A Machine Learning-Based Method and System for Compensating Antenna Phase Center Error

Abstract

This invention discloses a machine learning-based method for compensating antenna phase center error. First, it acquires frequency, attitude angle, and temperature information. Then, using a pre-trained lightweight model, it calculates the phase center error compensation value based on the acquired frequency, attitude angle, and temperature information. Finally, based on the phase center error compensation value, it determines the compensated ranging result. This compensation method introduces non-electromagnetic parameters such as temperature as input to compensate for the influence of changes in the on-orbit operating environment on the phase center. Simultaneously, it employs a machine learning model to calculate the compensation value. The machine learning model can approximate complex multidimensional nonlinear functions, eliminating interpolation errors and significantly improving compensation accuracy.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method and system for compensating antenna phase center error based on machine learning. Background Technology

[0002] Phase center error (PCO / PCV) compensation is a crucial step in high-precision GNSS positioning. It significantly improves positioning accuracy by correcting the deviation (PCO) between the antenna's phase center and geometric center, and the change in phase center with azimuth / elevation angle (PCV). Existing antenna phase center error (PCO / PCV) compensation schemes, such as the ATX files published by the international GNSS service organization IGS, primarily employ table-based interpolation methods. These methods interpolate from discrete calibration tables to obtain the PCV deviation corresponding to continuous satellite angles, accurately adapting to dynamic observation scenarios while balancing compensation efficiency and accuracy.

[0003] However, interpolation methods cannot accurately describe the complex nonlinear relationship between phase center and frequency, angle, and environmental conditions, and are prone to introducing large errors at non-sampling points. Especially at non-sampling points or when environmental parameters such as temperature change drastically, the error can reach the centimeter level, failing to meet the increasingly demanding accuracy requirements of current precision ranging systems. Furthermore, lookup table methods, based on static data calibrated in the laboratory, cannot cope with antenna characteristic drift caused by temperature gradients, mechanical stress, and material aging in the on-orbit environment, lacking adaptive capabilities. In addition, traditional error tables typically only include dimensions such as frequency, azimuth, and elevation, failing to consider key factors such as temperature and operating mode.

[0004] Based on this, some studies have attempted to introduce machine learning for navigation error modeling, but these are limited to multipath effects, ion layer delay, or phased array phase calibration. They have not yet been applied to system modeling and real-time compensation of antenna phase center errors, nor have they solved the problem of real-time deployment and updating of the model in resource-constrained spaceborne embedded environments. Summary of the Invention

[0005] To address some or all of the problems in existing technologies, and in order to improve the accuracy, adaptability, and coverage dimension of antenna phase center error compensation, the first aspect of this invention provides a machine learning-based method for compensating antenna phase center error, comprising:

[0006] Acquire frequency, attitude angle, and temperature information;

[0007] Using the pre-trained lightweight model, the phase center error compensation value is obtained based on the frequency, attitude angle, and temperature information; and

[0008] Based on the phase center error compensation value, the compensated ranging result is determined.

[0009] Furthermore, the compensation method also includes:

[0010] A reliability analysis is performed on the phase center error compensation value. If the reliability is lower than the threshold, a backup compensation method is adopted.

[0011] Furthermore, the backup compensation method includes a lookup-based interpolation method and / or the use of a default compensation value.

[0012] Furthermore, the pre-training of the lightweight model includes:

[0013] Obtain the calibration dataset;

[0014] The calibration dataset is supplemented by interpolation and / or simulation, while reducing the number of sampling points to obtain a training set;

[0015] Construct a mapping relationship between the training set and the phase center offset vector;

[0016] The mapping relationship is trained using a nonlinear fitting model; and

[0017] The trained model is pruned and quantized.

[0018] Furthermore, obtaining the calibration dataset includes:

[0019] Obtain historical data; and / or

[0020] Through experimental simulation, the radiation phase characteristics of the antenna were collected point-by-point at different frequencies, attitude angles, and temperatures; and / or

[0021] During in-orbit operation, actual observation data is measured.

[0022] Furthermore, the phase center offset vector includes the offset of the phase center in the east direction, the offset of the phase center in the north direction, and the offset of the phase center in the zenith direction.

[0023] Furthermore, the nonlinear fitting model includes a multilayer perceptron, a support vector regression model, and a Gaussian process regression model.

[0024] Based on the compensation method described above, a second aspect of the present invention provides a machine learning-based antenna phase center error compensation system, comprising:

[0025] The data acquisition module is used to acquire frequency, attitude angle, and temperature information; and

[0026] The inference compensation module is communicatively connected to the data acquisition module and is used to determine the phase center error compensation value based on the frequency, attitude angle and temperature information, and to determine the compensated ranging result based on the phase center error compensation value.

[0027] Furthermore, the inference compensation module includes:

[0028] A calculation unit is used to calculate the phase center error compensation value and, based on the phase center error compensation value, determine the compensated ranging result;

[0029] Storage unit, which is used to store model weights;

[0030] The model management and update unit is used to receive new models uploaded from the ground or models that have been fine-tuned in orbit; and

[0031] The extrapolation detection and safety rollback unit is used to determine the confidence level and trigger warnings and rollback based on the confidence level.

[0032] This invention provides a machine learning-based method and system for compensating antenna phase center errors. It introduces non-electromagnetic parameters such as temperature as input to compensate for the impact of on-orbit environmental changes on the phase center. The compensation method uses a machine learning model to calculate the compensation value. This model can approximate complex multidimensional nonlinear functions, eliminating interpolation errors and significantly improving compensation accuracy. It also supports online fine-tuning or incremental learning, dynamically adapting to antenna characteristic drift over time to ensure long-term accuracy. Furthermore, through model pruning, quantization, and other optimization techniques, it can operate efficiently on spaceborne, airborne, or embedded terminals, achieving real-time compensation. When the model encounters uncovered conditions, such as excessively high temperatures or extreme angles, it can automatically trigger confidence level judgment and revert to lookup table / default compensation, ensuring high security. Attached Figure Description

[0033] To further illustrate the above and other advantages and features of the various embodiments of the present invention, a more specific description of the various embodiments of the present invention will be presented with reference to the accompanying drawings. It is to be understood that these drawings depict only typical embodiments of the invention and are therefore not intended to limit its scope. In the drawings, identical or corresponding parts will be indicated by identical or similar reference numerals for clarity.

[0034] Figure 1 This diagram illustrates a flowchart of a machine learning-based method for compensating antenna phase center error according to an embodiment of the present invention.

[0035] Figure 2 This diagram illustrates the structure of a calibration dataset acquisition system according to an embodiment of the present invention; and

[0036] Figure 3 This diagram illustrates the structure of a machine learning-based antenna phase center error compensation system according to an embodiment of the present invention. Detailed Implementation

[0037] In the following description, the invention is described with reference to various embodiments. However, those skilled in the art will recognize that the embodiments may be practiced without one or more specific details or in conjunction with other alternatives and / or additional methods or components. In other instances, well-known structures or operations are not shown or described in detail so as not to obscure the inventive points of the invention. Similarly, for illustrative purposes, specific numbers and configurations are set forth to provide a comprehensive understanding of embodiments of the invention. However, the invention is not limited to these specific details. Furthermore, it should be understood that the embodiments shown in the drawings are illustrative representations and are not necessarily drawn to scale.

[0038] In this specification, references to "an embodiment" or "this embodiment" mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in at least one embodiment of the invention. The phrase "in one embodiment" appearing throughout this specification does not necessarily refer to the same embodiment in all instances.

[0039] It should be noted that the embodiments of the present invention describe the method steps in a specific order; however, this is only for illustrating the specific embodiment and not for limiting the order of the steps. On the contrary, in different embodiments of the present invention, the order of the steps can be adjusted according to actual needs.

[0040] To improve the accuracy and adaptability of antenna phase center error compensation, this invention provides a machine learning-based method and system for compensating antenna phase center error. Firstly, it explicitly introduces temperature T as input, combining this with the nonlinear fitting capability of the machine learning model to compensate for electromagnetic characteristic drift caused by temperature variations in antenna material parameters. Variables such as frequency, azimuth, elevation, and temperature are simultaneously incorporated into the input features to achieve multi-physics coupled modeling. This effectively compensates for the effects of environmental temperature changes, structural stress, and material aging on the phase center. The machine learning model can approximate complex high-dimensional nonlinear function relationships, eliminating interpolation errors from traditional lookup table methods, and maintaining high fitting accuracy even in non-sampling points and complex environments. Furthermore, the machine learning model supports online fine-tuning or incremental learning, allowing it to evolve with antenna performance changes during long-term on-orbit operation, maintaining long-term accuracy stability without requiring remeasurement and calibration. Specifically, by designing an online-updateable training interface, the machine learning model can be fine-tuned by incorporating some actual observation data during on-orbit operation, gradually reducing the deviation between the model and the actual environment, thereby achieving a compensation function that evolves over time and improving the model's adaptability. Finally, to reduce storage space and simplify computational logic, the trained model is further implemented in a lightweight embedded manner. After quantization, the neural network model occupies only a small amount of storage, approximately KB to MB. The inference process only involves forward computation, and the computational complexity is far lower than that of interpolation table lookup and higher-order interpolation. Furthermore, the pruned and quantized lightweight model can run on resource-constrained embedded platforms such as FPGAs, DSPs, and NPUs, and can be directly run using the matrix acceleration unit of the embedded platform, meeting the real-time requirements of spaceborne or airborne systems. The observation data compensated by the aforementioned compensation method and system has higher quality, and the positioning / ranging algorithm simplifies complex error modeling, improving convergence speed and solution stability. Compared to the traditional method of decomposing the phase center error into fixed offset (PCO) and variable phase (PCV) for separate compensation, this invention directly establishes an end-to-end mapping relationship between the observation geometry and physical environment parameters to the total phase center offset through a machine learning model, achieving integrated, high-precision, joint compensation of PCO and PCV, avoiding the error accumulation and model mismatch problems that may result from step-by-step compensation.

[0041] The technical solution of the present invention will be further described below with reference to the accompanying drawings of the embodiments.

[0042] Figure 1 This diagram illustrates a flowchart of a machine learning-based antenna phase center error compensation method according to an embodiment of the present invention. Figure 1 As shown, a machine learning-based method for compensating antenna phase center error includes:

[0043] First, in step 101, data acquisition occurs. Frequency, attitude angle, and temperature information are acquired, where the attitude angle information includes azimuth angle Az and pitch angle E1.

[0044] Next, in step 102, the compensation value is calculated. Using the pre-trained lightweight model, based on the frequency, attitude angle, and temperature information, a phase center error compensation value is obtained. This phase center error compensation value includes the offset vector (ΔE, ΔN, ΔU) of the antenna phase center relative to the antenna reference point (ARP) in a local horizontal coordinate system, such as the ENU coordinate system. Here, ΔE (East) refers to the offset of the phase center in the east direction, ΔN (North) refers to the offset of the phase center in the north direction, and ΔU (Up) refers to the offset of the phase center in the zenith direction, i.e., the vertically upward direction. In one embodiment of the invention, the lightweight model is obtained through training and can be fine-tuned and optimized during on-orbit operation. In one embodiment of the invention, the pre-training of the lightweight model includes: first, acquiring a calibration dataset; then, performing data augmentation and sampling optimization to obtain a training set; then, constructing a mapping relationship between the training set and the phase center offset vector; training the mapping relationship using a nonlinear fitting model; and finally, pruning and quantizing the trained model. In one embodiment of the invention, the calibration dataset may, for example, be historical data. In another embodiment of the present invention, the calibration dataset can also be constructed through experimental simulation. Specifically, the radiation phase characteristics of the antenna at different frequencies, attitude angles, and temperatures are collected point by point through experimental simulation. Figure 2 A schematic diagram of the structure of a calibration dataset acquisition system according to an embodiment of the present invention is shown. Figure 2As shown, the acquisition system includes a control computer 201, a three-dimensional turntable 202, a temperature-controlled chamber 203, a vector network analyzer 204, a standard antenna 205, and an antenna under test 206. The acquisition system is located in a microwave anechoic chamber. The control computer 201 controls the three-dimensional turntable 202, the temperature-controlled chamber 203, and the vector network analyzer 204 to collect antenna phase center data point-by-point under different frequency, attitude angle, and temperature combinations, obtaining a calibration dataset. In one embodiment of the invention, as mentioned above, some real-time measurement data can also be introduced as a calibration dataset during on-orbit operation to update and optimize the model. Specifically, during long-term missions, the satellite obtains partial high-precision baseline ranging results for fine-tuning through inter-satellite link mutual measurement or comparison with high-precision reference signals injected from the ground. Using these partial high-precision baseline ranging results or ground differential correction data, the compensation model is periodically fine-tuned and updated to the onboard units, thereby ensuring that the compensation accuracy remains stable during long-term missions despite antenna aging / environmental drift. In one embodiment of the present invention, data augmentation and sampling optimization mainly include supplementing the calibration dataset through interpolation and / or simulation, while reducing sampling points to obtain a training set. In one embodiment of the present invention, sampling points are reduced through a Design of Experiments (DoE) method. In one embodiment of the present invention, the nonlinear fitting model includes neural network models such as multilayer perceptrons, support vector regression models, and Gaussian process regression models.

[0045] Finally, in step 103, the ranging result is compensated. Based on the phase center error compensation value, the compensated ranging result is determined. For example, in high-precision inter-satellite ranging scenarios such as gravity field measurement satellites, where the inter-satellite link ranging system requires nanosecond-level phase measurement accuracy, the compensated high-precision ranging result can be output based on the phase center error compensation value. The compensated ranging data can then be used for gravity field inversion, effectively reducing the cumulative effect of antenna errors in long-period gravity field calculations and overcoming the accuracy bottleneck of traditional lookup table methods. Compared to the traditional IGS ATX file lookup table compensation method, the phase center error compensation residual can be reduced by more than 50%, significantly improving the gravity field recovery accuracy. For another example, when mapping is performed using a high-precision GNSS reference station receiver, where the mapping-level reference station requires millimeter-level positioning accuracy, the pseudorange and carrier observations can be corrected in real time based on the phase center error compensation value to improve the purity of the observation data, shorten the RTK initialization time, and enhance the stability and robustness of network calculations.

[0046] In one embodiment of the present invention, when the input exceeds the training distribution, i.e., the model encounters an uncovered condition, such as excessively high temperature or extreme angle, a warning is automatically triggered, and a confidence level assessment is performed. Based on the confidence level assessment, the model then reverts to a backup compensation method. In another embodiment of the present invention, a confidence level estimate is provided for each inference result; if it is below a threshold, a backup compensation method is automatically activated. In another embodiment of the present invention, the backup compensation method includes a lookup-based interpolation method and / or the use of a default compensation value.

[0047] Based on the compensation method described above Figure 3 This diagram illustrates the structure of a machine learning-based antenna phase center error compensation system according to an embodiment of the present invention. Figure 3 As shown, a machine learning-based antenna phase center error compensation system includes a data acquisition module 301 and an inference compensation module 302. The data acquisition module 301 acquires frequency, attitude angle, and temperature information. The inference compensation module 302 is communicatively connected to the data acquisition module 301. It determines a phase center error compensation value based on the frequency, attitude angle, and temperature information using a pre-trained lightweight model, and determines a compensated ranging result based on the compensated phase center error compensation value. In one embodiment of the invention, the data acquisition module 301 mainly includes external interfaces, such as a frequency interface 311, an attitude angle interface 312, and a temperature sensor interface 313, thereby receiving frequency, attitude angle, and temperature information measured by external devices or sensors.

[0048] like Figure 3As shown, the inference compensation module includes a processing unit 321, a storage unit 322, a model management and update unit 323, and an extrapolation detection and safety rollback unit 324. The processing unit 321 is communicatively connected to the data acquisition module and includes an embedded processor, such as an FPGA, DSP, or an MCU with an NPU. Based on the frequency, attitude angle, and temperature information acquired by the data acquisition module, the processing unit calculates the phase center error compensation value using a lightweight model and determines the compensated ranging result based on the phase center error compensation value. As mentioned earlier, in one embodiment of the present invention, the lightweight model occupies little storage and can run on resource-limited embedded platforms such as FPGAs, DSPs, and NPUs. Specifically, it runs directly through the matrix acceleration unit of the embedded platform. The storage unit 322 is used to store model weights. The model management and update unit 323 is communicatively connected to the storage unit 322 and is used to receive new models uploaded from the ground or models fine-tuned in orbit, and store the weights of the new models or models fine-tuned in orbit in the storage unit. The extrapolation detection and safety rollback unit 324 is used for confidence level determination and triggers warnings and rollbacks based on the confidence level. The lightweight model file is smaller than traditional high-density error tables, which can effectively reduce storage requirements. At the same time, embedded inference requires only a small amount of computing resources, saving hardware overhead compared to interpolation lookup tables. In addition, in one embodiment of the present invention, the modules interact through well-defined data interfaces, such as input parameter streams and output compensation vectors, which can be easily integrated into existing ranging and navigation systems.

[0049] In one embodiment of the present invention, the inference compensation module 302 can be regarded as the application layer of the compensation system, which is embedded in the target system and outputs correction quantities for real-time tasks. The compensation system further includes a basic layer and a core computing layer. The basic layer is a system for acquiring index-defined datasets, which provides input-output correspondence for subsequent modeling. Specifically, it stores the antenna phase center offsets (ΔE, ΔN, ΔU) measured at different operating frequencies f, azimuth angles Az, elevation angles E1, and temperatures T in a database or file system using standard data formats such as CSV and JSON. This data is then read by the training platform to construct an input-label mapping, ensuring that the training dataset covers typical operating conditions. The core computing layer refers to the training platform, which is responsible for converting discrete data into a general model, i.e., the lightweight model described above. The training platform transmits data to the inference compensation module 302 through an internal bus or API interface to provide trained, validated, and compressed machine learning models, such as quantized neural network parameter files, thereby enabling migration from offline learning to online applications. The inference compensation module 302 can transmit the real-time predicted phase center offset (ΔE, ΔN, ΔU) to the navigation calculation module via the internal bus or API interface, so that the error compensation amount enters the interface of the system ranging link and ensures that the observation value is dynamically corrected.

[0050] As previously described, the acquisition system measures the antenna pattern phase under controlled conditions by controlling the turntable angle, frequency setting, and temperature control environment, and derives the target antenna phase center position using the relative reference antenna method. Compared to traditional testing only at standard temperatures, this adds the dimension of a temperature-controlled chamber, allowing data to cover multi-physics field variations and providing more features from the source. The training platform models the relationship between (f, Az, E1, T) and (ΔE, ΔN, ΔU) as a nonlinear regression problem, using machine learning models, such as multilayer perceptrons (MLPs), to approximate it. Through weights and activation functions, it learns high-order nonlinear feature combinations, capturing complex coupling effects. Compared to traditional lookup table methods that can only perform linear or bilinear interpolation and cannot characterize the interaction effects of temperature and frequency, the MLP model can automatically learn these implicit patterns. The inference compensation module uses a lightweight neural network to input (f, Az, E1, T) in real time and outputs the predicted phase center offset. Since the inference process only involves matrix operations and nonlinear function calculations, it is fast and resource-efficient. Furthermore, by employing model compression techniques, such as pruning and quantization, the running efficiency is far superior to high-dimensional lookup table interpolation, while memory requirements are significantly reduced.

[0051] The core principle of the compensation method and system provided by this invention differs from the traditional lookup table interpolation method. Specifically, the lookup table interpolation method stores error values ​​at discrete sampling points and estimates the error at non-sampling points through mathematical interpolation, such as bilinear interpolation. This invention, however, utilizes machine learning models, such as neural networks, to construct a continuous nonlinear function mapping from input parameters to error values. In comparison, the machine learning modeling method outperforms the lookup table interpolation method in multiple dimensions, including fitting ability, dimensionality scalability, adaptability, storage and computational efficiency, and extrapolation and security. Specifically, the lookup table interpolation method uses piecewise linear fitting, which cannot characterize complex nonlinear relationships and results in large errors between sampling points and outside the boundaries. The machine learning modeling method, on the other hand, uses global nonlinear fitting, which can approximate complex physical phenomena with extremely high accuracy and small fitting errors. The lookup table interpolation method has poor dimensionality scalability; if a dimension, such as temperature, is added, the data volume increases exponentially, making it impractical. The model structure of the machine learning modeling method is easily expandable; new dimensions, such as temperature, humidity, and aging time, can be introduced simply by adding nodes to the input layer, resulting in excellent dimensionality scalability. The table lookup interpolation method lacks adaptability; its data is fixed once calibrated, making it unable to cope with characteristic drift caused by changes in the on-orbit environment and device aging. Machine learning modeling, on the other hand, supports online learning / fine-tuning, allowing for the updating of model parameters using new on-orbit data, achieving long-term adaptability. The table lookup interpolation method incurs high storage overhead, requiring a large number of sampling points, and is computationally complex, involving table lookups, interpolation calculations, and even high-dimensional interpolation. Machine learning modeling, however, has low storage overhead, storing only model parameters, resulting in a smaller file size after quantization, and is computationally efficient, requiring only one forward propagation, making it suitable for embedded acceleration. Furthermore, the table lookup interpolation method is undefined outside the data range and lacks an effective anomaly handling mechanism. Machine learning modeling, however, can integrate uncertainty estimation or anomaly detection modules, triggering a safety fallback mechanism for inputs exceeding the training range.

[0052] Although various embodiments of the invention have been described above, it should be understood that they are presented by way of example only and not as limitations. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the breadth and scope of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined solely by the appended claims and their equivalents.

Claims

1. A method for compensating for an antenna phase center error based on machine learning, characterized in that, The method comprises: acquiring frequency, attitude angle and temperature information; obtaining a phase center error compensation value based on the frequency, attitude angle and temperature information through a lightweight model obtained through pre-training, wherein the pre-training of the lightweight model comprises: acquiring historical data, simulating experiments, collecting the radiation phase characteristics of an antenna at different frequencies, attitude angles and temperatures point by point, acquiring a calibration data set in an on-orbit operation by measuring actual observation data, supplementing the calibration data set by interpolation and simulation while reducing sampling points to obtain a training set, constructing a mapping relationship between the training set and a phase center offset vector, training the mapping relationship using a nonlinear fitting model, pruning and quantizing the trained model, wherein the phase center offset vector comprises an offset amount of a phase center in an east direction, an offset amount of a phase center in a north direction, and an offset amount of a phase center in a zenith direction; and determining a compensated ranging result based on the phase center error compensation value; and in a long-term task of a satellite, acquiring part of high-precision baseline ranging results for fine tuning through inter-satellite link mutual measurement or comparison with a high-precision reference signal injected from the ground, periodically fine-tuning the compensation of the lightweight model using the part of high-precision baseline ranging results or ground differential correction data, and updating to a satellite-borne unit.

2. The compensation method of claim 1, wherein, The method further comprises: performing reliability analysis on the phase center error compensation value, and if the reliability is lower than a threshold, adopting a backup compensation method.

3. The compensation method of claim 2, wherein, The backup compensation method comprises an interpolation method based on a lookup table and adopting a default compensation value.

4. The compensation method of claim 1, wherein, The nonlinear fitting model comprises a multilayer perception machine, a support vector regression model and a Gaussian process regression model. 5.A system for compensating antenna phase center error based on machine learning, characterized in that, The method comprises: a data acquisition module configured to acquire frequency, attitude angle and temperature information; and an inference compensation module communicatively connected with the data acquisition module and configured to determine a phase center error compensation value based on the frequency, attitude angle and temperature information through a lightweight model obtained through pre-training, and determine a compensated ranging result based on the phase center error compensation value, wherein the pre-training of the lightweight model comprises: acquiring historical data, simulating experiments, collecting the radiation phase characteristics of an antenna at different frequencies, attitude angles and temperatures point by point, acquiring a calibration data set in an on-orbit operation by measuring actual observation data, supplementing the calibration data set by interpolation and simulation while reducing sampling points to obtain a training set, constructing a mapping relationship between the training set and a phase center offset vector, training the mapping relationship using a nonlinear fitting model, pruning and quantizing the trained model, wherein the phase center offset vector comprises an offset amount of a phase center in an east direction, an offset amount of a phase center in a north direction, and an offset amount of a phase center in a zenith direction, and in a long-term task of a satellite, acquiring part of high-precision baseline ranging results for fine tuning through inter-satellite link mutual measurement or comparison with a high-precision reference signal injected from the ground, periodically fine-tuning the compensation of the lightweight model using the part of high-precision baseline ranging results or ground differential correction data, and updating to a satellite-borne unit.

6. The compensation system of claim 5, wherein, The inference compensation module comprises: a processing unit communicatively connected with the data acquisition module and comprising an embedded processor, the processing unit being configured to calculate a phase center error compensation value through a lightweight model based on frequency, attitude angle and temperature information acquired by the data acquisition module, and determine a compensated ranging result based on the phase center error compensation value; a storage unit configured to store model weights; a model management and updating unit communicatively connected with the storage unit and configured to receive a new model uploaded from the ground or a model fine-tuned in orbit, and store weights of the new model or the model fine-tuned in orbit to the storage unit; and an extrapolation detection and safety fallback unit configured to make a confidence judgment, and trigger a warning and fallback based on the confidence.

7. The compensation system of claim 6, wherein, The lightweight model is run through a matrix acceleration unit of the embedded processor.

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