25 results about "Eigendecomposition of a matrix" patented technology

Provided in the present application are a channel information feedback method, a channel information receiving method, and related apparatuses. The channel information feedback method provided in the present application comprises: a terminal device receiving first indication information, wherein the first indication information is used for indicating M space-frequency units for which the terminal device feeds back channel information, M being an integer greater than or equal to 1; and then, on the basis of the first indication information, the terminal device sending the channel information of the M space-frequency units, wherein the channel information of the M space-frequency units is obtained by means of measuring a first reference signal, the first reference signal is carried on N space-frequency units, and the M space-frequency units are some or all of the N space-frequency units, with N being an integer greater than or equal to 1. Therefore, a network device can conveniently perform inference on the basis of the channel information of the M space-frequency units, so as to obtain channel information of the N space-frequency units. A terminal device directly feeds back channel information of some space-frequency units, without the need to perform eigenvalue decomposition and DFT calculation on a downlink measurement channel so as to obtain a precoding matrix. Therefore, the terminal complexity is reduced.

The application discloses a kind of conformal array rotation interference amplitude-phase error correction design methods, first, construct rotating array signal receiving model, according to the radius of rotating platform and angular velocity calculation rotating guide vector, construct rotating array channel amplitude-phase error model, correction source incident signal information acquisition, record the rotation angle of precision turntable;Covariance matrix is solved to the received data and eigenvalue decomposition, construct amplitude-phase error calculation equation;Solve amplitude-phase error matrix, construct amplitude-phase error correction matrix and correct the received data;Solve adaptive weight vector, and weighted output is carried out to the corrected data.The application compared with traditional array amplitude-phase error correction scheme, system structure is simple and easy to realize, without specific algorithm can be completed to the amplitude-phase error caused by array receiving channel is accurately corrected, effectively solve the receiving channel mismatch problem, improve array anti-interference performance.

This invention discloses a method and system for separating AIS aliasing signals using a four-circular array antenna. The steps are as follows: S100: AIS signals are received through multiple antennas to obtain the spatial baseband signal matrix X, and the phase error Δφ is calculated using interval calculation. k S200: Calculate the phase compensation matrix p; S200: Compensate the baseband signal according to the phase compensation matrix to obtain the baseband signal X. comp S300: For baseband signal X comp By expanding the spatial and temporal dimensions, we obtain the spatiotemporal snapshot matrix X. st (t); S400: The covariance matrix R is obtained by estimating the spatiotemporal snapshot matrix. xx S500: For the covariance matrix R xx Eigenvalue decomposition is performed to obtain the signal subspace and noise subspace; S600: DOA estimation is performed using the MUSIC algorithm to construct the spatial spectrum P(θ); S700: The beam w at the optimal solution is obtained using the space-time constrained minimum variance algorithm; S800: The separated signal is output through the sparse separation method of protocol features. This method can significantly improve the availability of AIS self-organizing network and provide more reliable protection for ship navigation safety.

A system and method for spectral learning in persistent cognitive machines implements learning through controlled evolution of a spectral decomposition of a cognitive manifold. The spectral decomposition, comprising eigenvectors and eigenvalues, encodes long-term memory as global geometric structure rather than as stored data or network parameters. The system performs inference operations by projecting incoming data onto the cognitive manifold using a fixed spectral decomposition without modification. Geometric invariants including principal angles, spectral gap ratios, projection residuals, and curvature statistics are continuously monitored to detect structural inadequacy. When invariants exceed thresholds, a learning event modifies the spectral decomposition through eigen decomposition with warm-start initialization while enforcing mode-specific plasticity bounds that are tighter for low-frequency eigenvectors than high-frequency eigenvectors, thereby preventing catastrophic forgetting. The system operates continuously by alternating between inference using fixed spectral decompositions and learning events that modify spectral decompositions through controlled spectral evolution.

This invention discloses a method for detecting respiratory signals using through-wall radar based on PCA and VMD. First, eigenvalue decomposition is performed on the ultra-wideband radar echo data matrix after removing the DC component. Then, mode decomposition is performed on the clutter-free dynamic signal matrix in the slow-time dimension. Relevant mode components within the respiratory frequency band are selected. The selected mode components are reconstructed. Fourier transform is performed in the slow-time dimension to construct a range-frequency spectrum. Finally, a two-dimensional Gaussian template conforming to the spectral characteristics of human respiration is constructed and matched. The range and frequency estimates of the human respiratory signal are calculated. This invention addresses the problems of weak anti-interference capability and high false alarm probability of single clutter suppression methods, thereby achieving accurate respiratory signal detection in strong clutter environments.

The application discloses a matrix space domain filtering and feature vector towed line array sonar array shape estimation method, and belongs to the field of array signal processing and sonar technology. The method firstly uses heading sensor measurement information to preliminarily estimate array element positions through an interpolation fitting method; based on the positions, conventional beam forming is carried out to obtain a coarse estimation azimuth angle of a target signal; a space domain matrix filter is constructed with the azimuth as the center to filter received data to suppress interference; finally, a covariance matrix of the filtered data is calculated and feature decomposition is carried out to extract main feature vector phase information, and the heading sensor information is combined to obtain accurate position coordinates of each array element through a coordinate rotation solution to realize array shape estimation. The application can effectively filter out interference in a complex environment with multiple signal incidence, significantly improves the precision and robustness of array shape estimation, and solves the technical bottleneck that the traditional feature vector method fails under multiple interference conditions.

The application belongs to the technical field of oil and gas exploration, and discloses a frequency space domain feature decomposition denoising method, a device and an analysis method. The denoising method comprises the following steps: transforming original time-space domain data to a frequency space domain; setting a frequency processing range; randomly extracting a part of proportional data as data analysis points on a frequency slice data, taking a rectangular window to expand each data analysis point into a feature analysis sample, traversing all data analysis points to obtain a feature analysis sample set; calculating a covariance matrix of the feature analysis sample set matrix, and performing feature decomposition to obtain a feature vector of an effective signal; taking a rectangular window and expanding the whole frequency slice data point by point, and calculating the effective signal feature vector through inner product to obtain the frequency slice data after denoising; and transforming the seismic effective signal in the frequency space domain back to a time-space domain to obtain the seismic data after final denoising. The application can realize amplitude-preserving denoising of the seismic signal.

A system and method for adaptive geometric diffusion projection enables mapping of heterogeneous high-dimensional representations onto a shared low-dimensional manifold without neural network training. The system maintains landmark points in source spaces and computes their spectral coordinates through graph Laplacian eigen decomposition based on semantic similarities. New input points are projected via harmonic extension, computing weighted interpolations of nearby landmark spectral coordinates. A geometric optimization process refines positions while maintaining manifold constraints through tangent space projections. The system continuously monitors geometric invariants including principal angles, spectral gaps, and curvature distributions. When invariants exceed thresholds, targeted adaptations occur: spectral basis updates using warm-started iterations, landmark set augmentation in high-residual regions, or parameter adjustments. The approach supports logarithmic computational scaling, enables streaming operation on continuous data, and handles multimodal inputs through reliability-weighted consensus. The system maintains projection quality indefinitely through continuous geometric monitoring and local adaptations.

This application relates to the technical field of intelligent measurement, and in particular to a method, system, device, and medium for component measurement path planning based on sparse images. The method includes: expanding the boundaries of the sparse image and filling the mask matrix; obtaining 3D visual mask points based on the fine mask; generating an initial sparse point cloud based on the 3D visual mask points; constructing a coarse 3D data model based on the initial sparse point cloud; performing clustering and redundant region removal on the coarse 3D data model; constructing a covariance matrix based on the working area of ​​the effective measurement unit; performing eigenvalue decomposition on the covariance matrix; calculating the camera spatial position based on the surface normal vector field and the preset vertical measurement height; modeling the camera measurement posture using the camera spatial position; performing field-of-view coverage analysis on the working area of ​​the effective measurement unit and the surface normal vector field using the camera measurement posture model; analyzing the scanning spatial position and calculating the optimal path objective function, thereby improving the efficiency of component measurement.

The application relates to the technical field of computer data processing, and discloses a portfolio optimization method based on matrix decomposition technology and related equipment; the method comprises the following steps: obtaining portfolio data from an external memory or a local memory; the portfolio data comprises asset names of all assets in a portfolio and historical price data of a preset time period; based on the portfolio data, the average yield of the portfolio and a covariance matrix are calculated; the covariance matrix is subjected to eigenvalue decomposition to obtain a first matrix Q and a second matrix D; an auxiliary variable is constructed, a target function and a constraint condition are constructed based on the auxiliary variable; the target function and the constraint condition are input into an SQP algorithm for solving to obtain a solution of the auxiliary variable; and the weight distribution of each asset in the portfolio is calculated based on the solution of the auxiliary variable. The application can greatly improve the solving efficiency of the model, reduce the memory occupation, save the computer data processing time, and reduce the computer energy consumption.

The application belongs to the technical field of cross of graph signal processing and complex network analysis, and particularly relates to an expected graph Hilbert transform method and system for uncertain graph topology, which comprises the following steps: 1. constructing a graph topology probability space to form a graph topology probability distribution model; 2. calculating an expected shift operator; 3. performing characteristic decomposition on the expected shift operator to obtain eigenvalues and eigenvectors, forming an expected graph Fourier basis, designing a Hilbert mask function according to the type of the graph, performing expected graph Hilbert transform to obtain an EGHT result; 4. constructing an expected graph analytic signal according to the original graph signal and the EGHT result; and 5. extracting a robust feature, calculating an instantaneous amplitude and an instantaneous phase. The method overcomes phase jump and amplitude distortion caused by spectrum basis instability, and improves the robustness and feature fidelity of the analytic signal construction and extraction method.

In an embodiment, an apparatus of a digital unit (DU) is provided. The apparatus can include a transceiver, a memory to store instructions, and a processor. The instructions, when executed by the processor, can direct the apparatus to obtain a channel frequency response from a reference signal from a terminal, obtain an eigenvector by eigen decomposition of the channel frequency response, obtain a transformed vector by performing a two-dimensional Fourier transform on the eigenvector, identify, according to the transformed vector, a basis vector of a plurality of basis vectors of an enhanced type 2 codebook by a decision metric, determine a precoding matrix using the identified basis vector, and transmit, by a radio unit (RU), downlink data to the terminal to which the precoding matrix is applied.

The application discloses a kind of main distribution network power flow model no solution traceability and correction method, it is related to power system dispatching technical field, including, acquisition real-time measurement data pre-processing, obtain quantum noise intensity coefficient;Quantum state density matrix is generated based on quantum noise intensity coefficient, and quantum fidelity is obtained by characteristic decomposition mapping;Based on quantum fidelity, the minimum eigenvalue is extracted, and the fault node coordinates are located by no solution traceability mapping, and the fault severity index is obtained by negative exponential mapping;Based on fault severity index, no solution traceability grade is divided, and fault scene is output;Based on fault scene, the set of power flow inversion control instructions is obtained, and the power flow no solution risk early warning value is corrected.The quantum fidelity mapping accurately locates the power grid fault source, eradicates the main distribution network model no solution problem, promotes the landing of quantum sensing industry and improves the fault response speed.

The application discloses a method for direction finding of unknown coherent sources based on double relaxation solution, and belongs to the technical field of array signal processing. The application calculates the covariance matrix of array receiving signals, and performs eigenvalue decomposition on the covariance matrix, then sorts the eigenvalues to obtain the eigenvectors corresponding to the maximum eigenvalue and the minimum eigenvalue, constructs a dictionary matrix of beam domain steering vectors, and realizes convex optimization solution of the linear relationship between the dictionary matrix and the maximum and minimum eigenvectors by introducing a relaxation factor, and completes accurate calculation of the signal wave direction. The application can provide a high-precision direction finding method for the passive detection field under the condition that there are related sources and the number of sources is unknown.

This application provides a channel information feedback method, a channel information reception method, and related apparatus. The method includes: a terminal device measuring a first reference signal to obtain channel information for N space-frequency units, where the first reference signal carries the N space-frequency units, and N is an integer greater than or equal to 1. Then, the terminal device sends first indication information and channel information for M space-frequency units. The first indication information indicates the M space-frequency units, where the M space-frequency units are some or all of the N space-frequency units, and M is an integer greater than or equal to 1. A network device infers the channel information for the N space-frequency units based on the channel information of these partial space-frequency units. The terminal device does not need to perform eigenvalue decomposition and DFT calculation on the precoding matrix; instead, it directly feeds back the channel information of a partial space-frequency unit, thereby reducing terminal complexity.

This invention discloses a hybrid distributed source DOA estimation method based on the rank deficiency principle. First, a distributed source model is established where circular and non-circular signals are simultaneously incident on an array antenna. Second, the received signal is augmented using the conjugate of the received signal, and its covariance matrix is ​​calculated. Next, eigenvalue decomposition is performed on the covariance matrix to obtain the noise subspace under hybrid source conditions. Finally, based on the rank deficiency principle, a cost function is derived, and direction-of-arrival estimation is completed through one-dimensional spectral peak search. This method is applicable to scenarios where both circular and non-circular sources exist simultaneously in space. Compared to algorithms requiring two-dimensional search, this algorithm effectively reduces computational complexity while maintaining good angle estimation performance.

This invention discloses a method for estimating the spatial power spectrum of a small-aperture linear array based on ellipsoidal semi-axis measurement, comprising: S1. acquiring a time-domain data matrix; S2. calculating a frequency-domain data matrix; S3. calculating a set of frequency indices; S4. decimating the frequency-domain data matrix; S5. determining a set of scanning directions; S6. calculating a time compensation vector; S7. calculating a phase compensation matrix; S8. performing phase compensation on the decimated frequency-domain data matrix; S9. constructing and solving a positive semi-definite programming problem; S10. calculating the ellipsoidal semi-axis measurement; and S11. calculating the spatial power spectrum based on the ellipsoidal semi-axis measurement. This method directly utilizes the frequency-domain data matrix to estimate the spatial power spectrum, eliminating the need to calculate the signal covariance matrix or perform eigenvalue decomposition. While reducing computational complexity, compared to traditional spatial power spectrum estimation methods based on conventional beamformers, it is more advantageous for estimating target directions when the number of array elements is small or the element spacing is much smaller than half the signal wavelength.

This application provides a channel information feedback method, a channel information receiving method, and related apparatus. The method includes: a terminal device receiving first indication information, which instructs the terminal device to feed back M space-frequency units (SQUs) of channel information, where M is an integer greater than or equal to 1; then, the terminal device transmits the channel information of the M SQUs according to the first indication information. The channel information of the M SQUs is obtained by measuring a first reference signal, which is carried by N SQUs. The M SQUs are some or all of the N SQUs, where N is an integer greater than or equal to 1. This facilitates network devices inferring the channel information of the N SQUs based on the channel information of the M SQUs. The terminal device does not need to perform eigenvalue decomposition and DFT calculation on the downlink measurement channel to obtain a precoding matrix, but directly feeds back the channel information of a portion of the SQUs, thereby reducing terminal complexity.

This invention discloses a kernelized inverse nearest neighbor discriminant analysis method, comprising the following steps: obtaining training image samples; mapping the input data to a high-dimensional space using a Gaussian kernel function; obtaining the representations of the intra-class and inter-class scatter matrices of the training image samples in the high-dimensional space using kernel tricks and the inverse nearest neighbor algorithm; learning the projection matrix that maximizes the inter-class scatter matrix and minimizes the intra-class scatter matrix through feature decomposition; extracting features from the training and test image samples using the projection matrix; and classifying the test samples using the nearest neighbor algorithm. This invention, for the first time, extends the inverse nearest neighbor linear discriminant analysis method to a high-dimensional space to solve the classification problem of nonlinear data. It proposes using a Gaussian kernel function for high-dimensional mapping, kernelizing the algorithm, and using kernel tricks for non-explicit mapping derivation. High-dimensional inverse nearest neighbors are established in the space after Gaussian function mapping to obtain the scatter matrix, wherein the kernel trick is used to realize the distance representation in the high-dimensional space.

The application discloses a noise estimation method, device, storage medium and computer program product, relates to the technical field of communication, and the method comprises the following steps: determining a noise-free frequency domain channel correlation matrix and a least square channel estimation based on a pilot signal; performing eigenvalue decomposition on the noise-free frequency domain channel correlation matrix to obtain a noise space eigenvector; and calculating noise estimation by projecting the noise space eigenvector to the least square channel estimation. The application solves the problem that the traditional method depending on a signal space is greatly affected by the filter passband width and the passband ripple, and has a large error in a high SNR multipath channel, improves the accuracy of noise estimation, improves the performance of equalization under high SNR high-order modulation, reduces BLER, solves the problem of large correlation matrix calculation amount, and reduces the complexity of system design.

This application provides a dynamic ad hoc network positioning method and system based on multi-UAV cooperation, belonging to the field of UAV communication and positioning technology. First, this application acquires the arrival angle spectrum and bit error rate data of the communication link, and corrects the spatial covariance matrix using a weighting factor mapped by the bit error rate. Then, it determines the relative azimuth vector and constructs the observation matrix through eigenvalue decomposition and orthogonal projection. Next, it maps the observation matrix to a geometric configuration constraint space to establish a topological cost function, and uses gradient iteration to update and solve for the target configuration. Finally, it combines the reference position information to complete the coordinate transformation, achieving global positioning of the UAV swarm. This application can effectively improve the accuracy of UAV swarm cooperative positioning in dynamic environments by introducing bit error rate-weighted correction of angle estimation and combining it with geometric manifold constraint optimization.

This application presents a high-resolution velocity and angle measurement method based on a frequency-domain dimensionality reduction sparse Bayesian algorithm, applicable to radar signal processing in two-dimensional uniform rectangular array (URA) systems. The method constructs locally continuous frequency-domain feature matrices in both the azimuth and Doppler dimensions, and generates a dimensionality reduction matrix using eigenvalue decomposition, achieving bidirectional frequency-domain dimensionality reduction of the original observation data. Then, it combines this with the Sparse Bayesian Learning (SBL) algorithm to perform two-dimensional sparse spectrum reconstruction on the dimensionality-reduced observation signal, thereby obtaining accurate and high-resolution joint estimation results for angle and velocity. This method, combining frequency-domain dimensionality reduction and Bayesian sparse reconstruction, significantly reduces computational complexity while maintaining excellent super-resolution capability and noise resistance, making it particularly suitable for velocity and angle measurement scenarios with dense target groups and low signal-to-noise ratios.

This invention discloses a geomagnetic interference separation method based on sliding window dynamic principal component analysis, belonging to the field of magnetic field signal processing and positioning technology. The method includes: continuously acquiring magnetic field signals to form a data stream; dynamically capturing the current window data using a sliding window; performing principal component analysis on the window data to establish a dynamic background field model through eigenvalue decomposition; adaptively selecting the top k principal components based on the cumulative contribution rate of eigenvalues ​​to reconstruct the geomagnetic background field estimate; subtracting the background field estimate from the original data to obtain the target magnetic signal; and iteratively executing the sliding window to achieve continuous real-time separation. This invention extends static PCA to dynamic sliding window PCA, effectively solving the problem that traditional PCA cannot adapt to real-time dynamic data streams through adaptive principal component selection and a unique reconstruction method. It can efficiently suppress geomagnetic interference, significantly improve target signal quality and magnetic positioning accuracy, and eliminates the need for sensor fusion and external calibration.

This invention discloses a method for calculating polarization parameters of radar array signals based on the vector MUSIC algorithm, relating to the field of radar array signal processing technology. First, this invention obtains the polarization signal steering vector matrix and noise subspace corresponding to the radar array signal, and performs matrix multiplication to obtain a 2×2 complex Hermitian matrix. By extracting the ratio of the imaginary to the real part of the second element in the first row of the complex Hermitian matrix, the arctangent function is directly applied to obtain the polarization phase difference, avoiding the process of solving for eigenvectors. Then, the minimum eigenvalue of the complex Hermitian matrix is ​​calculated, and combined with the trace of the complex Hermitian matrix, the arctangent value is calculated, and the polarization auxiliary angle is directly derived, eliminating the need for a complete eigenvalue decomposition process. Therefore, when calculating polarization parameters, the calculation starts from the definition of polarization parameters, i.e., directly from the definition of polarization phase difference and polarization auxiliary angle, directly avoiding the complex calculations brought about by eigenvalue decomposition, thereby reducing computational complexity and improving computational accuracy.

This invention relates to a coherent calculation method for gradient structure tensors based on Gaussian differential operators. It includes: preprocessing a 3D seismic data volume; performing a Hilbert transform on the processed data volume and calculating the instantaneous phase, using the calculated instantaneous phase information as input data for constructing the structure tensor; using multi-scale Gaussian differential operators to calculate the gradients in the traverse, trace, and time directions to construct the gradient structure tensor; using Gaussian smoothing in the approximate fault and stratigraphic directions to enhance the lateral discontinuities in the gradient structure tensor corresponding to fault and stratigraphic features; performing matrix eigenvalue decomposition; and finally, performing different coherence solutions. This invention's gradient structure tensor coherent calculation method based on Hilbert transform and Gaussian smoothing can highlight narrow channels and small-impact faults; by utilizing the structure tensor, it reduces the sensitivity of coherence algorithms to noise, reduces signal clutter and strong noise interference at the intersections of channels and small-scale faults, and improves the accuracy of coherence identification.