Real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar
By constructing a hybrid refractive index profile model and incorporating data from the Global Navigation Satellite System and numerical weather prediction, the accuracy problem of neutral atmospheric refraction error compensation for ground-based distributed radar was solved, achieving high-precision and low-cost calculation of neutral atmospheric refraction error and improving the detection and imaging performance of the radar system.
Patent Information
- Application Number
- CN202511892246.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-16
- Publication Date
- 2026-03-17
AI Technical Summary
Existing neutral atmospheric refraction error compensation methods in ground-based distributed radar systems cannot accurately characterize the atmosphere, leading to reduced detection or imaging accuracy. Furthermore, high-precision meteorological equipment is costly and has low spatiotemporal resolution, failing to meet the requirements of ground-based distributed radar systems.
By employing a hybrid refractive index profile model, combining meteorological methods from the Global Navigation Satellite System and numerical weather prediction data, and optimizing parameters through simulated annealing, a cost function containing observation loss terms and structural similarity loss terms is constructed to achieve real-time, high-precision compensation of the neutral atmospheric refractive index profile.
It improves the accuracy of neutral atmospheric refraction error calculation, reduces the cost of meteorological data acquisition, adapts to different geographical environments, and significantly enhances the detection and imaging accuracy of radar systems.
Smart Images
Figure CN121679503A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar signal processing technology, and specifically relates to a real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar. Background Technology
[0002] Ground-based distributed radar systems represent an important direction for future radar development, possessing the potential to achieve high-precision observation of extremely distant targets. This system can support all-weather, all-day observation and overcomes the physical limitations of centralized radar systems through signal synchronization technology, thereby enabling high-precision detection and imaging of deep-space targets such as asteroids.
[0003] Ground-based distributed radar observation of celestial objects relies on high-precision signal transmission and reception synchronization technology. This involves correcting the phase and time delay differences between individual radar units to ensure phase consistency during signal superposition, thereby improving the detection and imaging performance of the radar system. However, radar signal propagation is inevitably affected by the non-uniform refractive index of the neutral atmosphere. Besides introducing atmospheric phase errors, this also causes signal propagation path curvature, leading to deviations in the synthetic beam of the ground-based distributed radar, reducing its detection or imaging accuracy, and even preventing target detection. Therefore, compensation for neutral atmospheric refraction errors is essential.
[0004] Currently, methods for compensating neutral atmospheric refraction errors in ground-based distributed radar can be broadly categorized into three types: The first involves establishing a neutral atmospheric refraction error model based on the characteristics of neutral atmospheric refraction errors and long-term radar data; the second involves establishing an average refraction profile model based on long-term meteorological data and then calculating the neutral atmospheric refraction error according to the law of refraction; and the third involves directly measuring meteorological profiles in the neutral atmosphere using high-precision meteorological equipment and converting them into refractive index profiles to calculate the neutral atmospheric refraction error. However, compensation methods based on average refraction profile modeling cannot accurately characterize the atmosphere; high-precision meteorological equipment suffers from low spatiotemporal resolution, sparse spatial distribution, and excessive cost. Although compensation methods based on global navigation satellite meteorological methods may overcome these problems, existing research focuses only on the troposphere and cannot support the neutral atmospheric refraction error compensation requirements of ground-based distributed radar systems. Summary of the Invention
[0005] To address these limitations, this invention proposes a real-time, high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar. The calculation results of this method are closer to the actual atmospheric conditions, and can effectively improve the accuracy of neutral atmospheric refraction error calculation.
[0006] The technical solution for implementing the present invention is as follows: Firstly, this invention proposes a real-time, high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar, the specific process of which is as follows: Step 1: Construct the neutral atmospheric refractive index profile model in segments based on altitude, and set the initialization parameters of the model; Step 2: The line-of-sight neutral atmospheric delay estimated by the meteorological method of the real-time global navigation satellite system is introduced as the observation loss term of the cost function, and the tropospheric partial refractive index profile provided by numerical weather prediction data is introduced as the structural similarity loss term. A cost function containing the observation loss term and the structural similarity loss term is constructed. Step 3: Based on the cost function, update the parameters to be optimized in the neutral atmospheric refractive index profile model to obtain the optimal profile model and determine the current optimal neutral atmospheric refractive index profile. Step four: Use the neutral atmospheric refractive index profile to achieve neutral atmospheric refractive error compensation.
[0007] Optionally, the neutral atmospheric refractive index profile model of the present invention is as follows:
[0008] in, This represents the atmospheric refractive index of the surface where the ground-based distributed radar is located. This indicates the elevation of the surface where the ground-based distributed radar is located. Altitude Indicates the parameter to be estimated. , and This refers to the set altitude value.
[0009] Optionally, the present invention described =1km =6km and =86km.
[0010] Optionally, the observation loss term described in this invention for:
[0011] in, The atmospheric refractive index profile is determined by the estimated parameters. This represents the ray tracing operator. The first real-time measurement for global navigation satellites The neutral atmospheric delay along the line of sight of a satellite. For the first Geometric elevation angle of the satellite.
[0012] Optionally, the structural similarity loss term described in this invention for:
[0013] in, This is the proportionality coefficient. C is the Pearson correlation coefficient, which is used to characterize the similarity between the estimated profile and the reference profile. The more similar they are, the larger the C value.
[0014] Optionally, the Pearson correlation coefficient described in this invention for:
[0015] in, Indicates the neutral atmospheric height. Layer refractive index estimate, This indicates the neutral atmospheric height provided by numerical weather prediction data. Layer refractive index.
[0016] Optionally, in step three of this invention, random jitter is introduced into the parameters to be estimated in the current model based on the simulated annealing algorithm for updating and iterating until the iteration reaches a specified number, thereby obtaining the optimal neutral atmospheric refractive index model parameters.
[0017] In a second aspect, the present invention provides a real-time high-precision neutral atmospheric refraction error compensation device for ground-based distributed radar, comprising: The model building module is used to construct the neutral atmospheric refractive index profile model in segments according to altitude and to set the model's initialization parameters. The objective function construction module is used to introduce the line-of-sight neutral atmospheric delay estimated by the meteorological method of the real-time global navigation satellite system as the observation loss term of the cost function, and to introduce the tropospheric partial refractive index profile provided by numerical weather prediction data as the structural similarity loss term, and to construct a cost function that includes the observation loss term and the structural similarity loss term. The neutral atmospheric refractive index calculation module updates the parameters to be optimized in the neutral atmospheric refractive index profile model based on the cost function, obtains the optimal profile model, and determines the current optimal neutral atmospheric refractive index profile. The error compensation module utilizes the neutral atmospheric refractive index profile to achieve atmospheric refractive index error compensation.
[0018] Beneficial effects: First, higher accuracy: By combining two high-accuracy refractive index profile models to construct a higher-accuracy neutral atmospheric refractive index profile model, and by introducing real-time meteorological data from the Global Navigation Satellite System and numerical weather prediction data products to jointly constrain the high-accuracy estimation of model parameters, compared with existing traditional methods, the refractive index profile obtained can cover the neutral atmosphere, and the corresponding neutral atmospheric refractive error calculation results are closer to the actual atmospheric conditions, thus effectively improving the accuracy of neutral atmospheric refractive error calculation.
[0019] Second, the cost is relatively low: the required meteorological data sources are readily available, global navigation and positioning receivers and surface sensors are low-cost and easy to deploy, and numerical weather prediction data are open-source resources, avoiding the need for high-cost radiosonde stations or specialized equipment construction.
[0020] Third, the method has strong adaptability: the refractive correction method that introduces a hybrid refractive index profile model and a multi-source fusion cost function is applicable to distributed radar systems. It can overcome the limitations of traditional empirical formulas and average modeling methods in terms of applicable scope, geographical differences and model assumptions, and significantly improve the accuracy of refractive index calculation.
[0021] In summary, this invention has significant innovation and practical value in terms of method architecture, data fusion method, and accuracy assurance mechanism. Attached Figure Description
[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 Invention implementation flowchart; Figure 2 Statistical results of the accuracy of fitting neutral atmosphere profile models with different refractive indices; (a) Chongqing area, (b) Hong Kong, China; Figure 3 : Statistics on the accuracy of neutral atmospheric error estimation based on different neutral atmospheric refraction error calculation methods; (a) NARE accuracy in Chongqing, (b) NARE accuracy in Hong Kong, (c) NADE accuracy in Chongqing, (d) NADE accuracy in Hong Kong; Figure 4 Comparison of ZTD calculated based on real-time PPP and ZTD calculated based on nearby radiosonde data (March 2025); Table 1: Comparison of compensation accuracy of different neutral atmospheric refraction error methods; Figure 5 Statistical analysis of the accuracy of neutral atmospheric refractive index profiles obtained by different methods; Figure 6 Statistical analysis of residual sequences of neutral atmospheric refraction error compensation using different methods (March 2025). Detailed Implementation
[0024] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0025] It should be noted that, unless otherwise specified, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.
[0026] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0027] This application provides a real-time, high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar. The specific process is as follows: Step 1: Construct the neutral atmospheric refractive index profile model in segments based on altitude, and set the initialization parameters of the model; Step 2: The line-of-sight neutral atmospheric delay estimated by the meteorological method of the real-time global navigation satellite system is introduced as the observation loss term of the cost function, and the tropospheric partial refractive index profile provided by numerical weather prediction data is introduced as the structural similarity loss term. A cost function containing the observation loss term and the structural similarity loss term is constructed. Step 3: Based on the cost function, update the parameters to be optimized in the neutral atmospheric refractive index profile model to obtain the optimal profile model and determine the current optimal neutral atmospheric refractive index profile. Step four: Use the neutral atmospheric refractive index profile to achieve neutral atmospheric refractive error compensation.
[0028] The above process is explained in detail below, and the implementation procedure is attached. Figure 1 .
[0029] Step 1: Construction of a high-precision mixed neutral atmospheric refractive index profile model In this embodiment, a segmented profile model is used to model the area from the ground surface to an altitude of 6 kilometers, while a Hopfield model is used to model the area from 6 kilometers to 85 kilometers, together forming a high-precision mixed neutral atmospheric refractive index profile model. The surface meteorological parameters provided by ground meteorological measurement equipment are used as the input to the surface refractive index of this model, wherein the surface meteorological parameters... It can be acquired by ground sensors. This represents the atmospheric refractive index of the surface where the ground-based distributed radar is located. This represents the elevation of the surface where the ground-based distributed radar is located, and the parameters to be estimated within the model. Perform initialization, and the corresponding initialization parameters are: The neutral atmospheric refractive index profile is calculated based on the current model parameters, and the formula is expressed as: (1) In the formula, Indicates height as The atmospheric refractive index will be used to initialize the parameters. Let this be the current optimal parameter.
[0030] Step 2: Calculate the cost function based on global navigation satellite meteorological observation data and numerical weather prediction data. In the design of the cost function, the line-of-sight neutral atmospheric delay estimated by the meteorological method of the real-time global navigation satellite system is introduced as the observation loss term of the cost function; the tropospheric partial refractive index profile provided by numerical weather prediction data is introduced as the structural similarity loss term; the above two items together constitute the innovative cost function. This step combines global navigation satellite meteorological observation data and numerical weather prediction data. The cost function is shown below: (2) (3) In the formula, Let cost function be This is an evaluation item for observation accuracy based on real-time global navigation satellite meteorological line-of-sight atmospheric delay products. This is a morphological evaluation item based on numerical weather prediction data. This is the atmospheric refractive index profile determined by the estimated parameters. This represents the ray tracing operator. The first real-time measurement for global navigation satellites The amount of neutral atmospheric delay in the line-of-sight direction of a satellite. For the first Geometric elevation angle of the satellite. This is a scaling factor used to adjust the weight of the morphological evaluation term in the total cost function. The Pearson correlation coefficient is shown in (4): (4) In the formula, The first digit representing the neutral atmospheric altitude layer superscript Indicates the estimation result, superscript This indicates the result provided by numerical weather prediction data.
[0031] The initial cost function value can be calculated based on the initial neutral atmospheric refractive index profile data, the real-time line-of-sight atmospheric delay results measured by global navigation satellites, and the current numerical weather prediction data.
[0032] Step 3: Estimation of Neutral Atmospheric Refractive Index Parameters Based on Simulated Annealing Combining the neutral atmospheric refractive index profile model and initial neutral atmospheric refractive index profile parameters constructed in step one, and the innovative cost function and initial cost function value constructed in step two, the simulated annealing algorithm is used to introduce random jitter to update the current model parameters. The calculation of neutral atmospheric refractive index profile and cost function in steps one and two is repeated. When the iteration reaches the specified number of times, the optimal neutral atmospheric refractive index model parameters can be obtained, and the optimal neutral atmospheric refractive index profile at this time can be determined.
[0033] Step 4: Calculation and Compensation of Neutral Atmospheric Refraction Error in Ground-Based Distributed Radar System Combining the optimal neutral atmospheric refractive index profile obtained in step three, and taking the geometric elevation angle of the celestial target as a reference, the propagation path of electromagnetic waves in the neutral atmosphere and the target elevation angle are searched along different paths. The neutral atmospheric refraction error at a specific theoretical observation elevation angle is calculated using the ray tracing method. This refraction error is then superimposed on the theoretical observation elevation angle of the ground-based distributed radar unit, thereby achieving neutral atmospheric refraction error compensation in the ground-based distributed radar system.
[0034] Another embodiment of this application provides a real-time high-precision neutral atmospheric refraction error compensation device for ground-based distributed radar, comprising: The model building module is used to construct the neutral atmospheric refractive index profile model in segments according to altitude and to set the model's initialization parameters. The objective function construction module is used to introduce the line-of-sight neutral atmospheric delay estimated by the meteorological method of the real-time global navigation satellite system as the observation loss term of the cost function, and to introduce the tropospheric partial refractive index profile provided by numerical weather prediction data as the structural similarity loss term, and to construct a cost function that includes the observation loss term and the structural similarity loss term. The neutral atmospheric refractive index calculation module updates the parameters to be optimized in the neutral atmospheric refractive index profile model based on the cost function, obtains the optimal profile model, and determines the current optimal neutral atmospheric refractive index profile. The error compensation module utilizes the neutral atmospheric refractive index profile to achieve atmospheric refractive index error compensation.
[0035] Implementation example: Simulation experiments were conducted using this invention to further verify and analyze the feasibility and effectiveness of the proposed technology.
[0036] First, the accuracy of the proposed mixed refractive index profile model was verified using reference profile data from Chongqing and Hong Kong, China. The reference profile dataset consists of three types of data. Radiosonde data provides refractive index profiles from the surface to an altitude of 12 km, while the fifth-generation European Centre for Medium-Range Weather Forecasts (ERA5) reanalysis data provides refractive index profiles from 12 km to 45 km. Data for the remaining altitudes are supplemented by the US Standard Atmospheric Model (USA76).
[0037] To fully demonstrate the accuracy of the hybrid model, hybrid and traditional models, including the piecewise model, Hopfield model, and CRPL model, were used to fit the neutral atmospheric refraction profile dataset for the aforementioned region from 2022 to 2024. The fitting accuracy and corresponding neutral atmospheric error of each model were statistically compared using root mean square error (RMSE), standard deviation (STD), and mean absolute error (MAE). The statistical results are attached. Figure 2 and attached Figure 3 As shown. According to the appendix Figure 2 It can be seen that, within both regions, the proposed hybrid model achieves the highest profile fitting accuracy in neutral atmosphere. (Appendix) Figure 3 Furthermore, the neutral atmospheric refraction error and statistical results calculated based on each model are presented. It can be seen that the hybrid model proposed in this invention is significantly superior to the traditional model.
[0038] Secondly, this invention further verifies the performance of the proposed method based on measured GNSS data from Hong Kong, China, in March 2025. A neutral atmospheric refractive index profile was constructed using radiosonde data, ERA5 data, and the USA76 model. The corresponding neutral atmospheric refractive error was calculated using the ray tracing method as reference data. Global Navigation Satellite System data was obtained from the Stonecutters Island station. The numerical weather prediction data used were Global Forecast System (GFS) products provided by the National Center for Atmospheric Research (NCAR).
[0039] Appendix Figure 4 The zenith tropospheric delay (ZTD) obtained by real-time precise point positioning (PPP) was compared with that calculated based on radiosonde data from the same period. Using the radiosonde data ZTD as a reference, the RMSE of the ZTD obtained by the real-time PPP method was 1.9981 cm. After mapping the ZTD obtained by the real-time PPP method onto the navigation satellite line of sight, the corresponding tilted neutral atmospheric delay was obtained, which was used for subsequent verification of neutral atmospheric refraction error compensation.
[0040] The accuracy of the neutral atmospheric refractive index profiles estimated by different methods in the experiment is shown in the attached figure. Figure 5As shown. The method proposed in this invention achieves estimation accuracies of 9.7433 N-unit and 7.6361 N-unit at altitudes of 10 km and 50 km, respectively, which are superior to other methods. Appendix Table 1 summarizes the neutral atmospheric refraction error accuracy calculated by different methods and models.
[0041] Table 1 Comparison of compensation accuracy of different neutral atmospheric refraction error methods
[0042] The results show that the method proposed in this invention has the highest accuracy, with an RMSE of 0.0404 arcseconds, an STD of 0.0395 arcseconds, and a maximum absolute error (AEM) of 0.1743 arcseconds. (Appendix) Figure 6 The time series of neutral atmospheric refraction error compensation accuracy of different methods were compared, and it was also shown that the accuracy of the method proposed in this invention is better than that of other methods.
[0043] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar, characterized in that, The specific process is: Step one, the neutral atmosphere refractive index profile model is segmented according to the altitude, and the initialization parameters of the model are set; Step two, the line-of-sight direction neutral atmosphere delay estimated by the real-time global navigation satellite system meteorology method is introduced as the observation loss term of the cost function, and the troposphere part of the refractive index profile provided by the numerical weather prediction data is introduced as the structural similar loss term, and the cost function including the observation loss term and the structural similar loss term is constructed; Step three, based on the cost function, the to-be-optimized parameters of the neutral atmosphere refractive index profile model are updated, the optimal profile model is obtained, and the current optimal neutral atmosphere refractive index profile is determined; Step four, the neutral atmosphere refractive index profile is used to realize the neutral atmosphere refraction error compensation.
2. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The specific process is: The neutral atmosphere refractive index profile model is: wherein, represents the atmospheric refractivity of the ground surface on which the ground-based distributed radar is located, represents the altitude of the ground surface on which the ground-based distributed radar is located, is the altitude, represents the to-be-estimated parameter, , and is the set altitude value.
3. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The = 1 km, = 6 km and = 86 km.
4. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The observation loss term is: wherein, is the atmospheric refractive index profile determined from the estimated parameters, denotes the ray tracing operator, is the global navigation satellite system real-time measured first order ionospheric delay, is the neutral atmospheric delay in the line-of-sight direction of the nth satellite, is the geometric elevation angle of the nth satellite.
5. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The structural similarity loss term is: wherein, is a proportionality factor, is the Pearson correlation coefficient.
6. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The Pearson correlation coefficient is: wherein represents the neutral atmospheric height of the layer refractive index estimate, represents the neutral atmospheric height of the layer refractive index provided by the numerical weather prediction data.
7. The real-time high-precision neutral atmospheric refraction error compensation method for ground-based distributed radar according to claim 1, characterized in that, The step three introduces random jitter to the to-be-estimated parameters of the current model based on the simulated annealing algorithm for updating iteration until the iteration reaches a specified number of times, and the optimal neutral atmosphere refractive index model parameters are obtained.
8. A real-time high-precision neutral atmospheric refraction error compensation device for ground-based distributed radar, characterized in that, It comprises: The model construction module is used for segmenting the neutral atmosphere refractive index profile model according to the altitude, and setting the initialization parameters of the model; The objective function construction module is used for introducing the line-of-sight direction neutral atmosphere delay estimated by the real-time global navigation satellite system meteorology method as the observation loss term of the cost function, and introducing the troposphere part of the refractive index profile provided by the numerical weather prediction data as the structural similar loss term, and constructing the cost function including the observation loss term and the structural similar loss term; The neutral atmosphere refractive index calculation module updates the to-be-optimized parameters of the neutral atmosphere refractive index profile model based on the cost function, obtains the optimal profile model, and determines the current optimal neutral atmosphere refractive index profile; The error compensation module uses the neutral atmosphere refractive index profile to realize the atmospheric refraction error compensation.
9. The real-time high-precision neutral atmospheric refraction error compensation device for ground-based distributed radar according to claim 1, characterized in that, The specific process is: The neutral atmosphere refractive index profile model is: wherein, represents the atmospheric refractivity of the ground surface on which the ground-based distributed radar is located, represents the altitude of the ground surface on which the ground-based distributed radar is located, is the altitude, represents the parameter to be estimated, , and is the set altitude value.
10. The real-time high-precision neutral atmospheric refraction error compensation device for ground-based distributed radar according to claim 9, characterized in that, The observation loss term is: in, The atmospheric refractive index profile is determined by the estimated parameters. This represents the ray tracing operator. The first real-time measurement for global navigation satellites The neutral atmospheric delay along the line of sight of a satellite. For the first Geometric elevation angle of the satellite; The structural similarity loss term is: wherein, is a proportionality factor, is the Pearson correlation coefficient.