Digital beamforming based electronic reconnaissance positioning method and system

Abstract

The present application relates to electronic reconnaissance technical field, specifically for electronic reconnaissance positioning method and system based on digital beam forming, including the following steps: using fractional Fourier transform to eliminate interference and purify signal, constructing four-order parallel decomposition tensor model, calculating robust nulling weight through second-order cone programming and executing space domain filtering, reconstructing covariance matrix based on atomic norm minimization, and generating atomic norm grid reconnaissance orientation parameter set. In the present application, interference suppression is realized by self-adaptive search transformation energy gathering point, Gaussian noise interference is eliminated by using tensor blind source separation, guidance vector matching degree is improved by means of spherical uncertainty set constraint, deep null formation ability is strengthened, off-grid error is reconstructed and angle of arrival precision is optimized, and information reliability is dynamically evaluated by Mahalanobis distance, which effectively solves the positioning ambiguity problem under complex interference, significantly enhances the robustness of radiation source coordinate calculation, and realizes accurate reconnaissance and real-time tracking of three-dimensional space target.

Description

Technical Field

[0001] This invention relates to the field of electronic reconnaissance technology, and in particular to an electronic reconnaissance and positioning method and system based on digital beamforming. Background Technology

[0002] Electronic reconnaissance technology encompasses the acquisition, analysis, and processing of electromagnetic signals, aiming to obtain battlefield information by monitoring and locating signals emitted by enemy electronic equipment. The core tasks of this field involve electromagnetic wave detection and signal analysis, achieving target detection and identification by collecting signal characteristics from the radio spectrum. Electronic reconnaissance not only covers traditional airspace and frequency domain signal monitoring but also includes the fusion and processing of multi-band, multi-source signals. With the increasing complexity of the battlefield environment, electronic reconnaissance faces more and more challenges, especially in environments with dense signals and severe interference, requiring more precise and efficient technical means to improve reconnaissance and location accuracy.

[0003] Traditional electronic reconnaissance and positioning methods based on digital beamforming refer to a approach that uses digital beamforming technology to process and locate signals in electronic reconnaissance. This method primarily uses an array antenna to receive signals from different directions and employs a self-matching algorithm to filter, enhance, and locate the signals. The aim is to improve signal quality and accurately predict the target's location in complex electromagnetic environments. Traditional digital beamforming methods rely on the assumption of an array manifold and perform signal processing under conditions of low signal-to-noise ratio, multipath effects, and interference. However, in complex electromagnetic environments, traditional methods encounter problems such as fuzzy or failed angle-of-arrival estimation, thus affecting positioning accuracy. While current technologies employ spatial filtering and interference suppression techniques, issues such as array errors and steering vector mismatch still exist, leading to the failure to effectively form deep nulls in the target signal, thereby affecting target positioning.

[0004] Traditional digital beamforming-based electronic reconnaissance and positioning methods rely excessively on the assumption of an ideal array manifold. This leads to problems such as fuzzy or even failed angle-of-arrival estimation in complex electromagnetic environments with low signal-to-noise ratios or significant multipath effects, severely limiting positioning accuracy. Existing technologies cannot effectively address the negative impacts of array amplitude and phase errors and steering vector mismatch when dealing with signal-dense and highly interference environments. This makes it difficult to accurately form the deep null effect of the target signal, resulting in insufficient interference suppression capabilities and difficulty in ensuring the robustness and reliability of target radiation source parameter extraction, leading to significant deviations in subsequent three-dimensional positioning calculations. Summary of the Invention

[0005] To address the technical problems existing in the prior art, embodiments of the present invention provide an electronic reconnaissance and positioning method based on digital beamforming, comprising the following steps:

[0006] To achieve the above objectives, the present invention adopts the following technical solution: an electronic reconnaissance and positioning method based on digital beamforming, comprising the following steps:

[0007] S1: Based on the polarization-sensitive multi-channel array antenna, a four-dimensional received data matrix is ​​obtained. An adaptive rotation order step search is performed in the preset time and frequency planes. The non-stationary interference energy is gathered by fractional Fourier transform. A band-stop filter is configured to remove the interference impulse component in the transform domain. An inverse fractional Fourier transform is performed to generate a transform domain interference suppression and purification signal sequence.

[0008] S2: Call the transform domain interference suppression and purification signal sequence, calculate the fourth-order cumulant matrix to eliminate Gaussian noise sensitivity, construct a fourth-order parallel decomposition tensor model, perform tensor dimensionality reduction and blind source separation, extract the target radiation source component, and obtain the tensor dimensionality reduction separated target source estimated component.

[0009] S3: Based on the tensor dimensionality reduction separation of the target source estimation components, a spherical uncertainty set is introduced to define the neighborhood of the guiding vector error for the array amplitude and phase error. The problem is transformed into a second-order cone programming problem through the matrix inversion lemma. The null weighted vector is calculated, and spatial filtering is performed to obtain the robust second-order cone programming null weighted vector.

[0010] S4: Based on the robust second-order cone programming zero-trap weighted vector, construct an atomic set in the spatial domain and perform atomic norm minimization reconstruction. Recover the covariance matrix through semi-positive definite programming, extract spatial arrival angle features, and generate an atomic norm grid reconnaissance and positioning azimuth parameter set.

[0011] As a further aspect of the present invention, the transform domain interference suppression and purification signal sequence includes time-domain sampling amplitude, phase distribution sequence, and polarization state vector; the tensor dimensionality reduction separation of target source estimation components includes component power spectral density, tensor factor matrix, and source signal estimation vector; the robust second-order cone programming null weighted vector includes weight vector magnitude, null center frequency, and spatial gain attenuation value; and the atomic norm grid reconnaissance and positioning azimuth parameter set includes angle of arrival estimation value, atomic decomposition coefficient, and spatial frequency parameter.

[0012] As a further aspect of the present invention, the step of suppressing and purifying the signal sequence in the transform domain interference specifically comprises:

[0013] S101: Receives the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, performs a self-matched fractional Fourier transform on it, searches for the rotation order corresponding to the energy peak in the transform domain, and locates the energy accumulation point of the linear frequency modulation sweep interference.

[0014] The four-dimensional received data matrix consists of four dimensions: spatial array elements, time-domain sampling, frequency, and polarization.

[0015] S102: Based on the time-frequency coordinates corresponding to the energy gathering point, configure a blocking filter with a key cutoff bandwidth to block the values ​​in the transform domain that are within the envelope of the interference energy to zero, perform an inverse fractional Fourier transform and restore the time-domain waveform of the electromagnetic signal to obtain a preliminary de-interference signal stream.

[0016] S103: Extract the preliminary de-interference signal stream, calculate the correlation of the multi-channel polarization manifold, use the minimum mean square error criterion to correct the residual phase fluctuations between channels, and generate a transform domain interference suppression and purification signal sequence.

[0017] As a further aspect of the present invention, the step of tensor dimensionality reduction to separate the target source estimation components specifically comprises:

[0018] S201: Call the transform domain interference suppression and purification signal sequence, calculate the fourth-order cumulant matrix in multiple channels, remove background Gaussian co-frequency crosstalk components, and construct a fourth-order parallel decomposition tensor model based on the topological prior structure of the antenna array manifold matrix.

[0019] S202: Based on the fourth-order parallel decomposition tensor model, execute the alternating least squares iterative algorithm. In each iteration, fix the factor matrix of the remaining dimensions and perform least squares update on the current dimension until the Frobenius norm objective loss function converges to obtain the dimensionality-reduced factor matrix.

[0020] S203: Based on the reduced factor matrix, extract the component estimation vector of the target radiation source, calculate the power spectral density of the component energy, and obtain the tensor-based dimensionality reduction separation of the target source estimation components.

[0021] As a further aspect of the present invention, the steps of the robust second-order cone programming zero-trap weighted vector are specifically as follows:

[0022] S301: Extract the source signal estimation vector from the target source estimation component separated by tensor dimensionality reduction, derive the nominal steering vector of the target radiation source, and introduce a spherical uncertainty set. Define the steering vector mismatch range through the bounded spherical error neighborhood to obtain the nominal steering vector of the target radiation source.

[0023] S302: Based on the nominal steering vector of the target radiation source, the output interference plus noise ratio is the objective function. It is equivalently transformed into the dual form of minimizing the output power. It is then relaxed using the Lagrange multiplier method, transformed into a second-order cone constraint condition, and an inverse lemma is constructed for the covariance matrix.

[0024] S303: Extract the covariance matrix of the inverse lemma pair, iteratively calculate the optimal weight vector of the joint dimension of polarization and spatial domain, apply the weight vector to the strong interference direction of the antenna receiving manifold, and generate a robust second-order cone programming zero-trap weighted vector.

[0025] As a further aspect of the present invention, the steps of establishing the atomic norm grid reconnaissance and positioning azimuth parameter set are specifically as follows:

[0026] S401: Call the filter signal corresponding to the zero-trap weighted vector of the robust second-order cone programming, construct an atom set within the range of pitch and azimuth angles in the continuous spatial domain, and establish a continuous parameter sparse reconstruction model based on the atom norm.

[0027] S402: The continuous parameter sparse reconstruction model is transformed into a convex semi-positive definite programming problem. Its dual variables are solved using the interior point method, and the signal covariance matrix without off-grid error is identified. Eigenvalue decomposition is performed on the matrix to divide the signal subspace and noise subspace.

[0028] S403: Extract the signal subspace and noise subspace, locate the spatial direction vector that is orthogonal to the signal subspace in the continuous angular domain by searching for spectral peaks, and generate an atomic norm grid reconnaissance and positioning azimuth parameter set.

[0029] As a further aspect of the present invention, the method further includes step S5:

[0030] S5: Integrate the atomic norm grid reconnaissance and positioning azimuth parameter set with the time difference of arrival data captured by the external image sensor, calculate the Mahalanobis distance between the predicted state and the multi-station observation data, dynamically evaluate the statistical reliability of the observation information, filter information data that meets the statistical characteristics, input the capacitive Kalman filter for state update and three-dimensional nonlinear observation equation solution, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

[0031] As a further aspect of the present invention, the Mahalanobis distance refers to the calculation of predicted observations based on the predicted state, obtaining the difference between the predicted observations and the joint observation vector as the observation information vector, and calculating the product of the observation information vector, the inverse of the observation information covariance matrix, and the transpose of the observation information vector to obtain the Mahalanobis distance.

[0032] The coordinate values ​​of the volumetric Kalman filter radiation source include longitude coordinates, latitude coordinates, and altitude coordinates.

[0033] As a further aspect of the present invention, the step of determining the coordinate values ​​of the volumetric Kalman filter radiation source specifically includes:

[0034] S501: Based on the atomic norm grid reconnaissance and positioning azimuth parameter set, the arrival time difference data captured by external image sensors is fused to construct a nonlinear state estimation equation, and the least squares solution is used for initial rendezvous and positioning to obtain the initial state vector of the target radiation source.

[0035] S502: Extract the initial state vector, generate a Gaussian volume point set using the third-order spherical radial volume rule, propagate it to the observation space through a nonlinear observation equation, calculate the statistical information sequence of the observation prediction value and the real-time multi-station observation value, and derive the Mahalanobis distance.

[0036] S503: Determine whether the Mahalanobis distance is within the preset statistical confidence interval, perform adaptive weight decay or hard isolation on abnormal information that exceeds the interval, input the corrected information into the capacitive Kalman filter, iteratively update the state covariance matrix and Kalman gain matrix, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

[0037] Electronic reconnaissance and positioning systems based on digital beamforming include:

[0038] The interference removal module acquires the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, searches for the optimal rotation order in the two-dimensional time and frequency plane by performing an adaptive fractional Fourier transform, locates the energy accumulation point of linear frequency modulation sweep interference, configures a band-stop filter to block the interference impact in the transform domain, and performs an inverse fractional Fourier transform to generate a transform domain interference suppression and purification signal sequence.

[0039] The tensor separation module, based on the transform domain interference suppression and purification signal sequence, calculates the fourth-order cumulant matrix between signal components and suppresses Gaussian color noise, constructs a fourth-order parallel decomposition tensor model, and uses the alternating least squares method to perform tensor dimensionality reduction and blind separation of source signals to obtain the tensor dimensionality reduction separation target source estimated component.

[0040] The robust shaping module separates the target source estimation components based on the tensor dimensionality reduction, introduces a spherical uncertainty set constraint for array guide vector mismatch, constructs a second-order conical convex optimization function with the output interference plus noise ratio as the target, uses the matrix inversion lemma to iteratively calculate the adaptive weight vector of the joint dimension of polarization and spatial domain, performs zero-trap weighted filtering processing, and obtains the robust second-order conical programming zero-trap weighted vector.

[0041] The orientation extraction module constructs an atomic set in the continuous spatial dimension based on the robust second-order cone programming zero-trap weighted vector and performs atomic norm minimization reconstruction. It recovers the complete signal covariance matrix using semi-positive definite programming and searches for direction vectors orthogonal to the noise subspace from the signal subspace to generate an atomic norm grid reconnaissance and positioning orientation parameter set.

[0042] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0043] In this invention, by performing an adaptive rotation order step search in a preset time and frequency plane and combining it with fractional Fourier transform to gather energy, non-stationary interference is accurately eliminated and the purified signal is restored. A fourth-order cumulant tensor dimensionality reduction and blind source separation mechanism are used to completely eliminate Gaussian noise sensitivity and extract target radiation source components. A spherical uncertainty set is introduced to address array errors and transformed into a second-order cone programming problem. Robust null weights are dynamically calculated, significantly enhancing the spatial filtering depth and optimizing interference suppression capabilities. Atom norm minimization reconstruction and semi-positive definite programming are used to recover the covariance matrix, achieving angular domain feature extraction without off-grid errors, significantly enhancing the accuracy of spatial angle of arrival estimation. Time difference of arrival data is fused and combined with capacitive Kalman filtering for state updates, effectively solving the problem of positioning instability under nonlinear observation environments, comprehensively improving the reliability of three-dimensional coordinate calculation of radiation sources, ensuring real-time electromagnetic situational awareness in complex battlefields, and ultimately achieving a significant optimization of the robustness and detection efficiency of the electronic reconnaissance and positioning system. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic diagram of the steps of the present invention;

[0046] Figure 2 This is a detailed schematic diagram of S1 of the present invention;

[0047] Figure 3 This is a detailed schematic diagram of S2 of the present invention;

[0048] Figure 4 This is a detailed schematic diagram of S3 of the present invention;

[0049] Figure 5 This is a detailed schematic diagram of S4 of the present invention;

[0050] Figure 6 This is a detailed schematic diagram of S5 of the present invention;

[0051] Figure 7 This is a system module diagram of the present invention. Detailed Implementation

[0052] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0053] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0054] Please see Figure 1 This invention provides an electronic reconnaissance and positioning method based on digital beamforming, comprising the following steps:

[0055] S1: Based on the polarization-sensitive multi-channel array antenna, a four-dimensional received data matrix is ​​obtained. An adaptive rotation order step search is performed in the preset time and frequency planes. The non-stationary interference energy is gathered by fractional Fourier transform. A band-stop filter is configured to remove the interference impulse component in the transform domain. An inverse fractional Fourier transform is performed to generate a transform domain interference suppression and purification signal sequence.

[0056] S2: Call the transform domain interference suppression to purify the signal sequence, calculate the fourth-order cumulant matrix to eliminate Gaussian noise sensitivity, construct a fourth-order parallel decomposition tensor model, use the alternating least squares method to perform tensor dimensionality reduction and blind source separation, extract the target radiation source component, and obtain the tensor dimensionality reduction separated target source estimated component.

[0057] S3: Based on tensor dimensionality reduction, separate the target source estimation components. For the array amplitude and phase error, introduce a spherical uncertainty set to define the neighborhood of the guiding vector error. Construct a convex optimization objective function constrained by the interference plus noise ratio. Transform it into a second-order cone programming problem through the matrix inversion lemma. Calculate the null weighted vector and perform spatial filtering to obtain the robust second-order cone programming null weighted vector.

[0058] S4: Based on robust second-order cone programming zero-trap weighted vector, an atomic set is constructed in the spatial domain and atomic norm minimization reconstruction is performed. The covariance matrix is ​​recovered through positive semidefinite programming, spatial angle of arrival features are extracted, and an atomic norm grid reconnaissance and positioning azimuth parameter set is generated.

[0059] S5: Integrate the atomic norm grid reconnaissance and positioning azimuth parameter set with the time difference of arrival data captured by external image sensors, calculate the Mahalanobis distance between the predicted state and multi-station observation data, dynamically evaluate the statistical reliability of the observation information, filter information data that meets statistical characteristics, input the capacitive Kalman filter for state update and three-dimensional nonlinear observation equation solution, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

[0060] Mahalanobis distance refers to the distance between the predicted observations calculated based on the predicted state, the difference between the predicted observations and the joint observation vector as the observation information vector, and the product of the observation information vector, the inverse of the observation information covariance matrix, and the transpose of the observation information vector.

[0061] The transform domain interference suppression and purification signal sequence includes time-domain sampling amplitude, phase distribution sequence, and polarization state vector; the tensor dimensionality reduction separation of target source estimation components includes component power spectral density, tensor factor matrix, and source signal estimation vector; the robust second-order cone programming null weighted vector includes weight vector magnitude, null center frequency, and spatial gain attenuation value; the atomic norm grid reconnaissance and positioning azimuth parameter set includes angle of arrival estimation value, atomic decomposition coefficient, and spatial frequency parameter; and the volumetric Kalman filter radiation source coordinate values ​​include longitude coordinates, latitude coordinates, and altitude coordinates.

[0062] Please see Figure 2 The specific steps for transform domain interference suppression and purification of the signal sequence are as follows:

[0063] S101: Receives the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, performs a self-matched fractional Fourier transform on it, searches for the rotation order corresponding to the energy peak in the transform domain, and locates the energy accumulation point of the linear frequency modulation sweep interference.

[0064] The four-dimensional received data matrix consists of four dimensions: spatial array elements, time-domain sampling, frequency, and polarization.

[0065] The system receives a four-dimensional received data matrix from a polarization-sensitive multi-channel array antenna. This matrix integrates electromagnetic characteristics across four dimensions: spatial array elements, time-domain sampling, frequency, and polarization. For example, in a broadband radar reconnaissance scenario, the antenna array consists of eight dual-polarized dipole elements. Data is acquired at a sampling rate of 200 MHz within a 10-millisecond observation period, forming a data architecture containing 512 frequency elements and two polarization channels. By accessing the antenna's underlying high-speed buffer memory, the digital quantities of the original RF signal, after orthogonal demodulation and analog-to-digital conversion, are arranged to construct a four-dimensional tensor structure. A self-matched fractional Fourier transform is then performed on this matrix. Instead of a fixed transform angle, a preset step scanning mechanism is used to adjust the rotation order in steps of 0.01 within the range of 0 to 2, projecting the signal from the conventional time or frequency domain to the fractional-order processing space. At each rotation order, the squared magnitude of all sampling points in the transform domain is calculated to obtain the energy distribution function. For each distribution function, a peak detection operation is performed. This involves comparing the energy value of the current sampling point with the modulus of its eight neighboring points. If the energy of the current point exceeds that of all its neighbors and is greater than five times the preset average background noise energy, it is identified as a candidate energy peak. A global search is used to determine the rotation order with the highest energy concentration. For example, when dealing with linear frequency modulation (LFM) interference, when the rotation order is adjusted to 0.85, the time-domain overlapping and frequency-domain broadened interference signal exhibits an extremely narrow pulse-like energy concentration. When locating the energy concentration point of LFM sweep interference, the fractional-order frequency coordinates and rotation angle corresponding to the peak are recorded. The interference intensity is quantified by calculating the energy ratio between the peak point and the surrounding background noise region. When the ratio reaches 12 dB or higher, it is defined as a strong interference feature point. Typical interference envelope features from the historical scan database are retrieved and compared with the full width at half maximum (FWHM) of the current energy distribution to accurately define the extension range of the interference signal in the transform domain.

[0066] S102: Based on the time-frequency coordinates corresponding to the energy accumulation point, configure a blocking filter with a key cutoff bandwidth to block the values ​​in the transform domain that are within the envelope of the interference energy to zero, perform an inverse fractional Fourier transform and restore the time-domain waveform of the electromagnetic signal to obtain a preliminary de-interference signal stream.

[0067] Based on the time-frequency coordinates corresponding to the energy accumulation point obtained above, the broadening of the energy accumulation point on the fractional-order frequency axis is measured. The center frequency is set as the energy peak point, and the initial stopband is defined based on the width at which the interference energy drops by 3 dB. To address energy leakage caused by non-ideal sampling, this width is extended to both sides by a 20% redundancy interval to construct the critical cutoff bandwidth. For example, if the interference energy accumulation point is located at the 120 MHz equivalent fractional-order frequency, and the measured broadening is 5 MHz, then the cutoff range of the configured bandstop filter is set to 114 MHz to 126 MHz. Subsequently, the values ​​in the transform domain that are within the envelope of the interference energy are zeroed out. The transformed matrix indexes are traversed, and all complex values ​​falling within the cutoff bandwidth are forcibly assigned to 0, retaining all original signal components outside the bandwidth. The interference energy is physically removed. When performing the inverse fractional Fourier transform, a negative rotation order that corresponds exactly to the above is used. For example, if the rotation order is 0.85, then a negative 0.85 inverse transform is performed here to remap the processed data from the transform domain back to the original time domain. During the restoration of the time-domain waveform of the electromagnetic signal, the phase rotation factor introduced during the compensation transformation ensures the continuity of the signal phase, resulting in a preliminary de-interference signal stream. At this point, the strong linear frequency modulated component is eliminated from the signal stream, improving the quantization quality. The peak-to-sidelobe ratio of the signal before and after processing is calculated. If this ratio increases from -3 dB to 15 dB, it proves that the interference suppression is effective. In this process, the signals of each channel are restored in parallel, maintaining the initial amplitude consistency between polarization channels, laying the foundation for subsequent utilization of polarization information.

[0068] S103: Extract the initial interference-reducing signal stream, calculate the correlation of the multi-channel polarization manifold, use the minimum mean square error criterion to correct the residual phase fluctuations between channels, and generate a transform domain interference suppression and purification signal sequence.

[0069] By retrieving the complex analytic signals of two orthogonally polarized channels at the same sampling time, the cross-correlation coefficient between them is calculated. Specifically, the conjugate signal of the horizontally polarized channel is multiplied by the signal of the vertically polarized channel, and the sum is obtained, then divided by the square root of the product of their respective energies to obtain the correlation quantization value. For example, under ideal consistency, this value is 1, while in practical scenarios affected by channel imbalance, the initial correlation value is only 0.82. When correcting the residual phase fluctuations between channels using the minimum mean square error criterion, a reference channel is set, and the horizontally polarized channel of the first element with the most stable energy distribution is selected as the benchmark. An error objective function is constructed, defined as the square of the magnitude of the difference between the reference signal and the signal to be corrected. Through gradient descent iteration, the complex gain factor of the channel to be corrected is adjusted, and the phase compensation value is updated along the negative gradient direction of the error function in each iteration. For example, with an iteration step size of 0.005, after 150 iterations, the phase fluctuation error is reduced from the initial 15 degrees to below 0.5 degrees. A transform-domain interference suppression and purification signal sequence is generated, and the calculated optimal compensation factor is applied to all data points to perform full data correction. To verify the purification effect, a signal purity index is introduced, defined as the ratio of useful signal power to residual interference plus noise power. Comparison shows that the polarization correlation improved from 0.82 to 0.98 after correction. The advantage of this operational logic is that, through closed-loop feedback correction of polarization manifold correlation, residual phase noise caused by RF device inconsistencies is eliminated, improving the characteristic stability of subsequent spatial spectrum estimation.

[0070] Please see Figure 3 The specific steps for tensor dimensionality reduction to separate the target source estimation components are as follows:

[0071] S201: Call the transform domain interference suppression and purification signal sequence, calculate the fourth-order cumulant matrix in multiple channels, remove background Gaussian co-frequency crosstalk components, and construct a fourth-order parallel decomposition tensor model based on the topological prior structure of the antenna array manifold matrix.

[0072] The transform domain interference suppression and purification signal sequence is invoked, and complex signal samples from each channel are extracted. Combination operations are performed according to the definition of fourth-order moments, i.e., the expected product of the signal with its conjugate and replicas with different time delays is calculated. In this execution, 1024 sampling points are acquired through a sliding window, and the cross-cumulative amount between each group of array elements is calculated. When removing background Gaussian co-frequency crosstalk components, the statistical property that fourth-order and higher cumulative amounts of Gaussian processes are always equal to 0 is utilized to directly filter out terms contributing to Gaussian noise from the calculated matrix, retaining the non-Gaussian target radiation source characteristics. Based on the topological prior structure of the antenna array manifold matrix, preset array element geometric coordinate information is read from the storage unit. For example, for a uniform linear array, parameter values ​​with an adjacent element spacing of half a wavelength are read to construct a fourth-order parallel decomposition tensor model. The fourth-order cumulative matrix is ​​re-tensified and rearranged according to spatial domain, frequency, polarization, and sampling dimensions to form a fourth-order tensor. This model decomposes the complex received data into four interrelated factor matrices reflecting spatial direction, polarization state, signal waveform, and amplitude attenuation. For example, for a detection mission involving two target sources, if the rank of the tensor decomposition is set to 2, the model can fully describe the physical properties of the two independent radiation sources.

[0073] S202: Based on the fourth-order parallel decomposition tensor model, an alternating least squares iterative algorithm is executed. In each iteration, the factor matrix of the remaining dimensions is fixed and the least squares update is performed on the current dimension until the Frobenius norm objective loss function converges, and the dimensionality-reduced factor matrix is ​​obtained.

[0074] Based on a fourth-order parallel decomposition tensor model, a step-by-step optimization strategy is adopted. First, the four-dimensional factor matrices are initialized, with initial values ​​set to random complex number sequences following a standard normal distribution. In each iteration, the factor matrices of the remaining dimensions are fixed, and a least-squares update is performed on the current dimension. Specifically, the original tensor is expanded along the current dimension to obtain a large matrix. The observation matrix is ​​constructed using the Kronecker product of the remaining factors, and the optimal estimate of the current factor is solved through generalized inverse operations. For example, when updating the spatial factor matrix, the polarization, frequency, and sampling factors are kept constant, and the known values ​​of the factors are used to fit the current spatial manifold. Subsequently, the current Frobenius norm objective loss function is calculated, which is defined as the sum of squares of the differences between the original tensor and the tensor reconstructed from the product of the four factors. The rate of decrease of this loss value is monitored, and a convergence threshold of 0.0001 is set; that is, iteration stops when the percentage change in the loss value between two consecutive iterations is less than this threshold. Experimental test data shows that for a signal-to-noise ratio of 10 dB, the algorithm converges within 35 iterations. The process continues until the target loss function converges, yielding the dimensionality-reduced factor matrix. The factor matrix corresponds to the main feature components of the signal in each dimension. In this way, the originally massive amount of raw data is compressed into a very low-dimensional feature space, while preserving crucial orientation and polarization information.

[0075] S203: Based on the reduced factor matrix, extract the component estimation vector of the target radiation source, calculate the power spectral density of the component energy, and obtain the tensor dimension reduction separation of the target source estimation components;

[0076] Based on the dimensionality-reduced factor matrix, each column is extracted from the factor matrix corresponding to the time dimension. These columns represent independent estimates of the original waveforms of the target source. When calculating the power spectral density of the component energy, a fast Fourier transform is performed on each component vector, the square of the magnitude is calculated, and normalization is performed to obtain the energy distribution curve of the signal in the frequency domain. For example, for a detected frequency-hopping signal, its power spectral density will show a significant narrowband bulge at the corresponding center frequency, allowing for the tensor dimensionality reduction and separation of the estimated target source components. The components are sorted according to the peak intensity of the power spectrum, and pseudo-components with extremely scattered power spectral density distributions and energy values ​​lower than 10% of the principal components are removed, thus locking in the true target signal. To verify the separation performance, the waveform similarity between the separated signal components and the known reference signal is calculated. The advantage of this operational logic is that it utilizes the multidimensional structure preservation capability of tensors to thoroughly suppress background co-frequency crosstalk through fourth-order statistics while reducing dimensionality, improving the purity of the extracted target source components.

[0077] Please see Figure 4 The specific steps for robust second-order cone programming with zero-trap weighted vectors are as follows:

[0078] S301: Extract the source signal estimation vector from the target source estimation component by tensor dimensionality reduction and separation, derive the nominal steering vector of the target radiation source, and introduce a spherical uncertainty set. Define the steering vector mismatch range through the bounded spherical error neighborhood to obtain the nominal steering vector of the target radiation source.

[0079] The source signal estimation vector is extracted from the target source estimation component by tensor dimensionality reduction. Utilizing the directional features in the aforementioned spatial factor matrix, combined with the antenna array wavelength, element spacing, and estimated incident angle, a complex exponential ideal steering vector is constructed. For example, for a signal with an incident angle of 30 degrees, its nominal steering vector is a complex sequence with a fixed phase difference between elements. When introducing a spherical uncertainty set, considering actual element position perturbations and channel coupling, a Euclidean sphere with the nominal steering vector as its center and a preset constant radius is defined. The steering vector mismatch range is defined through a bounded spherical error neighborhood. Setting the uncertainty set radius to 0.1 means that the Euclidean distance offset between the actual steering vector and the nominal vector is limited to this range, thus obtaining the nominal steering vector of the target radiation source. This vector is used as the reference core for robust beamforming, ensuring that the algorithm maintains gain stability even with angular pointing errors within 0.5 degrees or amplitude errors within 2%.

[0080] S302: Based on the nominal steering vector of the target radiation source, the output interference plus noise ratio is the objective function. It is equivalently transformed into the dual form of minimizing the output power. It is relaxed using the Lagrange multiplier method, and then transformed into a second-order cone constraint condition. The inverse lemma is constructed for the covariance matrix.

[0081] Based on the nominal steering vector of the target radiation source, the sampling covariance matrix of the received data is first calculated. This is obtained by extracting and purifying the signal sequence and performing autocorrelation operations. It is then equivalently transformed into a dual form that minimizes the output power. That is, while ensuring the target direction gain is not less than 1, a set of weight vectors is found that minimizes the total output power of the array, thus suppressing strong interference in non-target directions. The Lagrange multiplier method is used for relaxation, transforming the originally complex nonlinear constraint problem into an easily solvable convex optimization form, further transforming it into a second-order cone constraint condition. Specifically, the mismatch range constraint term of the steering vector is expressed using norm inequalities, constructing a conical solution space, and constructing an inverse lemma for the covariance matrix. The sampling covariance matrix is ​​iteratively updated using the matrix inversion lemma, avoiding the computational load caused by direct large-scale inversion. For example, when the number of sampling points increases from 500 to 1000, the computational efficiency is improved by more than 60% through incremental updates. At this point, a mathematical framework for searching the optimal weights is ready, which can automatically balance target gain preservation with interference null depth.

[0082] S303: Extract the covariance matrix of the inverse lemma pair, iteratively calculate the optimal weight vector of the joint dimension of polarization and spatial domain, apply the weight vector to the strong interference direction of the antenna receiving manifold, and generate a robust second-order cone programming null weighted vector.

[0083] The covariance matrix of the inverse lemma is extracted, and optimization is performed under second-order cone constraints using the interior-point method or quasi-Newton method. In each iteration, the array output response under the current weight vector is calculated. When the change in the objective function is less than 0.0001, the current weight is output as the final solution. For example, for a strong interference source located at an azimuth angle of 45 degrees and an elevation angle of 10 degrees, the generated weight vector will produce a gain attenuation exceeding 40 dB in that coordinate direction. The weight vector is applied to the strong interference direction of the antenna receiving manifold, and a robust second-order cone programming null weight vector is generated by weighted summation of the weight vector with the multi-channel signal. To verify the null effect, the radiation pattern of the synthetic beam is measured. If a depression of 45 dB is formed in the known interference direction, and the gain fluctuation in the target direction is less than 0.5 dB, the weight vector is considered robust. The advantage of this operational logic is that the introduction of a spherical uncertainty set avoids the algorithm's self-dissipation phenomenon caused by model mismatch, significantly improving the signal enhancement capability in complex electromagnetic environments.

[0084] Please see Figure 5 The specific steps for obtaining the atomic norm grid reconnaissance and positioning azimuth parameter set are as follows:

[0085] S401: Call the filter signal corresponding to the zero-trap weighted vector of the robust second-order cone programming, construct the atom set within the range of pitch and azimuth angles in the continuous space, and establish a continuous parameter sparse reconstruction model based on the atom norm.

[0086] By invoking the filtered signal corresponding to the zero-trap weighted vector of robust second-order cone programming, the spatial domain is divided into countless extremely small continuous intervals, no longer limited to traditional discrete grid points. The atom set consists of normalized manifold vectors corresponding to different spatial angles, covering the entire space from -180 degrees to 180 degrees azimuth and from -90 degrees to 90 degrees pitch. A continuous parameter sparse reconstruction model based on the atom norm is established, representing the filtered signal as a linear combination of a very small number of atoms in the atom set. This model induces the sparsity of the signal by minimizing the atom norm, which is defined as the infimum of the sum of the magnitudes of the coefficients in all atom decomposition forms. For example, if there are 3 radiation sources in space, the model strives to accurately reconstruct the signal features using 3 corresponding spatial atoms. In this way, the angle estimation problem is transformed into a sparse representation optimization problem in continuous space.

[0087] S402: The continuous parameter sparse reconstruction model is transformed into a convex semi-positive definite programming problem. The dual variables are solved using the interior point method, and the signal covariance matrix without off-grid error is identified. Eigenvalue decomposition is performed on the matrix to divide the signal subspace and noise subspace.

[0088] The continuous parameter sparse reconstruction model is transformed into a convex positive semi-definite programming problem. This process utilizes duality theory, converting atomic norm minimization into a positive semi-definite constraint optimization involving the Hermitian matrix. The optimal solution within the feasible region is found by iteratively calculating the gradient of the barrier function of the Hermitian matrix. During the solution process, the off-grid error-free signal covariance matrix is ​​identified. This matrix is ​​the Toplitz matrix constructed through the dual solution, whose structure ensures that the estimated angle can lie at any continuous value, completely eliminating the quantization error caused by the target not being on the grid point in traditional grid search. Eigenvalue decomposition is performed on the matrix, decomposing it into a signal subspace composed of eigenvectors corresponding to the larger eigenvalues, thus separating the signal subspace from the noise subspace. For example, for an 8-element array, if there are 2 signals, the decomposition yields 2 signal eigenvectors and 6 noise eigenvectors.

[0089] S403: Extract the signal subspace and noise subspace, locate the spatial direction vector that is orthogonal to the signal subspace in the continuous angular domain by searching for spectral peaks, and generate an atomic norm grid reconnaissance and positioning azimuth parameter set;

[0090] The process involves extracting the signal and noise subspaces, constructing a spatial spectral function whose value is defined as the reciprocal of the projection modulus of the spatial atomic vector and the noise subspace. The entire angular domain is traversed to find the maxima of the spectral function. Due to the continuous reconstruction model, the spectral peaks are extremely sharp and precisely located, generating an atomic norm grid for reconnaissance and positioning azimuth parameters. The azimuth and elevation angles corresponding to all spectral peaks that pass a preset energy threshold are recorded. For example, the azimuth angle of a target is measured to be 125.43 degrees, and the elevation angle to be 12.15 degrees. The advantage of this operational logic is that by using continuous spatial sparse modeling, it overcomes the accuracy bottleneck of discrete search and achieves sub-beam-level angular measurement accuracy.

[0091] Please see Figure 6 The specific steps for obtaining the coordinates of the radiation source using volumetric Kalman filtering are as follows:

[0092] S501: Based on the atomic norm grid reconnaissance and positioning azimuth parameter set, the arrival time difference data captured by external image sensors is fused to construct a nonlinear state estimation equation, and the least squares solution is used for initial rendezvous and positioning to obtain the initial state vector of the target radiation source.

[0093] Based on the atomic norm grid-based reconnaissance and positioning azimuth parameter set, image synchronization trigger signals from different stations are retrieved from a high-speed data bus. The microsecond-level time difference of the signal arrival at each station is calculated and converted into a range difference constraint. A nonlinear state estimation equation is constructed, with azimuth, elevation, and range difference as observation terms, and the target's coordinates in three-dimensional space as the state variables to be determined. Initial rendezvous and positioning is performed using the least squares solution. The initial coordinate values ​​are solved using the Gauss-Newton method by constructing the sum of squared observation residuals. For example, the initial iteration point is set as the center of the observation area. After five rapid iterations, the initial state vector of the target radiation source is obtained. This vector contains the target's initial longitude, latitude, altitude, and preliminary velocity estimates, such as longitude 116.32 degrees, latitude 39.95 degrees, and altitude 500.2 meters.

[0094] S502: Extract the initial state vector, generate a Gaussian volume point set using the third-order spherical radial volume rule, propagate it to the observation space through the nonlinear observation equation, calculate the statistical information sequence of the observation prediction value and the real-time multi-station observation value, and derive the Mahalanobis distance;

[0095] An initial state vector is extracted. Based on the covariance matrix of the current state, a set of deterministic sampling points is symmetrically selected in the state space, with the number of sampling points being twice the state dimension. The data is propagated to the observation space through nonlinear observation equations. Each volume point is substituted into complex coordinate transformation and geometric projection formulas to obtain the predicted set of observations. A statistical information sequence is calculated between the predicted and real-time multi-station observations. The information is defined as the difference between the mean of the actual and predicted observation vectors. The Mahalanobis distance is derived by calculating the quadratic product of the information vector and the inverse of its covariance matrix. For example, for a set of azimuth observations, if the actual value is 45 degrees, the predicted value is 44.8 degrees, and the observation standard deviation is 0.1 degrees, the calculated Mahalanobis distance reflects the degree to which the observed value deviates from the predicted trajectory.

[0096] S503: Determine whether the Mahalanobis distance is within the preset statistical confidence interval, perform adaptive weight decay or hard isolation on abnormal information that exceeds the interval, input the corrected information into the capacitive Kalman filter, iteratively update the state covariance matrix and Kalman gain matrix, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

[0097] To determine if the Mahalanobis distance falls within a preset statistical confidence interval, the chi-square distribution table is used, with a significance level set to 0.05. If the Mahalanobis distance is less than the critical value of 7.81, the observation is considered normal. For outliers exceeding the interval, adaptive weight decay or hard isolation is applied. For outliers caused by multipath effects or momentary occlusion, their corresponding Kalman gain weights are forcibly reduced, for example, from 1.0 to 0.1, to weaken their impact on state updates. The corrected information is then input into the capacitive Kalman filter, iteratively updating the state covariance matrix and Kalman gain matrix. Specifically, the information is used to correct the currently predicted state vector, and the covariance range is narrowed based on the prediction error to obtain the coordinates of the capacitive Kalman filter radiation source. These coordinates represent the optimal position estimate after multi-time-step filtering and smoothing. For example, after 10 observation cycles of filtering, the positioning error was reduced from 50 meters at the initial intersection to 8.5 meters in steady state. The advantage of this operation logic is that it effectively solves the mean and covariance drift problem caused by nonlinear transformation through volume point sampling. Combined with anti-outlier logic, it ensures the robustness of dynamic positioning.

[0098] Please see Figure 7 An electronic reconnaissance and positioning system based on digital beamforming includes:

[0099] The interference removal module acquires the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, searches for the optimal rotation order in the two-dimensional time and frequency plane by performing an adaptive fractional Fourier transform, locates the energy accumulation point of linear frequency modulation sweep interference, configures a band-stop filter to block the interference impact in the transform domain, and performs an inverse fractional Fourier transform to generate a transform domain interference suppression and purification signal sequence.

[0100] The tensor separation module purifies the signal sequence based on transform domain interference suppression, calculates the fourth-order cumulant matrix between signal components and suppresses Gaussian color noise, constructs a fourth-order parallel decomposition tensor model and uses alternating least squares to perform tensor dimensionality reduction and blind separation of source signals, and obtains the tensor dimensionality reduction separation target source estimated components.

[0101] The robust shaping module separates the target source estimation components based on tensor dimensionality reduction. It introduces a spherical uncertainty set constraint to address the array guide vector mismatch. It constructs a second-order conical convex optimization function with the output interference plus noise ratio as the objective. It iteratively calculates the adaptive weight vector of the joint dimension of polarization and spatial domain using the matrix inversion lemma, and performs null weighted filtering to obtain the robust second-order conical programming null weighted vector.

[0102] The azimuth extraction module is based on robust second-order cone programming with zero-trap weighted vectors. It constructs an atomic set in the continuous spatial dimension and performs atomic norm minimization reconstruction. It uses semi-positive definite programming to recover the complete signal covariance matrix, searches for direction vectors orthogonal to the noise subspace from the signal subspace, and generates an atomic norm grid reconnaissance and positioning azimuth parameter set.

[0103] The collaborative positioning module is based on the atomic norm grid reconnaissance and positioning azimuth parameter set, and integrates the time difference of arrival data captured by external image sensors. It performs statistical reliability verification by calculating the Mahalanobis distance between the predicted state and the multi-station observation information. The verified information sequence is input into the capacitive Kalman filter to perform nonlinear state update and coordinate convergence operations, and constructs the coordinate values ​​of the capacitive Kalman filter radiation source.

[0104] The above embodiments illustrate preferred embodiments of the present invention. Any equivalent adjustments to the technical solution based on software engineering methods are within the scope of protection, including but not limited to: implementing algorithm logic using different programming languages, refactoring functional modules into services, adjusting data interaction protocols, and optimizing resource scheduling strategies. Any implementation scheme derived from reasonable modifications to the data processing flow, service call chain, or system architecture layer without departing from the core technology of the present invention should be considered within the protection scope defined by the technical solution of the present invention.

Claims

1. An electronic reconnaissance and positioning method based on digital beamforming, characterized in that, Includes the following steps: S1: Based on the polarization-sensitive multi-channel array antenna, a four-dimensional received data matrix is ​​obtained. An adaptive rotation order step search is performed in the preset time and frequency planes. The non-stationary interference energy is gathered by fractional Fourier transform. A band-stop filter is configured to remove the interference impulse component in the transform domain. An inverse fractional Fourier transform is performed to generate a transform domain interference suppression and purification signal sequence. S2: Call the transform domain interference suppression and purification signal sequence, calculate the fourth-order cumulant matrix to eliminate Gaussian noise sensitivity, construct a fourth-order parallel decomposition tensor model, perform tensor dimensionality reduction and blind source separation, extract the target radiation source component, and obtain the tensor dimensionality reduction separated target source estimated component. S3: Based on the tensor dimensionality reduction separation of the target source estimation components, a spherical uncertainty set is introduced to define the neighborhood of the guiding vector error for the array amplitude and phase error. The problem is transformed into a second-order cone programming problem through the matrix inversion lemma. The null weighted vector is calculated, and spatial filtering is performed to obtain the robust second-order cone programming null weighted vector. S4: Based on the robust second-order cone programming zero-trap weighted vector, construct an atomic set in the spatial domain and perform atomic norm minimization reconstruction. Recover the covariance matrix through semi-positive definite programming, extract spatial arrival angle features, and generate an atomic norm grid reconnaissance and positioning azimuth parameter set.

2. The electronic reconnaissance and positioning method based on digital beamforming according to claim 1, characterized in that, The transform domain interference suppression and purification signal sequence includes time-domain sampling amplitude, phase distribution sequence, and polarization state vector; the tensor dimensionality reduction separation of target source estimation components includes component power spectral density, tensor factor matrix, and source signal estimation vector; the robust second-order cone programming null weighted vector includes weight vector magnitude, null center frequency, and spatial gain attenuation value; and the atomic norm grid reconnaissance and positioning azimuth parameter set includes angle of arrival estimation value, atomic decomposition coefficient, and spatial frequency parameter.

3. The electronic reconnaissance and positioning method based on digital beamforming according to claim 1, characterized in that, The specific steps for suppressing and purifying the signal sequence in the transform domain interference are as follows: S101: Receives the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, performs a self-matched fractional Fourier transform on it, searches for the rotation order corresponding to the energy peak in the transform domain, and locates the energy accumulation point of the linear frequency modulation sweep interference. The four-dimensional received data matrix consists of four dimensions: spatial array elements, time-domain sampling, frequency, and polarization. S102: Based on the time-frequency coordinates corresponding to the energy gathering point, configure a blocking filter with a key cutoff bandwidth to block the values ​​in the transform domain that are within the envelope of the interference energy to zero, perform an inverse fractional Fourier transform and restore the time-domain waveform of the electromagnetic signal to obtain a preliminary de-interference signal stream. S103: Extract the preliminary de-interference signal stream, calculate the correlation of the multi-channel polarization manifold, use the minimum mean square error criterion to correct the residual phase fluctuations between channels, and generate a transform domain interference suppression and purification signal sequence.

4. The electronic reconnaissance and positioning method based on digital beamforming according to claim 3, characterized in that, The steps for tensor dimensionality reduction to separate the target source estimation components are as follows: S201: Call the transform domain interference suppression and purification signal sequence, calculate the fourth-order cumulant matrix in multiple channels, remove background Gaussian co-frequency crosstalk components, and construct a fourth-order parallel decomposition tensor model based on the topological prior structure of the antenna array manifold matrix. S202: Based on the fourth-order parallel decomposition tensor model, execute the alternating least squares iterative algorithm. In each iteration, fix the factor matrix of the remaining dimensions and perform least squares update on the current dimension until the Frobenius norm objective loss function converges to obtain the dimensionality-reduced factor matrix. S203: Based on the reduced factor matrix, extract the component estimation vector of the target radiation source, calculate the power spectral density of the component energy, and obtain the tensor-based dimensionality reduction separation of the target source estimation components.

5. The electronic reconnaissance and positioning method based on digital beamforming according to claim 4, characterized in that, The specific steps of the robust second-order cone programming zero-trap weighted vector are as follows: S301: Extract the source signal estimation vector from the target source estimation component separated by tensor dimensionality reduction, derive the nominal steering vector of the target radiation source, and introduce a spherical uncertainty set. Define the steering vector mismatch range through the bounded spherical error neighborhood to obtain the nominal steering vector of the target radiation source. S302: Based on the nominal steering vector of the target radiation source, the output interference plus noise ratio is the objective function. It is equivalently transformed into the dual form of minimizing the output power. It is then relaxed using the Lagrange multiplier method, transformed into a second-order cone constraint condition, and an inverse lemma is constructed for the covariance matrix. S303: Extract the covariance matrix of the inverse lemma pair, iteratively calculate the optimal weight vector of the joint dimension of polarization and spatial domain, apply the weight vector to the strong interference direction of the antenna receiving manifold, and generate a robust second-order cone programming zero-trap weighted vector.

6. The electronic reconnaissance and positioning method based on digital beamforming according to claim 5, characterized in that, The specific steps for setting the atomic norm grid reconnaissance and positioning azimuth parameter set are as follows: S401: Call the filter signal corresponding to the zero-trap weighted vector of the robust second-order cone programming, construct an atom set within the range of pitch and azimuth angles in the continuous spatial domain, and establish a continuous parameter sparse reconstruction model based on the atom norm. S402: The continuous parameter sparse reconstruction model is transformed into a convex semi-positive definite programming problem. Its dual variables are solved using the interior point method, and the signal covariance matrix without off-grid error is identified. Eigenvalue decomposition is performed on the matrix to divide the signal subspace and noise subspace. S403: Extract the signal subspace and noise subspace, locate the spatial direction vector that is orthogonal to the signal subspace in the continuous angular domain by searching for spectral peaks, and generate an atomic norm grid reconnaissance and positioning azimuth parameter set.

7. The electronic reconnaissance and positioning method based on digital beamforming according to claim 1, characterized in that, The method also includes step S5: S5: Integrate the atomic norm grid reconnaissance and positioning azimuth parameter set with the time difference of arrival data captured by the external image sensor, calculate the Mahalanobis distance between the predicted state and the multi-station observation data, dynamically evaluate the statistical reliability of the observation information, filter information data that meets the statistical characteristics, input the capacitive Kalman filter for state update and three-dimensional nonlinear observation equation solution, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

8. The electronic reconnaissance and positioning method based on digital beamforming according to claim 7, characterized in that, The Mahalanobis distance refers to the calculation of the predicted observation value based on the predicted state, obtaining the difference between the predicted observation value and the joint observation vector as the observation information vector, and calculating the product of the observation information vector, the inverse of the observation information covariance matrix, and the transpose of the observation information vector to obtain the Mahalanobis distance. The coordinate values ​​of the volumetric Kalman filter radiation source include longitude coordinates, latitude coordinates, and altitude coordinates.

9. The electronic reconnaissance and positioning method based on digital beamforming according to claim 7, characterized in that, The specific steps for obtaining the coordinates of the volumetric Kalman filter radiation source are as follows: S501: Based on the atomic norm grid reconnaissance and positioning azimuth parameter set, the arrival time difference data captured by external image sensors is fused to construct a nonlinear state estimation equation, and the least squares solution is used for initial rendezvous and positioning to obtain the initial state vector of the target radiation source. S502: Extract the initial state vector, generate a Gaussian volume point set using the third-order spherical radial volume rule, propagate it to the observation space through a nonlinear observation equation, calculate the statistical information sequence of the observation prediction value and the real-time multi-station observation value, and derive the Mahalanobis distance. S503: Determine whether the Mahalanobis distance is within the preset statistical confidence interval, perform adaptive weight decay or hard isolation on abnormal information that exceeds the interval, input the corrected information into the capacitive Kalman filter, iteratively update the state covariance matrix and Kalman gain matrix, and obtain the coordinate values ​​of the capacitive Kalman filter radiation source.

10. An electronic reconnaissance and positioning system based on digital beamforming, characterized in that, The system is used to implement the electronic reconnaissance and positioning method based on digital beamforming as described in any one of claims 1-9, and the system comprises: The interference removal module acquires the four-dimensional received data matrix captured by the polarization-sensitive multi-channel array antenna, searches for the optimal rotation order in the two-dimensional time and frequency plane by performing an adaptive fractional Fourier transform, locates the energy accumulation point of linear frequency modulation sweep interference, configures a band-stop filter to block the interference impact in the transform domain, and performs an inverse fractional Fourier transform to generate a transform domain interference suppression and purification signal sequence. The tensor separation module, based on the transform domain interference suppression and purification signal sequence, calculates the fourth-order cumulant matrix between signal components and suppresses Gaussian color noise, constructs a fourth-order parallel decomposition tensor model, and uses the alternating least squares method to perform tensor dimensionality reduction and blind separation of source signals to obtain the tensor dimensionality reduction separation target source estimated component. The robust shaping module separates the target source estimation components based on the tensor dimensionality reduction, introduces a spherical uncertainty set constraint for array guide vector mismatch, constructs a second-order conical convex optimization function with the output interference plus noise ratio as the target, uses the matrix inversion lemma to iteratively calculate the adaptive weight vector of the joint dimension of polarization and spatial domain, performs zero-trap weighted filtering processing, and obtains the robust second-order conical programming zero-trap weighted vector. The orientation extraction module constructs an atomic set in the continuous spatial dimension based on the robust second-order cone programming zero-trap weighted vector and performs atomic norm minimization reconstruction. It recovers the complete signal covariance matrix using semi-positive definite programming and searches for direction vectors orthogonal to the noise subspace from the signal subspace to generate an atomic norm grid reconnaissance and positioning orientation parameter set.

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