A radar signal amplitude equalization calibration method and system

Abstract

The present application relates to the technical field of radar signal, disclose a kind of radar signal amplitude equalization calibration method and system, the method comprises: radar echo signal is decomposed in time-frequency domain, obtain the signal characteristics of radar, signal characteristics are carried out unsupervised manifold learning, obtain the distorted signal manifold representation of radar, based on the ideal working parameter of radar, radar standard signal is carried out target manifold construction, obtain the ideal signal manifold table of radar, distorted signal manifold representation and ideal signal manifold table are coupled with Riemann geometry, obtain the differential homeomorphism relationship of radar, based on differential homeomorphism relationship, real-time echo signal of radar is carried out differential homeomorphism mapping, obtain the amplitude equalization calibration signal of radar;The present application can improve the equalization calibration efficiency of a kind of radar signal amplitude.

Description

Technical Field

[0001] This invention relates to the field of radar signal technology, and in particular to a radar signal amplitude equalization calibration method and system. Background Technology

[0002] Radar, as an active detection technology, achieves target positioning, velocity measurement, and identification by emitting electromagnetic waves and receiving reflected echoes from targets. It is widely used in many key fields such as national defense, aerospace, traffic control, and meteorological monitoring. With the increasing complexity of detection scenarios and the upgrading requirements for detection accuracy, multi-channel array radar, with its spatial diversity advantage, has become a core technology for improving target resolution and anti-jamming performance.

[0003] Existing radar signal amplitude equalization calibration techniques suffer from insufficient accuracy in fusing spatiotemporal and frequency multidimensional features of multi-channel signals. This makes it difficult to construct a unified feature system that takes into account dynamic changes in the time dimension, distribution patterns in the frequency dimension, and array characteristics in the spatial dimension, resulting in incomplete representation of distorted signals in complex scenarios. Furthermore, existing calibration methods often rely on linear mapping models or local feature matching logic, lacking distortion correction mechanisms based on global geometric topology relationships. This makes it impossible to achieve a smooth adaptation mapping between distorted signals and ideal signals, failing to meet the stringent requirements of calibration accuracy and signal stability in high-precision detection scenarios. Therefore, improving the efficiency of radar signal amplitude equalization calibration has become an urgent problem to be solved. Summary of the Invention

[0004] This invention provides a radar signal amplitude equalization calibration method and system to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides a radar signal amplitude equalization calibration method, comprising: S1. Perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar; S2. Perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar; S3. Based on the ideal operating parameters of the radar, construct the target manifold of the standard signal of the radar to obtain the ideal signal manifold representation of the radar. S4. Perform Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. S5. Based on the differential homeomorphism relationship, perform differential homeomorphism mapping on the real-time echo signal of the radar to obtain the amplitude equalization calibration signal of the radar.

[0006] In a preferred embodiment, the radar echo signal is decomposed in the time and frequency domain to obtain the signal characteristics of the radar, including: Based on the radar's receiver array geometry and channel configuration parameters, the original echo data stream of the radar is spatially manifold aligned to obtain the radar's multi-channel complex signal. Short-time Fourier analysis is performed on the multi-channel complex signal to obtain the joint time-frequency distribution of the radar; The time-frequency joint distribution is subjected to magnitude extraction to obtain the time-frequency amplitude information of the radar; Based on the geometric configuration of the receiving array, the time-frequency amplitude information is structurally integrated to obtain the signal characteristics of the radar.

[0007] In a preferred embodiment, the unsupervised manifold learning of the signal features to obtain the distorted signal manifold representation of the radar includes: The signal characteristics of the radar are normalized to obtain the normalized time-frequency data of the radar; The standardized time-frequency data is subjected to neighborhood measurement to obtain the multi-channel range information of the radar; Based on the multi-channel distance information, the standardized time-frequency data is divided into topological neighborhoods to obtain the local neighborhood structure of the radar's time-frequency data. Based on the local structure of the time-frequency data, a nonlinear dimensionality reduction mapping is performed on the standardized time-frequency data to obtain the low-dimensional manifold embedding shape of the radar. The distortion mode structure of the radar is obtained by performing intrinsic identification on the low-dimensional manifold embedding morphology. Based on the distortion mode structure, the low-dimensional manifold embedding morphology is topologically reconstructed to obtain the distortion signal manifold representation of the radar.

[0008] In a preferred embodiment, based on the distortion mode structure, topological reconstruction is performed on the low-dimensional manifold embedding morphology to obtain the distorted signal manifold representation of the radar, including: Attribute mining is performed on the distortion pattern structure to obtain the distortion topology features of the radar; Based on the distorted topological features, information is embedded into the low-dimensional manifold embedding morphology to obtain the topologically regular manifold of the radar. The distortion shaping of the topologically regular manifold is performed to obtain the distorted signal manifold characterization of the radar.

[0009] In a preferred embodiment, based on the ideal operating parameters of the radar, a target manifold is constructed from the standard signal of the radar to obtain an ideal signal manifold representation of the radar, including: In the standard signal space of the radar, the ideal operating parameters of the radar are theoretically mapped to obtain the theoretical distortion-free signal of the radar; The ideal signal parameter space of the radar is obtained by performing feature geometry deconstruction on the theoretically undistorted signal. The ideal topological connection structure of the radar is obtained by performing topological correlation analysis on the proximity relationships of relevant points in the ideal signal parameter space. By performing spatial topology fusion on the ideal signal parameter space and the ideal topology connection structure, the ideal signal manifold representation of the radar is obtained.

[0010] In a preferred embodiment, the distorted signal manifold representation and the ideal signal manifold representation are coupled using Riemannian geometry to obtain the differential homeomorphism of the radar, including: By geometrically aligning the intrinsic geometric properties of the distorted signal manifold representation and the ideal signal manifold representation, the coupled Riemannian metric structure of the radar is obtained. Based on the coupled Riemannian metric structure, the tangential correspondence between the distorted signal manifold representation and the ideal signal manifold representation is spatially mapped to obtain the tangential spatial isomorphism of the radar. Based on the tangential spatial isomorphism, the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation is tensor-coupled to obtain the inter-manifold connectivity tensor field of the radar. Based on the manifold connectivity tensor field, tensor-constrained registration is performed on the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar.

[0011] In a preferred embodiment, based on the tangential spatial isomorphism, a tensor coupling is performed on the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation to obtain the intermanifold connectivity tensor field of the radar, including: Based on the tangential spatial isomorphism, the distortion signal manifold representation and the ideal signal manifold representation are deduced together to obtain the local geometric correspondence of the radar. A compatibility test is performed on the local geometric correspondences to obtain the consistent communication structure of the radar; Tensor expansion is performed on the consensus communication structure to obtain the inter-manifold connectivity tensor field of the radar.

[0012] In a preferred embodiment, based on the differential homeomorphism relation, differential homeomorphic mapping is performed on the real-time echo signal of the radar to obtain the amplitude equalization calibration signal of the radar, including: The real-time echo signal of the radar is subjected to time-frequency deconvolution extraction to obtain the signal time-frequency characteristics of the radar; Based on the differential homeomorphism relation, the time-frequency characteristics of the signal are smoothed by homeomorphism correction to obtain the regularized time-frequency characteristics of the radar. The regular time-frequency characteristics are reconstructed by inverse time-frequency transformation to obtain the amplitude equalization calibration signal of the radar.

[0013] In a preferred embodiment, the formula for calculating the amplitude equalization calibration signal is as follows: ; In the formula, The amplitude equalization calibration signal is... The signal time-frequency characteristics of the radar are... For the differential homeomorphism relation, The inverse time-frequency transform reconstruction operator for the regular time-frequency features.

[0014] To address the above problems, the present invention also provides a radar signal amplitude equalization calibration system, the system comprising: The time-frequency decomposition module is used to perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar. The manifold learning module is used to perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar. The manifold construction module is used to construct the target manifold of the standard signal of the radar based on the ideal operating parameters of the radar, so as to obtain the ideal signal manifold representation of the radar. A geometric coupling module is used to perform Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. The mapping calibration module is used to perform differential homeomorphic mapping on the real-time echo signal of the radar based on the differential homeomorphism relationship, so as to obtain the amplitude equalization calibration signal of the radar.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention utilizes the radar receiver array's geometric configuration and channel configuration parameters to perform spatial manifold alignment, short-time Fourier analysis, modulus extraction, and structured integration on the original echo data stream. This constructs a signal feature system encompassing time, frequency, and space dimensions, eliminating signal misalignment and phase deviation caused by antenna position differences and channel configuration, and removing redundant phase information. Further, through normalization processing, topological neighborhood partitioning, nonlinear dimensionality reduction mapping, and distortion mode intrinsic identification, unsupervised manifold learning is completed. This accurately mines distortion topological features and reconstructs the distortion signal manifold representation, comprehensively capturing the overall morphology and core features of signal distortion in complex scenarios. This forms a unified feature system that considers dynamics, distribution patterns, and array characteristics, solving the problems of insufficient multi-dimensional feature fusion accuracy and incomplete distortion representation in existing technologies.

[0016] 2. This invention uses an ideal signal manifold representation constructed with ideal operating parameters as a reference benchmark. By performing Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation, and through geometric alignment, tangent space isomorphic mapping, tensor coupling, and constraint registration, a globally consistent differential homeomorphic relationship is constructed, achieving a smooth mapping between the two manifolds. Based on this relationship, the time-frequency characteristics of the real-time echo signal are smoothed by homeomorphic correction and inverse time-frequency transformation reconstruction. While retaining the effective information of the target, the amplitude distortion is thoroughly corrected, ensuring the spatiotemporal continuity and consistency of the calibrated signal, and meeting the stringent requirements of high-precision detection scenarios for calibration accuracy and signal stability. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a radar signal amplitude equalization calibration method according to an embodiment of the present invention. Figure 2 This is a functional block diagram of a radar signal amplitude equalization calibration system provided in an embodiment of the present invention; The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0019] This application provides a radar signal amplitude equalization calibration method. The execution subject of this radar signal amplitude equalization calibration method includes, but is not limited to, at least one of the following electronic devices that can be configured to execute the method provided in this application embodiment: a server, a terminal, etc. In other words, the radar signal amplitude equalization calibration method can be executed by software or hardware installed on a terminal device or a server device. The server includes, but is not limited to, a single server, a server cluster, a cloud server, or a cloud server cluster. The server can be an independent server or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDNs), and big data and artificial intelligence platforms.

[0020] Reference Figure 1 The diagram shown is a flowchart illustrating a radar signal amplitude equalization calibration method according to an embodiment of the present invention. In this embodiment, the radar signal amplitude equalization calibration method includes: S1. Perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar; In this embodiment of the invention, the radar echo signal is decomposed in the time and frequency domain to obtain the signal characteristics of the radar, including: Based on the radar's receiver array geometry and channel configuration parameters, the original echo data stream of the radar is spatially manifold aligned to obtain the radar's multi-channel complex signal. Short-time Fourier analysis is performed on the multi-channel complex signal to obtain the joint time-frequency distribution of the radar; The time-frequency joint distribution is subjected to magnitude extraction to obtain the time-frequency amplitude information of the radar; Based on the geometric configuration of the receiving array, the time-frequency amplitude information is structurally integrated to obtain the signal characteristics of the radar.

[0021] Based on the radar's receiver array geometry and channel configuration parameters, the raw echo data stream of the radar is spatially manifold aligned to obtain the radar's multi-channel complex signal. The receiver array geometry refers to the physical arrangement of the radar's antenna array for receiving signals, defining the specific spatial relationships of each receiving antenna. The channel configuration parameters are the setting information for each signal receiving channel of the radar, including the channel's signal reception timing, signal transmission path, etc. Both of these are known information determined at the radar's manufacturing stage or before use. The raw echo data stream is the set of unprocessed raw signal data reflected back from the target after the radar transmits a signal, containing all signal information related to the target and its environment. During the spatial manifold alignment process, the spatial coordinates of each receiving antenna and their distance and angular relationships are first determined based on the geometric configuration of the receiving array. Then, the time sequence and data transmission rules of the received signals for each channel are determined in combination with the channel configuration parameters. Subsequently, the original echo data stream is matched and organized one by one according to the spatial position and receiving time sequence corresponding to each receiving channel, so that the echo signals of the same detection target received by different channels maintain a consistent arrangement order in the spatial dimension. At the same time, the signal phase misalignment caused by antenna position differences and channel transmission delay is corrected. The final multi-channel complex signal is a set of complete data containing signal amplitude and phase information corresponding to each receiving channel. The multiple sets of data together constitute a signal set that can reflect the receiving characteristics of different channels.

[0022] Short-time Fourier analysis was performed on the multi-channel complex signal to obtain the joint time-frequency distribution of the radar. The multi-channel complex signal contains the amplitude and phase information of each channel, but its time-domain characteristics cannot directly reflect the change of signal frequency over time. In short-time Fourier analysis, the continuous signal of each channel in the multi-channel complex signal is first divided into multiple continuous and non-overlapping time segments with a fixed time length. The time length is chosen to ensure that the frequency characteristics of the signal within each segment are relatively stable, and is usually determined based on the speed of the target's movement and the signal frequency range. Next, an appropriate window function is selected for each time segment. The window function highlights the signal characteristics within the current time segment while suppressing interference from adjacent time segments. The shape and length of the window function are determined according to the signal stationarity requirements to ensure that the signal frequency characteristics are not distorted due to improper window function selection. Then, a Fourier transform is performed on each windowed time segment to convert the time-domain signal of each time segment into a frequency-domain signal, obtaining all frequency components and their intensities for each time segment. Finally, the frequency domain analysis results of all time segments are arranged in chronological order to form a two-dimensional data distribution that simultaneously includes the time dimension, the frequency dimension, and the intensity of the corresponding frequency components, i.e., the time-frequency joint distribution.

[0023] The time-frequency joint distribution is subjected to modulus extraction to obtain the time-frequency amplitude information of the radar. The time-frequency joint distribution is a two-dimensional data set containing time, frequency, and corresponding complex form data of the signal. The complex form of each data point simultaneously contains the amplitude and phase information of the signal. During the modulus extraction process, each data point in the time-frequency joint distribution is traversed one by one. For the complex form signal corresponding to each data point, the modulus of the complex number is obtained through mathematical operations. This operation process only retains the amplitude value that can reflect the strength of the signal energy and completely removes the phase information that does not affect the amplitude equalization calibration. Then, all the calculated amplitude values ​​are strictly retained according to the time and frequency arrangement order in the original time-frequency joint distribution. The final time-frequency amplitude information is a two-dimensional data set containing only the time dimension, the frequency dimension, and the magnitude of the corresponding signal amplitude.

[0024] Based on the geometric configuration of the receiving array, the time-frequency amplitude information is structurally integrated to obtain the signal characteristics of the radar. The geometric configuration of the receiving array clearly defines the spatial positional relationship of each receiving antenna, and the time-frequency amplitude information includes the time, frequency, and signal amplitude data corresponding to each channel. During the structural integration process, firstly, according to the spatial arrangement order of each receiving antenna in the geometric configuration of the receiving array, the time-frequency amplitude data corresponding to different channels in the time-frequency amplitude information are classified and collected to ensure that the signal data received by the antenna at the same spatial position are grouped into one category; then, a one-to-one correspondence between the time dimension, frequency dimension, spatial position dimension, and signal amplitude is established to integrate the time-frequency amplitude data scattered in each channel into a unified data system; finally, the format of the integrated data is standardized to ensure that the data arrangement logic is consistent in the three dimensions of time, frequency, and space, and the resulting signal characteristics are a structured data set that can comprehensively reflect the amplitude characteristics of the radar echo signal in the three dimensions of time, frequency, and space.

[0025] The beneficial effects are: eliminating signal misalignment and phase deviation caused by differences in antenna spatial location and channel configuration; enabling multi-channel complex signals to accurately reflect the echo characteristics of the same target; providing a consistent and accurate basic signal in spatial dimension; transforming time-domain signals into an intuitive time-frequency joint distribution containing time and frequency features; clearly presenting the dynamic changes of signal frequency over time; providing clear time-frequency dimension data support for amplitude feature extraction; filtering signal energy intensity data related to amplitude calibration; eliminating irrelevant phase information; reducing data processing redundancy; improving subsequent processing efficiency; establishing multi-dimensional correlations between time, frequency, space, and amplitude; forming comprehensive and rigorous signal features; providing complete and accurate input data for unsupervised manifold learning; and ensuring the accuracy of constructing distorted signal manifold representations.

[0026] S2. Perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar; In this embodiment of the invention, unsupervised manifold learning is performed on the signal features to obtain the distorted signal manifold representation of the radar, including: The signal characteristics of the radar are normalized to obtain the normalized time-frequency data of the radar; The standardized time-frequency data is subjected to neighborhood measurement to obtain the multi-channel range information of the radar; Based on the multi-channel distance information, the standardized time-frequency data is divided into topological neighborhoods to obtain the local neighborhood structure of the radar's time-frequency data. Based on the local structure of the time-frequency data, a nonlinear dimensionality reduction mapping is performed on the standardized time-frequency data to obtain the low-dimensional manifold embedding shape of the radar. The distortion mode structure of the radar is obtained by performing intrinsic identification on the low-dimensional manifold embedding morphology. Based on the distortion mode structure, the low-dimensional manifold embedding morphology is topologically reconstructed to obtain the distortion signal manifold representation of the radar.

[0027] Based on the aforementioned distortion mode structure, topological reconstruction is performed on the low-dimensional manifold embedding morphology to obtain the distortion signal manifold representation of the radar, including: Attribute mining is performed on the distortion pattern structure to obtain the distortion topology features of the radar; Based on the distorted topological features, information is embedded into the low-dimensional manifold embedding morphology to obtain the topologically regular manifold of the radar. The distortion shaping of the topologically regular manifold is performed to obtain the distorted signal manifold characterization of the radar.

[0028] Normalization processing is performed on the radar signal characteristics to obtain standardized time-frequency data. The radar signal characteristics are obtained through time-frequency domain decomposition and contain structured data related to time-frequency amplitude information and the geometry of the receiving array. This data may exhibit inconsistencies in dimensions and dispersed value ranges due to hardware differences between different radar channels and intensity fluctuations during signal transmission. Normalization processing first clarifies the value ranges and data distribution of the signal characteristics for each channel. Then, through a unified adjustment method, the time-frequency amplitude data of all channels are adjusted to the same numerical range, eliminating interference caused by dimensional differences and value fluctuations. The resulting standardized time-frequency data is uniformly formatted and free of irrelevant interference, providing a consistent analytical basis for subsequent neighborhood measurements.

[0029] Neighborhood measurement is performed on standardized time-frequency data to obtain multi-channel range information for the radar. Standardized time-frequency data is time-frequency data that has undergone format unification and interference removal, containing signal correlation data of each radar channel at different times and frequencies. Neighborhood measurement requires comparing the values ​​of each data point with all other data points in the same channel, as well as with data points at the corresponding time and frequency positions in different channels. The distance is determined by quantifying the numerical differences between data points; for example, the smaller the numerical difference between two data points, the smaller the corresponding distance, and vice versa. The final multi-channel range information is a quantified result of the proximity relationship between all data points, clarifying the degree of adjacency of each data point in different channels.

[0030] Based on multi-channel distance information, topological neighborhood division is performed on standardized time-frequency data to obtain the local neighborhood structure of radar time-frequency data. Multi-channel distance information is the quantification result of the proximity relationships between data points. Topological neighborhood division requires first setting a fixed distance threshold, which is determined based on the normal fluctuation range of the radar signal and the characteristics of data distribution to ensure accurate differentiation between adjacent and non-adjacent data points. Then, all distance values ​​corresponding to each data point are compared with this threshold. Data points with distance values ​​less than the threshold are classified as the neighborhood of that data point, forming a set for each data point that includes itself and its neighboring data points. All these sets together constitute the local neighborhood structure of the time-frequency data, clearly presenting the distribution of neighboring data around each data point.

[0031] Based on the local neighborhood structure of time-frequency data, a nonlinear dimensionality reduction mapping is performed on the standardized time-frequency data to obtain the low-dimensional manifold embedding form of the radar. The local neighborhood structure of the time-frequency data clarifies the adjacent distribution relationship of each data point. The standardized time-frequency data is high-dimensional time-frequency correlated data, containing some redundant dimensional information. The nonlinear dimensionality reduction mapping needs to select the key dimensions that can reflect the core features of the radar signal while strictly preserving the local neighborhood relationships between each data point, and discarding secondary dimensions that do not affect the essential attributes of the signal. This transforms the high-dimensional standardized time-frequency data into a low-dimensional data representation. The final low-dimensional manifold embedding form is a simplified form of the high-dimensional data, which retains the core local topological relationships while reducing the complexity of the data.

[0032] Intrinsic identification of low-dimensional manifold embedding morphology yields the radar's distortion mode structure. Low-dimensional manifold embedding morphology is simplified data that preserves core topological relationships and reflects the main characteristics of the radar signal. Intrinsic identification requires a comprehensive analysis of the distribution patterns of data points within the low-dimensional manifold embedding morphology, including data point clustering areas, dispersion, and trends. By comparing this distribution with the signal data distribution characteristics under normal radar operation, anomalous features inconsistent with the normal distribution are identified. These anomalous features are the essential manifestations of radar signal distortion. These anomalous features are then categorized and integrated according to their distribution patterns and manifestations to form the distortion mode structure, clarifying the specific types and distribution characteristics of radar signal distortion.

[0033] Attribute mining is performed on the distortion pattern structure to obtain the distortion topology features of the radar. The distortion pattern structure is a collection of identified radar signal distortion types and distribution characteristics. Attribute mining requires in-depth analysis of the specific attributes of each distortion type, including the time-frequency range of distortion occurrence, the degree of signal strength distortion, the duration of distortion, and distribution differences in different radar channels. These attributes are extracted and organized in detail to ensure that no key information is missed. The resulting distortion topology features are a precise summary of the core attributes of each distortion pattern, clarifying the key characteristic parameters of distortion.

[0034] Based on distortion topological features, information embedding is performed on the low-dimensional manifold embedding morphology to obtain the radar's topologically regularized manifold. Distortion topological features are the core attribute parameters of the distortion mode, while the low-dimensional manifold embedding morphology is simplified data that retains the core topological relationships of the signal. Information embedding requires matching the attribute parameters corresponding to each distortion topological feature one by one to the corresponding distortion data points and neighborhood structures in the low-dimensional manifold embedding morphology. For example, the intensity attribute of a certain distortion is mapped to the numerical features of the related data points, and the distribution range attribute is mapped to the coverage range of the related neighborhood structure. During the embedding process, the original local topological relationships of the low-dimensional manifold embedding morphology are strictly maintained. The resulting topologically regularized manifold is a regularized data structure that integrates the core distortion attributes, preserving both the core topological relationships of the original data and fully carrying the key attribute information of the distortion.

[0035] Distortion shaping is performed on a topologically regular manifold to obtain a manifold representation of the radar's distorted signal. A topologically regular manifold is a regular data structure that incorporates the core attributes of distortion, already possessing key distortion information and the core topological relationships of the original data. Distortion shaping requires targeted adjustments to the overall structure of the manifold based on the distortion topological features it carries. For example, for regions with high distortion intensity, the data point distribution density in that region is adjusted accordingly; for the distribution range of distortion, the coverage area of ​​the manifold is adjusted accordingly. This ensures that the adjusted manifold accurately and completely reflects the overall shape and distribution characteristics of the radar signal distortion. The resulting distorted signal manifold representation is a comprehensive topological presentation of the radar signal distortion state, clearly showing the overall structure and core features of the distortion.

[0036] The beneficial effects include: eliminating interference in signal features, unifying data formats, providing reliable basic data for subsequent processing, quantifying the proximity relationships of multi-channel data points, providing accurate basis for topological neighborhood division, clarifying the local distribution range of data, avoiding the loss of core topological information during dimensionality reduction, reducing data complexity while preserving core topological relationships, reducing computational load and improving processing efficiency, accurately identifying the essential characteristics and distribution patterns of signal distortion, improving the targeting of distortion processing, analyzing core distortion attributes, providing accurate support for information integration, improving manifold integration accuracy, achieving accurate fusion of distortion attributes and low-dimensional manifold topology, enhancing the manifold's ability to express distortion, fully presenting the overall topology and core features of signal distortion, and providing high-quality data support for subsequent geometric coupling and amplitude calibration.

[0037] S3. Based on the ideal operating parameters of the radar, construct the target manifold of the standard signal of the radar to obtain the ideal signal manifold representation of the radar. In this embodiment of the invention, based on the ideal operating parameters of the radar, a target manifold is constructed on the standard signal of the radar to obtain an ideal signal manifold representation of the radar, including: In the standard signal space of the radar, the ideal operating parameters of the radar are theoretically mapped to obtain the theoretical distortion-free signal of the radar; The ideal signal parameter space of the radar is obtained by performing feature geometry deconstruction on the theoretically undistorted signal. The ideal topological connection structure of the radar is obtained by performing topological correlation analysis on the proximity relationships of relevant points in the ideal signal parameter space. By performing spatial topology fusion on the ideal signal parameter space and the ideal topology connection structure, the ideal signal manifold representation of the radar is obtained.

[0038] Operations are conducted within the radar's standard signal space, a dedicated space for interference-free and distortion-free signals pre-defined during radar design. Its scope and attributes are clearly defined by the radar's design specifications and operating frequency band. Ideal operating parameters are a set of parameters specified in the radar design documents that ensure distortion-free signal transmission and reception, encompassing specific pre-defined values ​​such as transmit power, receive gain, and signal bandwidth. When theoretically mapping these ideal operating parameters, the physical laws and design logic of radar signal transmission are strictly followed. Each parameter is mapped one-to-one to a specific dimension of the standard signal space; for example, transmit power corresponds to signal strength, and signal bandwidth corresponds to signal frequency range. Through this precise one-to-one correspondence, a theoretically distortion-free signal that conforms to the attributes of the standard signal space and contains no distortion components is directly generated. This signal completely replicates the signal form and all characteristics that the radar should possess under ideal operating conditions.

[0039] For the acquired theoretically distortion-free signal, a feature geometry deconstruction is performed. First, multiple quantifiable features contained in the signal are separated and extracted. These features include the amplitude variation pattern, frequency distribution range, and phase stability of the signal. Then, following the construction logic of geometric space, each extracted feature is treated as an independent dimension, and the specific value of the feature is used as the coordinate point on that dimension. Based on the physical correlation of signal transmission, all dimensions are arranged in an orderly manner, ultimately forming a multi-dimensional spatial structure. This spatial structure is the ideal signal parameter space, which clearly presents the value range of each feature parameter of the radar signal under ideal conditions and their relative positions.

[0040] The focus is on relevant points within the ideal signal parameter space. These relevant points refer to parameter coordinate points with physical connections, such as amplitude parameter points and frequency parameter points corresponding to the same moment. Proximity is determined based on a preset threshold, which is determined by the accuracy requirements of the radar signal parameters. Two points are considered adjacent when the numerical difference in any dimension does not exceed 5% of the design accuracy. During topology analysis, all relevant points within the ideal signal parameter space are traversed first, calculating the spatial distance between each point and other points. Point pairs that meet the proximity criteria are selected. Then, according to the timing logic of signal transmission and parameter association logic, these adjacent point pairs are connected to form a continuous and unbroken network structure. This network structure is the ideal topology connection structure, which accurately reflects the connection order and association strength between relevant points within the ideal signal parameter space.

[0041] Using the ideal signal parameter space as the basic carrier, which clearly presents the value range and positional relationship of each characteristic parameter of the ideal signal, the ideal topology connection structure is then fully embedded into the ideal signal parameter space according to its own connection logic and parameter association relationship. This ensures that each connection node in the ideal topology connection structure accurately corresponds to the corresponding coordinate point in the ideal signal parameter space, while maintaining the dimensional attributes of the ideal signal parameter space and the network form of the ideal topology connection structure without change. Through this embedding and integration method, a comprehensive representation that combines parameter dimensional information and topology connection information is formed. This comprehensive representation is the ideal signal manifold representation, which fully presents the parameter distribution and structural association characteristics of radar signals under ideal conditions.

[0042] The beneficial effects are as follows: generating a theoretically undistorted signal that truly reflects the ideal working state, ensuring the accuracy and purity of the basic signal, providing a reliable ideal reference for amplitude equalization calibration, transforming abstract signal characteristics into a multi-dimensional parameter space, clearly defining the value range and positional relationship of each characteristic parameter, providing a foundation for structured analysis, improving the intuitiveness and operability of the ideal signal feature representation, accurately selecting relevant neighboring point pairs and constructing a topological connection structure, truly reflecting the correlation law and connection order of ideal signal parameters, ensuring the integrity and rationality of the ideal signal structural features, and integrating the parameter space and topological connection structure to form an ideal signal manifold representation that covers complete information, accurately presenting the overall characteristics of the ideal radar signal, providing a complete and accurate reference for geometric coupling, and ensuring the accuracy of obtaining differential homeomorphism relationships.

[0043] S4. Perform Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. In this embodiment of the invention, the distorted signal manifold representation and the ideal signal manifold representation are coupled using Riemannian geometry to obtain the differential homeomorphism of the radar, including: By geometrically aligning the intrinsic geometric properties of the distorted signal manifold representation and the ideal signal manifold representation, the coupled Riemannian metric structure of the radar is obtained. Based on the coupled Riemannian metric structure, the tangential correspondence between the distorted signal manifold representation and the ideal signal manifold representation is spatially mapped to obtain the tangential spatial isomorphism of the radar. Based on the tangential spatial isomorphism, the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation is tensor-coupled to obtain the inter-manifold connectivity tensor field of the radar. Based on the manifold connectivity tensor field, tensor-constrained registration is performed on the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar.

[0044] Based on the tangential spatial isomorphism, a tensor coupling is performed on the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation to obtain the inter-manifold connectivity tensor field of the radar, including: Based on the tangential spatial isomorphism, the distortion signal manifold representation and the ideal signal manifold representation are deduced together to obtain the local geometric correspondence of the radar. A compatibility test is performed on the local geometric correspondences to obtain the consistent communication structure of the radar; Tensor expansion is performed on the consensus communication structure to obtain the inter-manifold connectivity tensor field of the radar.

[0045] The distorted signal manifold representation is a manifold morphology containing the distorted topological features of radar signals, obtained through unsupervised manifold learning. The ideal signal manifold representation is a manifold representation containing an ideal topological connection structure, constructed based on ideal radar operating parameters. The intrinsic geometric properties of both encompass core information reflecting the geometric characteristics of the manifold, such as curvature, dimension, and neighborhood association mode. After extracting the intrinsic geometric property information of each manifold, the geometric properties of the distorted signal manifold representation are adjusted according to the same dimensional division and association logic, using the geometric parameters of the ideal signal manifold representation as a reference benchmark. This ensures that the geometric framework of the two manifolds remains unified, ultimately forming a coupled Riemannian metric structure. This structure is a metric standard that simultaneously carries the geometric characteristics of both manifolds and matches them, clarifying the metric rules for the two manifolds in the same geometric space.

[0046] The Coupled Riemannian Metric Structure (CRM) provides a unified benchmark for the geometric correlation analysis of two manifolds. Tangential correspondence refers to the correlation of tangent directions at corresponding points on the two manifolds. Based on the metric rules defined by the CRM, the tangential vector of each point on the distorted signal manifold representation is extracted one by one. Simultaneously, the corresponding point on the ideal signal manifold representation is found, and its tangential vector is extracted. By comparing the direction and amplitude ratio of the two sets of tangential vectors, a one-to-one mapping relationship is established. This ensures that the mapping process strictly follows the requirements of the CRM, making the mapped tangential vectors meet the standards in terms of direction consistency and amplitude ratio rationality. The resulting tangential space isomorphism relationship clarifies the equivalent correlation law between the tangential spaces of the two manifolds, providing a tangential-level basis for subsequent global geometric correlation analysis.

[0047] The tangential isomorphism relation has clarified the correspondence rules of the tangential spaces of the two manifolds. Based on this rule, multiple adjacent points on the two manifolds are selected to form local regions. The extent of each local region is determined by its ability to fully reflect the geometric change trends within that region. The geometric change trends, such as the connection paths, angle changes, and distance ratios between points represented by the distorted signal manifold within each local region, are analyzed. Simultaneously, the geometric change trends of the same range of local regions in the ideal signal manifold representation are analyzed. By comparing and deriving the correlation between the geometric features of the two manifolds within this local region, a local geometric correspondence is obtained. This relationship accurately reflects the specific geometric correlation details of the two manifolds in each local region.

[0048] Local geometric correspondences are the geometric associations of various local regions, and there is a possibility of conflicting association rules between different local regions. Each local region's local geometric correspondence is checked individually to verify whether the geometric association logic of adjacent local regions can be smoothly connected. It is determined whether there are contradictions in the association rules of different local regions. Using the geometric rules expressed by the ideal signal manifold as a unified basis, conflicting local geometric correspondences are adjusted and corrected to ensure that all local region geometric correspondences follow the same logical system, ultimately forming a consistent connection structure. This structure integrates all local regions and forms a conflict-free geometric association system, providing a unified connection standard for subsequent global expansion.

[0049] The consistent connection structure is a unified system of local geometric associations. Each specific parameter of the geometric association rule in this structure is transformed into a tensor form, where each component of the tensor corresponds to a parameter in the geometric association, ensuring the integrity and correspondence of the parameters. Following the global distribution patterns of the two manifolds, these tensors are extended to all regions of both manifolds, ensuring that each region has a corresponding tensor to describe the geometric associations of the two manifolds within that region. During the extension process, the geometric association rules carried by the tensors remain unchanged, ultimately forming an inter-manifold connection tensor field. This tensor field is a set of tensors that comprehensively reflects the global geometric associations of the two manifolds, covering all regions of both manifolds and clearly defining the geometric connection methods of each region.

[0050] The inter-manifold connectivity tensor field provides comprehensive constraints for the registration of the two manifolds. Using the geometric connectivity of each region in this tensor field as constraints, the distorted signal manifold representation is registered and adjusted towards the ideal signal manifold representation. During the adjustment process, each point in the distorted signal manifold representation finds its corresponding point in the ideal signal manifold representation based on the corresponding tensor constraints. This ensures that the distorted signal manifold representation retains its original topological structure after registration and perfectly matches the geometric structure of the ideal signal manifold representation, ultimately yielding a differential homeomorphism. This relationship clarifies the specific rules for mapping each point in the distorted signal manifold representation to its corresponding point in the ideal signal manifold representation, achieving a smooth mapping between the two manifolds.

[0051] The beneficial effects include ensuring consistency between the two manifold geometric frameworks, laying a reliable foundation for subsequent processing, improving the accuracy of data processing, clarifying the tangential correspondence rules of manifolds, improving the accuracy of the correlation between manifolds, accurately capturing local geometric correlation details, improving the comprehensiveness of global correlation analysis, eliminating conflicts in local correlation rules, improving the reliability of the overall correlation system, achieving local correlation to global coverage, improving the comprehensiveness and accuracy of the registration process, ensuring smooth mapping between manifolds, and improving the effect and accuracy of radar signal amplitude equalization calibration.

[0052] S5. Based on the differential homeomorphism relationship, perform differential homeomorphism mapping on the real-time echo signal of the radar to obtain the amplitude equalization calibration signal of the radar.

[0053] In this embodiment of the invention, based on the differential homeomorphism relation, differential homeomorphic mapping is performed on the real-time echo signal of the radar to obtain the amplitude equalization calibration signal of the radar, including: The real-time echo signal of the radar is subjected to time-frequency deconvolution extraction to obtain the signal time-frequency characteristics of the radar; Based on the differential homeomorphism relation, the time-frequency characteristics of the signal are smoothed by homeomorphism correction to obtain the regularized time-frequency characteristics of the radar. The regular time-frequency characteristics are reconstructed by inverse time-frequency transformation to obtain the amplitude equalization calibration signal of the radar.

[0054] The specific formula for calculating the amplitude equalization calibration signal is as follows: ; In the formula, The amplitude equalization calibration signal is... The signal time-frequency characteristics of the radar are... For the differential homeomorphism relation, The inverse time-frequency transform reconstruction operator for the regular time-frequency features.

[0055] After acquiring the real-time radar echo signal, the time span and frequency coverage of the signal are first determined. The real-time echo signal is then divided into several continuous signal segments at fixed and uniform time intervals, each segment corresponding to a specific time node. For each signal segment, the variation pattern of its vibration amplitude is analyzed to identify all frequency components contained in the segment, and the vibration intensity of each frequency component is recorded. Each time node is then correlated with its corresponding frequency component and vibration intensity, forming structured data that simultaneously contains three-dimensional information of time, frequency, and intensity. This data constitutes the radar signal's time-frequency characteristics.

[0056] After obtaining the differential homeomorphism relation and the signal's time-frequency characteristics, each time-frequency-intensity combination in the signal's time-frequency characteristics is checked one by one, based on the correspondence rules between the distorted signal and the ideal signal determined in the differential homeomorphism relation. When a combination is found to be mismatched with the corresponding combination in the ideal signal manifold representation, the intensity value of that combination is gradually corrected according to the continuous adjustment path set by the differential homeomorphism relation. During the correction process, the intensity changes between adjacent time nodes and adjacent frequency components are kept to a smooth transition, without sudden numerical jumps. The time-frequency-intensity structured data formed after comprehensive correction, which fully conforms to the requirements of the ideal signal manifold representation, is the radar's regularized time-frequency characteristics.

[0057] The frequency components and their intensity data corresponding to all time nodes in the regularized time-frequency characteristics are collected. Following the chronological order of the time nodes, the intensity values ​​of all frequency components at each time node are superimposed to calculate the comprehensive signal amplitude corresponding to that time node. The comprehensive signal amplitudes of all time nodes are then arranged sequentially to form a continuous and complete time-domain signal. This time-domain signal accurately reflects the true information of the target and eliminates the amplitude distortion in the original signal; it serves as the radar's amplitude equalization calibration signal.

[0058] In the formula, The amplitude equalization calibration signal is the final output of the calibration method of this invention. It is used to eliminate the amplitude distortion of the radar real-time echo signal, enabling the radar to accurately detect targets in the future. It is obtained by reconstructing the regularized time-frequency characteristics through inverse time-frequency transform. The inverse time-frequency transform reconstruction operator for regularized time-frequency features originates from a dedicated transformation rule designed to convert regularized time-frequency features into a time-domain calibration signal. Its purpose is to reconstruct regularized time-frequency features after smooth homeomorphic correction by performing an inverse time-frequency transform, transforming the structured regularized time-frequency features containing three-dimensional correlation information of time, frequency, and intensity into a continuous and complete time-domain amplitude equalization calibration signal. The differential homeomorphism relation is derived from the Riemannian geometric coupling of the distorted signal manifold representation and the ideal signal manifold representation of radar. Specifically, it involves first geometrically aligning the intrinsic geometric properties of the two manifolds, and then gradually constructing the relation through steps such as tangential correspondence mapping, global geometric correlation tensor coupling, and tensor constraint registration. Its purpose is to establish continuous correspondence rules between distorted and ideal signals, providing a precise mapping basis for the correction of signal time-frequency characteristics. The time-frequency characteristics of radar signals are derived from time-frequency deconstruction and extraction of real-time radar echo signals. Specifically, the real-time echo signal is divided into several signal segments at fixed time intervals, the frequency components and vibration intensity of each segment are analyzed, and then the time nodes are correlated with the corresponding frequencies and intensities to form structured data. The purpose is to serve as input data for differential homeomorphism mapping, providing basic data support for subsequent smooth homeomorphism correction based on differential homeomorphism relationships.

[0059] The logic of the overall formula is as follows: first, use the differential homeomorphism relation... Time-frequency characteristics of the signal Smooth homeomorphism correction is performed to obtain well-formed time-frequency characteristics that conform to the ideal signal standard, and then the inverse time-frequency transform is used to reconstruct the operator. The regular time-frequency characteristics are reconstructed by inverse time-frequency transform, and the final output is an amplitude equalization calibration signal that can accurately reflect the true information of the target. This fully realizes the amplitude equalization calibration of radar signals.

[0060] The beneficial effects are as follows: it accurately separates the core time and frequency information of real-time echo signals, forming structured signal time-frequency characteristics, providing a clear processing target for subsequent calibration, improving the targeting and accuracy of subsequent processing, eliminating distortion components in the signal time-frequency characteristics, ensuring the spatiotemporal continuity and consistency of the regularized time-frequency characteristics, conforming to ideal signal standards, improving the accuracy and reliability of signal calibration, providing high-quality basic data for calibration signal generation, completely restoring the regularized time-frequency characteristics into a time-domain signal, retaining the effective information of the ideal signal to the maximum extent, solving the problem of radar signal amplitude distortion, improving radar signal quality, ensuring accurate detection and identification of targets by the radar, and enhancing radar performance.

[0061] like Figure 2 The diagram shown is a functional block diagram of a radar signal amplitude equalization calibration system provided in an embodiment of the present invention.

[0062] The radar signal amplitude equalization calibration system 100 described in this invention can be installed in an electronic device. Depending on the functions implemented, the radar signal amplitude equalization calibration system 100 may include a time-frequency decomposition module 101, a manifold learning module 102, a manifold construction module 103, a geometric coupling module 104, and a mapping calibration module 105. The modules described in this invention can also be referred to as units, which are a series of computer program segments that can be executed by the processor of an electronic device and perform a fixed function, and are stored in the memory of the electronic device.

[0063] In this embodiment, the functions of each module / unit are as follows: The time-frequency decomposition module 101 is used to perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar. The manifold learning module 102 is used to perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar. The manifold construction module 103 is used to construct the target manifold of the standard signal of the radar based on the ideal operating parameters of the radar, so as to obtain the ideal signal manifold representation of the radar. The geometric coupling module 104 is used to perform Riemann geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. The mapping calibration module 105 is used to perform differential homeomorphic mapping on the real-time echo signal of the radar based on the differential homeomorphism relationship, so as to obtain the amplitude equalization calibration signal of the radar.

[0064] In the several embodiments provided by this invention, it should be understood that the disclosed methods and systems can be implemented in other ways. For example, the system embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and other division methods may be used in actual implementation.

[0065] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0066] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional modules.

[0067] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0068] This application embodiment can acquire and process relevant data based on artificial intelligence technology. Artificial intelligence is the theory, method, technology, and application system that uses digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use that knowledge to obtain optimal results.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A radar signal amplitude equalization calibration method, characterized in that, The method includes: S1. Perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar; S2. Perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar; S3. Based on the ideal operating parameters of the radar, construct the target manifold of the standard signal of the radar to obtain the ideal signal manifold representation of the radar. S4. Perform Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. S5. Based on the differential homeomorphism relationship, perform differential homeomorphism mapping on the real-time echo signal of the radar to obtain the amplitude equalization calibration signal of the radar.

2. The radar signal amplitude equalization calibration method as described in claim 1, characterized in that, The radar echo signal is decomposed in the time and frequency domain to obtain the signal characteristics of the radar, including: Based on the radar's receiver array geometry and channel configuration parameters, the original echo data stream of the radar is spatially manifold aligned to obtain the radar's multi-channel complex signal. Short-time Fourier analysis is performed on the multi-channel complex signal to obtain the joint time-frequency distribution of the radar; The time-frequency joint distribution is subjected to magnitude extraction to obtain the time-frequency amplitude information of the radar; Based on the geometric configuration of the receiving array, the time-frequency amplitude information is structurally integrated to obtain the signal characteristics of the radar.

3. The radar signal amplitude equalization calibration method as described in claim 1, characterized in that, Unsupervised manifold learning is performed on the signal features to obtain the distorted signal manifold representation of the radar, including: The signal characteristics of the radar are normalized to obtain the normalized time-frequency data of the radar; The standardized time-frequency data is subjected to neighborhood measurement to obtain the multi-channel range information of the radar; Based on the multi-channel distance information, the standardized time-frequency data is divided into topological neighborhoods to obtain the local neighborhood structure of the radar's time-frequency data. Based on the local structure of the time-frequency data, a nonlinear dimensionality reduction mapping is performed on the standardized time-frequency data to obtain the low-dimensional manifold embedding shape of the radar. The distortion mode structure of the radar is obtained by performing intrinsic identification on the low-dimensional manifold embedding morphology. Based on the distortion mode structure, the low-dimensional manifold embedding morphology is topologically reconstructed to obtain the distortion signal manifold representation of the radar.

4. The radar signal amplitude equalization calibration method as described in claim 3, characterized in that, Based on the aforementioned distortion mode structure, topological reconstruction is performed on the low-dimensional manifold embedding morphology to obtain the distortion signal manifold representation of the radar, including: Attribute mining is performed on the distortion pattern structure to obtain the distortion topology features of the radar; Based on the distorted topological features, information is embedded into the low-dimensional manifold embedding morphology to obtain the topologically regular manifold of the radar. The distortion shaping of the topologically regular manifold is performed to obtain the distorted signal manifold characterization of the radar.

5. The radar signal amplitude equalization calibration method as described in claim 1, characterized in that, Based on the ideal operating parameters of the radar, a target manifold is constructed from the standard signal of the radar to obtain an ideal signal manifold representation of the radar, including: In the standard signal space of the radar, the ideal operating parameters of the radar are theoretically mapped to obtain the theoretical distortion-free signal of the radar; The ideal signal parameter space of the radar is obtained by performing feature geometry deconstruction on the theoretically undistorted signal. The ideal topological connection structure of the radar is obtained by performing topological correlation analysis on the proximity relationships of relevant points in the ideal signal parameter space. By performing spatial topology fusion on the ideal signal parameter space and the ideal topology connection structure, the ideal signal manifold representation of the radar is obtained.

6. The radar signal amplitude equalization calibration method as described in claim 1, characterized in that, By performing Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation, the differential homeomorphism of the radar is obtained, including: By geometrically aligning the intrinsic geometric properties of the distorted signal manifold representation and the ideal signal manifold representation, the coupled Riemannian metric structure of the radar is obtained. Based on the coupled Riemannian metric structure, the tangential correspondence between the distorted signal manifold representation and the ideal signal manifold representation is spatially mapped to obtain the tangential spatial isomorphism of the radar. Based on the tangential spatial isomorphism, the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation is tensor-coupled to obtain the inter-manifold connectivity tensor field of the radar. Based on the manifold connectivity tensor field, tensor-constrained registration is performed on the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar.

7. The radar signal amplitude equalization calibration method as described in claim 6, characterized in that, Based on the tangential spatial isomorphism, a tensor coupling is performed on the global geometric correlation between the distorted signal manifold representation and the ideal signal manifold representation to obtain the inter-manifold connectivity tensor field of the radar, including: Based on the tangential spatial isomorphism, the distortion signal manifold representation and the ideal signal manifold representation are deduced together to obtain the local geometric correspondence of the radar. A compatibility test is performed on the local geometric correspondences to obtain the consistent communication structure of the radar; Tensor expansion is performed on the consensus communication structure to obtain the inter-manifold connectivity tensor field of the radar.

8. The radar signal amplitude equalization calibration method as described in claim 1, characterized in that, Based on the aforementioned differential homeomorphism, the real-time echo signal of the radar is subjected to differential homeomorphic mapping to obtain the amplitude equalization calibration signal of the radar, including: The real-time echo signal of the radar is subjected to time-frequency deconvolution extraction to obtain the signal time-frequency characteristics of the radar; Based on the differential homeomorphism relation, the time-frequency characteristics of the signal are smoothed by homeomorphism correction to obtain the regularized time-frequency characteristics of the radar. The regular time-frequency characteristics are reconstructed by inverse time-frequency transformation to obtain the amplitude equalization calibration signal of the radar.

9. The radar signal amplitude equalization calibration method as described in claim 8, characterized in that, The specific formula for calculating the amplitude equalization calibration signal is as follows: ； In the formula, The amplitude equalization calibration signal is... The signal time-frequency characteristics of the radar are... For the differential homeomorphism relation, The inverse time-frequency transform reconstruction operator for the regular time-frequency features.

10. A radar signal amplitude equalization calibration system, characterized in that, The system for implementing the radar signal amplitude equalization calibration method according to claim 1 includes: The time-frequency decomposition module is used to perform time-frequency domain decomposition on the radar echo signal to obtain the signal characteristics of the radar. The manifold learning module is used to perform unsupervised manifold learning on the signal features to obtain the distorted signal manifold representation of the radar. The manifold construction module is used to construct the target manifold of the standard signal of the radar based on the ideal operating parameters of the radar, so as to obtain the ideal signal manifold representation of the radar. A geometric coupling module is used to perform Riemannian geometric coupling between the distorted signal manifold representation and the ideal signal manifold representation to obtain the differential homeomorphism of the radar. The mapping calibration module is used to perform differential homeomorphic mapping on the real-time echo signal of the radar based on the differential homeomorphism relationship, so as to obtain the amplitude equalization calibration signal of the radar.

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