearity problems and non-convergence of parameters in the traditional radio telescope direction error correction method, resulting in a decrease in model prediction accuracy and stability, especially in high-frequency band observations.
The redundant correction terms were eliminated by stepwise regression analysis method, combined with the Markov chain Monte Carlo (MCMC) method to verify the parameter distribution to ensure the stability and convergence of the model, reduce the correlation of independent variables through stepwise regression analysis, and use the MCMC method to provide the credible interval of each parameter to quantify its uncertainty.
It significantly improves the accuracy and stability of the direction error correction of radio telescopes, improves the reliability and accuracy of observation data, solves the problems of multicollinearity and non-convergence of parameters, and ensures the effectiveness of the model in complex situations.
Smart Images
Figure CN120296980A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for correcting the pointing error of a radio telescope based on parameter optimization, and belongs to the technical field of radio telescope pointing correction. Background Technique
[0002] Radio telescopes are core equipment in astronomical research, and their pointing accuracy directly determines the quality and reliability of observational data. Radio telescopes have played a key role in many major astronomical discoveries, such as the discovery of gravitational waves in 2014, the observation of neutron star mergers in 2017, the photographing of a black hole image in 2019, and the detection of fast radio burst sources in 2020. These achievements all rely on the high-precision pointing ability of radio telescopes. With the increasing observational requirements, the challenges faced by radio telescopes are becoming increasingly severe, especially in high-frequency band observations, where stricter requirements for pointing accuracy are imposed.
[0003] High-precision pointing ability is the basis for radio telescopes to conduct space target observations. If the pointing error is not effectively corrected, it will lead to antenna efficiency loss. In high-frequency band observations such as the Ka band, the impact of pointing error is particularly significant. For example, in the observations of the 65-meter Tianma Telescope in China above 32 GHz, the pointing error must be controlled within 4 arcseconds. However, due to external factors such as servo control error, temperature change, coupling error, etc., this accuracy requirement is often difficult to achieve. Therefore, the pointing error correction technology is crucial, as it can not only improve the observational accuracy of radio telescopes but also significantly enhance the observational efficiency and data reliability.
[0004] Currently, traditional pointing error correction methods usually adopt multiple regression models. This method corrects the pointing error of radio telescopes through trigonometric function terms and their combinations (such as cos(az), sin(az), etc.). Trigonometric function terms are usually used to describe the influence of factors such as the azimuth angle and elevation angle of the telescope on the pointing accuracy. However, there is a significant problem with such multiple regression models based on trigonometric functions, namely multicollinearity.
[0005] Multicollinearity refers to a high degree of correlation between independent variables in the model, resulting in unstable estimation of regression coefficients. In a multiple regression model, if the correlation between independent variables is too high, especially when trigonometric function terms are involved, the parameter estimation of the regression model will become unreliable and cannot accurately reflect the true relationship between independent variables. Although multicollinearity does not directly affect the result of data fitting, it will cause the variance of the regression coefficients to increase sharply, thereby leading to a decrease in the accuracy of model prediction. This situation will affect the stability of the regression model in the prediction stage, especially when the correlation of independent variables changes, which may lead to serious distortion of the prediction results.
[0006] In addition, when the traditional model uses the ordinary least squares (OLS) method for parameter estimation, it also faces the situation that some parameters do not converge. Especially when the data set is complex or contains strong collinearity, the parameter estimation values of some correction terms cannot converge to stable values. This will cause large inconsistencies in the fitting results of the model among different data sets, thereby reducing the accuracy and prediction ability of the model.
[0007] In the multiple regression model adopted by the traditional pointing error correction method, due to the strong correlation between each correction term, there is a problem of multicollinearity, and when using the ordinary least squares (OLS) method for parameter estimation, some parameters cannot converge, resulting in unstable estimation of the model, which in turn affects the accuracy and reliability of prediction. Summary of the Invention
[0008] The technical problem to be solved by the present invention is to provide a radio telescope pointing error correction method based on parameter optimization to overcome the problems of multicollinearity and parameter non-convergence, and improve the accuracy and stability of pointing correction.
[0009] The technical solution of the present invention is: a radio telescope pointing error correction method based on parameter optimization, and the method is specifically as follows:
[0010] Step1: Collect the error sources affecting the pointing accuracy of the radio telescope, analyze the error sources, and establish a 22-parameter model as the original regression model.
[0011] Step2: Apply the stepwise regression analysis method to optimize the original regression model, eliminate the correction terms with redundant contributions, thereby reducing the correlation between independent variables and eliminating the problem of multicollinearity; stepwise regression not only helps to eliminate irrelevant correction terms, but also can test the contribution of each correction term to the model, thereby ensuring the simplicity and efficiency of the model.
[0012] Step3: After the stepwise regression analysis is completed, use the MCMC method to further verify the corrected parameters; through the sampling technique, the MCMC method can provide a credible interval for each parameter, quantify its uncertainty, especially solve the problem that the ordinary least squares method cannot converge, and ensure the convergence of the parameters and the stability of the model.
[0013] Step4: Determine the correction model according to the parameter distribution obtained by the MCMC method, and further adjust the model parameters by verifying the degree of agreement between the corrected model and the measured data to ensure its high accuracy and stability.
[0014] Step5: Correct the pointing accuracy of the radio telescope through the optimized pointing error correction model, thereby improving the reliability and accuracy of the observation data and completing the error correction.
[0015] The error sources include the linear and non - linear errors of the antenna device itself, servo control errors, and temperature variations.
[0016] The specific step - wise regression analysis method is as follows:
[0017] Step2.1: Read the input data and divide the training set and test set according to the source name;
[0018] Step2.2: Calculate the feature matrix of the correction terms and create a corresponding parameter list for each correction term;
[0019] Step2.3: Use the variance inflation factor to evaluate the multicollinearity between features, and calculate the VIF and P - value of each correction term;
[0020] Step2.4: Calculate the VIF value and P - value of each correction term;
[0021] Step2.5: Eliminate redundant correction terms through the VIF value and eliminate invalid correction terms through the P - value;
[0022] Step2.6: Calculate the AIC value and evaluate the model performance through the AIC value;
[0023] Step2.7: When the VIF values of all remaining features are less than the set threshold, the P - values are less than the significance level, and the AIC value is minimized, the step - wise regression process terminates.
[0024] The parameters in the parameter list include:
[0025] az_labels: Labels of the Azimuth correction terms;
[0026] el_labels: Labels of the Elevation correction terms.
[0027] The calculation of the VIF value is:
[0028]
[0029] where, is the R - square of the model after removing this feature in the regression process.
[0030] The calculation of the P - value is:
[0031] P = 2×(1 - Φ(|t|));
[0032] where: t is the ratio of the regression coefficient to its standard error, called the t - statistic, and Φ is the cumulative distribution function of the standard normal distribution.
[0033] The elimination of redundant correction terms through the VIF value is specifically:
[0034] In each regression, check the VIF values of all features. If the VIF value of a certain feature is greater than the set threshold, it is considered that the feature is highly correlated with other features, and then this feature is removed;
[0035] By calculating the VIF value of each feature, find the feature with the largest VIF value that exceeds the threshold and remove it.
[0036] The specific method of removing invalid correction terms through the P-value is as follows:
[0037] After removing the high-VIF features, recalculate the P-values of the remaining features;
[0038] If the P-value of a certain feature is greater than the set significance level, it indicates that the contribution of this feature to the model is not significant, and it is removed;
[0039] Gradually remove the feature with the largest P-value until the P-values of all remaining features are less than the set significance level.
[0040] The calculation of the AIC value is as follows:
[0041] AIC = 2k - 2ln(L)
[0042] Where: k is the number of estimated parameters in the model, and L is the maximum likelihood estimate value of the model.
[0043] To solve the problem of prediction distortion caused by multicollinearity and the problem of non-convergence of some parameters in traditional models, the present invention proposes a method of optimizing traditional parametric models. Specifically, stepwise regression analysis is used to remove the correction terms with overlapping contributions, thereby effectively reducing the correlation between independent variables and reducing the impact of multicollinearity on the regression model. Stepwise regression not only helps to remove redundant terms, but also can test the significance of each correction term one by one, ensuring the simplicity and efficiency of the model, thereby enhancing the stability and prediction ability of the model.
[0044] After the stepwise regression analysis is completed, the MCMC (Markov Chain Monte Carlo) method is further used to verify the rationality of the parameter distribution obtained after removing the multicollinearity correction terms. The MCMC method can provide a credible interval for each parameter through sampling technology to quantify its uncertainty. By continuously sampling, the MCMC method can also optimize the parameter estimation, thereby enhancing the stability and reliability of the model in complex situations. This advantage of MCMC enables us to ensure that the optimized parameter estimation is not only numerically effective but also has a reasonable distribution statistically. In this way, it can be ensured that the final obtained correction model is effective and stable in the high-precision pointing correction task, especially in the face of complex data, it can effectively avoid the problem of non-convergence of some parameters when using the least squares method for parameter estimation.
[0045] The beneficial effects of the present invention are as follows: By combining stepwise regression and the MCMC method, the problem of multicollinearity in the model can be effectively eliminated, and at the same time, the problem that some parameters cannot converge caused by the least squares method can be solved. The MCMC method further improves the stability and prediction accuracy of the model by providing the credible interval of each parameter, ensuring high-precision correction of the pointing error of the radio telescope. Compared with traditional regression methods, the present invention has obvious advantages in solving the challenges of complex non-linear error sources and parameter non-convergence. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] Figure 1 is the flowchart of the steps of the present invention;
[0047] Figure 2 is the schematic diagram of the stepwise regression process of the present invention;
[0048] Figure 3 is the 22-parameter MCMC sampling trajectory diagram of the present invention, where the arrows indicate the partial parameters that cannot converge;
[0049] Figure 4 is the 19-parameter MCMC sampling trajectory diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention. It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other arbitrarily.
[0051] In the correction of the pointing error of a radio telescope, the pointing accuracy is one of the important technical indicators for evaluating the performance of the telescope, and it is affected by various error factors, such as non-linear errors of antenna equipment, servo control errors, external factors such as temperature changes. Traditional regression models usually use a 22-parameter model to describe the functional relationship between the pointing error and the current pointing (azimuth angle and elevation angle). However, due to the multicollinearity among the independent variables of this model and the fact that some parameters cannot converge during the least squares fitting process, the parameter estimation is unstable and the prediction effect is not good. Specifically, in the regression results of the initial 22-parameter model, the estimated values of some parameters show extremely large or extremely small values, and there are problems with low statistical significance, which will significantly affect the accuracy and stability of the model.
[0052] To solve the above problems, in this embodiment, the traditional 22-parameter model is optimized by using stepwise regression and MCMC methods, gradually reducing redundant parameters, solving the problems of multicollinearity and non-convergence of some parameters, thereby improving the robustness and convergence of the model;
[0053] As Figure 1 shown, the specific steps are as follows:
[0054] First, a pointing error correction model of a radio telescope is established, adopting the internationally common 22-parameter model. This model includes multiple correction terms, which describe the influence of azimuth (az) and elevation (el) on pointing accuracy through trigonometric functions and their combinations, and comprehensively considers other error sources:
[0055] ΔAZ = P0 + tan(el)cos(az)P2 + tan(el)sin(az)P3 + tan(el)P4 - sec(el)P5
[0056] + azP 11 + cos(az)P 12 + sin(az)P 13 + cos(2az)P 16 + sin(2az)P 17 ;
[0057] ΔEL = P1 + sin(az)P2 + cos(az)P3 + cos(el)P6 + cot(el)P7 + elP8 + cos(el)P9 + sin(el)P 10
[0058] + cos(2az)P 14 + sin(2az)P 15 + cos(8el)P 18 + sin(8el)P 19 + cos(az)P 20 + sin(az)P 21 ;
[0059] The 22-parameter model takes into account various error factors and can describe the pointing error relatively accurately. However, due to the large number of trigonometric function terms in the model, the correlation between independent variables is relatively high, resulting in the emergence of the multicollinearity problem.
[0060] Therefore, it is necessary to optimize the 22-parameter model through stepwise regression analysis, as Figure 2 shown, specifically:
[0061] First, calculate the variance inflation factor (VIF) and the P-value of each parameter to eliminate redundant correction terms. The core idea of stepwise regression is to eliminate variables that contribute little or are redundant to the model, ensuring the simplicity and efficiency of the final model. Before stepwise regression, some correction terms in the 22-parameter model had high VIF values, indicating a high degree of multicollinearity problem, which led to unstable parameter estimation. After stepwise regression analysis, correction terms with redundant contributions (such as el*P[8], cos(el)*P[9], sin(el)*P
[10] ) were eliminated, thus reducing the original 22 parameters to 19 effective parameters.
[0062] The detailed steps of the stepwise regression process are as follows:
[0063] Step 1: Initial preparation work;
[0064] Load data: Read the input data from a file and divide the training set and test set according to the source name.
[0065] Construct the feature matrix: Calculate the feature matrices of the correction terms (az_X_train and el_X_train), and create corresponding parameter lists for each correction term. The parameters include:
[0066] az_labels: Labels of the Azimuth correction terms.
[0067] el_labels: Labels of the Elevation correction terms.
[0068] Step 2: Calculate the VIF and P-value of each correction term;
[0069] VIF calculation: Use the variance inflation factor (VIF) to evaluate the multicollinearity between features. For each feature, calculate its VIF value. The VIF value is used to judge the correlation between independent variables. The higher the VIF, the higher the correlation between this feature and other features, and this feature may need to be eliminated.
[0070] Calculate the VIF value of each feature:
[0071]
[0072] Among them, is the R-squared of the model after removing this feature in the regression process.
[0073] P-value calculation: Evaluate whether each correction term is significant through the P-value.
[0074] Calculate the P-value of each feature:
[0075] P = 2×(1 - Φ(|t|));
[0076] Among them, t is the ratio of the regression coefficient to its standard error, called the t-statistic, and Φ is the cumulative distribution function of the standard normal distribution.
[0077] When the P-value is less than the set significance level (usually 0.05), the correction term is considered significant and retained in the model.
[0078] Step 3: Preliminary check: At this stage, check the VIF value and P-value of each correction term;
[0079] If the VIF value of a certain correction term exceeds the set threshold (usually 10), then this correction term is considered redundant.
[0080] If the P-value of a certain correction term is greater than the set significance level (usually 0.05), then this correction term may not contribute to the model.
[0081] Gradually eliminate redundant correction terms;
[0082] Identify redundant correction terms through VIF values:
[0083] In each regression, check the VIF values of all features. If the VIF value of a certain feature is high (e.g., greater than 10), then this feature is considered highly correlated with other features and may cause a multicollinearity problem. At this time, this feature needs to be removed.
[0084] By calculating the VIF value of each feature, find the feature with the largest VIF value that exceeds the threshold and remove it.
[0085] Further eliminate invalid correction terms through P-values:
[0086] After removing the high-VIF features, recalculate the P-values of the remaining features.
[0087] If the P-value of a certain feature is greater than 0.05 (the usual significance level), it indicates that this feature does not contribute significantly to the model and can be removed.
[0088] Gradually remove the feature with the largest P-value until the P-values of all remaining features are less than the set significance level.
[0089] Step 4: Check the AIC (Akaike Information Criterion) value and evaluate the model performance;
[0090] AIC is a criterion used to measure the balance between the goodness of fit and complexity of the model. A lower AIC value indicates a better model. The specific calculation of AIC is:
[0091] AIC = 2k - 2ln(L);
[0092] Among them, k is the number of parameters estimated in the model (including regression coefficients), and L is the maximum likelihood estimate value of the model.
[0093] The AIC value is used to ensure the simplicity and accuracy of the model. After each feature is removed, the AIC value of the model is recalculated, and it is ensured that the AIC value gradually decreases or remains unchanged; if removing a feature causes the AIC value to increase, then this feature should not be removed, which means that removing this feature destroys the fitting effect of the model.
[0094] Step 5: Termination condition and final model;
[0095] When the VIF values of all remaining features are less than a set threshold (e.g., 10), and the P values are less than the significance level (e.g., 0.05), and the AIC value is minimized, the stepwise regression process terminates.
[0096] The final 19-parameter corrected model is:
[0097] ΔAZ = P0 + tan(el)cos(az)P2 + tan(el)sin(az)P3 + tan(el)P4 - sec(el)P5
[0098] + azP8 + cos(az)P9 + sin(az)P 10 + cos(2az)P 13 + sin(2az)P 14 ;
[0099] ΔEL = P1 + sin(az)P2 + cos(az)P3 + cos(el)P6 + cot(el)P7 + cos(2az)P 11
[0100] + sin(2az)P 12 + cos(8el)P 15 + sin(8el)P 16 + cos(az)P 17 + sin(az)P 18 ;
[0101] Such as Figure 3As shown, after stepwise regression optimization, to further verify the stability and convergence of the model, the Markov Chain Monte Carlo (MCMC) method was used to conduct posterior analysis on 19 corrected parameters. The MCMC method analyzes the credible intervals of each corrected parameter by generating a large number of samples, thereby quantifying its uncertainty. In the initial 22-parameter model, the estimation of some parameters did not converge, resulting in unstable results. However, the problem of multicollinearity has been successfully solved through stepwise regression, and the stability of the parameters has been optimized. At this time, the MCMC method is mainly used to verify whether the distribution of the corrected parameters in the model converges after stepwise regression optimization, ensuring that all corrected parameters have a good posterior distribution. The results of MCMC show the credible intervals of all corrected parameters in the optimized 19-parameter model. Compared with the 22-parameter model, the optimized model shows significant improvement in terms of convergence and credible intervals, and the parameter distribution is more reasonable.
[0102] As Figure 4 shown, through stepwise regression and MCMC optimization, a corrected model containing 19 effective parameters was finally obtained, which significantly improved the stability and convergence of the model compared to the original 22-parameter model.
[0103] Through the above embodiments, the present invention significantly reduces the correlation between independent variables, eliminates the problem of multicollinearity, and improves the stability of the model by stepwise regression to eliminate redundant parameters.
[0104] The MCMC method ensures the convergence of all parameters through posterior analysis and quantifies the credible intervals of each parameter, ensuring the reliability of parameter estimation.
[0105] Finally, the optimized 19-parameter model can be used for the pointing correction of radio telescopes. Applying this optimized model to the pointing correction of radio telescopes significantly improves the accuracy of observation data and ensures higher-quality observation results.
[0106] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.
Claims
1. A method for correcting the pointing error of a radio telescope based on parameter optimization, characterized in that , The method is specifically as follows: Step1: Collect the error sources that affect the pointing accuracy of the radio telescope, analyze the error sources, and establish a 22-parameter model as the original regression model; Step2: Apply the stepwise regression analysis method to optimize the original regression model, eliminate the correction terms with redundant contributions, and eliminate the problem of multicollinearity; Step3: After the stepwise regression analysis is completed, use the MCMC method to further verify the corrected parameters; Step4: Determine the correction model according to the parameter distribution obtained by the MCMC method, and adjust the model parameters by verifying the degree of agreement between the corrected model and the measured data; Step5: Correct the pointing accuracy of the radio telescope through the optimized pointing error correction model to complete the error correction.
2. The radio telescope pointing error correction method based on parameter optimization according to claim 1, characterized in that: The error sources include the linear and non-linear errors of the antenna equipment itself, servo control errors, and temperature changes.
3. The radio telescope pointing error correction method based on parameter optimization according to claim 1, wherein The stepwise regression analysis method is specifically as follows: Step2.1: Read the input data and divide the training set and test set according to the source name; Step2.2: Calculate the characteristic matrix of the correction terms and create a corresponding parameter list for each correction term; Step2.3: Use the variance inflation factor to evaluate the multicollinearity between features, and calculate the VIF and P values of each correction term; Step2.4: Calculate the VIF value and P value of each correction term; Step2.5: Eliminate the redundant correction terms through the VIF value, and eliminate the invalid correction terms through the P value; Step2.6: Calculate the AIC value and evaluate the model performance through the AIC value; Step2.7: When the VIF values of all remaining features are less than the set threshold, and the P values are less than the significance level, and the AIC value is minimized, the stepwise regression process terminates.
4. The method for correcting the pointing error of a radio telescope based on parameter optimization according to claim 3, characterized in that, The parameters in the parameter list include: az_labels: Labels of the Azimuth correction terms; el_labels: Labels of the Elevation correction terms.
5. The method for correcting the pointing error of a radio telescope based on parameter optimization according to claim 3, characterized in that, The calculation of the VIF value is: Among them, is the R-squared of the model after removing this feature during the regression process. The calculation of the P value is: P = 2×(1 - Φ(|t|)); where: t is the ratio of the regression coefficient to its standard error, called the t statistic, and Φ is the cumulative distribution function of the standard normal distribution.
6. The method for correcting the pointing error of a radio telescope based on parameter optimization according to claim 3, characterized in that, The elimination of redundant correction terms through the VIF value is specifically as follows: In each regression, check the VIF values of all features. If the VIF value of a certain feature is greater than the set threshold, it is considered that this feature is highly correlated with other features, and then this feature is eliminated; By calculating the VIF values of each feature, find the feature with the largest VIF value that exceeds the threshold and remove it.
7. The method for correcting the pointing error of a radio telescope based on parameter optimization according to claim 3, wherein The elimination of invalid correction terms through the P value is specifically as follows: After removing the high-VIF features, recalculate the P values of the remaining features; If the P value of a certain feature is greater than the set significance level, it indicates that the contribution of this feature to the model is not significant, and it is eliminated; Gradually remove the feature with the largest P value until the P values of all remaining features are less than the set significance level.
8. The method for correcting the pointing error of a radio telescope based on parameter optimization according to claim 3, characterized in that, The calculation of the AIC value is: AIC = 2k - 2ln(L) where: k is the number of parameters estimated in the model, and L is the maximum likelihood estimate value of the model.