Multi-path fusion phased array radar antenna unit coordinate determination method and system

Abstract

The invention provides a multipath fusion phased array radar antenna unit coordinate determination method and system, and the method comprises the steps: obtaining an antenna array surface power distribution diagram, recognizing the boundary and geometric center of an array, and planning a spiral and cross-shaped composite sampling path; on the planned sampling path, collecting phase data at a plurality of inclination angles and frequencies; based on the signal-to-noise ratio and the angle correction factor, carrying out adaptive weighted fusion calculation on the adjacent point phase difference under multiple conditions; establishing an overdetermined equation set by using the fused phase difference, and iteratively solving the accurate coordinates of the antenna unit through two rounds of weighted least squares; and establishing a drift model to perform dynamic compensation, and performing real-time calibration by using a unit with determined coordinates as a reference point. According to the invention, through a multi-angle and multi-frequency redundancy measurement strategy and in combination with a signal-to-noise ratio-based adaptive weighting algorithm, environmental interference can be effectively identified and suppressed. Even in a complex electromagnetic environment, the system can still keep stable measurement precision.

Description

Technical Field

[0001] This invention relates to the field of electronic information technology, specifically to a method and system for determining the coordinates of phased array radar antenna elements using multipath fusion. Background Technology

[0002] As a core technology of modern radar systems, the precise coordinates of each radiating element in the phased array radar antenna array play a decisive role in the beam pointing accuracy, sidelobe suppression capability, and target positioning accuracy of the entire system. Traditional antenna element coordinate measurement methods mainly rely on a single measurement path and fixed parameter settings, which have many technical bottlenecks.

[0003] In existing technologies, commonly used near-field measurement methods typically employ linear scanning or simple grid scanning paths. This single-path strategy is susceptible to interference from local electromagnetic anomalies, multipath effects, and random noise, leading to insufficient reliability of the measurement results. Especially in complex electromagnetic environments, the phase data from a single measurement often contains significant uncertainty, making it difficult to meet the sub-millimeter coordinate accuracy requirements of modern high-precision phased array systems.

[0004] Traditional measurement systems also suffer from significant limitations in environmental adaptability. Changes in temperature, humidity, and atmospheric pressure alter the propagation characteristics of electromagnetic waves, leading to systematic drift in phase measurements. Existing methods lack effective real-time compensation mechanisms, and accumulated errors during long-term measurements severely impact the final accuracy.

[0005] Furthermore, existing technologies also face challenges in terms of measurement efficiency. For large-scale phased array antennas, traditional unit-by-unit measurement methods are extremely inefficient, often requiring hours or even days to determine the coordinates of the entire array. They lack intelligent parameter optimization and path planning capabilities, and cannot adaptively adjust measurement strategies based on specific antenna types and environmental conditions.

[0006] In data processing, traditional methods mainly rely on simple mathematical models and statistical methods, failing to fully utilize the rich information contained in multi-dimensional and multi-condition measurement data. The lack of advanced signal processing algorithms and artificial intelligence technologies makes it difficult to extract optimal coordinate information from complex phase data. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention proposes a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. It integrates cutting-edge algorithms such as Physical Information Neural Network (PINN), tensor decomposition, and Bayesian optimization, enabling it not only to fit measurement data but also to ensure that the results satisfy the physical constraints of the electromagnetic field. The system possesses self-learning capabilities, continuously optimizing algorithm parameters based on historical measurement data to adapt to different types of phased array antennas.

[0008] To achieve the above objectives, this invention proposes a method for intelligent determination of phased array radar antenna element coordinates based on multipath phase fusion, comprising the following steps: Step S1: Obtain the antenna array power distribution map by broadband frequency sweeping, identify the array boundary and geometric center, and plan a spiral and cross-shaped composite sampling path; Step S2: On the planned sampling path, phase data is acquired at multiple tilt angles and frequencies, and filtering and phase unwrapping preprocessing are performed; Step S3: Based on the signal-to-noise ratio and angle correction factor, perform adaptive weighted fusion calculation on the phase difference between adjacent points under multiple conditions; Step S4: Establish a set of indeterminate equations using the fused phase difference, and solve for the precise coordinates of the antenna elements through two rounds of weighted least squares iterative solution; Step S5: Establish a temperature-phase drift model for dynamic compensation, and use the cells with determined coordinates as reference points for real-time calibration.

[0009] Furthermore, step S1 is detailed as follows: Step S1.1: Obtain the reflection power distribution map of the entire antenna array by broadband frequency sweep (operating frequency ±10%), and identify the boundary contour of the antenna array; Step S1.2: Use image processing algorithms to perform edge detection and morphological analysis on the power distribution map to automatically identify the geometric center region of the antenna array; Step S1.3: Based on prior knowledge of antenna design (cell spacing, array size), plan a spiral sampling path around the central region, and initially set the sampling point spacing d to 1 / 3 of the antenna cell spacing; Step S1.4: On the basis of the spiral path, a cross-shaped dense sampling path is superimposed to form a composite sampling strategy.

[0010] Furthermore, step S2 is detailed as follows: Step S2.1: Set the probe tilt angle to three angles: 0°, 15°, and 30°, and collect phase data for each sampling point respectively; Step S2.2: For each sampling point, perform phase measurement at five frequency points: operating frequency f0, f0±5%, and f0±10%. Step S2.3: Collect 10 data points under each measurement condition, remove outliers using median filtering, and then calculate the average value as the phase measurement value for that point; S2.4: Utilize the phase continuity of adjacent points to perform phase unwinding processing and eliminate 2π ambiguity.

[0011] Furthermore, step S3 is as follows: Step S3.1: Calculate the phase difference matrix Δφ(i,j,θ,f) of adjacent sampling points under different measurement conditions, where i and j are the sampling point indices, θ is the probe angle, and f is the measurement frequency; Step S3.2: Calculate the confidence weight of each phase difference based on the signal-to-noise ratio (SNR) (i,j,θ,f), using the following formula: ; Adjacent sampling point pairs ( At the probe angle and frequency Normalized weights under Adjacent sampling point pairs ( At the probe angle and frequency Signal-to-noise ratio : Index number of the first sampling point : The index number of the second sampling point (and (adjacent) θ: Probe tilt angle (values: 0°, 15°, 30°) : Measurement frequency (value: , ±5%, ±10%) Step S3.3: Considering the influence of probe angle on measurement accuracy, an angle correction factor is introduced, as shown in the following formula: α(θ) = cos(θ) × (1 + 0.1×sin²(θ)); α(θ) is the correction factor corresponding to the probe tilt angle θ. Step S3.4: Calculate the phase difference after weighted fusion, using the following formula: ; Adjacent sampling point pairs The fusion phase difference; Adjacent sampling point pairs At the probe angle and frequency The original phase difference.

[0012] Furthermore, step S4 is detailed as follows: Step S4.1: Establish a system of indeterminate equations, expressing the phase difference-distance relationship of all adjacent point pairs as: ; Where λ: operating wavelength , : No. The horizontal and vertical coordinates of each antenna element; , : No. The horizontal and vertical coordinates of each antenna element; : Beam pointing angle in the horizontal direction; : Beam pointing angle in the vertical direction; Step S4.2: Use the weighted least squares method to solve for the initial estimated values ​​of the antenna element coordinates; Step S4.3: Based on the initial coordinates, calculate the theoretical phase difference and compare it with the measured phase difference to identify abnormal measurement points; Step S4.4: After removing outliers, perform a second round of least squares optimization to obtain accurate coordinates.

[0013] Furthermore, step S5 is detailed as follows: Step S5.1: Establish the temperature-phase drift model: Where β is the temperature coefficient, obtained through experimental calibration. Phase shift caused by temperature change; T: Current ambient temperature; Reference temperature or initial temperature; Step S5.2: Monitor temperature changes during the measurement process and compensate for phase drift caused by temperature in real time; Step S5.3: Using the antenna element with determined coordinates as a reference point, perform system calibration periodically; Step S5.4: Use the Kalman filter algorithm to fuse historical measurement data and current measurement values ​​to improve the accuracy of coordinate estimation.

[0014] Furthermore, the spiral sampling path in step S1.3 is specifically designed as follows: The helical equation is: r = a + b×θ, where a is the initial radius and b is the pitch coefficient. The helical parameters are adaptively adjusted according to the antenna array size to ensure coverage of the entire region of interest. Sampling is performed at equal intervals of arc length along the helical line, with an interval of d / 2. Helical sampling can effectively avoid aliasing effects caused by periodic sampling.

[0015] Furthermore, it also includes a measurement uncertainty assessment step: The error sources are evaluated based on the GUM (Guide to Measurement Uncertainty) method; Type A uncertainty (statistical method) and Type B uncertainty (non-statistical method) are considered; the combined standard uncertainty and expanded uncertainty are calculated; and confidence intervals are provided for each coordinate measurement result.

[0016] Furthermore, it also includes data traceability and quality assurance steps: Record complete measurement process data, including timestamps, environmental parameters, equipment status, etc.; establish blockchain storage for measurement data to ensure data immutability; generate measurement reports that comply with ISO / IEC 17025 standards; and support complete reproduction and verification of the measurement process.

[0017] Furthermore, step S3 also includes a phase gradient consistency check: Calculate the phase gradient field ∇φ(x,y) in the local region; check whether the curl of the gradient field is close to zero, i.e., verify ∇×∇φ ≈ 0; for regions with abnormal curl, increase the sampling density and remeasure; improve the reliability of coordinate determination by utilizing the continuity constraint of the phase gradient.

[0018] Furthermore, step S4 also includes constraint optimization: Introduce prior constraints on antenna element spacing: |d measured - d design |<0.1×d design Add array regularity constraints: antenna elements in adjacent rows / columns should be arranged in a straight line; use a constrained least squares algorithm to ensure the physical rationality of the solution; trigger a retest mechanism for solutions that do not meet the constraints.

[0019] The system for determining the coordinates of phased array radar antenna elements by implementing the above-mentioned multi-path fusion method includes an intelligent probe module, a high-precision mechanical scanning platform, a multi-channel phase measurement module, an intelligent data processing and analysis module, and a system integration and control module. The intelligent probe module includes: Broadband dual-polarization probe, operating frequency coverage 1-40GHz; built-in triaxial angle sensor for real-time probe attitude monitoring; integrated temperature sensor with measurement accuracy ±0.1℃; programmable gain amplifier with dynamic range 80dB. The high-precision mechanical scanning platform includes: Five-axis linkage robotic arm with repeatability of ±0.05mm; maximum scanning range: 3m×3m×1m; integrated laser rangefinder to measure the distance between the probe and the array in real time; vibration-proof design with vibration amplitude <0.01mm during operation; The multi-channel phase measurement module includes: FPGA-based parallel data acquisition system; 16-bit ADC, sampling rate 1GSps; real-time FFT processing capability, latency <1ms; phase measurement accuracy ±0.1°; The intelligent data processing and analysis module includes: An embedded GPU computing platform that supports parallel algorithm acceleration; an adaptive filter bank that can automatically select filtering parameters based on signal characteristics; a machine learning algorithm library that includes algorithms such as support vector machines and random forests; and a real-time data visualization interface that supports 3D display. The system integration and control module includes: A unified hardware abstraction layer supports measurement equipment from different manufacturers; state machine-based measurement process control; fault diagnosis and self-recovery mechanisms; and a remote monitoring interface that supports networked operation.

[0020] Furthermore, the intelligent probe module also includes: Automatic near-field / far-field switching function, automatically selects the working mode according to the measurement distance; adjustable polarization function, supports linear polarization and circular polarization measurement; built-in calibration source, can perform self-calibration; electromagnetic shielding design, suppresses external interference >60dB.

[0021] It also includes a rapid positioning step for batch antenna units: Based on the accurate positioning result of the first antenna element, combined with the design parameters of the antenna array, a template matching algorithm is used to quickly locate the approximate positions of the remaining antenna elements. Local fine measurement is performed on each predicted position, reducing the number of sampling points to 5. Through parallel processing, multiple antenna elements are measured simultaneously, improving efficiency by more than 10 times.

[0022] Furthermore, it also includes an environmental adaptation module: Air pressure compensation unit: corrects the electromagnetic wave propagation speed according to air pressure changes; humidity compensation unit: considers the influence of humidity on the dielectric constant; electromagnetic environment monitoring unit: detects the background electromagnetic noise level in real time; adaptive operating parameter adjustment: optimizes measurement parameters according to environmental conditions.

[0023] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention provides a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. It employs fusion strategies using multiple sampling paths, such as cross-shaped, star-shaped, and circular paths, and intelligently fuses the measurement results from different paths using a weighted standard deviation formula, effectively suppressing random errors and systematic biases in single-path measurements. After optimization with a weight allocation of 40% for cross-shaped, 35% for star-shaped, and 25% for circular paths, the final coordinate measurement accuracy reaches ±0.3mm (95% confidence level).

[0024] 2. This invention provides a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. By employing a redundant measurement strategy using multiple angles (0°, 15°, 30°) and multiple frequencies, combined with an adaptive weighting algorithm based on signal-to-noise ratio, this invention can effectively identify and suppress environmental interference. Even in complex electromagnetic environments, the system maintains stable measurement accuracy, and its interference suppression capability is improved by more than 60dB.

[0025] 3. This invention provides a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. It introduces an intelligent prediction algorithm based on an LSTM neural network and a genetic algorithm for parameter optimization, enabling automatic selection of optimal measurement parameters according to antenna type and environmental conditions. In batch measurement mode, efficiency can be improved by utilizing the reference information of already determined coordinate elements. The parallel data acquisition capability of the 4×1 linear phased array probe allows phase information from four different angles to be obtained in a single measurement, significantly shortening the measurement time.

[0026] 4. This invention provides a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. It establishes a comprehensive temperature-phase drift compensation model and, combined with real-time environmental monitoring and a Kalman filter algorithm, can dynamically compensate for measurement drift caused by environmental factors such as temperature, humidity, and air pressure. The strategy of combining the physical model with neural network residual compensation ensures measurement stability under various operating conditions and expands the environmental adaptability range.

[0027] 5. This invention provides a multi-path fusion method and system for determining the coordinates of phased array radar antenna elements. It features a modular hardware architecture and a unified software interface, supports 5G / WiFi dual-mode communication and cloud data processing, and possesses remote monitoring and expert diagnostic capabilities. The system's self-diagnosis and self-recovery mechanisms significantly reduce maintenance costs and operational complexity. Attached Figure Description

[0028] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the invention. Detailed Implementation The technical solution of the present invention will be more clearly and completely explained below with reference to the accompanying drawings and through the description of preferred embodiments of the present invention.

[0030] As one specific implementation, an initial scan is first performed to determine the approximate central region of the antenna array. Unlike traditional power peak search, this method calculates the power gradient field: ; Power value; : Power gradient vector; , Spatial coordinates; Starting from multiple random initial points, the tracing path follows the gradient ascent direction: ; Where r(t) is the position vector at time t, and α is the step size parameter (typically 0.1-0.5). Tracking stops when the gradient magnitude |∇P| < ε. The DBSCAN clustering algorithm is then used to cluster all convergence points, and the centroid of the largest cluster is determined as the array center. This method has stronger noise resistance compared to traditional peak search.

[0031] After the center is determined, the sampling points are arranged according to an adaptive spacing. The sampling point positions in the X-axis direction are: ; : No. sampling points coordinate; Array center coordinate; : Basic spacing; Total number of sampling points; The similarity in the Y-axis direction results in dense sampling in the central region and sparse sampling in the edge region, which improves efficiency while ensuring measurement accuracy.

[0032] Frequency selection employs an optimization algorithm based on information entropy. The information gain for each frequency is defined as: ; in For frequency point The signal-to-noise ratio, To assess phase stability, a greedy algorithm is used to select M frequency points, maximizing the total information entropy of the selected frequency point set. This ensures that the selected frequency points have the maximum information content, avoiding the problem of missing the optimal frequency point that may occur with traditional equal-interval selection.

[0033] Phase difference calculation employs an iterative phase expansion algorithm, identifying phase transition points by calculating the closed-path integral ∮Δφ·dl to ensure the continuity of the phase difference. For multi-frequency data, an improved dispersion model is established: ; in Frequency is The phase difference at time A is the principal propagation term (proportional to distance), B is the dispersion term (reflecting the dispersive properties of the medium), C is the constant term (systematic bias), and D is the higher-order term (nonlinear effect). A weighted overall least squares method is used for fitting, considering both frequency and phase measurement errors. The objective function is: Weight ; in, : No. The weight of each data point; : No. Uncertainty of a phase measurement; : No. Uncertainty of a frequency measurement; : No. Each measured phase difference; : Phase difference predicted by the model; Balance factor; Frequency measurement value.

[0034] Environmental compensation employs a combination of physical modeling and neural network residual compensation. The physical model includes compensation formulas for temperature, humidity, and air pressure, while the neural network is used to learn nonlinear relationships that the physical model fails to capture. The total compensation amount is: in, Temperature compensation item; Humidity compensation item; : Air pressure compensation item; : Neural network residual compensation term; The weights w1 and w2 are adaptively adjusted based on historical prediction errors to achieve optimal fusion of the physical model and the data-driven model.

[0035] An adaptive unscented Kalman filter is used to optimize the estimation of the compensated phase difference. The state vector contains the phase value and its first and second time derivatives, and nonlinear propagation is handled through Sigma point sampling. The innovation lies in introducing an adaptive noise estimation mechanism based on the innovation v. k = Z k - Ẑ k The covariance matrices of process noise Q and measurement noise R are dynamically updated, where v k : The innovation vector at time k; Z k : The observation value at time k; Ẑ k : The predicted value at time k.

[0036] The X and Y plane coordinates are calculated using a multi-dimensional phase difference joint solution method based on tensor decomposition. A third-order tensor T∈ℝ^(2N+1)×(2N+1)×M is constructed, where T(i,j,k) represents the phase difference between the i-th and j-th sampling points at the k-th frequency. This is achieved through CP decomposition. Where ⊗ represents the outer product, vectors aᵣ and bᵣ contain spatial coordinate information, vector cᵣ corresponds to the frequency response characteristics, and λᵣ are the decomposition coefficients. This method fully utilizes the inherent structure of multi-frequency data, improving the accuracy and robustness of coordinate solution.

[0037] The depth information Z is calculated using the frequency-dependent characteristics of electromagnetic waves penetrating a radome. First, the penetration phase is extracted: ; Penetration Phase Total phase c: speed of light Then, spectral analysis was performed. After performing the FFT transformation, the peak position k peak The relationship with depth is: Where c is the speed of light, Z is the depth value, and εᵣ is the relative permittivity of the radome material. If multiple significant peaks exist in the spectrum, it indicates the presence of a multi-layered structure, and the depth resolution can be improved using the MUSIC algorithm.

[0038] Machine learning employs a Physical Information Neural Network (PINN), which adds physical constraints to traditional neural networks. The loss function is designed as follows: ; in For data fitting loss, physical constraint loss Ensure the phase field satisfies the irrotational condition (physical law), smoothness loss. Ensure the smoothness of the solution; These are the weighting coefficients. For curl operator; The network input includes 115 dimensions, including phase difference features, environmental parameters, and geometric parameters, and the output is three-dimensional coordinates [x,y,z].

[0039] The validation employs a strategy combining multipath measurement and Bayesian optimization. Four measurement paths are designed: cross-shaped (basic path), star-shaped (adding diagonal directions), Archimedes spiral (continuous coverage), and random walk (Monte Carlo validation).

[0040] Bayesian optimization is used for intelligent selection of validation points. A Gaussian process model is constructed. , where μ(x) is the mean function and k(x,x') is the covariance kernel function. The acquisition function is defined as: ; Where κ is the exploration-utilization balance parameter and σ(x) is the prediction standard deviation. An efficient validation strategy is achieved by maximizing the acquisition function to select the next validation point.

[0041] Consistency determination uses the Hausdorff distance metric to measure the difference in measurement results across different paths. When d H When the sample density exceeds the preset threshold (typically 0.5 mm), the system automatically increases the sampling density in areas with large differences and remeasures to ensure the reliability of the final result.

[0042] The intelligent probe array employs a 4×1 linear phased array configuration, with four receiving units arranged at equal intervals, the spacing being 0.5λ at the center frequency. Each unit receives signals independently, and electronic beam scanning is achieved through phase control.

[0043] During operation, the central processing unit sends phase control commands to the four receiving units, causing them to form receiving beams pointing in a specific direction. By rapidly switching between different phase configurations, beam scanning can be achieved within a range of ±60°, with a scanning speed of up to 1000 times per second. Each receiving channel is equipped with an independent low-noise amplifier and analog-to-digital converter to ensure high-fidelity signal acquisition.

[0044] Simultaneous reception from multiple directions is achieved through digital beamforming technology. The four received signals are digitized and processed in parallel within the FPGA, simultaneously forming four receiving beams pointing in different directions. This design allows for the acquisition of phase information from multiple angles in a single measurement, improving measurement efficiency by more than four times compared to traditional single-probe systems.

[0045] The signal processing employs an adaptive beamforming algorithm, which automatically adjusts the weighting coefficients of each channel based on the signal-to-noise ratio of the received signal to suppress interference and enhance the target signal. When strong interference is detected, the system automatically forms a null in that direction, with a depth of up to -40dB.

[0046] The input feature engineering for Long Short-Term Memory (LSTM) networks first preprocesses the raw data. Historical measurement data is obtained by taking the phase difference sequence of the most recent 50 measurements and extracting temporal features using a sliding window. Environmental parameters include the current values ​​and rates of change of temperature, humidity, and air pressure. Antenna type is represented by one-hot encoding, supporting eight common phased array types. The operating frequency is normalized to the [0,1] interval.

[0047] The network architecture consists of two layers of LSTM units: the first layer has 128 hidden units, and the second layer has 64 hidden units. The state update of each LSTM unit follows a standard formula, but an adaptive mechanism is introduced in the forget gate to dynamically adjust according to the rate of change of the input data, enabling the network to better adapt to different measurement scenarios.

[0048] The training process employs a phased strategy. First, pre-training is performed using simulated data to establish basic coordinate prediction capabilities. Then, fine-tuning is performed using measured data, requiring at least 1000 sets of labeled data for each antenna type. In addition to mean squared error, the loss function incorporates physical consistency constraints to ensure that the predicted coordinates conform to the geometry of the antenna array.

[0049] During inference, the network outputs not only predicted coordinates but also a confidence score. When the confidence score falls below a threshold, the system automatically switches to a traditional algorithm or requests manual verification to ensure the reliability of the measurement.

[0050] Batch measurements begin by establishing a reference coordinate system through precise measurement of the first antenna element. Based on the antenna design parameters (element spacing, arrangement), affine transformations are used to predict the theoretical positions of the remaining elements. To account for manufacturing and installation errors, a search area of ​​±10% is defined around each theoretical position.

[0051] The path planning employs an improved traveling salesman algorithm, aiming to minimize the total measurement time. The algorithm considers the robot arm's kinematic constraints, acceleration limitations, and obstacle avoidance requirements. A large-scale array is decomposed into multiple sub-regions using dynamic programming, with each sub-region employing a serpentine scanning path, and sub-regions connected by the shortest path.

[0052] Parallel measurements are achieved by deploying multiple independent probe modules. The main control system divides the antenna array into multiple non-overlapping measurement areas and assigns tasks to each probe. Probes maintain a distance of at least 2 meters from each other to avoid mutual interference. A real-time communication protocol ensures that the measurement progress of each probe is synchronized, and automatically assists other probes when one probe completes its task.

[0053] The database employs a distributed architecture and includes fields such as antenna element ID, 3D coordinates, measurement time, environmental parameters, and measurement uncertainty. A spatial index supports fast proximity queries. Historical data is used to train predictive models and anomaly detection; when the coordinates of an element deviate from the historical mean by more than 3σ, it is automatically marked as a potential fault point.

[0054] The cross-shaped path uses dense sampling along the row and column where the antenna element is located, with a sampling interval of d / 4. The star-shaped path adds two diagonals at 45° and 135° to the cross-shaped path. The ring-shaped path samples on concentric circles with radii ranging from 0.5d to 2d, centered on the antenna element. The antenna element coordinates are calculated independently for each path.

[0055] The standard deviation is calculated using a weighted method, considering the number of measurement points and coverage area for different paths. The weight allocation is: 40% for the cross-shaped pattern, 35% for the star-shaped pattern, and 25% for the circular pattern. The calculation formula is as follows: in For the weights of each path, For the measurement results of each path, This is a weighted average, where n is the total number of paths; When the standard deviation exceeds 0.5 mm, adaptive encrypted measurement is initiated. The system analyzes the difference patterns of the results for each path and identifies the direction with the largest deviation. In this direction, the sampling interval is reduced to d / 8, and the measurement range is expanded to 3d. At the same time, the presence of metallic obstacles or strong reflectors in this area is checked, and the probe angle or measurement power is adjusted as necessary.

[0056] The verification results are displayed in real time through a visual interface. Measurement results for different paths are represented by different colors, and points with deviations exceeding the limits are highlighted in red. The system automatically generates a verification report, including detailed data for each path, statistical analysis, and improvement suggestions.

[0057] As a specific implementation method, the remote monitoring module is implemented as follows: 5G / WiFi dual-mode communication ensures reliable connectivity in different environments. The 5G module supports SA / NSA dual-mode and prioritizes the use of low-latency URLLC slicing. The WiFi module supports the 802.11ax standard, providing stable high-speed connectivity in indoor environments. The communication protocol adopts MQTT to ensure the reliability and real-time performance of data transmission.

[0058] Data transmission employs a tiered strategy. Critical data (coordinates, anomaly alarms) is transmitted in real-time with a latency of less than 100ms. Raw phase data is compressed and transmitted in batches; the compression algorithm is optimized for the characteristics of phase data, achieving a compression ratio of up to 10:1. The video stream uses H.265 encoding, with the bitrate adaptively adjusted based on network bandwidth.

[0059] The remote expert system is built on a knowledge graph and incorporates expertise in areas such as antenna fault diagnosis and measurement anomaly analysis. When an anomaly is detected, the system automatically matches similar cases and generates preliminary diagnostic suggestions. Experts can remotely view the on-site situation using AR glasses, mark problem areas on the 3D model, and guide on-site operations.

[0060] Cloud storage utilizes object storage services, with data organized hierarchically by project, date, and antenna type. Hot and cold data are separated, with recent data stored in high-speed storage and historical data migrated to low-cost storage. The data analytics platform supports SQL queries and machine learning tasks, enabling cross-project big data analysis to identify common problems and optimization opportunities.

[0061] As a specific implementation method, adaptive parameter optimization is achieved as follows: adaptive adjustment of the sampling interval is based on spatial spectrum analysis of the antenna array. First, coarse sampling is performed to calculate the spatial spectral density. In regions with drastic spectral changes (such as array edges or defect locations), the sampling interval is automatically reduced to d / 4, and increased to 2d in uniform regions. The dynamic range is limited to [d / 4, 2d] to balance accuracy and efficiency.

[0062] The measured power is adjusted based on the real-time signal-to-noise ratio (SNR). The system maintains a power-SNR lookup table with the goal of keeping the SNR within the 40-50 dB range. When ambient electromagnetic noise increases, the transmit power is automatically increased, but not exceeding regulatory limits. The integration time is inversely proportional to the SNR, ensuring that the standard deviation of the phase measurement is less than 0.5°.

[0063] The genetic algorithm optimization involves a population of 20 individuals, each encoded with parameters including sampling interval, measurement power, integration time, frequency selection, and filtering parameters. The fitness function comprehensively considers measurement accuracy (60% weight), measurement time (30% weight), and energy consumption (10% weight).

[0064] The evolutionary process employs an elite preservation strategy, with the two best individuals directly inherited by the next generation. Uniform crossover is used with a crossover probability of 0.8. Adaptive mutation rates are employed, dynamically adjusted based on population diversity. After each generation, the parameters of the best individuals are selected and applied to actual measurements, and the fitness assessment is updated based on the measurement results.

[0065] Through 20-30 generations of evolution, the system can find the optimal combination of parameters suitable for the current antenna type and environmental conditions. Compared with fixed parameters, the measurement efficiency is improved by more than 30%, while maintaining sub-millimeter level measurement accuracy.

[0066] As one specific implementation method, the approach begins with a comprehensive system initialization. The intelligent probe array (a linear phased array with four receiving units) is mounted on the robotic arm, with the spacing between each receiving unit set to 0.5λ at the center frequency. The system self-test program is then initiated to ensure all hardware modules are functioning correctly.

[0067] Depending on the type of phased array under test, the system automatically downloads relevant prior knowledge from a cloud database, including parameters such as typical cell spacing and operating frequency range. These parameters are input into an LSTM neural network, which predicts the optimal initial measurement parameters based on historical measurement data. Simultaneously, a genetic algorithm runs in the background, preparing to optimize the measurement parameters in real time.

[0068] The environmental sensing module begins operation, collecting current temperature, humidity, and air pressure data to establish an environmental baseline. The remote monitoring module establishes a connection with the cloud via 5G / WiFi, ensuring real-time data transmission and enabling remote intervention by experts.

[0069] The robotic arm drives the probe array to perform a wide-area coarse scan at a distance of approximately 1 meter from the antenna array. The four receiving units of the probe array operate simultaneously, using digital beamforming technology to create four receiving beams pointing in different directions, covering a range of ±60°. This parallel reception significantly improves scanning efficiency.

[0070] During the scanning process, the system calculates the power distribution P(i,j) and the power gradient field ∇P in real time. A gradient flow tracing algorithm is used to simultaneously trace from multiple starting points, stopping when the gradient magnitude is less than a threshold. The convergence points of all tracing paths are clustered using DBSCAN to determine the geometric center of the array.

[0071] Based on the identified center location and array boundaries, the system automatically plans subsequent fine-grained measurement paths. The main path adopts a spiral shape, upon which a cross-shaped dense sampling path is superimposed. The genetic algorithm adjusts the initial value of the sampling interval d based on the coarse scan results.

[0072] The probe array is moved to a near-field position at a distance of λ / 2π from the array surface to begin fine measurements. At each sampling point, the system first performs a frequency band quality assessment, calculating the signal-to-noise ratio and phase stability at each frequency. Based on an information entropy optimization algorithm, M optimal frequency points are selected to ensure that the acquired data has the maximum information content.

[0073] The four units of the intelligent probe array collect data at three angles: 0°, 15°, and 30°. Each angle is measured 10 times at M selected frequency points. The LSTM network processes this data in real time and predicts the most likely phase value for the next sampling point to verify the rationality of the measurement.

[0074] Environmental compensation is performed simultaneously. The physical model calculates the phase drift caused by temperature, humidity, and air pressure based on real-time environmental parameters, while the neural network compensates for nonlinear effects that the physical model fails to capture. The compensated phase data is further optimized using an adaptive unscented Kalman filter, with the filter's noise parameters dynamically adjusted based on the innovation.

[0075] During the measurement process, the genetic algorithm continuously optimizes the parameters. After each region is measured, the algorithm evaluates the measurement quality and updates the population, gradually converging to the optimal parameter combination. For regions with low signal-to-noise ratios, the measurement power and integration time are automatically increased, while for high-quality regions, the measurement speed is accelerated.

[0076] The multi-frequency phase data from all sampling points constitute a third-order tensor T. Spatial coordinate information and frequency response characteristics are extracted through CP decomposition, and an overdetermined system of equations is established to solve for the X and Y coordinates. Depth Z is determined by analyzing the penetration phase differences at different frequencies, and the peak position after FFT transformation directly corresponds to the depth value.

[0077] After the initial coordinates are determined, the system initiates a cross-validation procedure. In addition to the original spiral path, cross-shaped, star-shaped, and circular path measurements are performed. A Bayesian optimization algorithm intelligently selects validation points to maximize information acquisition efficiency. The weighted standard deviation of the measurement results from different paths is calculated, and measurements are automatically densified in the area if the deviation exceeds 0.5 mm.

[0078] The Physical Information Neural Network (PINN) performs global optimization on all measurement data. The network not only fits the measurement data but also ensures that the results satisfy the physical laws of the electromagnetic field (such as the irrotationality of the phase field). This physical constraint significantly improves prediction accuracy in sparse regions at the measurement points.

[0079] Once the precise coordinates of the first antenna element are determined, the system enters an efficient batch measurement mode. Based on the antenna design parameters and the measured coordinates, the positions of the remaining elements are predicted. Rapid verification measurements are performed within ±10% of the predicted positions, requiring only 5 sampling points per element.

[0080] If multiple probe systems are deployed, the main controller divides the antenna array into multiple zones, with each probe operating in parallel. Probes synchronize their progress via a real-time communication protocol, dynamically adjusting task allocation. Probes that have completed their tasks automatically support probes that are progressing slower.

[0081] All measurement data is transmitted to the cloud in real time, with key data (coordinate values, anomaly markers) transmitted first, and raw phase data uploaded in batches after compression. The cloud database automatically builds a spatial index, supporting fast querying and analysis. The anomaly detection algorithm runs continuously, automatically issuing an alarm when a coordinate deviation exceeds 3σ.

[0082] Remote experts can view real-time measurement status through an AR interface and intervene to provide guidance when necessary. The expert system provides fault diagnosis suggestions based on a knowledge graph, and historical case matching helps to quickly resolve problems.

[0083] After measurement, the system performs a comprehensive uncertainty assessment. Considering all error sources, including measurement repeatability, environmental variations, and equipment accuracy, the expanded uncertainty for each coordinate is calculated. The results are expressed as confidence intervals, with a typical accuracy of ±0.3 mm (95% confidence level).

[0084] The generated measurement report contains complete process data: measurement timestamps, environmental parameters, equipment status, raw data, processing algorithms, final coordinates, uncertainty analysis, etc. All data is stored using blockchain technology to ensure traceability and immutability.

[0085] The LSTM network uses new measurement data for incremental learning, continuously improving prediction accuracy. The genetic algorithm saves the optimized parameter combinations to a knowledge base, serving as initial parameters for subsequent similar tasks. The entire system becomes increasingly intelligent and efficient through continuous learning.

[0086] In this way, a complete and coherent measurement process is formed from system initialization to final report generation. The output of each stage serves as the input for the next stage, collectively achieving high-precision and high-efficiency antenna element coordinate measurement.

[0087] like Figure 1 As shown, the present invention is as follows: Step S1: Obtain the antenna array power distribution map by broadband frequency sweeping, identify the array boundary and geometric center, and plan a spiral and cross-shaped composite sampling path; Step S2: On the planned sampling path, phase data is acquired at multiple tilt angles and frequencies, and filtering and phase unwrapping preprocessing are performed; Step S3: Based on the signal-to-noise ratio and angle correction factor, perform adaptive weighted fusion calculation on the phase difference between adjacent points under multiple conditions; Step S4: Establish a set of indeterminate equations using the fused phase difference, and solve for the precise coordinates of the antenna elements through two rounds of weighted least squares iterative solution; Step S5: Establish a temperature-phase drift model for dynamic compensation, and use the cells with determined coordinates as reference points for real-time calibration.

[0088] Specifically, it includes: Broadband frequency sweeping technology was used to acquire the reflected power distribution map of the entire antenna array within ±10% of the operating frequency. The reflected power value at each frequency point was recorded during the sweep, forming a two-dimensional power distribution matrix. The Canny edge detection algorithm was used to process the power distribution map and identify the boundary contour of the antenna array. Morphological opening and closing operations were used to eliminate edge noise and accurately extract the array's shape contour. The centroid algorithm was used to calculate the geometric center coordinates of the array, serving as the starting reference point for subsequent sampling. Based on prior knowledge of the antenna design, including element spacing and array size, the sampling density parameters were determined. Starting from the geometric center, a spiral sampling path was planned according to the Archimedes' spiral equation. The initial sampling point spacing d was set to 1 / 3 of the antenna element spacing to ensure sufficient spatial resolution. A cross-shaped dense sampling path was superimposed on the spiral path, with the cross lines passing through the array center and extending to the boundary. This composite sampling strategy ensured high-density sampling in key areas and full array coverage. The generated sampling point coordinate sequence will serve as the measurement position input for the next step.

[0089] Following the planned sampling path, the probe was moved to each sampling point for measurement. The probe tilt angle was set sequentially to 0°, 15°, and 30° to acquire the phase response at different incident angles. At each angle, phase measurements were performed at five frequency points: the operating frequency f0 and f0±5% and f0±10%. This multi-frequency measurement strategy improves the robustness and anti-interference capability of phase measurements. Ten data points were continuously collected under each measurement condition to form a dataset. A median filtering algorithm was used to identify and remove outliers, effectively suppressing random noise. The arithmetic mean of the filtered data was calculated as the phase value under that measurement condition. A three-dimensional phase data matrix φ(x,y,θ,f) was established to store the multi-condition phase data of all sampling points. Two-dimensional phase unwinding was performed using the phase continuity constraint between adjacent sampling points. The unwinding algorithm adopted a quality map-guided path tracing method, expanding from high-quality regions to low-quality regions. After eliminating 2π phase ambiguity, a continuous phase distribution map was obtained. The preprocessed phase data was then passed to S3 for phase difference calculation.

[0090] Based on the phase data described above, the phase difference between all adjacent sampling point pairs under different measurement conditions is calculated. A four-dimensional phase difference matrix is ​​constructed. Simultaneously, the signal-to-noise ratio (SNR) of each measurement is extracted to quantify the measurement quality. Normalized confidence weights are calculated based on the SNR. Measurements with high SNR receive greater weights, while the influence of low SNR measurements is suppressed. Considering the influence of the probe tilt angle on the electromagnetic wave propagation path, an angle correction factor is introduced to compensate for the oblique incidence effect. The confidence weights are multiplied by the angle correction factor to obtain a comprehensive weighting coefficient. The phase differences under all measurement conditions are weighted and summed to calculate the fused phase difference. The fusion process fully utilizes the redundant information from multi-angle and multi-frequency measurements. The weighted fusion strategy adaptively enhances high-quality measurements and suppresses low-quality measurements. The generated fused phase difference matrix will serve as the core input for the coordinate solution in the next step.

[0091] Using the fused phase difference data from the previous step, a mathematical model for solving the antenna element coordinates is established. Based on the phase-space relationship of the phased array antenna, the phase difference between each pair of adjacent points satisfies the equation... ; The equations for all adjacent point pairs are combined to form a system of indeterminate equations. The number of equations is much greater than the number of unknowns, providing redundancy in the solution. A weighted least squares method is used, with the weight matrix constructed from the signal-to-noise ratio information obtained in the previous step. Initial estimates of the antenna element coordinates are obtained through matrix operations. The theoretical phase difference is calculated based on the initial coordinates and compared with the measured fused phase difference. Residuals are calculated, and a threshold is set to identify point pairs with measurement anomalies. After removing the anomaly point pairs, the system of equations is reconstructed for a second round of optimization. This iterative optimization process improves the accuracy and reliability of the coordinate estimation. The output precise coordinates will be used for the next step of dynamic calibration.

[0092] A mathematical model of temperature-phase drift is established. The temperature coefficient is determined through calibration experiments controlling temperature changes. Ambient temperature changes are monitored in real time throughout the measurement process. Based on the temperature drift model, the phase deviation caused by temperature is calculated and compensated. The high-precision antenna element coordinates determined in the previous step are used as reference points. The phase of the reference point is measured periodically to detect the system drift. The drift information from the reference point is used to correct system errors at other test points. A dynamic estimation model is established using the Kalman filter algorithm. Optimal estimation is achieved by fusing historical measurement data and current observations. The prediction-update mechanism of the Kalman filter effectively suppresses random errors. The dynamically compensated results can be fed back to all the above steps, forming a closed-loop optimization. Real-time calibration ensures the stability and consistency of long-term measurements. Finally, high-precision antenna element coordinates after temperature compensation and dynamic calibration are output.

[0093] The above-described specific embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Various modifications, substitutions, and improvements made by those skilled in the art to the technical solutions of the present invention based on the provided textual description and drawings, without departing from the design concept and spirit of the present invention, should all fall within the scope of protection of the present invention. The scope of protection of the present invention is determined by the claims.

Claims

1. A method for determining the coordinates of phased array radar antenna elements using multi-path fusion, characterized in that, Includes the following steps: Step S1: Obtain the antenna array power distribution map by broadband frequency sweeping, identify the array boundary and geometric center, and plan a spiral and cross-shaped composite sampling path; Step S2: On the planned sampling path, phase data is acquired at multiple tilt angles and frequencies, and filtering and phase unwrapping preprocessing are performed; Step S3: Based on the signal-to-noise ratio and angle correction factor, perform adaptive weighted fusion calculation on the phase difference between adjacent points under multiple conditions; Step S4: Establish a set of indeterminate equations using the fused phase difference, and solve for the precise coordinates of the antenna elements through two rounds of weighted least squares iterative solution; Step S5: Establish a temperature-phase drift model for dynamic compensation, and use the cells with determined coordinates as reference points for real-time calibration.

2. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S1 is as follows: Step S1.1: Obtain the reflection power distribution map of the entire antenna array by broadband frequency sweeping, and identify the boundary contour of the antenna array; Step S1.2: Use image processing algorithms to perform edge detection and morphological analysis on the power distribution map to automatically identify the geometric center region of the antenna array; Step S1.3: Based on prior knowledge of antenna design, including element spacing and array size, plan a spiral sampling path around the central region, with the initial sampling point spacing d set to 1 / 3 of the antenna element spacing; Step S1.4: On the basis of the spiral path, a cross-shaped dense sampling path is superimposed to form a composite sampling strategy.

3. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S2 is as follows: Step S2.1: Set the probe tilt angle to three angles: 0°, 15°, and 30°, and collect phase data for each sampling point respectively; Step S2.2: For each sampling point, at the operating frequency , ±5% and Phase measurements were performed at five frequency points, with a range of ±10%. Step S2.3: Collect 10 data points under each measurement condition, remove outliers using median filtering, and then calculate the average value as the phase measurement value at that point; S2.4: Utilize the phase continuity of adjacent points to perform phase unwinding processing and eliminate 2π ambiguity.

4. The method for determining the coordinates of phased array radar antenna elements by multi-path fusion according to claim 1, characterized in that, Step S3 is as follows: Step S3.1: Calculate the phase difference matrix Δφ of adjacent sampling points under different measurement conditions. ),in Here is the sampling point index, and θ is the probe angle. For measuring frequency; Step S3.2: Calculate the confidence weight of each phase difference based on the signal-to-noise ratio (SNR) (i,j,θ,f), using the following formula: ； Adjacent sampling point pairs ( At the probe angle and frequency Normalized weights under Adjacent sampling point pairs ( At the probe angle and frequency Signal-to-noise ratio : Index number of the first sampling point : Index number of the second sampling point θ: Probe tilt angle : Measurement frequency; Step S3.3: Considering the influence of probe angle on measurement accuracy, an angle correction factor is introduced, as shown in the following formula: α(θ) = cos(θ) × (1 + 0.1×sin²(θ)); α(θ) is the correction factor corresponding to the probe tilt angle θ. Step S3.4: Calculate the phase difference after weighted fusion, using the following formula: ； Adjacent sampling point pairs The fusion phase difference; Adjacent sampling point pairs At the probe angle and frequency The original phase difference.

5. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S4 is as follows: Step S4.1: Establish a system of indeterminate equations, expressing the phase difference-distance relationship of all adjacent point pairs as: ； in λ: Operating wavelength , : No. The horizontal and vertical coordinates of each antenna element; , : No. The horizontal and vertical coordinates of each antenna element; : Beam pointing angle in the horizontal direction; : Beam pointing angle in the vertical direction; Step S4.2: Use the weighted least squares method to solve for the initial estimated values ​​of the antenna element coordinates; Step S4.3: Based on the initial coordinates, calculate the theoretical phase difference and compare it with the measured phase difference to identify abnormal measurement points; Step S4.4: After removing outliers, perform a second round of least squares optimization to obtain accurate coordinates.

6. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S5 is as follows: Step S5.1: Establish the temperature-phase drift model: Where β is the temperature coefficient, obtained through experimental calibration. Phase shift caused by temperature change; T: Current ambient temperature; Reference temperature or initial temperature; Step S5.2: Monitor temperature changes during the measurement process and compensate for phase drift caused by temperature in real time; Step S5.3: Using the antenna element with determined coordinates as a reference point, perform system calibration periodically; Step S5.4: Use the Kalman filter algorithm to fuse historical measurement data and current measurement values ​​to improve the accuracy of coordinate estimation.

7. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, The spiral sampling path in step S1.3 is specifically designed as follows: The equation for a helix is: r = a + b × θ, where a is the initial radius and b is the pitch coefficient. The spiral parameters are adaptively adjusted according to the antenna array size to ensure coverage of the entire region of interest. Samples are taken at equal intervals along the spiral, with an interval of d / 2. Spiral sampling can effectively avoid the aliasing effect caused by periodic sampling.

8. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S3 also includes a phase gradient consistency check: Calculate the phase gradient field ∇φ(x,y) in the local region; check whether the curl of the gradient field is close to zero, i.e., verify ∇×∇φ ≈ 0; for regions with abnormal curl, increase the sampling density and remeasure; improve the reliability of coordinate determination by utilizing the continuity constraint of the phase gradient.

9. The method for determining the coordinates of phased array radar antenna elements by multipath fusion according to claim 1, characterized in that, Step S4 also includes constraint optimization: Introduce prior constraints on antenna element spacing: |d measured - d design | < 0.1×d design Add array regularity constraints: antenna elements in adjacent rows / columns should be arranged in a straight line; use a constrained least squares algorithm to ensure the physical rationality of the solution; trigger a retest mechanism for solutions that do not meet the constraints.

10. A system for implementing the multipath fusion phased array radar antenna element coordinate determination method according to any one of claims 1-9, characterized in that, It includes an intelligent probe module, a high-precision mechanical scanning platform, a multi-channel phase measurement module, an intelligent data processing and analysis module, and a system integration and control module; The intelligent probe module includes: Broadband dual-polarization probe, operating frequency coverage 1-40GHz; Built-in three-axis angle sensor to monitor probe attitude in real time; Integrated temperature sensor with a measurement accuracy of ±0.1℃; Programmable gain amplifier with a dynamic range of 80dB; The high-precision mechanical scanning platform includes: Five-axis linkage robotic arm with repeatability of ±0.05mm; Maximum scanning range: 3m × 3m × 1m; Integrated laser rangefinder to measure the distance between the probe and the array surface in real time; Vibration-resistant design, vibration amplitude <0.01mm during operation; The multi-channel phase measurement module includes: FPGA-based parallel data acquisition system; 16-bit ADC, sampling rate 1GSps; Real-time FFT processing capability with latency <1ms; Phase measurement accuracy ±0.1°; The intelligent data processing and analysis module includes: Embedded GPU computing platform, supporting parallel algorithm acceleration; An adaptive filter bank can automatically select filtering parameters based on signal characteristics; A machine learning algorithm library, including algorithms such as support vector machines and random forests; Real-time data visualization interface, supporting 3D display; The system integration and control module includes: A unified hardware abstraction layer supports measurement equipment from different manufacturers; Measurement process control based on state machine; Fault diagnosis and self-recovery mechanism; Remote monitoring interface, supporting networked operation.

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