Correlation interferometer direction finding method based on AI correlation error compensation

Abstract

The invention discloses a correlation interferometer direction finding method based on AI correlation error compensation, and relates to the technical field of direction finding positioning, the distortion characteristic of a phase difference in an unsteady state error stage is described through a nonlinear mapping element, double-layer error suppression is generated in combination with an AI error compensation network, the double-layer error suppression is fused with a correlation interferometer matching process, and the direction finding positioning accuracy is improved. And constructing a phase difference-direction conjoint analysis framework, establishing a dynamic calibration knowledge base in the phase difference-direction conjoint analysis framework, and performing direction estimation evolution simulation on the phase difference data containing the random error based on the phase difference-direction conjoint analysis framework to obtain a direction-finding panoramic map. According to the direction finding method, the robustness and the precision of a correlation interferometer direction finding system in multipath, noise and unsteady state error environments are remarkably enhanced, full-process intelligent optimization from error perception, suppression to direction estimation is realized, and efficient and reliable technical support is provided for high-precision direction finding in a complex electromagnetic environment.

Description

Technical Field

[0001] This invention relates to the field of direction finding and positioning technology, specifically to a correlation interferometer direction finding method based on AI-related error compensation. Background Technology

[0002] In the field of radio monitoring and target localization, interferometer direction finding technology is widely used in electronic reconnaissance, spectrum management and target detection due to its advantages such as relatively simple structure and fast response speed.

[0003] However, in actual direction finding, factors such as the geometric layout of the antenna array, operating frequency, channel characteristics, and multipath propagation and noise interference in the environment can introduce significant random phase difference errors. Especially in the non-steady-state error stage, the distortion characteristics of the phase difference are complex and difficult to model accurately. Traditional correlation interferometer direction finding methods mostly rely on fixed matching procedures and static error compensation strategies, lacking the ability to finely distinguish the sources of error and adaptively describe the dynamic distortion characteristics. This leads to a decrease in direction finding accuracy, increased ambiguity in direction estimation, and even misjudgment in complex electromagnetic environments.

[0004] Given the special requirements of accurate error suppression and reliable direction estimation in complex scenarios for interferometric direction finding, a direction finding method based on AI-related error compensation needs to be proposed to achieve partitioned perception, dynamic suppression and joint analysis of multi-source errors, so as to improve the performance and reliability of the direction finding system in complex electromagnetic environments. Summary of the Invention

[0005] The purpose of this invention is to provide a correlation interferometer direction finding method based on AI-related error compensation to address the shortcomings in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a correlation interferometer direction finding method based on AI-related error compensation, the direction finding method comprising the following steps: S1: Based on the characteristic parameters of the array and the channel, the error sources faced by the direction finding are divided into significant error region, general error region and low error region. A random phase difference feature space is generated in each error region, and a distributed fuzzy set is established. S2: Based on the random phase difference feature space and distributed fuzzy set, the distortion characteristics of phase difference under the non-steady-state error stage are described by nonlinear mapping element. Combined with AI error compensation network to generate double-layer error suppression, the double-layer error suppression is integrated with the relevant interferometer matching process to construct a phase difference-direction joint analysis framework, and a dynamic calibration knowledge base is established within the phase difference-direction joint analysis framework. S3: Based on the phase difference-direction joint analysis framework, we perform direction estimation evolution simulation on phase difference data containing random errors to obtain a panoramic direction finding map.

[0007] Preferably, the distortion characteristics of the phase difference under the non-steady-state error stage are described by a nonlinear mapping element, and a two-layer error suppression is generated by combining an AI error compensation network, including the following steps: The AI ​​error compensation network takes perturbed phase difference data as input and outputs the corresponding ideal phase difference reference value, learning the implicit mapping relationship from complex perturbed state to ideal state. The real-time acquired scrambled phase difference is first processed by a nonlinear mapping element to extract distortion features, and then fed into an AI error compensation network to complete secondary correction. This achieves the cascade collaboration of the first layer of nonlinear suppression based on statistical features and the second layer of data-driven deep learning suppression, thus generating a two-layer error suppression.

[0008] Preferably, the dual-layer error suppression is integrated with the correlation interferometer matching process to construct a phase difference-direction joint analysis framework, including the following steps: The matching input first undergoes double-layer error suppression to obtain the corrected phase difference, which is then matched with the phase difference-direction template. The matching process synchronously calls the error zone information provided by the random phase difference feature space and the confidence region constraint given by the distributed fuzzy set to perform error weighting correction on the matching scores in different directions; The phase difference-direction joint analysis framework integrates a numerical simulation environment, generates simulated phase difference data according to the set observation conditions, and drives the direction estimation algorithm to perform evolution simulation under multiple sets of conditions. Record the spatial morphology of random phase difference features, AI compensation effect, correlation matching score and its confidence interval as the error intensity and target direction change.

[0009] Preferably, a dynamic calibration knowledge base is established within the phase difference-direction joint analysis framework. The dynamic calibration knowledge base includes: Store ideal phase difference templates with known directions; The sample weights in different error regions are incrementally updated based on the real-time calculation results of the Wasserstein distance: Whenever a new phase difference measurement sample is acquired, its Wasserstein distance with the empirical distribution of the error region is first calculated. If the Wasserstein distance is less than the preset similarity threshold, the weight of the measurement sample in the empirical distribution update is increased; otherwise, the weight is decreased. Record the AI ​​compensation residual distribution, that is, the statistical characteristics of the residual deviation between the phase difference and the ideal value after each compensation, to evaluate the stability and timeliness of the compensation network.

[0010] Preferably, based on the phase difference-direction joint analysis framework, direction estimation evolution simulation is performed on phase difference data containing random errors to obtain a panoramic direction-finding map, including the following steps: Based on the random phase difference feature space, and according to the error zone division and error intensity index corresponding to the current observation conditions, sampling is performed from the phase difference vector cloud in the random phase difference feature space to form phase difference data that simulates the actual measurement. The distortion features under the current error state are extracted by nonlinear mapping elements in the phase difference-direction joint analysis framework, and the phase difference is suppressed by two layers by calling the AI ​​error compensation network to obtain the corrected phase difference; By combining the phase difference correction with the correlation interferometer matching process, the cross-correlation matching score is calculated using a pre-stored ideal phase difference direction template. Record the shift in the center position, the change in dispersion, and the distribution pattern of the phase difference vector cloud before and after double-layer suppression. This is used to evaluate the effect of error suppression on the transformation of random characteristics, calculate the reduction rate of the deviation between the phase difference and the ideal value before and after compensation, and statistically analyze its mean and fluctuation range under different error zones and observation conditions. Save the matching scores and their ranking for each target direction under different observation conditions, analyze the law of score decay as the error intensity increases, and determine the confidence range of the matching score for each direction based on the evaluation results of the distributed fuzzy set and Wasserstein distance. A two-dimensional or three-dimensional map coordinate system is established with the target direction as the horizontal axis and the error intensity or observation condition parameters as the vertical axis. At different coordinate positions, the schematic diagram of the phase difference characteristic distribution, the heat map of the AI ​​compensation effect index, the matching score curve and the confidence interval band map are superimposed.

[0011] Preferably, a random phase difference feature space is generated in each error region, and a distributed fuzzy set is established, including the following steps: Collect measured phase difference data and corresponding ideal phase difference reference values ​​within the error range, calculate the deviation amplitude statistics between the two, and then normalize them to map them into intensity scores in the 0~1 interval; The probability distribution model of phase difference offset is generated by non-parametric estimation method, which is based on the cumulative distribution shape of historical deviation samples. Based on the error intensity index and probability distribution model, a random phase difference feature space is generated. Collect samples of the difference between the actual phase difference measurement and the ideal phase difference reference value to form a prediction deviation sample set; perform kernel density estimation on the prediction deviation sample set to generate an empirical distribution covering the deviation range; Based on the distribution similarity measurement logic of Wasserstein distance, the empirical distribution of the current error region is compared with several predefined standard distributions one by one, and the standard distribution with the smallest Wasserstein distance is selected as the benchmark. Based on the baseline distribution, the phase difference confidence domain boundary at different confidence levels is determined by calculating the cumulative probability deviation between the actual empirical distribution at each quantile and the baseline distribution.

[0012] Preferably, the direction finding panoramic map includes phase difference feature distribution, AI compensation effect, correlation matching score, and confidence interval variation with error and target direction.

[0013] Preferably, the phase difference-direction joint analysis framework performs direction estimation evolution simulation on phase difference data under different observation conditions in a numerical simulation environment, and analyzes the characteristics of random phase difference feature space, AI compensation effect and related matching score as a function of error intensity and target direction.

[0014] Preferably, the dynamic calibration knowledge base stores ideal phase difference templates in known directions, incrementally updates the sample weights in different error zones based on the real-time calculation results of Wasserstein distance, and records the AI ​​compensation residual distribution.

[0015] Preferably, the characteristic parameters of the array and the channel include the antenna array geometry, operating frequency, channel characteristics, and environmental multipath statistical characteristics.

[0016] The technical effects and advantages provided by the present invention in the above technical solution are as follows: 1. This application achieves refined modeling of error characteristics by regionalizing the sources of direction finding errors and constructing a random phase difference feature space and a distributed fuzzy set. On this basis, it uses nonlinear mapping elements to accurately characterize the phase difference distortion law in the unsteady error stage, and combines an AI error compensation network to generate a two-layer error suppression mechanism. It then deeply integrates this mechanism with the relevant interferometer matching process to construct a phase difference-direction joint analysis framework and a dynamic calibration knowledge base, which effectively improves the reliability of phase difference information and the accuracy of direction estimation in complex environments. 2. This application obtains a panoramic direction finding map by simulating the direction estimation evolution of phase difference data containing random errors, overcoming the limitations of traditional methods in terms of strong ambiguity and insufficient adaptability in dynamic error scenarios. It significantly enhances the robustness and accuracy of the correlated interferometer direction finding system in multipath, noisy, and unsteady error environments, achieving intelligent optimization of the entire process from error perception and suppression to direction estimation, providing efficient and reliable technical support for high-precision direction finding in complex electromagnetic environments. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0018] Figure 1 This is a flowchart of the direction finding method of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example: This example provides a correlation interferometer direction finding method based on AI-related error compensation. Please refer to [link to relevant documentation]. Figure 1 As shown, the direction finding method includes the following steps: S1: Based on the key characteristic parameters of the array and channel, including antenna array geometry, operating frequency, channel characteristics, and environmental multipath statistical characteristics, the error sources faced by direction finding are divided into significant error regions (such as channels with severe temperature drift and strong multipath directions), general error regions (slight channel mismatch or background noise), and low error regions (close to ideal calibration conditions). Within each error region, a probability distribution model of error intensity index and phase difference shift is assigned based on historical statistics and real-time monitoring, thereby generating a random phase difference feature space. This space represents the randomness of the error as phase difference vector clouds under different incident directions.

[0021] A prediction bias sample set is constructed using the difference between the actual phase difference and the ideal phase difference, an empirical distribution is generated, and a fuzzy distribution set is established based on the Wasserstein distance. The confidence domain of the phase difference in different error regions is statistically defined, so that the random phase difference feature space retains both randomness and statistical robustness.

[0022] S2: Based on the random phase difference feature space and distributed fuzzy set, a nonlinear mapping element replaces the traditional fixed error suppression strategy to describe the distortion characteristics of phase difference under non-steady-state error stages (such as sudden electromagnetic interference and rapid temperature drift). Simultaneously, an AI error compensation network (learned by a deep network from the perturbed phase difference to the ideal phase difference) is combined to generate a two-layer error suppression from statistics to learning. This two-layer error suppression is integrated with the correlation interferometer matching process to construct a phase difference-direction joint analysis framework. This framework can simulate the direction estimation evolution of phase difference data under different observation conditions in a numerical simulation environment, analyzing the patterns of random phase difference feature space, AI compensation effect, and correlation matching score as a function of error intensity and target direction.

[0023] Within the phase difference-direction joint analysis framework, a dynamic calibration knowledge base is established simultaneously. The base not only stores ideal phase difference templates with known directions, but also incrementally updates the sample weights of different error zones based on the real-time calculation results of Wasserstein distance, and records the distribution of AI-compensated residuals.

[0024] S3: Based on the phase difference-direction joint analysis framework, direction estimation evolution simulation is performed on phase difference data containing random errors under different frequency bands, signal-to-noise ratios, and array element health conditions. This results in a panoramic direction finding map that includes phase difference feature distribution, AI compensation effect, correlation matching score, and confidence interval changes with error and target direction.

[0025] This embodiment also provides a detailed description of each step, as follows: In step S1, based on the key characteristic parameters of the array and channel, including the antenna array geometry, operating frequency, channel characteristics and environmental multipath statistical characteristics, a systematic identification and partitioning of the sources of direction finding error is carried out, which is the basic premise for constructing a high-precision random phase difference feature space.

[0026] A multidimensional analysis was conducted on the potential error causes of the direction finding system under all operating conditions, dividing the error sources into three categories: significant error region, general error region, and low error region. Significant error regions mainly include channels with severe temperature drift (such as receiving channels whose phase response deviates from the calibration value due to device aging or changes in ambient temperature) and directions dominated by strong multipath (such as the incident direction of high-power delayed signals formed by reflections from buildings in urban environments). The general error zone corresponds to scenarios with mild channel mismatch (such as channel gain differences within the allowable range but not reaching the optimal matching state) or background noise at a moderate level (noise power does not reach the level of drowning out the signal, but causes some disturbance to the phase measurement). The low error region refers to the state where the system is close to the ideal calibration conditions (such as constant temperature environment, consistent channel amplitude and phase, negligible multipath effects or extremely low residual amount after previous suppression).

[0027] If a direction finding system operates at a frequency of 3 GHz, the antenna array is a uniform linear array with an element spacing of 0.5λ, and the channel characteristics are obtained through factory testing, the standard deviation of the phase response of each channel under the calibration environment is σ_cal<0.5°, and the environmental multipath statistical characteristics are measured in an urban environment, the main multipath power ratio (the power ratio of the strongest reflection path to the direct path) can reach 20dB.

[0028] When performing multidimensional analysis under full operating conditions, phase drift data for each channel at different ambient temperatures are first collected: For example, if the phase of channel 3 is φ3=60° at 25℃ and the phase changes to φ3'=72° at 45℃, the temperature drift Δφ=12°. The logic for judging severe temperature drift is that Δφ exceeds the threshold Δφ_th=8° (an empirical value set according to the calibration stability requirements). Then channel 3 is classified into the significant error zone.

[0029] For multipath direction identification, based on spatial spectrum estimation, the peak power spectrum of a certain direction θ=120° is P_120°=-30dBm, and the peak power of the direct direction θ=0° is P_0°=-10dBm. The main multipath power ratio R_p=P_120°-P_0°=-20dB (that is, the power of the reflected path is 1 / 100 of that of the direct path). If R_p exceeds the multipath influence threshold R_p_th=-15dB, then the direction 120° is classified into the significant error region.

[0030] The determination of the general error zone combines channel mismatch and background noise level: Assuming the gain difference ΔG between channel 5 and channel 1 is 1.2dB (the nominal consistency requirement is ≤1.0dB for optimal matching), it is judged as a slight channel mismatch; the background noise power measured at the observation direction θ=60° is N=-80dBm, the signal power is S=-60dBm, and the signal-to-noise ratio SNR=SN=20dB. If the SNR is in the medium level range (for example, 15dB≤SNR<25dB is judged as medium noise disturbance), then this condition is classified into the general error range.

[0031] The low-error region requires simultaneous fulfillment of the following conditions: constant temperature environment (ambient temperature fluctuation ≤ ±2℃, temperature drift Δφ < 1°), consistent channel amplitude and phase (phase standard deviation σ_ph < 0.5°, gain difference ≤ 0.5dB for each channel), and negligible multipath effects (main multipath power ratio R_p < -25dB). A calculation example is shown below: The ambient temperature is 30±1℃, the phase change of channel 2 is Δφ2=0.6°, the phase standard deviation between channels is σ_ph=0.3°, the gain difference is 0.4dB, and the measured power ratio of the strongest reflection direction is R_p=-28dB. All of the above indicators meet the threshold conditions of the low error zone. Therefore, this operating condition is classified as the low error zone.

[0032] By using this quantitative discrimination logic based on characteristic parameters (comparing temperature drift Δφ with Δφ_th, power ratio R_p with R_p_th, and gain difference with phase standard deviation and set tolerance), the possible error causes encountered by the direction finding system can be systematically divided into significant error region, general error region and low error region, providing a clear partitioning basis and statistical foundation for the subsequent construction of random phase difference feature space.

[0033] Specifically, within each error zone, a quantifiable error intensity index and a probability distribution model of phase difference shift need to be assigned to that zone, combining historical statistical patterns and real-time monitoring data. The error intensity index is constructed as follows: A large amount of measured phase difference data and corresponding ideal phase difference benchmark values ​​were collected in the region. The deviation amplitude statistics of the two (such as average deviation, standard deviation of deviation, and maximum deviation) were calculated. Then, the data were normalized and mapped to intensity scores in the range of 0 to 1. The higher the score, the greater the potential impact of the error in the region on the direction finding results. The probability distribution model of the phase difference offset was generated by non-parametric estimation method based on the cumulative distribution pattern of historical deviation samples. For example, for the phase difference offset caused by temperature drift in the significant error area, its distribution may show a wide tail characteristic. It is necessary to select an empirical distribution form that can cover extreme deviations to ensure that the model is consistent with the randomness of the actual error.

[0034] Based on the error intensity index and probability distribution model, a random phase difference feature space is generated. The core representation of this space is: Using all possible incident directions of the antenna array as the dimension index, for each incident direction, based on the phase difference offset probability distribution model of the error region, a set of phase difference vectors is generated through Monte Carlo random sampling (each vector corresponds to one possible superposition result of error states). After a large number of samples, a phase difference vector cloud is formed in that direction. The density distribution of the cloud reflects the probability concentration trend of the phase difference value, and the dispersion reflects the intensity of the random error, thus intuitively representing the random characteristics of the phase difference under different incident directions. For example, in the low error region, the phase difference vector cloud in a certain incident direction will be tightly clustered around the ideal phase difference vector, while in the significant error region, the cloud in the same direction will show a large-scale dispersion.

[0035] For a specific incident direction (e.g., 120°) within a significant error region, the ideal phase difference vector is [40°, 55°, 70°] (corresponding to three array elements). Based on historical statistics and real-time monitoring data, the deviation between the measured phase difference and the ideal value is calculated: 100 samples were collected, yielding mean deviations of [5°, 8°, 12°], standard deviations of [3°, 4°, 6°], and maximum deviations of [10°, 15°, 20°]. A weighted summation normalization method (mean deviation + standard deviation + maximum deviation) was used (weights of 0.3, 0.3, and 0.4, which can be adjusted according to system sensitivity) to calculate the intensity score. The normalized mean deviation = (5+8+12) / (10+15+20) = 25 / 45 ≈ 0.556, and the normalized standard deviation = (3+4+6) / (10+15+20) = 13 / 45 ≈ 0.289; The normalized value of the maximum deviation = (10+15+20) / (10+15+20) = 45 / 45 = 1, and the intensity score = 0.3×0.556+0.3×0.289+0.4×1≈0.167+0.087+0.4=0.654 (If the extreme error is highlighted according to the proportion of the maximum deviation, the weight can be adjusted to make the score higher. Here, the threshold of the intensity index of the significant error area is set to 0.6, so it is judged as a significant error).

[0036] The probability distribution model of phase difference shift uses nonparametric kernel density estimation. Based on 100 sets of deviation samples [Δφ1,Δφ2,…,Δφ100] (such as Δφ1=[6°,9°,14°], Δφ2=[4°,7°,11°], etc.), each sample point is smoothed by Gaussian kernel function to generate an empirical distribution covering ±3 times the standard deviation. Its cumulative distribution shape shows a wide tail (the probability density is low but not zero) when the positive deviation is above 15°, which is consistent with the characteristics of extreme shift caused by temperature drift. Based on this model, Monte Carlo random sampling (sampling times N=500) is performed on the incident direction. Each sampling randomly generates a phase difference offset vector [δ1, δ2, δ3] from the empirical distribution, which is added to the ideal value to obtain the perturbed phase difference vector [40+δ1, 55+δ2, 70+δ3]. For example, the k-th sampling yields [43°, 59°, 81°] (δ=[3°, 4°, 11°]), and the m-th sampling yields [48°, 68°, 92°] (δ=[8°, 13°, 22°], falling into the wide-tail region). After 500 samplings, the frequency distribution of the phase difference values ​​for each array element is statistically analyzed. Element 1 has a phase difference that occurs 150 times in the 38°~42° range (high density), 80 times in the 45°~50° range (medium density), and 20 times above 50° (wide tail). Element 2 has a phase difference that occurs 140 times in the 53°~57° range, 90 times in the 60°~65° range, and 30 times above 68°. Element 3 has a phase difference that occurs 120 times in the 68°~72° range, 100 times in the 75°~80° range, and 50 times above 85° (wide tail is more pronounced).

[0037] The phase difference vector clouds formed by these sampling results show that the probability concentration trends of array elements 1 to 3 are around 41°, 56°, and 71° (close to the ideal value), respectively. The dispersion (measured by the sampling standard deviation) is 3.2°, 4.5°, and 7.8°, respectively (significantly greater than 1.0°, 1.2°, and 1.5° in the low error region). This intuitively demonstrates the large-scale diffusion characteristics of the phase difference in the significant error region. In contrast, in the low error region, due to the concentrated probability distribution and small sampling offset, the clouds will tightly cluster around the ideal value. For example, in the low error region, the ideal value in a certain direction [30°, 45°, 60°] has a sampling standard deviation of only 1.0°, 1.2°, and 1.5°, and the clouds have almost no diffusion.

[0038] Specifically, to improve the statistical robustness of the random phase difference feature space, it is necessary to introduce a mechanism for constructing distributed fuzzy sets and defining confidence regions: Collect samples of the difference between the actual phase difference measurement and the ideal phase difference reference value to form a prediction deviation sample set; perform kernel density estimation on the sample set to generate an empirical distribution covering the main deviation range (the construction of the empirical distribution must ensure that it contains at least 95% of the sample points to avoid loss of tail information).

[0039] Based on the distribution similarity measurement logic of Wasserstein distance, the empirical distribution of the current error region is compared one by one with several predefined standard distributions (such as normal distribution and Laplace distribution). The standard distribution with the smallest Wasserstein distance is selected as the benchmark. Then, based on this benchmark distribution, the cumulative probability deviation between the actual empirical distribution and the benchmark distribution at each quantile is calculated to determine the boundary of the phase difference confidence region at different confidence levels (such as 90% and 95%). The confidence region definition must satisfy the following: Within this region, the Wasserstein distance increment between the empirical distribution and the benchmark distribution does not exceed a set threshold (e.g., 0.05), thus ensuring that the random phase difference feature space not only fully preserves the random characteristics of the error but also has clear statistical constraint boundaries, providing a reliable prior statistical basis for subsequent error suppression and direction estimation.

[0040] In a certain incident direction within a significant error region, 100 sets of difference samples between actual phase difference measurements and ideal phase difference reference values ​​are collected to form a prediction deviation sample set. The deviation samples for array element 1 are [5°, 7°, 4°, 9°, ..., 12°] (unit: degrees). First, kernel density estimation is performed on this sample set (using a Gaussian kernel, with bandwidth adaptively selected based on the sample standard deviation). An empirical distribution covering the main deviation range is generated. After verification, this empirical distribution contains more than 95% of the sample points (e.g., when the cumulative frequency reaches ±1.96 times the sample standard deviation, it covers 96 samples, meeting the ≥95% requirement), ensuring that extreme deviations at the tail are not missed.

[0041] Based on the distribution similarity measurement logic of Wasserstein distance, this empirical distribution is compared with a predefined normal distribution N(μ1,σ1). 2 ), comparing the Laplace distribution L(μ2,b2) one by one: The Wasserstein distance is calculated by taking the average distance between the corresponding quantiles of the cumulative distribution functions (CDF) of the two distributions. For example, the Wasserstein distance W1 between the empirical distribution and the normal distribution is calculated by multiplying |ECDF(x) - N_CDF(x)| by the sum of the corresponding probability masses for all quantiles x. The Wasserstein distance W2 between the empirical distribution and the Laplace distribution is calculated similarly. If W1 = 0.18 and W2 = 0.32, then the normal distribution with the smaller Wasserstein distance is selected as the benchmark distribution. Subsequently, a series of quantiles (e.g., 10%, 50%, 90%) are taken on the benchmark normal distribution, and the difference between the cumulative probability of the empirical distribution at these quantiles and the cumulative probability of the benchmark distribution is calculated. For example, at the 10% quantile, the cumulative probability of the empirical distribution is 0.12, while the benchmark distribution is 0.10, resulting in a deviation of +0.02; at the 90% quantile, the cumulative probability of the empirical distribution is 0.88, while the benchmark distribution is 0.90, resulting in a deviation of -0.02. For a 90% confidence level, interpolation is used to find the range where the sum of the absolute values ​​of the deviations between the cumulative probability of the empirical distribution and the cumulative probability of the benchmark distribution is minimized within the interval of 0.05 to 0.95. The corresponding phase difference boundary is then determined, ensuring that the Wasserstein distance increment between the empirical distribution and the benchmark distribution within this region does not exceed a set threshold (e.g., 0.05). The values ​​are as follows: If the increment of the Wasserstein distance between the baseline distribution and the empirical distribution within the phase difference interval [34°, 46°] is 0.03 (less than 0.05), then this interval is the boundary of the 90% confidence region. If it is expanded to [33°, 47°], the increment increases to 0.06 (exceeding the threshold), and the expanded range is discarded. The confidence region obtained in this way can both retain the random characteristics of the empirical distribution (the wide tail is still marked outside the confidence region) and provide clear statistical constraints for subsequent error suppression and direction estimation. For example, when performing correlation matching score weighting, only phase difference samples within the confidence region can be used, thereby avoiding excessive influence of extreme biases on the direction finding results and ensuring statistical robustness.

[0042] In step S2, based on the completion of the construction of the random phase difference feature space and distributed fuzzy set, a more adaptive error suppression system needs to be established for the complex distortion characteristics of the non-steady-state error stage. A complementary two-layer suppression capability is formed from both statistical and learning perspectives. Finally, the phase difference-direction joint analysis framework is constructed by integrating it into the matching process of the relevant interferometer. At the same time, a dynamically updated calibration knowledge base is established within the framework to support the continuous optimization and high-precision maintenance of the direction finding process.

[0043] Specifically, a non-linear mapping element is adopted to replace the traditional fixed error suppression strategy to capture the distortion law of the phase difference in the non-steady error stage. The situations in the non-steady error stage include sudden electromagnetic interference (such as the phase mutation of the channel caused by the short-term radiation of adjacent high-power equipment) and rapid temperature drift (such as the rapid drift of the phase response of the array channel caused by the high-speed crossing of the carrier through a region with significant temperature difference). The processing logic of the non-linear mapping element is as follows: Taking the phase difference vector clouds corresponding to different error regions in the random phase difference feature space as the input space, by analyzing the deformation trajectory of this space when the error intensity changes rapidly, a mapping rule from error state characteristics (such as the change trend of the error intensity index and the fluctuation amplitude of the phase difference deviation between adjacent moments) to the phase difference distortion mode is established. This mapping rule is not a linear proportional adjustment, but rather刻画 the non-linear behavior of approximate linear response of the phase difference under small perturbations and saturation or reverse offset under large perturbations or across error regions through piecewise fitting and smooth transition with multiple inflection points.

[0044] For example, when the system instantaneously enters a significant error region from a low error region, the non-linear mapping element will apply a progressive non-linear correction to the original phase difference according to the error intensity jump rate and the type of error region it is in, so that the distortion characteristics can be continuously expressed rather than a hard switch.

[0045] Suppose the system instantaneously enters a significant error region (error intensity index 0.85) from a low error region (error intensity index 0.2) at a certain moment. The error intensity jump rate can be calculated by dividing the difference between the error intensity indices of two adjacent frames by the time interval. Assuming the time interval is 0.1 seconds, then the jump rate = (0.85 - 0.2) / 0.1 = 6.5 (intensity index / second), which belongs to a rapid transition.

[0046] The input of the non-linear mapping element is the original phase difference vector [30°, 45°, 60°] (ideal value) corresponding to the incident direction (such as 90°) in the random phase difference feature space at this moment and the current error state characteristics: error intensity index I = 0.85, jump rate R = 6.5, and the phase difference deviation fluctuation amplitude σ0 = 1.0° in the previous frame (low error region) (reflecting the stable state under small perturbations). The mapping rule adopts piecewise fitting and smooth transition with multiple inflection points, defining the piecewise interval of the error intensity I and the corresponding non-linear correction coefficient k(I): when I ≤ 0.3 (low error region), k = 1.0 (approximate linear response, no correction); when 0.3 < I ≤ 0.6 (transition region), k = 1 + 2 * (I - 0.3) (linear increasing correction); when I > 0.6 (significant error region), k = 1.6 + 0.4tanh(R - 5) (saturation characteristic, when R > 5, tanh(R - 5) approaches 1, and k approaches 2.0 to avoid infinite growth).

[0047] Substituting I=0.85 and R=6.5, we calculate k=1.6+0.4tanh(1.5)≈1.6+0.40.905≈1.6+0.362=1.962 (close to the saturation value of 2.0). The phase difference distortion correction amount Δφ=k(current deviation vector). Let the current deviation vector be [5°,8°,12°] (the deviation caused by temperature drift and multipath after entering the significant error region). Then the correction amount Δφ≈1.962*[5°,8°,12°]≈[9.81°,15.70°,23.54°]. After correction, the phase difference vector = ideal value + correction amount = [39.81°,60.70°,83.54°].

[0048] If a traditional fixed error suppression strategy is used (k is always 1.0), the correction amount is only [5°, 8°, 12°], and the phase difference vector is [35°, 53°, 72°], which cannot reflect the large-amplitude distortion in the significant error region. Nonlinear mapping, by dynamically adjusting k with I and R, allows for a continuous expression of distortion characteristics: When R is small (e.g., R=3, tanh(-2)≈-0.964), k=1.6+0.4*(-0.964)≈1.214, the correction amount decreases, avoiding over-correction; when R is extremely large (e.g., R=10, tanh(5)≈0.9999), k≈2.0, the correction amount reaches saturation, preventing extreme transitions from causing correction instability. In this example, the nonlinear mapping smoothly transitions the phase difference vector from a tightly clustered region in the low error region (standard deviation of deviation 1.0°) to a wide-ranging dispersion in the significant error region (standard deviation of deviation after correction ≈√[(9.81-5)]). 2 +(15.70-8) 2 +(23.54-12) 2 ] / √3≈√[(23.1)+(59.3)+(133.3)] / √3≈√215.7 / 1.732≈14.69 / 1.732≈8.48°).

[0049] Specifically, an AI error compensation network is constructed and, together with the aforementioned nonlinear mapping element, forms a two-layer error suppression structure. The AI ​​error compensation network is essentially a mapping learner composed of multiple deep neural networks, and its processing is as follows: During the training phase, the input is perturbed phase difference data (i.e., the phase difference sequence or its feature vector after preprocessing by nonlinear mapping elements), and the output is the corresponding ideal phase difference reference value. The network continuously reduces the difference between the predicted output and the ideal value through backpropagation and gradient optimization, thereby learning the implicit mapping relationship from the complex perturbed state to the ideal state.

[0050] During the network inference phase, the real-time acquired scrambled phase difference is first processed by a nonlinear mapping element to extract distortion features, and then fed into an AI error compensation network for secondary fine correction. This achieves the cascade collaboration between the first layer of statistical feature-based nonlinear suppression and the second layer of data-driven deep learning suppression. The advantages of this two-layer structure are: The statistical layer can provide physically interpretable distortion trend constraints, avoiding overfitting of purely data-driven networks in areas with scarce samples; the learning layer can capture complex nonlinear and cross-interference effects that are difficult for the statistical layer to model, thereby improving the overall suppression accuracy.

[0051] If, in a significant error region at a certain incident direction (e.g., 60°), the real-time acquired perturbed phase difference data is [38°, 56°, 84°], and the ideal phase difference reference value is [30°, 45°, 60°]. In the first layer of statistical suppression, the nonlinear mapping element, based on the current error intensity index I=0.85 and the rise rate R=6.5 (calculated in the same way as the previous example), obtains a correction coefficient k≈1.962, and extracts the distortion feature vector F=[I,R, deviation fluctuation amplitude σ], where the deviation fluctuation amplitude σ is calculated from the current perturbed phase difference and the ideal value, σ=√[(38-30)]. 2 +(56-45) 2 +(84-60) 2 ] / √3=√[64+121+576] / √3=√761 / 1.732≈27.586 / 1.732≈15.93°. Therefore, the preprocessed phase difference of the nonlinear mapping output = ideal value + k× deviation vector = [30°,45°,60°]+1.962×[8°,11°,24°]≈[30+15.70,45+21.58,60+47.09]≈[45.70°,66.58°,107.09°]. This value is used as one of the input features of the AI ​​error compensation network (it can be concatenated with F to form a complete input vector X).

[0052] During the training phase, the network input consists of a large number of similar X samples, and the output is the corresponding ideal phase difference Y=[30°,45°,60°]. The network adopts a multilayer perceptron structure (e.g., 10 nodes in the input layer, 64 nodes with ReLU activation in the first hidden layer, 32 nodes with ReLU activation in the second hidden layer, and 3 nodes with linear activation in the output layer). The loss function is the mean squared error (for a batch of N samples, the squared difference between the output of each sample and the ideal value on the three array elements is calculated, the sums are taken and the average is taken, and then the network weights are adjusted by backpropagation).

[0053] Suppose that in a certain batch of training, the network's predicted output for a certain input X is [31.2°, 44.1°, 59.3°], then the single sample error = [(31.2-30)]. 2 (44.1-45)2 (59.3-60) 2 = [1.44, 0.81, 0.49], mean square error = (1.44 + 0.81 + 0.49) / 3 ≈ 0.913. Through backpropagation and gradient descent optimization, the average loss of this batch is gradually reduced. The network learns to further eliminate residual distortion based on the output of the statistical layer.

[0054] During the inference phase, the preprocessed phase difference [45.70°, 66.58°, 107.09°] is concatenated with feature F and input into the network. The network outputs a second-corrected phase difference of [30.4°, 44.8°, 60.2°]. At this point, the total bias = |30.4-30|+|44.8-45|+|60.2-60|=0.4+0.2+0.2=0.8°, compared to the bias of |45.70-30|+|66.58-45|+|107.09-60|=15.70+21.58+47.09=84.37° using only nonlinear mapping, demonstrating a significant suppression effect. The advantages of this two-layer structure are: The statistical layer uses physical quantities such as error intensity and rise rate to establish interpretable distortion trend constraints, providing reasonable correction directions even in areas with scarce samples (such as rare cases of sudden strong interference), thus preventing the purely data-driven network from overfitting to common patterns due to insufficient training samples. The learning layer, on the other hand, captures cross-interference (such as the nonlinear change of inter-channel coupling with temperature) and higher-order distortions that are difficult for the statistical layer to characterize, achieving fine correction. For example, in this case, the statistical layer has already pulled the widely diffuse phase difference back to near the ideal value region, and the learning layer further eliminates residual small deviations, making the final output almost coincide with the ideal value, thereby improving the overall suppression accuracy and system robustness.

[0055] Specifically, the aforementioned two-layer error suppression mechanism is deeply integrated with the traditional matching process of related interferometers to construct a phase difference-direction joint analysis framework. The integration steps are as follows: In the traditional correlation interferometer matching process, the cross-correlation score between the phase difference measurement and the pre-stored phase difference-direction template is used as the matching basis. Under this framework, the matching input first undergoes double-layer error suppression to obtain the corrected phase difference, and then it is matched with the phase difference-direction template. At the same time, the matching process will synchronously call the error zone information provided by the random phase difference feature space and the confidence region constraint given by the distributed fuzzy set to perform error weighting correction on the matching scores in different directions.

[0056] The framework integrates a numerical simulation environment, which can generate simulated phase difference data according to the set observation conditions (such as different frequency bands, signal-to-noise ratio, array health status), drive the direction estimation algorithm to perform evolution simulation under multiple sets of conditions, and record the spatial morphology of random phase difference features, AI compensation effect (such as the phase difference deviation reduction rate before and after compensation), correlation matching score and its confidence interval as a function of error intensity and target direction, so as to analyze the system performance boundary and weak links.

[0057] Assume the system operates at a frequency of 3 GHz, with a signal-to-noise ratio of 20 dB, and the array is in normal health condition. The target direction set includes three candidate directions: 60°, 90°, and 120°. Their pre-stored direction-phase difference templates are T60=[30°, 45°, 60°], T90=[35°, 50°, 65°], and T120=[40°, 55°, 70°]. The real-time acquired perturbed phase difference data is M=[38°,56°,84°]. First, it enters a two-layer error suppression: the first layer nonlinear mapping calculates the correction coefficient k=1+2×(0.6-0.3)=1.6 based on the error intensity I=0.6 and the rise rate R=4.0, and the deviation vector D=M-T60=[8°,11°,24°], resulting in the preprocessed phase difference P1=T60+k×D=[30+12.8,45+17.6,60+38.4]=[42.8°,62.6°,98.4°]; the second layer AI error compensation network takes P1 and the feature vector F=[I,R,σ] as input (σ is the root mean square of D≈15.93°), and outputs the secondary corrected phase difference P2=[30.5°,44.9°,60.3°].

[0058] In the traditional matching process, the logic for calculating the cross-correlation score is as follows: For each directional template T, calculate the cosine similarity between P2 and T (i.e., the dot product of the corresponding matrix data after normalization), with a score S∈[0,1]. A larger score indicates a better match. The normalization method is to divide the matrix data of P2 and T by their respective moduli. For the 60° direction, the moduli of P2 ≈ √[(30.5)]. 2 +(44.9) 2 +(60.3) 2]≈√[930+2016+3636]=√6582≈81.13, T60 module length≈√[900+2025+3600]=√6525≈80.78, dot product=30.5×30+44.9×45+60.3×60=915+2020.5+3618=6553.5, S60=6553.5 / (81.13×80.78)≈6553.5 / 6555≈0.9998. Similarly, for the 90° direction, T90 = [35°, 50°, 65°], the dot product = 30.5 × 35 + 44.9 × 50 + 60.3 × 65 = 1067.5 + 2245 + 3919.5 = 7232, the modulus T90 ≈ √[1225 + 2500 + 4225] = √7950 ≈ 89.17, S90 = 7232 / (81.13 × 89.17) ≈ 7232 / 7235 ≈ 0.9996; For the 120° direction, the modulus of T120 is approximately √[1600+3025+4900]=√9525≈97.60, the dot product is 30.5×40+44.9×55+60.3×70=1220+2469.5+4221=7910.5, and S120=7910.5 / (81.13×97.60)≈7910.5 / 7918≈0.9990.

[0059] In the fusion framework, the random phase difference feature space is synchronously invoked to determine the current error region as a general error region (I=0.6). The distributed fuzzy set gives the 90% confidence region boundary of this region as the phase difference element deviations within ±5°, with a confidence weight W=0.9 (W decreases if the deviation exceeds the confidence region). Since the deviations between P2 and T60 are only approximately [0.5°, 0.1°, 0.3°], all within the confidence region, the final weighted score WS60=0.9998×0.9≈0.8998. The deviations in other directions are larger (such as the deviations from T90 [-4.5°, 5.1°, 4.7°], some exceeding the confidence region), so the weights are reduced to W=0.7, resulting in WS90=0.9996×0.7≈0.6997 and WS120≈0.9990×0.7≈0.6993. After sorting, the highest score is in the 60° direction, achieving a correct match.

[0060] The numerical simulation environment within the framework can generate batches of perturbed phase difference data under different observation conditions. For example, by reducing the signal-to-noise ratio to 10dB (increasing the noise standard deviation and causing the bias vector to diffuse), the above process can be repeated to obtain the bias reduction rate before and after compensation (the difference between the bias modulus before and after compensation divided by the bias modulus before compensation). The matching score as a function of error intensity and the confidence interval width can then be plotted. At I=0.6, the reduction rate ≈ (modulus length D - modulus length (P2 - T60)) / modulus length D ≈ (15.93 - 0.62) / 15.93 ≈ 96%. Simulations show that when I increases to 0.85 and the signal-to-noise ratio decreases to 5dB, the reduction rate drops to 80%, the matching score decreases, and the confidence interval widens. This reveals the system performance boundaries and weaknesses, providing a basis for error suppression parameter optimization and array health maintenance.

[0061] Specifically, during the operation of the phase difference-direction joint analysis framework, a dynamic calibration knowledge base is simultaneously established to support online adaptive optimization. This knowledge base consists of three parts: Store ideal phase difference templates with known directions, which are derived from a high-precision calibration process or obtained by averaging multiple measurements in a reliable environment.

[0062] Based on the real-time calculation results of the Wasserstein distance, the sample weights in different error regions are incrementally updated. The processing logic is as follows: Whenever a new phase difference measurement sample is acquired, its Wasserstein distance to the empirical distribution of the error region is calculated. If the distance is less than a preset similarity threshold, the weight of the sample in the empirical distribution update is increased; otherwise, the weight is decreased, so that the distribution model of the knowledge base can track environmental changes.

[0063] The AI ​​compensation residual distribution is continuously recorded, which is the statistical characteristic of the residual deviation between the phase difference and the ideal value after each compensation. This is used to evaluate the stability and timeliness of the compensation network and to trigger model retraining or parameter adjustment when the residual increases abnormally.

[0064] Suppose the knowledge base already stores an ideal phase difference template T90=[35°, 50°, 65°] for a certain direction (e.g., 90°). This template is derived from high-precision calibration (averaged by multiple measurements in a temperature-controlled laboratory, with a standard deviation less than 0.2°). When the system is running online, new phase difference measurement samples M=[36°, 49°, 67°] are acquired in real time. First, the error region to which this sample belongs is determined: based on the current array and channel characteristic parameters, it is determined to be a general error region (error intensity index I=0.55). This error region already has an empirical distribution E (obtained by kernel density estimation from historical deviation samples).

[0065] Calculate the deviation vector Δ = [1°, -1°, 2°] between sample M and the ideal template, and then calculate the Wasserstein distance W of this deviation vector based on the empirical distribution E: The similarity between the empirical distribution E and the single-point distribution centered at Δ is measured using the quantile average displacement method. Several cumulative probability quantiles (e.g., 10%, 50%, 90%) are selected, and the deviation vector of the corresponding quantile in E is found. The Euclidean distance between E and Δ is calculated and weighted averaged, with the weight being the probability quality of each quantile. The calculated result is W=0.12, and the preset similarity threshold θ=0.15. Since W<θ, it indicates that the sample has a high similarity to the empirical distribution. Therefore, its weight is increased in the update of the empirical distribution: the incremental update logic is w_new=w_old+α·(1-W / θ) (α is the learning step size, taken as 0.2). If the original weight w_old=0.05, then the incremental factor (1-W / θ)=(1-0.12 / 0.15)=0.2, w_new=0.05+0.2×0.2=0.09. The sample weight is increased, making the empirical distribution closer to the current environment.

[0066] Record the AI-compensated residual distribution. After double-layer error suppression, the corrected phase difference P2 = [35.2°, 49.9°, 65.1°] is obtained, and the residual vector R = P2 - T90 = [0.2°, -0.1°, 0.1°]. Calculate the residual magnitude |R| = √(0.2...). 2 +(-0.1) 2 +0.1 2 =√(0.04+0.01+0.01)=√0.06≈0.245°. The mean μ_R and standard deviation σ_R of the residual magnitude within the statistical window (e.g., the most recent 100 compensations) are used. Let μ_R=0.22° and σ_R=0.08°. The current residual of 0.245° falls outside the μ_R±2σ_R range (the upper limit of 0.22+0.16=0.38° is not actually exceeded, but the abnormal threshold is set as μ_R+3σ_R=0.46°, which is considered normal; this is just an example). If the residual magnitude exceeds μ_R+2σ_R multiple times consecutively, it is considered an abnormal increase in residual magnitude, triggering AI network retraining or learning rate adjustment.

[0067] In step S3, based on the established phase difference-direction joint analysis framework, it is necessary to conduct direction estimation evolution simulations for phase difference data with random errors under diverse observation conditions. This will systematically reveal the laws governing the changes in direction finding performance with error intensity and target direction, and form a comprehensive direction finding map covering key evaluation dimensions. The core objective of this process is to reproduce direction finding scenarios under different combinations of frequency bands, signal-to-noise ratios, and array element health states in a controlled numerical simulation environment. It will quantitatively capture the evolution characteristics of phase difference feature distribution, AI compensation effect, correlation matching scores, and their confidence intervals, thereby providing predictable performance boundaries and optimization basis for actual system deployment.

[0068] Specifically, the value range and stepping strategy of the simulation variables are determined to ensure coverage and extreme operating conditions. Frequency band variables are divided into several representative frequency points based on the system's operating bandwidth; for example, the low-frequency band focuses on multipath delay spread characteristics, while the high-frequency band emphasizes path loss and phase noise effects. Signal-to-noise ratio (SNR) variables are set at multiple levels with equal intervals, from an ideal high SNR to a low SNR close to the detection threshold, to observe the gradual impact of noise on phase difference measurement and related matching processes. Array element health status variables are simulated by artificially introducing different modes and degrees of array element failure or performance degradation, such as single-element gain attenuation, phase response shift, and complete failure, and multiple health defects can be combined to construct composite states. Each variable combination constitutes a set of independent observation conditions, and all combinations form a simulation experiment matrix.

[0069] For each set of observation conditions, generate a phase difference dataset containing random errors: Based on the random phase difference characteristic space, and according to the error zone division and error intensity index corresponding to the current observation conditions, samples are taken from the phase difference vector cloud in this space to form a set of phase difference data simulating actual measurements. The sampling process requires the introduction of random noise injection logic that matches the current signal-to-noise ratio. That is, random perturbations conforming to Gaussian or measured noise distributions are superimposed on the ideal phase difference, and predefined amplitude and phase distortions are applied to the phase difference of the corresponding channel according to the health status of the array elements. The perturbation-injected phase difference data obtained in this way retains the randomness of the error while reflecting the comprehensive influence of specific observation conditions.

[0070] The generated phase difference data, including random error, is input into the phase difference-direction joint analysis framework to perform a complete direction estimation process. This includes: First, the distortion features under the current error state are extracted by the nonlinear mapping element within the framework, and the AI ​​error compensation network is called to perform double-layer suppression of the phase difference to obtain the corrected phase difference. Then, the corrected phase difference is combined with the correlation interferometer matching process, and the cross-correlation matching score is calculated using the pre-stored ideal phase difference direction template. During this process, the distributed fuzzy set is called simultaneously to apply confidence region weighting to the matching scores of each direction, and the scores are corrected by error region weighting, so as to obtain the direction estimation result considering statistical robustness.

[0071] The system operating bandwidth is set to 2–4 GHz. Three representative frequency points are used for the frequency band variables: low frequency 2.2 GHz (emphasizing multipath delay spread), mid frequency 3.0 GHz (normal operating conditions), and high frequency 3.8 GHz (highlighting path loss and phase noise), with a step size of 0.8 GHz to cover typical and extreme characteristics. The signal-to-noise ratio (SNR) variable is set at three levels of 20 dB, 10 dB, and 5 dB with equal intervals (20 dB approaches the ideal high SNR, and 5 dB approaches the detection threshold). Three modes are set for the array element health status variable. Under normal conditions, with a single element (channel 2) gain attenuation of 3dB, a phase response shift of +15° for channel 2, and channel 3 completely disabled, three basic states can be combined: 1 (normal) + 1 (gain attenuation) + 1 (phase shift + failure) = 3. Here, the composite state of "channel 2 gain attenuation of 3dB + channel 3 completely disabled" is selected for example. Each variable combination constitutes an independent observation condition, and all combinations form 3 (frequency band) × 3 (signal-to-noise ratio) × 3 (health state) = 27 sets of simulation experiment matrices.

[0072] Taking the observation conditions "frequency band 3.8GHz, signal-to-noise ratio 10dB, array element health status = channel 2 gain attenuation 3dB + channel 3 complete failure" as an example, the ideal phase difference template T60 = [30°, 45°, 60°] for the target direction 60°. Based on the random phase difference characteristic space, the error region under this condition is determined to be a significant error region (error intensity index I = 0.85). The basic disturbed phase difference M_base = [35°, 52°, 75°] (reflecting the deviation introduced by multipath and temperature drift) is obtained by sampling from the phase difference vector cloud in this region. The random noise injection corresponding to a signal-to-noise ratio of 10dB is: The noise standard deviation σ_noise is estimated as an inverse relationship between noise power and signal power. Assuming the ideal phase difference power corresponds to a standard deviation of 1°, then σ_noise ≈ 1° × √(ideal power / noise power). A 10dB signal-to-noise ratio means the noise power is approximately 1 / 10 of the signal power, therefore σ_noise ≈ 1° × √10 ≈ 3.16°. A Gaussian random perturbation N(0,σ_noise) is then superimposed on M_base. 2We get M_noise = [35 + 2.8°, 52 - 1.1°, 75 + 3.5°] ≈ [37.8°, 50.9°, 78.5°]. Then, we apply amplitude and phase distortion based on the array element health status: The 3dB gain reduction of channel 2 causes the phase difference reading to be too large (equivalent to an increase in phase of about 1.25°). The complete failure of channel 3 sets the phase difference of that channel to an invalid value (NaN or interpolation is used in the simulation, but a fixed deviation of +20° is used here for demonstration). The final disturbed phase difference data M=[37.8°,50.9+1.25°,78.5+20°]≈[37.8°,52.15°,98.5°].

[0073] Using the phase difference-direction joint analysis framework with input M, the first-layer nonlinear mapping element extracts error state features (I=0.85, rise rate R=5.0, deviation fluctuation σ≈√[(37.8-30)]. 2 +(52.15-45) 2 +(98.5-60) 2 ] / √3≈√[60.84+51.12+1482.25] / 1.732≈√1594.21 / 1.732≈39.93 / 1.732≈23.05°), calculate the correction coefficient k=1.6+0.4×tanh(R-5)=1.6+0.4×tanh(0)=1.6, preprocessed phase difference P1=T60+k×(M-T60)=[30+1.6×7.8,45+1.6×7.15,60+1.6×38.5]≈[30+12.48,45+11.44,60+61.6]≈[42.48°,56.44°,121.6°]. The second-layer AI error compensation network takes P1 and the feature vector F=[I,R,σ] as input and outputs the second-corrected phase difference P2≈[30.6°,45.2°,60.4°].

[0074] In the matching process, the cross-correlation score (cosine similarity) between P2 and templates in each direction is calculated: For a 60° template T60, the dot product = 30.6×30 + 45.2×45 + 60.4×60 = 918 + 2034 + 3624 = 6576, the modulus length P2 ≈ √[936 + 2043 + 3648] = √6627 ≈ 81.41, the modulus length of T60 ≈ 80.78, and the score S60 = 6576 / (81.41 × 80.78) ≈ 6576 / 6577 ≈ 0.9998; For a 90° template T90 = [35°, 50°, 65°], the dot product = 30.6×35 + 45.2×50 + 60.4×65 = 10 71 + 2260 + 3926 = 7257, modulus length T90 ≈ 89.17, score S90 ≈ 7257 / (81.41 × 89.17) ≈ 7257 / 7260 ≈ 0.9996; For a 120° template T120 = [40°, 55°, 70°], modulus length ≈ 97.60, dot product = 30.6 × 40 + 45.2 × 55 + 60.4 × 70 = 1224 + 2486 + 4228 = 7938, score S120 ≈ 7938 / (81.41 × 97.60) ≈ 7938 / 7945 ≈ 0.9991.

[0075] Using the distributed fuzzy set, the significant error region has a 90% confidence region deviation of ±6°. The deviations between P2 and T60 are [0.6°, 0.2°, 0.4°] within the confidence region, with a weight W = 0.9. The weighted score WS60 = 0.9998 × 0.9 ≈ 0.8998. The deviations in other directions are out of the region, so the weights are reduced to 0.7, resulting in WS90 ≈ 0.6997 and WS120 ≈ 0.6993. After sorting, the highest direction is 60°, achieving a correct match.

[0076] Specifically, during the simulation, four types of key evaluation data need to be collected and quantified simultaneously to support the construction of the panoramic map.

[0077] The shift in the center position, changes in dispersion, and distribution morphology of the phase difference vector cloud before and after double-layer suppression are recorded to evaluate the effect of error suppression on the modification of stochastic characteristics. The rate of reduction in deviation between the phase difference and the ideal value before and after compensation is calculated, and its mean and fluctuation range are statistically analyzed under different error zones and observation conditions to measure the network's adaptability and stability. The matching scores and their ranking for each target direction under different observation conditions are saved, and the decay pattern of scores with increasing error intensity and possible direction confusion phenomena are analyzed. Based on the evaluation results of the distributed fuzzy set and Wasserstein distance, the confidence range of the matching score for each direction is determined, and the estimation uncertainty is reflected in the interval width in the figure.

[0078] To form a comprehensive orientation map, the above four types of data need to be structured, integrated, and visualized under all combinations of observation conditions: A two-dimensional or three-dimensional map coordinate system is established with the target direction as the horizontal axis and the error intensity or observation condition parameters as the vertical axis. The phase difference feature distribution pattern, AI compensation effect index heat map, matching score curve and confidence interval band map are superimposed at different coordinate positions, and different frequency bands or signal-to-noise ratio conditions are distinguished by color, transparency or texture. The impact of array element health status can be presented by layered slicing or multi-view linkage.

[0079] For example, in the significant error region and under low signal-to-noise ratio conditions, the map shows a general decrease in matching scores, a significant widening of the confidence interval, and a weakening of the AI ​​compensation effect. Conversely, in the low error region and under high signal-to-noise ratio conditions, the scores are concentrated, the confidence interval is narrow, and the compensation effect is stable. The resulting panoramic direction-finding map not only intuitively reflects the overall system performance but can also be used to identify high-risk operating conditions, guide the optimization of error suppression parameters, and formulate array maintenance strategies, ensuring reliable direction-finding accuracy in complex and ever-changing real-world environments.

[0080] If the target direction is 60°, and the ideal phase difference template T60 = [30°, 45°, 60°], under the observation conditions of "significant error zone (error intensity index I = 0.85), frequency band 3.8 GHz, signal-to-noise ratio 5 dB, array element health status = channel 2 gain attenuation 3 dB + channel 3 partial failure", the scrambled phase difference data M = [38°, 53°, 95°] is generated.

[0081] Phase difference vector cloud features were collected before and after double-layer suppression: The cloud cluster before suppression was obtained from 500 samplings. The center position C1 is the mean phase difference of each array element ≈ [38°, 53°, 95°]. The dispersion D1 is calculated using the standard deviation as √[((38-38)]. 2 +(53-53) 2 +(95-95) 2 ) / 3]=0 (This is a special case where the sample mean is unbiased; in practice, the sample variance should be used. In this example, the standard deviation of the true sample is assumed to be σ1≈[4°,5°,10°]); After nonlinear mapping and AI network suppression, the corrected phase difference P2≈[30.8°,45.3°,60.7°], the cloud center C2≈[30.8°,45.3°,60.7°], the standard deviation σ2≈[0.6°,0.7°,0.8°], and the center position offset ΔC=√[(30.8-38) 2 +(45.3-53) 2 +(60.7-95) 2] / √3≈√[51.84+59.29+1176.49] / 1.732≈√1287.62 / 1.732≈35.88 / 1.732≈20.72°, the dispersion change rate R_d=(σ1 mean-σ2 mean) / σ1 mean≈((4+5+10) / 3-(0.6+0.7+0.8) / 3) / ((4+5+10) / 3)≈(6.33-0.7) / 6.33≈88.9%, indicating that suppression significantly compresses the dispersion of random errors.

[0082] The AI ​​compensation effect for the second type of data is calculated using the deviation reduction rate RR: RR=(‖M-T60‖-‖P2-T60‖) / ‖M-T60‖, where ‖·‖ is the Euclidean modulus, and ‖M-T60‖=√[(8)] 2 +(8) 2 +(35) 2 ]=√(64+64+1225)=√1353≈36.78°, ‖P2-T60‖=√[(0.8) 2 +(0.3) 2 +(0.7) 2 =√(0.64+0.09+0.49)=√1.22≈1.10°, so RR≈(36.78-1.10) / 36.78≈97.0%. By statistically analyzing the mean and fluctuation under different error zones and observation conditions (e.g., the mean RR of 94% and the standard deviation of 2.5% for 10 groups of samples with significant error zones), the adaptability and stability of the network can be measured.

[0083] Third category data matching score: The cosine similarity between P2 and T60 is S60≈0.9995. The similarity with the 90° template T90=[35°,50°,65°] is S90≈0.995. The similarity with the 120° template T120=[40°,55°,70°] is S120≈0.990. The sorting remains correct, but the high score interval narrows under low signal-to-noise ratio. As the error intensity increases (e.g., I=0.9), the score may drop to 0.980 and there is a risk of orientation confusion.

[0084] Fourth type of confidence interval: Based on the distance W = 0.10 between the distributed fuzzy set and Wasserstein (less than the threshold of 0.15), the 90% confidence region bias boundary is determined to be ±4°. The interval width reflects the uncertainty. In this example, the bias of P2 is within the confidence region, so the width is narrow. If W increases to 0.25, the confidence region boundary expands to ±8°, and the width doubles.

[0085] To create a panoramic image, a two-dimensional coordinate system is established with the target direction as the horizontal axis and the error intensity I as the vertical axis. The coordinates at (60°, 0.85) are then superimposed. The diagram illustrates the phase difference feature cloud (C1→C2, dispersion decreasing), the AI ​​compensation effect heatmap (RR=97% represented in dark red), the matching score curve (high S60 and far from S90 and S120), and the confidence interval band diagram (narrow bars represent low uncertainty). Different frequency bands / signal-to-noise ratios are distinguished by color (e.g., red for 3.8GHz high frequency, diagonal stripes for 5dB low SNR), and the health status of array elements is presented using layered slices. For example, in the significant error region +I=0.85+5dB, the spectrum shows a general decrease in matching scores (S60 from 0.9995 to 0.985), a widening of the confidence interval (±4°→±7°), and a weakening of the compensation effect (RR decreasing to 91%); while in the low error region +I=0.2+20dB, the scores are concentrated in the high range (S60≈0.9999), the confidence interval is narrow (±1°), and RR≈99%. This panoramic map visually exposes high-risk operating conditions (low signal-to-noise ratio + significant error region), guiding the optimization of suppression parameters (such as improving the coverage of such conditions by AI network training samples) and array maintenance (prioritizing the detection of channel 2 gain stability), thereby maintaining reliable direction finding accuracy in variable environments.

[0086] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0087] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A correlation interferometer direction finding method based on AI related error compensation, characterized in that: The direction finding method includes the following steps: S1: Based on the characteristic parameters of the array and the channel, the error sources faced by the direction finding are divided into significant error region, general error region and low error region. A random phase difference feature space is generated in each error region, and a distributed fuzzy set is established. S2: Based on the random phase difference feature space and distributed fuzzy set, the distortion characteristics of phase difference under the non-steady-state error stage are described by nonlinear mapping element. Combined with AI error compensation network to generate double-layer error suppression, the double-layer error suppression is integrated with the relevant interferometer matching process to construct a phase difference-direction joint analysis framework, and a dynamic calibration knowledge base is established within the phase difference-direction joint analysis framework. S3: Based on the phase difference-direction joint analysis framework, we perform direction estimation evolution simulation on phase difference data containing random errors to obtain a panoramic direction finding map.

2. The AI-related error compensation based correlation interferometer direction finding method of claim 1, wherein: The distortion characteristics of phase difference under non-steady-state error stage are described by nonlinear mapping elements, and a two-layer error suppression is generated by combining AI error compensation network, including the following steps: The AI ​​error compensation network takes perturbed phase difference data as input and outputs the corresponding ideal phase difference reference value, learning the implicit mapping relationship from complex perturbed state to ideal state. The real-time acquired scrambled phase difference is first processed by a nonlinear mapping element to extract distortion features, and then fed into an AI error compensation network to complete secondary correction. This achieves the cascade collaboration of the first layer of nonlinear suppression based on statistical features and the second layer of data-driven deep learning suppression, thus generating a two-layer error suppression. 3.The AI-related error compensation based correlation interferometer direction finding method according to claim 2, wherein: By integrating two-layer error suppression with the correlation interferometer matching process, a phase difference-direction joint analysis framework is constructed, including the following steps: The matching input first undergoes double-layer error suppression to obtain the corrected phase difference, which is then matched with the phase difference-direction template. The matching process synchronously calls the error zone information provided by the random phase difference feature space and the confidence region constraint given by the distributed fuzzy set to perform error weighting correction on the matching scores in different directions; The phase difference-direction joint analysis framework integrates a numerical simulation environment, generates simulated phase difference data according to the set observation conditions, and drives the direction estimation algorithm to perform evolution simulation under multiple sets of conditions. Record the spatial morphology of random phase difference features, AI compensation effect, correlation matching score and its confidence interval as the error intensity and target direction change.

4. The AI-related error compensation based correlation interferometer direction finding method of claim 3, wherein: A dynamic calibration knowledge base is established within the phase difference-direction joint analysis framework. This dynamic calibration knowledge base includes: Store ideal phase difference templates with known directions; The sample weights in different error regions are incrementally updated based on the real-time calculation results of the Wasserstein distance: Whenever a new phase difference measurement sample is acquired, its Wasserstein distance with the empirical distribution of the error region is first calculated. If the Wasserstein distance is less than the preset similarity threshold, the weight of the measurement sample in the empirical distribution update is increased; otherwise, the weight is decreased. Record the AI ​​compensation residual distribution, that is, the statistical characteristics of the residual deviation between the phase difference and the ideal value after each compensation, to evaluate the stability and timeliness of the compensation network. 5.The AI-related error compensation based correlation interferometer direction finding method according to claim 1, wherein: Based on the phase difference-direction joint analysis framework, direction estimation evolution simulation is performed on phase difference data containing random errors to obtain a panoramic direction-finding map, including the following steps: Based on the random phase difference feature space, and according to the error zone division and error intensity index corresponding to the current observation conditions, sampling is performed from the phase difference vector cloud in the random phase difference feature space to form phase difference data that simulates the actual measurement. The distortion features under the current error state are extracted by nonlinear mapping elements in the phase difference-direction joint analysis framework, and the phase difference is suppressed by two layers by calling the AI ​​error compensation network to obtain the corrected phase difference; By combining the phase difference correction with the correlation interferometer matching process, the cross-correlation matching score is calculated using a pre-stored ideal phase difference direction template. Record the center position shift, dispersion change and distribution pattern of the phase difference vector cloud before and after double-layer suppression to evaluate the effect of error suppression on random characteristics, calculate the deviation reduction rate of the phase difference before and after compensation from the ideal value, and statistically analyze its mean and fluctuation range under different error zones and observation conditions. Save the matching scores and their ranking for each target direction under different observation conditions, analyze the law of score decay as the error intensity increases, and determine the confidence range of the matching score for each direction based on the evaluation results of the distributed fuzzy set and Wasserstein distance. A two-dimensional or three-dimensional map coordinate system is established with the target direction as the horizontal axis and the error intensity or observation condition parameters as the vertical axis. At different coordinate positions, the schematic diagram of the phase difference characteristic distribution, the heat map of the AI ​​compensation effect index, the matching score curve and the confidence interval band map are superimposed.

6. The AI-related error compensation based correlation interferometer direction finding method of claim 1, wherein: A random phase difference feature space is generated within each error region, and a distributed fuzzy set is established, including the following steps: Collect measured phase difference data and corresponding ideal phase difference reference values ​​within the error range, calculate the deviation amplitude statistics between the two, and then normalize them to map them into intensity scores in the 0~1 interval; The probability distribution model of phase difference offset is generated by non-parametric estimation method, based on the cumulative distribution shape of historical deviation samples. Based on the error intensity index and probability distribution model, a random phase difference feature space is generated; Collect samples of the difference between the actual phase difference measurement value and the ideal phase difference reference value to form a prediction deviation sample set; perform kernel density estimation on the prediction deviation sample set to generate an empirical distribution covering the deviation range; Based on the distribution similarity measurement logic of Wasserstein distance, the empirical distribution of the current error region is compared with several predefined standard distributions one by one, and the standard distribution with the smallest Wasserstein distance is selected as the benchmark. Based on the baseline distribution, the phase difference confidence domain boundary at different confidence levels is determined by calculating the cumulative probability deviation between the actual empirical distribution at each quantile and the baseline distribution. 7.The AI-related error compensation based correlation interferometer direction finding method according to claim 1, wherein: The direction finding panoramic map includes phase difference feature distribution, AI compensation effect, correlation matching score, and confidence interval as the error and target direction change.

8. The correlation interferometer direction finding method based on AI correlation error compensation according to claim 1, characterized in that: The phase difference-direction joint analysis framework simulates the direction estimation evolution of phase difference data under different observation conditions in a numerical simulation environment, and analyzes the characteristics of random phase difference feature space, AI compensation effect and related matching score as a function of error intensity and target direction.

9. The AI-related error compensation based correlation interferometer direction finding method of claim 8, wherein: The dynamic calibration knowledge base stores ideal phase difference templates for known directions, incrementally updates sample weights in different error zones based on real-time calculation results of Wasserstein distance, and records the AI-compensated residual distribution.

10. The AI-related error compensation based correlation interferometer direction finding method of claim 1, wherein: The characteristic parameters of the array and channel include antenna array geometry, operating frequency, channel characteristics, and environmental multipath statistical characteristics.

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