Method and system for determining coordinates of phased array radar antenna elements in multipath fusion

Abstract

The application provides a phased array radar antenna unit coordinate determination method and system, comprising: acquiring an antenna array surface power distribution map, identifying an array boundary and a geometric center, and planning a spiral and cross composite sampling path; collecting phase data at multiple inclination angles and frequencies on the planned sampling path; based on a signal-to-noise ratio and an angle correction factor, adaptively weighting and fusing phase difference of adjacent points under multiple conditions to calculate; using the fused phase difference to establish an overdetermined equation set, and solving the accurate coordinates of the antenna unit through two rounds of weighted least square method iteration; establishing a drift model for dynamic compensation, and using the unit with the determined coordinates as a reference point for real-time calibration. Through the redundant measurement strategy of multiple angles and multiple frequencies, combined with the adaptive weighting algorithm based on the signal-to-noise ratio, the application can effectively identify and suppress environmental interference. Even in a complex electromagnetic environment, the system can still maintain stable measurement accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electronic information technology, in particular to a phased array radar antenna unit coordinate determination method and system based on multi-path fusion. BACKGROUND

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

[0003] In existing technologies, the commonly used near-field measurement method usually adopts a straight-line scanning or simple grid scanning path. This single-path strategy is easily disturbed by local electromagnetic environment anomalies, multipath effects, and random noise, resulting in insufficient reliability of the measurement results. Especially in complex electromagnetic environments, the phase data of a single measurement often contains a large degree of uncertainty, making it difficult to meet the requirements of modern high-precision phased array systems for sub-millimeter level coordinate accuracy.

[0004] Traditional measurement systems also have significant defects in environmental adaptability. Changes in temperature, humidity, and atmospheric pressure can cause changes in electromagnetic wave propagation characteristics, which in turn cause systematic drift in phase measurement. Existing methods lack effective real-time compensation mechanisms, and the cumulative error during long measurement processes seriously affects the final accuracy.

[0005] In addition, existing technologies also face challenges in measurement efficiency. For large-scale phased array antennas, the traditional one-by-one unit measurement method is extremely inefficient, often taking hours or even days to complete the coordinate determination of the entire array. Lack of intelligent parameter optimization and path planning capabilities, the measurement strategy cannot be adaptively adjusted according to the specific antenna type and environmental conditions.

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

[0007] To overcome the shortcomings of existing technologies, the present application proposes a phased array radar antenna unit coordinate determination method and system based on multi-path fusion, which integrates physical information neural networks (PINN), tensor decomposition, Bayesian optimization, and other cutting-edge algorithms. Not only can it fit measurement data, but also ensure that the results meet the physical law constraints of electromagnetic fields. The system has self-learning capabilities and can continuously optimize algorithm parameters based on historical measurement data to adapt to different types of phased array antennas.

[0008] To achieve the above object, the application provides a phased array radar antenna unit coordinate intelligent determination method based on multi-path phase fusion, comprising the following steps:

[0009] Step S1: Obtain an antenna array surface power distribution map through broadband frequency sweeping, identify the array boundary and geometric center, and plan a spiral and cross composite sampling path;

[0010] Step S2: Collect phase data at multiple tilt angles and frequencies on the planned sampling path, and perform filtering and phase unwrapping preprocessing;

[0011] Step S3: Based on the signal-to-noise ratio and angle correction factor, adaptively weight and fuse the phase difference of adjacent points under multiple conditions;

[0012] Step S4: Use the fused phase difference to establish an overdetermined equation set, and solve the accurate coordinates of the antenna unit through two rounds of weighted least squares method iteration;

[0013] Step S5: Establish a temperature-phase drift model for dynamic compensation, and use the unit with determined coordinates as a reference point for real-time calibration.

[0014] Further, step S1 is specifically as follows:

[0015] Step S1.1: Obtain the reflected power distribution map of the entire antenna array surface by broadband frequency sweeping (working frequency ±10% range), and identify the boundary profile of the antenna array;

[0016] Step S1.2: Perform edge detection and morphological analysis on the power distribution map using image processing algorithms to automatically identify the geometric center area of the antenna array;

[0017] Step S1.3: Based on the prior knowledge (unit spacing, array size) of antenna design, plan a spiral sampling path around the center area, and set the initial sampling point spacing d to 1 / 3 of the antenna unit spacing;

[0018] Step S1.4: On the basis of the spiral path, superimpose a cross-shaped dense sampling path to form a composite sampling strategy.

[0019] Further, step S2 is specifically as follows:

[0020] Step S2.1: Set the probe tilt angle to 0°, 15°, and 30°, and collect phase data for each sampling point;

[0021] Step S2.2: For each sampling point, perform phase measurement at five frequency points of working frequency f0 and f0±5%, f0±10%;

[0022] Step S2.3: Collect 10 times of data under each measurement condition, use median filter to remove outliers, and then calculate the average value as the phase measurement value of the point;

[0023] S2.4: Use the phase continuity of adjacent points to perform phase unwrapping processing to eliminate the 2π ambiguity.

[0024] Further, step S3 is specifically as follows:

[0025] 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 indexes, θ is the probe angle, and f is the measurement frequency;

[0026] Step S3.2: Calculate the credibility weight of each phase difference based on the signal-to-noise ratio SNR(i,j,θ,f), and the formula is as follows:

[0027] ;

[0028] : the normalized weight of the adjacent sampling point pair ( ) under the probe angle and the frequency

[0029] : the signal-to-noise ratio of the adjacent sampling point pair ( ) under the probe angle and the frequency

[0030] : the index number of the first sampling point

[0031] : the index number of the second sampling point (adjacent to )

[0032] θ: probe tilt angle (value: 0°, 15°, 30°)

[0033] : measurement frequency (value: , ±5%, ±10%);

[0034] Step S3.3: Considering the influence of the probe angle on the measurement accuracy, an angle correction factor is introduced, and the formula is as follows:

[0035] α(θ) = cos(θ) × (1 + 0.1×sin²(θ));

[0036] α(θ) the correction factor corresponding to the probe tilt angle θ ​​

[0037] Step S3.4: Calculate the weighted fused phase difference, formula as follows:

[0038] ;

[0039] : fused phase difference of adjacent sampling point pair ;

[0040] : original phase difference of adjacent sampling point pair at probe angle and frequency .

[0041] Further, step S4 is specifically as follows:

[0042] Step S4.1: Establish overdetermined equation set, express phase difference-distance relationship of all adjacent point pairs as:

[0043] ;

[0044] Wherein λ: working wavelength

[0045] , : horizontal and vertical coordinates of the i-th antenna unit ;

[0046] , : horizontal and vertical coordinates of the i-th antenna unit ;

[0047] : horizontal beam pointing angle

[0048] : vertical beam pointing angle

[0049] Step S4.2: Solve initial estimated value of antenna unit coordinates by using weighted least square method;

[0050] Step S4.3: Based on initial coordinates, back-calculate theoretical phase difference, compare with measured phase difference, and identify abnormal measurement points;

[0051] Step S4.4: After removing abnormal points, perform second round of least square optimization to obtain accurate coordinates.

[0052] Further, step S5 is specifically as follows:

[0053] Step S5.1: Establish temperature-phase shift model: Wherein β is temperature coefficient, which is obtained by experiment calibration,

[0054] : phase shift caused by temperature change;

[0055] T: current ambient temperature;

[0056] : reference temperature or initial temperature;

[0057] Step S5.2: Monitor temperature changes during measurement, real-time compensate phase shift caused by temperature;

[0058] Step S5.3: Use the antenna unit with determined coordinates as reference point, periodically calibrate the system;

[0059] Step S5.4: Use Kalman filtering algorithm, fuse historical measurement data and current measurement value, improve coordinate estimation accuracy.

[0060] Further, the spiral sampling path in S1.3 is specifically designed as:

[0061] Spiral equation: r = a + b × θ, where a is the initial radius and b is the pitch coefficient; adaptively adjust the spiral parameters according to the size of the antenna array to ensure coverage of the entire region of interest; sample on the spiral line at equal intervals of arc length, with an interval of d / 2; spiral sampling can effectively avoid aliasing effects caused by periodic sampling.

[0062] Further, it also includes a measurement uncertainty evaluation step:

[0063] Based on the GUM (Guide to the Evaluation of Measurement Uncertainty) method to evaluate each error source; consider type A uncertainty (statistical method) and type B uncertainty (non-statistical method); calculate the combined standard uncertainty and expanded uncertainty; provide confidence intervals for each coordinate measurement result.

[0064] Further, it also includes a data traceability and quality assurance step:

[0065] Record complete measurement process data, including time stamp, environmental parameters, equipment status, etc.; establish block chain storage of measurement data to ensure data cannot be tampered with; generate measurement reports that meet ISO / IEC 17025 standards; support complete reproduction and verification of the measurement process.

[0066] Further, the S3 step also includes phase gradient consistency verification:

[0067] Calculate the phase gradient field ∇φ(x,y) in the local area; check if the curl of the gradient field is close to zero, i.e. verify ∇×∇φ ≈ 0; for areas with abnormal curl, increase the sampling density and re-measure; use the continuity constraint of the phase gradient to improve the reliability of coordinate determination.

[0068] Further, the S4 step further comprises constraint optimization:

[0069] Introducing the prior constraint of antenna element spacing: |d measured - d design |<0.1×d design ; Adding array regularity constraints: adjacent rows / columns of antenna elements should maintain a straight-line arrangement; using a least squares algorithm with constraints to ensure the physical reasonableness of the solution; for solutions that do not meet the constraints, triggering a re-measurement mechanism.

[0070] The system implementing the above-mentioned phased array radar antenna element coordinate determination method of multi-path fusion includes an intelligent probe head 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.

[0071] The intelligent probe head module includes:

[0072] A broadband dual-polarized probe with a working frequency covering 1-40GHz; a built-in three-axis angle sensor for real-time monitoring of probe attitude; an integrated temperature sensor with a measurement accuracy of ±0.1℃; a programmable gain amplifier with a dynamic range of 80dB;

[0073] The high-precision mechanical scanning platform includes:

[0074] A five-axis linkage mechanical arm with a repeat positioning accuracy of ±0.05mm; a maximum scanning range of 3m×3m×1m; an integrated laser range finder for real-time measurement of the distance between the probe and the array surface; a vibration-proof design with a vibration amplitude of <0.01mm during operation;

[0075] The multi-channel phase measurement module includes:

[0076] A parallel data acquisition system based on FPGA; a 16-bit ADC with a sampling rate of 1GSps; real-time FFT processing capability with a delay of <1ms; phase measurement accuracy of ±0.1°;

[0077] The intelligent data processing and analysis module includes:

[0078] An embedded GPU computing platform supporting parallel algorithm acceleration; an adaptive filter bank that can automatically select filter parameters according to signal characteristics; a machine learning algorithm library containing support vector machines, random forests, and other algorithms; a real-time data visualization interface supporting 3D display;

[0079] The system integration and control module includes:

[0080] A unified hardware abstraction layer supporting measurement devices from different manufacturers; a state machine-based measurement process control; a fault diagnosis and self-recovery mechanism; a remote monitoring interface supporting networked operation.

[0081] Further, the intelligent probe head module further comprises:

[0082] Near-field / far-field automatic switching function, automatically select the working mode according to the measurement distance; Polarization adjustable function, support linear polarization, circular polarization measurement; Built-in calibration source, self-calibration can be carried out; Electromagnetic shielding design, suppress external interference > 60dB.

[0083] Further comprising a batch antenna unit rapid positioning step:

[0084] Based on the accurate positioning result of the first antenna unit, combined with the design parameters of the antenna array; Adopt template matching algorithm, quickly locate the approximate position of the remaining antenna units; Local fine measurement is carried out for each predicted position, and the number of sampling points is reduced to 5; Through parallel processing, multiple antenna units are measured at the same time, and the efficiency is improved by more than 10 times.

[0085] Further, it further comprises an environment adaptation module:

[0086] Atmospheric pressure compensation unit: correct the electromagnetic wave propagation speed according to the change of atmospheric pressure; Humidity compensation unit: consider the influence of humidity on dielectric constant; Electromagnetic environment monitoring unit: real-time detection of background electromagnetic noise level; Adaptive working parameter adjustment: optimize the measurement parameters according to the environmental conditions.

[0087] Compared with the prior art, the beneficial effects of the present application are:

[0088] 1. The application provides a multi-path fusion phased array radar antenna unit coordinate determination method and system, which adopts a fusion strategy of multiple sampling paths such as cross-shaped, Chinese character-shaped and ring-shaped, intelligently fuses the measurement results of different paths through a weighted standard deviation formula, and effectively suppresses the random error and system deviation in single path measurement. After weight distribution optimization of cross-shaped 40%, Chinese character-shaped 35% and ring-shaped 25%, the final coordinate measurement accuracy reaches ±0.3mm (95% confidence).

[0089] 2. The application provides a multi-path fusion phased array radar antenna unit coordinate determination method and system, which can effectively identify and suppress environmental interference through a multi-angle (0°, 15°, 30°) and multi-frequency redundant measurement strategy, combined with an adaptive weighting algorithm based on signal-to-noise ratio. Even in complex electromagnetic environment, the system can still maintain stable measurement accuracy, and the interference suppression ability is improved by more than 60dB.

[0090] 3. The application provides a multi-path fused phased array radar antenna element coordinate determination method and system, which introduces an intelligent prediction algorithm based on an LSTM neural network and a genetic algorithm parameter optimization, and can automatically select optimal measurement parameters according to the antenna type and environmental conditions. In the batch measurement mode, the reference information of the determined coordinate elements can be used to realize efficiency improvement. The parallel data acquisition capability of the 4x1 linear phased array probe enables the acquisition of phase information at four different angles in a single measurement, greatly shortening the measurement time.

[0091] 4. The application provides a multi-path fused phased array radar antenna element coordinate determination method and system, which establishes a perfect temperature-phase shift compensation model, combines real-time environmental monitoring and Kalman filtering algorithm, and can dynamically compensate the measurement drift caused by environmental factors such as temperature, humidity and air pressure. The strategy of combining physical model and neural network residual compensation ensures the measurement stability under various working conditions and expands the environmental adaptation range.

[0092] 5. The application provides a multi-path fused phased array radar antenna element coordinate determination method and system, which has a modular hardware architecture and a unified software interface, supports 5G / WiFi dual-mode communication and cloud data processing, and has remote monitoring and expert diagnosis capabilities. The system fault self-diagnosis and self-recovery mechanism greatly reduces the maintenance cost and operation complexity. BRIEF DESCRIPTION OF DRAWINGS

[0093] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the following will briefly introduce the drawings needed to be used in the specific embodiments or prior art description. Obviously, the drawings described below are some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0094] Figure 1 is a flowchart of the present application DETAILED DESCRIPTION

[0095] The technical solutions of the present application will be described more clearly and completely by combining the drawings and the description of the preferred embodiments of the present application.

[0096] As a specific embodiment, first, an initial scan is performed to determine the approximate center region of the antenna array. Unlike the traditional power peak search, this method calculates the power gradient field:

[0097] ;

[0098] : power value;

[0099] : power gradient vector;

[0100] , : spatial coordinates;

[0101] From multiple random starting points, the tracking path is:

[0102] ;

[0103] where r(t) is the position vector at time t, and α is the step size parameter (typical value 0.1-0.5). When the gradient modulus |∇P| < ε, stop tracking, and use the DBSCAN clustering algorithm to cluster all convergent points. The center of the largest class is determined as the array center. This method has stronger anti-noise ability than traditional peak search.

[0104] After the center is determined, the sampling points are arranged according to the adaptive spacing. The sampling point position in the X-axis direction is:

[0105] ;

[0106] : the first sampling point coordinate;

[0107] : array center coordinate;

[0108] : basic spacing;

[0109] : total number of sampling points;

[0110] The Y-axis direction is similar, so that the center area is densely sampled, and the edge area is sparsely sampled, which improves the efficiency while ensuring the measurement accuracy.

[0111] The frequency point selection uses an optimization algorithm based on information entropy. Define the information gain of each frequency point as:

[0112] ;

[0113] where is the signal-to-noise ratio of the frequency point , and is the phase stability index. Select M frequency points through the greedy algorithm to maximize the total information entropy of the selected frequency point set. Ensure that the selected frequency points have the maximum amount of information, avoiding the problem of missing optimal frequency points that may occur in traditional equal-interval selection.

[0114] The phase difference calculation adopts the iterative phase unwrapping algorithm, and the phase jump point is identified by calculating the closed path integral ∮Δφ·dl to ensure the continuity of the phase difference. For multi-frequency point data, an improved dispersion model is established:

[0115] ;

[0116] where is the phase difference at frequency , A is the main propagation term (proportional to distance), B is the dispersion term (reflecting the dispersion characteristics of the medium), C is the constant term (systematic deviation), and D is the high-order term (nonlinear effect). The weighted total least squares method is used for fitting, considering the frequency measurement error and phase measurement error, and the objective function is:

[0117]

[0118] The weight ;

[0119] where, is the weight of the th data point;

[0120] is the uncertainty of the th phase measurement;

[0121] is the uncertainty of the th frequency measurement;

[0122] is the th measured phase difference;

[0123] is the phase difference predicted by the model;

[0124] is the balance factor;

[0125] is the frequency measurement value.

[0126] The environmental compensation adopts a method combining physical models and neural network residual compensation. The physical model includes compensation formulas for temperature, humidity, and air pressure, and the neural network is used to learn the nonlinear relationship that the physical model fails to capture. The total compensation amount is:

[0127]

[0128] where, is the temperature compensation term;

[0129] is the humidity compensation term;

[0130] : air pressure compensation term;

[0131] : neural network residual compensation term;

[0132] The weights w1, w2 are adaptively adjusted according to historical prediction errors, realizing optimal fusion of the physical model and the data-driven model.

[0133] 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 the Sigma point sampling is used to handle the nonlinear propagation. The innovation v k = Z k - Ẑ k The covariance matrices of the process noise Q and the measurement noise R are dynamically updated, where v k : innovation vector at the kth moment;

[0134] Z k : observation value at the kth moment;

[0135] Ẑ k : predicted value at the kth moment.

[0136] The X, Y plane coordinate calculation uses a multi-dimensional phase difference joint solving 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 of the i, j sampling point at the k frequency. Through CP decomposition:

[0137]

[0138] where ⊗ represents the outer product, the aᵣ, bᵣ vectors contain spatial coordinate information, the cᵣ vector corresponds to the frequency response characteristics, and λᵣ is the decomposition coefficient. This method fully utilizes the internal structure of multi-frequency point data, improving the accuracy and robustness of coordinate solving.

[0139] The calculation of the depth information Z utilizes the frequency-dependent characteristics of the electromagnetic wave penetration through the radome. First, the penetration phase is extracted:

[0140] ;

[0141] : penetration phase

[0142] : total phase

[0143] c: speed of light

[0144] Then, spectral analysis is performed. For After FFT transformation, the peak position k peak The relationship with depth is:

[0145]

[0146] Where c is the speed of light, Z is the depth value, and εᵣ is the relative permittivity of the radome material. If there are multiple significant peaks in the spectrum, indicating the presence of multiple layers, the depth resolution can be improved by the MUSIC algorithm.

[0147] Machine learning uses a physics-informed neural network (PINN), which adds physical constraints to the traditional neural network. The loss function is designed as:

[0148] ;

[0149] Where is the data fitting loss, and the physical constraint loss ensures that the phase field satisfies the irrotational condition (physical law), and the smoothness loss ensures the smoothness of the solution. is the weight coefficient, is the curl operator.

[0150] The network input includes 115 features such as phase difference characteristics, environmental parameters, and geometric parameters, and the output is three-dimensional coordinates [x, y, z].

[0151] Verification uses a combination of multi-path measurement and Bayesian optimization strategy. Four measurement paths are designed: cross shape (basic path), Chinese character shape (increasing diagonal direction), Archimedes spiral (continuous coverage), and random walk (Monte Carlo verification).

[0152] Bayesian optimization is used for intelligent selection of verification 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:

[0153] ;

[0154] Where κ is the exploration-exploitation balance parameter, and σ(x) is the predicted standard deviation. The next verification point is selected by maximizing the acquisition function, realizing an efficient verification strategy.

[0155] Consistency determination uses Hausdorff distance to measure the difference between different path measurement results. When d H exceeds the preset threshold (typical value 0.5mm), the system automatically increases the sampling density in the area with large differences and re-measures to ensure the reliability of the final results.

[0156] The smart probe array adopts a 4x1 linear phased array configuration, with four receiving units arranged at equal intervals with a spacing of 0.5λ at the center frequency. Each unit independently receives signals and achieves electronic scanning of the beam through phase control.

[0157] During operation, the central processing unit sends phase control instructions to the four receiving units to form a receiving beam pointing in a specific direction. By rapidly switching different phase configurations, beam scanning can be achieved within a range of ±60°, with a scanning speed of 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.

[0158] Multi-directional simultaneous reception is achieved through digital beamforming technology. After digitizing the four-way receiving signals, parallel processing is performed in the FPGA to simultaneously form four receiving beams pointing in different directions. This design allows multiple angle phase information to be obtained in a single measurement, with a measurement efficiency improvement of more than 4 times compared to traditional single-probe systems.

[0159] The signal processing uses an adaptive beamforming algorithm that automatically adjusts the weighting coefficients of each channel based on the signal-to-noise ratio of the received signal, suppressing interference and enhancing target signals. When strong interference is detected, the system automatically forms a null in that direction, with a depth of up to -40dB.

[0160] The input feature engineering of the long short-term memory network first preprocesses the original data. The historical measurement data takes the phase difference sequence of the last 50 measurements, and the time series features are extracted through a sliding window. The environmental parameters include the current values and change rates of temperature, humidity, and air pressure. The antenna type is represented by one-hot encoding, supporting 8 common phased array types. The operating frequency is normalized to the [0, 1] interval.

[0161] The network architecture contains two layers of LSTM units, with 128 hidden units in the first layer and 64 hidden units in the second layer. The state update of each LSTM unit follows the standard formula, but an adaptive mechanism is introduced in the forget gate to dynamically adjust based on the change rate of the input data, allowing the network to better adapt to different measurement scenarios.

[0162] The training process uses a phased strategy. First, use simulation data for pre-training to establish basic coordinate prediction capabilities. Then fine-tune using real measurement data, with at least 1000 labeled data sets for each antenna type. The loss function includes not only mean squared error but also a physical consistency constraint to ensure that the predicted coordinates meet the geometric rules of the antenna array.

[0163] During inference, the network not only outputs coordinate prediction values but also outputs confidence scores. When the confidence is below a threshold, the system automatically switches to a traditional algorithm or requests manual confirmation to ensure the reliability of the measurement.

[0164] Batch measurement first establishes a reference coordinate system by precisely measuring the first antenna element. According to the antenna design parameters (element spacing, arrangement), the theoretical positions of the remaining elements are predicted using affine transformation. Considering manufacturing and installation errors, a search area of ±10% is defined around each theoretical position.

[0165] Path planning adopts an improved Traveling Salesman Algorithm, aiming to minimize the total measurement time. The algorithm takes into account the kinematic constraints of the robotic arm, acceleration limits, and obstacle avoidance requirements. By dynamic programming, the large array is decomposed into multiple sub-regions, each using a serpentine scanning path within and the shortest path between sub-regions.

[0166] Parallel measurement is achieved by deploying multiple independent probe modules. The main control system divides the antenna array into multiple non-overlapping measurement regions and assigns tasks to each probe. Probes maintain at least 2 meters apart to avoid mutual interference. Real-time communication protocols ensure the synchronization of measurement progress among probes, and when a probe completes its task, it automatically assists other probes.

[0167] The database adopts a distributed architecture, containing fields such as antenna element ID, three-dimensional coordinates, measurement time, environmental parameters, and measurement uncertainty. Spatial indexing supports fast proximity queries. Historical data is used to train prediction models and detect anomalies, and when a unit's coordinates deviate from the historical mean by more than 3σ, it is automatically marked as a potential fault point.

[0168] The cross-shaped path densely samples along the rows and columns where the antenna elements are located, with a sampling interval of d / 4. The herringbone path adds two diagonal lines at 45° and 135° based on the cross. The ring path samples from the antenna element as the center, with a radius from 0.5d to 2d concentric circles. Each path calculates the antenna element coordinates independently.

[0169] The standard deviation calculation uses a weighted method, considering the number of measurement points and coverage of different paths. The weight distribution is: cross 40%, herringbone 35%, ring 25%. The calculation formula is:

[0170]

[0171] where is the weight of each path, is the measurement result of each path, is the weighted average value, n is the total number of paths;

[0172] When the standard deviation exceeds 0.5mm, adaptive encrypted measurement is started. The system analyzes the difference pattern of each path result 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, check whether there are metal obstacles or strong reflectors in this area, and adjust the probe angle or measurement power if necessary.

[0173] The verification results are displayed in real time through a visual interface, with different colors representing the measurement results of different paths, and red highlights for points with deviations exceeding the limit. The system automatically generates a verification report, including detailed data, statistical analysis, and improvement suggestions for each path.

[0174] As a specific implementation, the remote monitoring module is implemented as follows: 5G / WiFi dual-mode communication ensures reliable connection in different environments. The 5G module supports SA / NSA dual-mode, and preferentially uses the low-latency URLLC slice. The WiFi module supports the 802.11ax standard, providing stable high-speed connection in indoor environments. The communication protocol uses MQTT to ensure the reliability and real-time nature of data transmission.

[0175] Data transmission adopts a hierarchical strategy. Critical data (coordinates, abnormal alarms) are transmitted in real time with a delay of less than 100 ms. Raw phase data is compressed and transmitted in batches, with the compression algorithm optimized for phase data characteristics, achieving a compression ratio of up to 10:1. Video streams are encoded using H.265, with the code rate adaptively adjusted according to network bandwidth.

[0176] The remote expert system is based on a knowledge graph and contains professional knowledge such as antenna fault diagnosis and measurement anomaly analysis. When an anomaly is detected, the system automatically matches similar cases and generates preliminary diagnosis suggestions. Experts can remotely view the on-site situation through AR glasses and mark the problem areas on the three-dimensional model to guide on-site operations.

[0177] Cloud storage uses object storage services, and data is organized by project, date, and antenna type. Cold and hot data separation is implemented, with recent data saved in high-speed storage and historical data migrated to low-cost storage. The data analysis platform supports SQL queries and machine learning tasks, enabling cross-project big data analysis to identify common problems and optimization opportunities.

[0178] As a specific implementation, the adaptive parameter optimization is implemented as follows: adaptive sampling interval adjustment based on spatial spectrum analysis of antenna arrays. First, coarse sampling is performed to calculate the spatial spectrum density. In areas with intense spectral changes (such as array edges and defect locations), the sampling interval is automatically reduced to d / 4, and in uniform areas, it is increased to 2d. The dynamic range is limited to [d / 4, 2d] to balance accuracy and efficiency.

[0179] Measurement power is adjusted according to real-time signal-to-noise ratio. The system maintains a power-signal-to-noise ratio lookup table, aiming to keep SNR in the range of 40-50 dB. When environmental electromagnetic noise increases, the transmission power is automatically increased, but not exceeding the regulatory limit. The integration time is inversely proportional to the signal-to-noise ratio, ensuring that the standard deviation of phase measurement is less than 0.5°.

[0180] The genetic algorithm optimizes a population of 20 individuals, each encoding includes: sampling interval, measurement power, integration time, frequency selection, filtering parameters, etc. The fitness function considers the measurement accuracy (60% weight), measurement time (30% weight) and energy consumption (10% weight).

[0181] The evolution process adopts the elite reservation strategy, and the best 2 individuals are directly inherited to the next generation. The crossover operation uses uniform crossover with a crossover probability of 0.8. The mutation operation adopts adaptive mutation rate, which is dynamically adjusted according to population diversity. After each generation evolution, the parameters of the optimal individual are applied to the actual measurement, and the fitness evaluation is updated according to the measurement results.

[0182] Through 20-30 generations of evolution, the system can find the optimal parameter combination suitable for the current antenna type and environmental conditions, and compared with fixed parameters, the measurement efficiency is improved by more than 30%, while maintaining sub-millimeter level measurement accuracy.

[0183] As a specific implementation, the method starts with a comprehensive initialization of the system. The intelligent probe array (linear phased array of 4 receiving units) is installed on the mechanical arm, and the spacing between each receiving unit is set to 0.5λ center frequency. Start the system self-checking program to ensure that all hardware modules are working properly.

[0184] According to the type of phased array to be measured, the system automatically downloads the corresponding prior knowledge from the cloud database, including typical unit spacing, operating frequency range and other parameters. These parameters are input into the LSTM neural network, and the network predicts the optimal initial measurement parameters based on historical measurement data. At the same time, the genetic algorithm starts running in the background, preparing to optimize the measurement parameters in real time.

[0185] The environmental perception module starts working, collecting current temperature, humidity, and air pressure data to establish an environmental baseline. The remote monitoring module establishes a connection with the cloud through 5G / WiFi, ensuring that data can be transmitted in real time and experts can intervene remotely.

[0186] The mechanical arm drives the probe array to perform a wide-range coarse scan about 1 meter away from the antenna array. The 4 receiving units of the probe array work simultaneously, forming 4 different receiving beams through digital beamforming technology, covering a range of ±60°. This parallel reception greatly improves the scanning efficiency.

[0187] During the scanning process, the system calculates the power distribution P(i,j) and the power gradient field ∇P in real time. The gradient flow tracking algorithm is used to track from multiple starting points simultaneously, and stops when the gradient modulus is less than the threshold value. The convergence points of all tracking paths are clustered through DBSCAN to determine the geometric center of the array.

[0188] Based on the identified center position and array boundary, the system automatically plans the subsequent fine measurement path. The main path adopts a spiral shape, on which a cross-shaped dense sampling path is superimposed. The genetic algorithm adjusts the initial value of the sampling interval d according to the coarse scanning results.

[0189] The probe array moves to a near-field position at a distance of λ / 2π from the array surface, and fine measurement begins. At each sampling point, the system first performs a frequency band quality assessment to calculate the signal-to-noise ratio and phase stability of each frequency point. Based on the information entropy optimization algorithm, M optimal frequency points are selected to ensure that the collected data has the maximum amount of information.

[0190] The 4 units of the intelligent probe array collect data at 0°, 15°, and 30° angles, respectively, and measure 10 times at the selected M frequency points for each angle. The LSTM network processes these data in real time to predict the most likely phase value at the next sampling point, which is used to verify the rationality of the measurement.

[0191] Environmental compensation is carried out synchronously. The physical model calculates the phase drift caused by temperature, humidity, and air pressure based on real-time environmental parameters, and the neural network compensates for nonlinear effects that the physical model fails to capture. The compensated phase data is further optimized through adaptive unscented Kalman filtering, and the noise parameters of the filter are dynamically adjusted based on the innovation.

[0192] During the measurement process, the genetic algorithm continuously optimizes the parameters. After completing the measurement of a region, the algorithm evaluates the measurement quality and updates the population, gradually converging to the optimal parameter combination. Regions with low signal-to-noise ratio automatically increase the measurement power and integration time, while high-quality regions speed up the measurement.

[0193] The multi-frequency point phase data of all sampling points form a third-order tensor T. Through CP decomposition, spatial coordinate information and frequency response characteristics are extracted, and an overdetermined equation system is established to solve the X and Y coordinates. Depth Z is determined by analyzing the differences in penetration phase at different frequencies, and the peak position after FFT transformation directly corresponds to the depth value.

[0194] After the initial coordinates are determined, the system starts the cross-validation program. In addition to the original spiral path, cross-shaped, hiragana-shaped, and ring-shaped path measurements are additionally performed. The Bayesian optimization algorithm intelligently selects verification points to maximize information acquisition efficiency. The measurement results of different paths are calculated to obtain the weighted standard deviation, and when it exceeds 0.5 mm, the region is automatically encrypted for measurement.

[0195] The physical information neural network (PINN) globally optimizes all measurement data. The network not only fits the measurement data but also ensures that the results meet the physical laws of electromagnetic fields (such as the irrotational nature of the phase field). This physical constraint significantly improves the prediction accuracy in areas with sparse measurement points.

[0196] After the precise coordinates of the first antenna unit are determined, the system enters a high-efficiency batch measurement mode. Based on the antenna design parameters and the measured coordinates, the positions of the remaining units are predicted. A quick verification measurement is conducted within ±10% of the predicted position, requiring only 5 sampling points per unit.

[0197] If multiple probe systems are deployed, the main controller divides the antenna array into multiple regions, and each probe works in parallel. The probes are synchronized through a real-time communication protocol and dynamically adjust task allocation. Probes that have completed tasks automatically assist slower probes.

[0198] All measurement data is transmitted to the cloud in real time, with critical data (coordinate values, anomaly markers) being transmitted first and raw phase data being compressed and uploaded in batches. The cloud database automatically establishes a spatial index to support fast querying and analysis. Anomaly detection algorithms run continuously, and an alarm is automatically triggered when the coordinate deviation exceeds 3σ.

[0199] Remote experts can view real-time measurement status through an AR interface and intervene if necessary. The expert system provides fault diagnosis suggestions based on a knowledge graph, and historical case matching helps quickly solve problems.

[0200] After measurement is complete, the system conducts a comprehensive uncertainty evaluation. All error sources are considered, including measurement repeatability, environmental changes, equipment precision, etc., to calculate the expanded uncertainty of each coordinate. The result is expressed in the form of a confidence interval, with a typical precision of ±0.3mm (95% confidence).

[0201] The generated measurement report contains complete process data: measurement timestamps, environmental parameters, device status, raw data, processing algorithms, final coordinates, uncertainty analysis, etc. All data is saved through blockchain technology to ensure traceability and tamper resistance.

[0202] The LSTM network uses new measurement data for incremental learning, continuously improving prediction accuracy. Genetic algorithms save optimized parameter combinations to the knowledge base as initial parameters for subsequent similar tasks. The entire system becomes increasingly intelligent and efficient through continuous learning.

[0203] In this way, from system initialization to final report generation, a complete and coherent measurement process is formed. The output of each stage is the input of the next stage, together realizing high-precision and high-efficiency antenna unit coordinate measurement.

[0204] As shown in Figure 1 The present application is as follows:

[0205] Step S1: Obtain the antenna array power distribution map by wideband frequency sweeping, identify the array boundary and geometric center, and plan the spiral and cross composite sampling path;

[0206] Step S2: Collect phase data at multiple tilt angles and frequencies on the planned sampling path, and perform filtering and phase unwrapping preprocessing;

[0207] Step S3: Based on the signal-to-noise ratio and angle correction factor, the phase difference of adjacent points under multiple conditions is adaptively weighted and fused to calculate;

[0208] Step S4: Use the fused phase difference to establish an overdetermined equation system, and solve the antenna element accurate coordinates by two rounds of weighted least squares method iteration;

[0209] Step S5: Establish a temperature-phase drift model for dynamic compensation, and use the determined coordinates of the element as a reference point for real-time calibration.

[0210] Specifically includes:

[0211] The entire antenna array reflectivity distribution map is obtained within the range of ±10% of the working frequency through the wideband sweep frequency technology. The reflectivity value of each frequency point is recorded during the sweep process to form a two-dimensional power distribution matrix. The Canny edge detection algorithm is used to process the power distribution map to identify the boundary profile of the antenna array. The morphological opening and closing operation is used to eliminate edge noise and accurately extract the shape profile of the array. The centroid algorithm is used to calculate the geometric center coordinates of the array as the starting reference point for subsequent sampling. Based on the prior knowledge of antenna design, including the element spacing and array size, the sampling density parameters are determined. Starting from the geometric center, the spiral sampling path is planned according to the Archimedes spiral equation. The initial sampling point spacing d is set to 1 / 3 of the antenna element spacing to ensure sufficient spatial resolution. On the basis of the spiral path, a cross-shaped dense sampling path is superimposed, and the cross line passes through the array center and extends to the boundary. The composite sampling strategy ensures high-density sampling in key areas and full-array coverage. The generated sampling point coordinate sequence will be used as the measurement position input for the next step.

[0212] According to the sampling path planned above, the probe is moved to each sampling point for measurement. The probe inclination angle is set to 0°, 15°, 30° in turn to obtain the phase response under different incident angles. Under each angle, phase measurement is performed at the working frequency f0and f0±5%, f0±10% for a total of 5 frequency points. This multi-frequency measurement strategy improves the robustness and anti-interference ability of phase measurement. 10 times of data are continuously collected under each measurement condition to form a data set. The median filtering algorithm is used to identify and eliminate outliers, effectively suppressing random noise. The arithmetic mean of the filtered data is calculated as the phase value under the measurement condition. A three-dimensional matrix of phase data φ(x, y, θ, f) is established to store the multi-condition phase data of all sampling points. Using the continuity constraint of adjacent sampling points, two-dimensional phase unwrapping processing is performed. The unwrapping algorithm uses a quality map guided path tracking method to expand from high quality areas to low quality areas. After eliminating the 2π phase ambiguity, the continuous phase distribution map is obtained. The preprocessed phase data is passed to S3 for phase difference calculation.

[0213] Based on the above phase data, the phase difference between all adjacent sampling points under different measurement conditions is calculated. A four-dimensional phase difference matrix is constructed. At the same time, the signal-to-noise ratio of each measurement is extracted to quantify the measurement quality. According to the signal-to-noise ratio, the normalized reliability weight is calculated. High signal-to-noise ratio measurements are given greater weight, and low signal-to-noise ratio measurements are suppressed. Considering the influence of probe inclination angle on electromagnetic wave propagation path, an angle correction factor is introduced to compensate for the oblique incidence effect. Multiply the reliability weight by the angle correction factor to get the comprehensive weighting coefficient. Weighted sum of phase differences under all measurement conditions to calculate the fused phase difference. The fusion process makes full use of the redundant information of multi-angle and multi-frequency measurement. The weighted fusion strategy adaptively strengthens high-quality measurements and suppresses low-quality measurements. The generated fused phase difference matrix will be the core input for the next step of coordinate solving.

[0214] Using the fused phase difference data of the previous step, a mathematical model for solving the coordinates of the antenna elements is established. According to the phase-space relationship of phased array antennas, the phase difference of each pair of adjacent points satisfies the equation

[0215] ;

[0216] The equations of all adjacent point pairs are combined to form an overdetermined equation set. The number of equations is much larger than the number of unknowns, providing redundancy for solving. Weighted least squares method is used for solving, and the weight matrix is constructed from the signal-to-noise ratio information of the previous step. The initial estimate of the antenna element coordinates is obtained through matrix operations. Based on the initial coordinates, the theoretical phase difference is calculated and compared with the measured phase difference. The residual error is calculated and a threshold is set to identify abnormal point pairs. After removing abnormal point pairs, the equation set is reconstructed for the second round of optimization. The iterative optimization process improves the accuracy and reliability of the coordinate estimation. The output accurate coordinates will be used for the next step of dynamic calibration.

[0217] A mathematical model of temperature-phase drift is established. Through a calibration experiment of controlling temperature change, the value of the temperature coefficient is determined. During the entire measurement process, the change of the environmental temperature is monitored in real time. According to 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 points is measured regularly to detect the drift of the system. Using the drift information of the reference points, the system error of other points to be measured is corrected. The Kalman filtering algorithm is used to establish a dynamic estimation model. The historical measurement data and the current observation value are fused to achieve optimal estimation. The prediction-update mechanism of Kalman filtering effectively suppresses random errors. The results of dynamic compensation can be fed back to all the above steps to form a closed-loop optimization. Real-time calibration ensures the stability and consistency of long-time measurement. Finally, the high-precision antenna element coordinates are output after temperature compensation and dynamic calibration.

[0218] The above specific embodiments only describe the preferred embodiments of the present application, and do not limit the protection scope of the present application. Without departing from the design concept and spirit of the present application, various modifications, substitutions and improvements of the technical solutions of the present application made by those skilled in the art according to the description and drawings provided by the present application should all belong to the protection scope of the present application. The protection scope of the present application is determined by the claims.

Claims

1. A method for determining the coordinates of a phased array radar antenna element in a multipath environment, characterized in that The method comprises the following steps: Step S1: Obtain an antenna array surface power distribution map by wideband frequency sweeping, identify the array boundary and geometric center, and plan a spiral and cross composite sampling path; Step S2: Collect phase data at multiple tilt angles and frequencies on the planned sampling path, and perform filtering and phase unwrapping preprocessing; Step S3: Based on the signal-to-noise ratio and the angle correction factor, the phase differences of adjacent points under different probe tilt angles and measurement frequencies are adaptively weighted and fused; Step S4: Using the fused phase difference of adjacent points, according to the linear relationship between the phase difference and the spatial distance between the antenna elements, the over-determined equation set is established by combining the equations of all adjacent point pairs, and the accurate coordinates of the antenna elements are iteratively solved by two rounds of weighted least squares method; Step S5: Establish a temperature-phase shift model for dynamic compensation, and use the determined coordinates of the elements as reference points for real-time calibration.

2. The multipath-fused phased-array radar antenna element coordinate determination method of claim 1, wherein, Step S1 is as follows: Step S1.1: Obtain the reflected power distribution map of the entire antenna array by wideband frequency sweeping, and identify the boundary profile of the antenna array; Step S1.2: Perform edge detection and morphological analysis on the power distribution map using image processing algorithms to automatically identify the geometric center region of the antenna array; Step S1.3: Based on the prior knowledge of antenna design, including element spacing and array size, a spiral sampling path is planned around the center region, and the sampling point spacing dinitial is 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 of claim 1, wherein, Step S2 is as follows: Step S2.1: Set the probe tilt angle to 0°, 15°, and 30°, and collect phase data for each sampling point; Step S2.2: For each sampling point, phase measurements are made at five frequencies , ± 5% and ± 10% Step S2.3: Collect 10 sets of data under each measurement condition, remove outliers using median filtering, and then calculate the average value as the phase measurement value of the point; Step S2.4: Use the phase continuity of adjacent points to perform phase unwrapping processing to eliminate 2π ambiguity.

4. The method of claim 1, wherein, Step S3 is as follows: Step S3.1: Calculate the phase difference matrix Δφ for neighboring sample points under different measurement conditions, where is the sample point index, θ is the probe tilt angle, is the measurement frequency; Step S3.2: Based on the signal-to-noise ratio SNR(i,j,θ,f), the reliability weight of each phase difference is calculated, and the formula is as follows: ； : Normalized weights of adjacent sample point pairs ) at probe tilt angle and frequency ​ : signal-to-noise ratio of adjacent sample pairs ) at the probe tilt angle and frequency ​ : index number of the first sample point; : index number of the second sampling point; θ: probe tilt angle; : measurement frequency; Step S3.3: Considering the influence of probe tilt angle on measurement accuracy, an angle correction factor is introduced, and the formula is as follows: 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 weighted fused phase difference, and the formula is as follows: ； : pairs of adjacent sample points : fused phase difference; : pairs of adjacent samples at the probe tilt angle and frequency under the original phase difference.

5. The method of claim 1, wherein, Step S4 is as follows: Step S4.1: Establish an over-determined equation set, and express the phase difference-distance relationship of all adjacent point pairs as: ； wherein λ: working wavelength; , : No. The horizontal and vertical coordinates of each antenna element; , : No. The horizontal and vertical coordinates of each antenna element; : horizontal beam pointing angle; : vertical beam pointing angle; Step S4.2: Use the weighted least squares method to solve the initial estimate value of the antenna element coordinates; Step S4.3: Based on the initial coordinates, the theoretical phase difference is calculated, compared with the measured phase difference, and the abnormal measurement points are identified; Step S4.4: After removing the abnormal points, the second round of least squares optimization is performed to obtain the accurate coordinates.

6. The multipath-fused phased-array radar antenna element coordinate determination method of claim 1, wherein, Step S5 is as follows: Step S5.1: Establishing a temperature-phase drift model: where β is the temperature coefficient, obtained by experimental calibration, : amount of phase drift due to temperature change; T: current environmental temperature; : reference or initial temperature; Step S5.2: Monitor the temperature change during the measurement process, and compensate the phase drift caused by temperature in real time; Step S5.3: Use the antenna element with the determined coordinates as the reference point, and periodically calibrate the system; Step S5.4: Use Kalman filter algorithm to fuse historical measurement data and current measurement value, and improve the coordinate estimation accuracy.

7. The method of claim 2, wherein, The spiral sampling path in step S1.3 is specifically designed as: Spiral equation: r = a + b × θ, where a is the initial radius and b is the pitch coefficient; Adaptively adjust the spiral parameters according to the size of the antenna array to ensure coverage of the entire region of interest; Sample on the spiral line at equal intervals of arc length, with an interval of d / 2; Spiral sampling can effectively avoid the aliasing effect caused by periodic sampling.

8. The multipath-fused phased-array radar antenna element coordinate determination method of claim 1, wherein, The step S3 also includes phase gradient consistency test: Calculate the phase gradient field ∇φ(x,y) in the local area; test whether the curl of the gradient field is close to zero, i.e. verify ∇×∇φ ≈ 0; for the area with abnormal curl, increase the sampling density and re-measure; use the continuity constraint of phase gradient to improve the reliability of coordinate determination.

9. The multipath-fused phased-array radar antenna element coordinate determination method of claim 1, wherein, The 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 maintain straight alignment; Employ a least squares algorithm with constraints to ensure physical reasonableness of the solution; Trigger a re-measurement mechanism for solutions that do not satisfy the constraints.

10. A system for implementing the method of determining the coordinates of the elements of a phased array radar antenna with multipath fusion according to any one of claims 1-9, characterized in that, It includes intelligent probe head module, high-precision mechanical scanning platform, multi-channel phase measurement module, intelligent data processing and analysis module, and system integration and control module; The intelligent probe head module includes: Broadband dual-polarized probe, working frequency covering 1-40GHz; Built-in three-axis angle sensor, real-time monitoring of probe attitude; Integrated temperature sensor, measurement accuracy ±0.1℃; Programmable gain amplifier, dynamic range 80dB; The high-precision mechanical scanning platform includes: Five-axis linkage mechanical arm, repeat positioning accuracy ±0.05mm; Maximum scanning range: 3m × 3m × 1m; Integrated laser range finder, real-time measurement of probe and array distance; Anti-vibration design, vibration amplitude <0.01mm during work; The multi-channel phase measurement module includes: Parallel data acquisition system based on FPGA; 16-bit ADC, sampling rate 1GSps; Real-time FFT processing capability, delay <1ms; Phase measurement accuracy ±0.1°; The intelligent data processing and analysis module includes: Embedded GPU computing platform, supporting parallel algorithm acceleration; Adaptive filter bank, automatically selecting filter parameters according to signal characteristics; Machine learning algorithm library, including support vector machine, random forest and other algorithms; Real-time data visualization interface, supporting 3D display; The system integration and control module includes: Unified hardware abstraction layer, supporting measurement devices from different manufacturers; State machine-based measurement process control; Fault diagnosis and self-recovery mechanism; Remote monitoring interface, supporting networked operation.

Images