46 results about "Toeplitz matrix" patented technology

The invention provides a continuous wave sonar direct wave suppression method, device and equipment and a storage medium, and the method comprises the steps: intercepting a target segment signal from a received signal, the target segment signal being composed of continuous Nw sampling points in the received signal; an estimation channel corresponding to the target segment signal is solved through a basis tracking algorithm, a dictionary matrix of the basis tracking algorithm is an Nw * Nw Toeplitz matrix, the first column is the first to Nw sampling points of the transmitted signal, and the second to Nw elements of the first row are zero; if the current estimation channel meets a judgment condition, the current estimation channel is determined as a final channel, and the judgment condition includes that the maximum element value in the estimation channel is larger than a first threshold value; reconstructing a direct wave and a multipath signal thereof according to the transmitted signal and the final channel; and subtracting the direct wave and the multipath signal thereof from the received signal to obtain a suppression result. According to the invention, on the premise of ensuring that the target echo energy is not lost, the sidelobe interference of the direct wave is effectively eliminated.

The invention discloses a mechanical fault diagnosis method based on maximum correlation kurtosis depth unrolling, and relates to the technical field of mechanical state monitoring, and the method specifically comprises the following steps: obtaining a vibration signal sliding window segmentation calculation kurtosis, and generating a window priority sequence through cross-correlation correction sorting; a high-quality window is selected to be combined with a rotating speed integral and a fast Fourier transform detection angle period to form an angle domain period boundary set, a segmentation signal calculation error is subjected to quasi-Newton optimization de-convolution to obtain a deep de-convolution fault feature signal, a Toeplitz matrix is constructed, and a multi-layer fault feature vector is weighted and extracted; according to the method, vibration signal sorting is segmented through a sliding window, so that impact positioning is enhanced, noise is reduced, definition is improved, an angle domain period is dynamically recognized, feature synchronization is achieved, error optimization unrolling is performed, impact recovery is enhanced, and feature dimensions are expanded through matrix weighted mapping. And the recognition precision and adaptability are improved through multi-scale aggregation.

The invention provides an intelligent metasurface-assisted non-line-of-sight target DOA estimation method based on atom norm minimization. After a receiving end obtains an echo signal, the echo signal is left multiplied by a known channel vector pseudo-inverse, the influence of an RIS backward channel is eliminated, and an angle estimation problem is converted into a convex optimization problem; a convex optimization problem is solved by using a CVX toolbox in Matlab, two one-dimensional Toeplitz matrixes respectively containing DOD and DOA information are constructed, the two one-dimensional Toeplitz matrixes are respectively subjected to one-dimensional Vandermonde decomposition to solve a signal angle, and joint estimation of the DOD and the DOA is realized. According to the method, the active regulation and control capability of the RIS is enhanced, so that the problem that DOA estimation precision and calculation efficiency in a traditional non-line-of-sight scene are difficult to consider at the same time is effectively solved, and the real-time performance of azimuth angle estimation is remarkably improved while relatively low calculation complexity is kept; and particularly under the conditions of low signal-to-noise ratio and low snapshot number, high-precision estimation of the target orientation can still be realized.

The application provides a uniform plane array FDA-MIMO three-dimensional target positioning method and system based on complete decoupling atomic norm minimization. The method converts the problem into a semi-positive programming solution by constructing a low-dimensional observation matrix and using complete decoupling atomic norm, and realizes joint estimation of distance, pitch angle and azimuth angle through Vandermonde decomposition. Compared with high complexity algorithms (VANM, etc.), the application significantly reduces the calculation amount by decomposing the Toeplitz matrix, and improves the single snapshot precision by using the multi-slice constraint mechanism. Compared with low complexity algorithms (3D-DANM), the application introduces an auxiliary variable matrix to restore the distance-angle coupling structure, avoids the performance loss caused by excessive relaxation, and significantly improves the estimation accuracy and multi-target resolution capability while ensuring the calculation efficiency.

The invention discloses an ultra-wideband radar super-resolution imaging method based on spectrum mode decomposition. The method comprises the following steps: acquiring radar observation data; constructing a radar observation data vector and a frequency dependence factor set, and defining a frequency spectrum mode matrix for each frequency dependence factor, so as to obtain a Toeplitz matrix and a single-mode frequency spectrum vector corresponding to an optimal solution through solving a convex optimization problem; estimating scattering parameters of each scattering center in the scene according to the Toeplitz matrix and the single-mode spectrum vector; and carrying out spectrum extrapolation and radar image calculation according to the scattering parameters so as to output a super-resolution radar image of the target according to a calculation result. The radar spectrum is subjected to mode decomposition according to different frequency dependence factors, the estimation accuracy of target parameters is improved, the spectrum extrapolation precision under the large frequency span is improved, and then the radar super-resolution imaging quality is improved.

The invention belongs to the technical field of direction of arrival, and relates to a sparse array coherent signal source DOA estimation method based on Toeplitz matrix reconstruction. Comprising the following steps: S1, assuming that a coherent signal source is incident to a sparse array, further constructing a sparse array observation signal model, and further solving a theoretical covariance matrix of the sparse array observation signal model; s2, performing solution operation on the theoretical covariance matrix in the S1; s2, on the basis of the S2, further constructing a Hermitian Toeplitz matrix through virtual array interpolation, and further realizing DOA estimation based on the virtual array interpolation; and S3, obtaining a virtual ULA based on the sparse array of the S1 by combining the S2, performing solution operation on the virtual ULA, and then constructing a Toeplitz matrix based on physical array interpolation so as to realize DOA estimation based on virtual array interpolation. According to the algorithm provided by the invention, the coherent signal source can be accurately estimated under the condition that the degree of freedom and the array aperture are not lost. Simulation experiment results show that the proposed algorithm is superior to the existing algorithm in the aspect of estimating the coherent source.

The purpose of this invention is to provide a method for DOA estimation of acoustic vector arrays based on quaternion matrix dimensionality reduction, comprising the following steps: constructing a CAACIS acoustic vector coprime array at the receiver; establishing a quaternion model of the received signal based on the array output; estimating the quaternion covariance matrix; performing dimensionality reduction on the quaternion covariance matrix to obtain a virtual array received signal model of the acoustic vector coprime array; reconstructing the Hermitian-Toeplitz matrix; performing eigenvalue decomposition on the Hermitian-Toeplitz matrix and constructing a spatial spectral function; and obtaining the DOA estimation result through spectral peak search. This invention addresses the problem of how to achieve multi-objective DOA estimation with both low complexity and good performance based on a quaternion framework under acoustic vector coprime arrays.

The invention discloses a mode identification method based on an unsupervised optimization covariance random subspace method. The method comprises the following steps: arranging a vibration sensor on a to-be-detected structure with noise interference or a weak excitation mode to obtain a structure dynamic response; constructing a Hankel matrix, calculating a covariance matrix Ri, and constructing a Toeplitz matrix based on the Ri; calculating an extended observable matrix Oi and an extended controllable matrix Gamma i based on the weighted Toeplitz matrix; defining the range of the row block number i and the model order N of the Toeplitz matrix; analyzing the sensitivity of the row block number i of the Toeplitz matrix and the model order N based on a parameter optimization index kP (i, N); the singular entropy increment of the weighted Toeplitz matrix T1i is calculated; calculating the singular entropy increment curvature of the weighted Toeplitz matrix T1i, and determining a critical model order Nc (i); calculating an accumulated parameter optimization index kappa P value from a minimum model order Nmin to a critical model order Nc (i) under the condition of different Toeplitz matrix row block numbers i; selecting a parameter combination {iopt, Nopt} corresponding to the minimum parameter as an optimal parameter; identifying a system matrix and determining modal parameters, and drawing an original stability diagram; and on the basis of DBSCAN clustering, automatically identifying each order of physical modality from candidate modalities containing noise interference. A corresponding system is also disclosed.

The application provides a self-adaptive signal beam forming method, device, equipment and storage medium. The method is based on a 2N+1 element uniform linear array receiving signal. The method comprises the following steps: a multiple Toeplitz matrix is constructed, and a covariance matrix is obtained by merging; a signal direction vector is calculated according to an eigenvalue and an eigenvector, and an expected signal direction vector is obtained by optimization; a noise power is estimated by using a minimum eigenvalue, a corresponding relationship between a signal power and the eigenvector is established, and an expected signal power is determined; a covariance matrix of mutually independent noise is reconstructed according to the noise power, the corresponding relationship and the expected signal power; and the expected signal direction vector and the reconstructed covariance matrix are brought into a Cap on beam former, and an optimal weight vector is calculated to control beam forming. The method improves the performance and reliability of the beam forming system in a complex signal environment by constructing a multiple Toeplitz matrix and using the characteristics of the multiple Toeplitz matrix for signal decorrelation and covariance matrix reconstruction.

The application belongs to the technical field of radio positioning, and particularly relates to a kind of intelligent metasurface assisted user positioning method based on modified dimensionality reduction MUSIC.The method utilizes the phase reconfigurable characteristics of intelligent metasurface, constructs zero-mean orthogonal phase coefficients, separates out base station-user direct channel and base station-intelligent metasurface-user cascade channel, estimates intelligent metasurface-user channel under the assumption that base station-intelligent metasurface has good line-of-sight path, thereby calculates the left and right correlation coefficients of two channel sections, and reconstructs left and right pseudo-covariance matrix using the Toeplitz matrix of correlation coefficient, further obtains pseudo-covariance matrix, then performs eigenvalue decomposition on pseudo-covariance matrix, constructs modified dimensionality reduction MUSIC spatial spectrum using the orthogonality of signal space and noise space, thereby estimates the azimuth of base station-user and intelligent metasurface-user, and then calculates the user position using least square method.The application trades off higher estimation accuracy for complexity.

The invention discloses a coherent signal source DOA estimation method based on Toeplitz reconstruction and Schur decomposition, and the method comprises the following steps: S1, array receiving signal acquisition and covariance matrix calculation, S2, first Toeplitz matrix construction, S3, covariance matrix Schur decomposition and signal matrix construction, S4, second Toeplitz matrix construction, and S5, matrix fusion and DOA estimation. A first Toeplitz matrix is constructed; the method comprises the following steps: constructing a first Toeplitz matrix, performing Schur decomposition on a covariance matrix, constructing a signal matrix, constructing a second Toeplitz matrix by taking a mean value of each diagonal line of the signal matrix as a reference, fusing the two Toeplitz matrixes, performing subspace separation and spectral peak search on the fused matrix to realize DOA estimation, and performing simulation verification to obtain the DOA estimation result. The algorithm provided by the invention can effectively reduce the DOA estimation error of the coherent signal source under the scenes of low signal-to-noise ratio and few snapshots, and can effectively improve the stability of the estimation result.

The present application relates to the technical field of signal processing, in particular to a kind of sparse low-rank decomposition DOA estimation method based on virtual array interpolation, establish receiving signal model;The sampling covariance matrix of receiving signal model is calculated, and vectorization operation is carried out to sampling covariance matrix, since there is hole for a non-uniform virtual array in virtual array, virtual sensor is inserted at the hole position of virtual array, form virtual uniform array, reconstruct virtual uniform array receiving signal model as Toeplitz matrix, and carry out low-rank and sparse matrix decomposition into signal covariance matrix and noise covariance matrix;Signal covariance matrix is reconstructed using low-rank matrix recovery theory, and the expected signal covariance matrix is recovered, it is carried out eigenvalue decomposition using MUSIC algorithm, and the target DOA is estimated.This application makes full use of all virtual array element information, avoids the inaccuracy of DOA estimation caused by information loss.

The invention relates to the field of quantum key distribution, and discloses a key distribution anti-attack method and system based on decoy state coding and an irrelevant protocol, and the method comprises the steps: Alice generates a signal state quantum pulse and a three-intensity decoy state quantum pulse in a mixed manner, and transmits and monitors channel parameters in real time through a quantum channel; bob randomly selects a measurement base for measurement, records original data and delays to obtain a state type identifier; the Charlie transmits a random test state, collects Bell inequality verification parameters, and implements equipment-independent security verification; the two parties screen matched data through base comparison, evaluate channel security and correct a signal state bit error rate by using a decoy state bit error rate; and based on the screened keys, a Toeplitz matrix negotiation protocol is adopted for compression to generate a final key, 10% of the keys are randomly extracted for cross validation, and after the cross validation is passed, the keys are stored, and the decoy state strength and the measurement base group parameters are updated. According to the method, an Alice, Bob and Charlie three-party system is constructed to form an iterative security closed loop, attack is comprehensively resisted, and a security key is generated.

The invention discloses an array signal direction-of-arrival phase recovery method and system based on meshless compressed sensing, a computer and a storage medium, and the method comprises the steps: collecting the amplitude observation data of a target signal through a linear sampler, and forming an observation vector; a matrix variable is introduced, a linear relation between the observation vector and the matrix variable is established, and x is an array signal to be recovered; constructing a joint optimization model, wherein the model is a positive semidefinite programming model containing an atomic norm minimization constraint and a phase lifting constraint; performing numerical solution on the positive semidefinite programming model to obtain an optimal solution; and constructing a Toeplitz matrix according to the optimal solution to perform frequency estimation, and obtaining direction-of-arrival information of the target signal. According to the invention, under the condition of only signal amplitude measurement, phase information loss or serious distortion, high-precision recovery and direction-of-arrival estimation of array signals can be realized.

The invention relates to a self-adaptive quantum random number generation method based on real-time entropy estimation, and belongs to the technical field of quantum random number generation. According to an existing integrated quantum random number generator, due to the non-stationary characteristic of a physical entropy source, the entropy rate dynamically drifts, and after-processing parameters are fixed, randomness safety and generation efficiency are difficult to guarantee at the same time. According to the method, the state transition probability of the original random bit stream is counted in real time, the confidence interval correction is introduced to calculate the minimum entropy, the input bit width is dynamically adjusted accordingly, the Toeplitz matrix is reconstructed for random extraction, and self-adaptive adjustment of the compression ratio is achieved. According to the method, the compression ratio is increased to ensure the security of the output random number when the entropy source quality is reduced, and the compression ratio is reduced to improve the generation efficiency when the entropy source quality is improved, so that the dynamic balance between the randomness security and the generation efficiency is realized on the premise of keeping integration and low cost.

The invention relates to the technical field of ultrasonic communication, in particular to a design method of an ultrasonic cross-metal communication channel echo cancellation filter, which comprises the following steps of: acquiring a composite signal which is received by a receiving end and comprises a direct signal and an echo signal; creating a corresponding filter mask according to the length of a pre-selected filter; generating a Toeplitz matrix of the composite signal, and according to the filter mask, rejecting a column corresponding to a filter coefficient invalid for echo elimination in the Toeplitz matrix to form a new Toeplitz matrix; constructing a sparse optimization problem of a filter coefficient of the filter; solving the sparse optimization problem to obtain a sparse vector, and recovering the sparse vector into a corresponding filter coefficient according to the filter mask; and the filter is designed according to the filter coefficient obtained through recovery, so that the echo signal in the composite signal is filtered through the designed filter, interference can be avoided, and the filtering performance is improved.

The application provides a low-complexity target DOD-DOA and Doppler frequency joint estimation algorithm based on space-time nested sampling, and the joint estimation algorithm comprises the following steps: step 1: configuring a bistatic MIMO radar system into a space-time nested sampling model, and sampling a received signal {x q (l)} by using the space-time nested sampling model; q Step 2: performing multi-stage delay sampling on the received signal {x q (l)} to obtain {y(l)}; step 3: performing matched filtering on the received signal {y(l)} to obtain {y(t)}; step 4: solving a target echo signal covariance matrix R; step 5: vectorizing and de-redundantizing the target signal covariance matrix, and obtaining a new observation signal according to the obtained observation signal; step 6: performing three-dimensional Toeplitz matrix iterative reconstruction on the new observation signal to obtain an equivalent covariance matrix R xx in a virtual domain; and step 7: solving DOD-DOA and Doppler frequency parameters of the target by using an improved multi-dimensional ESPRIT algorithm.

A distributed acoustic sensing (DAS) system may include an optical fiber, a phase-sensitive OTDR (φ-OTDR) coupled to the optical fiber, and a processor cooperating with the φ-OTDR. The processor may be configured to generate a series of covariance matrices for DAS data from the φ-OTDR, and determine an acoustic event based upon comparing the series of covariance matrices with a corresponding Toeplitz matrix.

The invention discloses a near field source positioning method based on covariance fitting. Calculating a spatial correlation function of an array element and constructing single-snapshot equivalent data by utilizing a symmetric characteristic of a uniform linear array, and eliminating signal correlation by utilizing spatial smoothing; performing convex optimization reconstruction on the smoothed covariance matrix based on a covariance fitting criterion, and recovering an idealized Toeplitz matrix structure; solving the reconstructed covariance matrix by adopting a rooting MUSIC algorithm, and resolving a near-field source angle parameter; and constructing a distance sensitive steering vector according to an angle estimation result, and establishing a distance polynomial equation by using noise subspace orthogonality to realize joint optimization estimation of the angle and the distance. Through the covariance matrix reconstruction and polynomial rooting technology, the estimation precision under the conditions of low signal-to-noise ratio and few snapshots is improved, the operand is reduced, meanwhile, the cumulative effect of angle errors to distance estimation is avoided, and efficient matching of near-field source positions is achieved in a complex scene.

The invention provides a high-precision neighborhood joint tomography SAR (Synthetic Aperture Radar) super-resolution three-dimensional imaging method and device, and relates to the technical field of radar signal processing, and the technical key points are as follows: carrying out local windowing operation on a multi-channel SAR image subjected to registration processing, and constructing a multi-measurement vector MMV observation matrix; a Hankel-Toeplitz hybrid matrix structure is introduced to implement double constraints on an MMV matrix, wherein the Hankel matrix structure is used for enhancing the time-domain low-rank characteristic of each pixel signal in the MMV, and the Toeplitz matrix structure ensures that multiple pixels share consistent elevation frequency information; converting time-frequency domain double constraints into a joint optimization problem, and establishing a neighborhood joint tomography model; a projection gradient descent algorithm based on matrix decomposition is adopted to achieve efficient model solving, a high-precision SAR three-dimensional super-resolution reconstruction result is obtained, and high-resolution three-dimensional SAR imaging verification is achieved through land exploration No.1 satellite data.

The invention discloses a centrifugal pump tiny fault detection method based on improved pseudo-spectrum estimation. The method specifically comprises the following steps that 1, an autocorrelation function of a vibration signal is calculated; step 2, constructing a Toeplitz matrix R by using an autocorrelation function; step 3, decomposing the Toeplitz matrix R to obtain a feature vector matrix U; 4, calculating signal subspace energy and noise subspace energy; 5, calculating a model order evaluation cost function B (p); step 6, selecting an order po which minimizes B (p) as an optimal order; 7, calculating a pseudo frequency spectrum of each frequency component of the signal; and 8, performing feature extraction on the pseudo-spectrum, constructing a crack sensitive feature value J, and judging whether the centrifugal pump impeller has fine cracks or not according to the J. By adopting the method, tiny faults in the operation process of the centrifugal pump can be accurately identified.

This invention discloses a radar target recognition method based on a two-dimensional self-selected weighted convolutional neural network, comprising: first, constructing a two-dimensional data signal from the original one-dimensional time-domain signal obtained by the radar signal processing system using a Toeplitz matrix; then, generating training and test sets from the constructed two-dimensional data signal according to the categories of the original signal; constructing a coordinate attention module, and then constructing a convolutional neural network composed of self-selected weighting modules; inputting the training set data into the constructed network for training to obtain a trained network model; finally, using the test set to test the trained network model to complete the radar target recognition and classification. This invention can improve the accuracy of target recognition with very small computational parameter costs, and is suitable for use in situations where computational resources are very limited but high target recognition accuracy is required.

The invention discloses an interference detection method for two-dimensional difference frequency DOA (direction of arrival) estimation, which comprises the following steps of: obtaining a noiseless version of an augmented covariance matrix based on a virtual array by utilizing the structural characteristics of a parallel extended co-prime array through structuring a Toeplitz matrix and calling asymptotic maximum likelihood estimation of a structured covariance matrix. Time samples are integrated into a sample covariance matrix, a MUSIC spectrum of each difference frequency is obtained, the direction of a signal source is searched in a noise subspace, and a unique azimuth angle and a unique pitch angle are correspondingly matched. According to the method, a sparse array structure of a double-parallel extended co-prime array is adopted, a difference frequency Hadamard product principle is utilized, a Toeplitz matrix is structured, a difference frequency-based two-dimensional DOA estimation algorithm is realized, the method is applied to multi-target interference detection, a target function is optimized through mathematical modeling so as to obtain a pitch angle and an azimuth angle of an incident signal, and finally algorithm comparison is performed, so that the interference detection accuracy is improved. And quantitatively analyzing the performance difference between the power normalized spectrum of each method and the RMSE and the operation time, and well verifying the feasibility and the excellent performance.

The invention provides a modal parameter identification method, and relates to the technical field of structural health monitoring, vibration engineering and signal processing. The method comprises the following steps: acquiring an acceleration time domain signal; decomposing the acceleration time domain signal, and performing signal reconstruction on a plurality of multivariate intrinsic mode function components; smoothing each channel of data of the reconstructed signal, and constructing a Toeplitz matrix by using a cross-correlation function sequence; singular value decomposition is carried out on the matrix, and a discrete state space matrix is obtained through calculation by adopting a covariance-driven random subspace method; the discrete state space matrix is decomposed, and the inherent frequency, the damping ratio and the vibration mode vector of the ith-order mode are obtained through calculation; and carrying out statistical analysis on all modal parameters, and verifying to obtain a finally confirmed real modal parameter set. According to the method, multi-channel signals can be comprehensively processed, excitation interference of a complex environment is effectively suppressed, and a robustness method of full-automatic high-precision modal recognition is realized.

The invention provides a coherent signal high-resolution DOA estimation method based on Toeplitz matrix reconstruction and tensor PARAFAC decomposition, and belongs to the technical field of signal processing. According to the method, a plurality of full-rank Toeplitz matrixes are constructed by using all data of a covariance matrix, and the limitation that only one row of data is used in a traditional method is broken through. Meanwhile, a backward Toeplitz matrix is innovatively constructed, the information amount of data is further increased, and the rank defect problem of a covariance matrix is effectively solved. On the basis, all constructed Toeplitz matrixes are stacked according to a third dimension to form a third-order tensor PARAFAC model, and multi-dimensional features of the signals are extracted through PARAFAC decomposition. Due to the fact that multi-dimensional information of data can be fully mined through tensor decomposition, robustness of the algorithm to noise is remarkably improved, and finally efficient and stable DOA estimation is achieved.

The invention discloses an intelligent metasurface-assisted low-bit quantization array non-line-of-sight signal source DOA estimation method, and the method comprises the steps: processing a received signal through employing a low-precision ADC after a receiving array antenna receives an echo signal scattered by a target and reflected by an RIS, constructing an RIS equivalent channel, employing an RIS equivalent channel matrix as an auxiliary variable, and carrying out the estimation of the DOA of a low-bit quantization array non-line-of-sight signal source. The method comprises the following steps: quantizing a signal, estimating the quantized signal, converting an angle estimation problem into a convex optimization problem, solving the convex optimization problem by utilizing a CVX toolbox in Matlab software, constructing two one-dimensional Toeplitz matrixes respectively containing target DOA and DOD information, solving a signal angle by utilizing one-dimensional Vandermonde decomposition, and performing angle matching, and the DOA and DOD joint estimation of the non-line-of-sight signal source is realized. According to the method, the active regulation and control capability of the RIS, the low-bit quantization technology and the atom norm minimization algorithm are creatively fused, high-precision and real-time DOA and DOD estimation can be achieved in the non-line-of-sight environment while low-bit quantization is achieved, and the method has higher engineering practical value.

The application discloses a self-evaluation quantum random number generation system and method based on heterodyne detection, which comprises the following steps: a heterodyne detection-based method is used to simultaneously extract two corresponding orthogonal component fluctuations of a quantum state as an entropy source of a random number generator; original data of a two-component measurement are randomly extracted based on a synchronous clock to reconstruct a quantum state phase space distribution in real time, so that the safety of the entropy source is comprehensively evaluated, and then the evaluation result is fed back to a hardware hash post-processing link, the size of a Toeplitz matrix constructed in an FPGA is adjusted in real time, and the real-time safety of the generated quantum random number is ensured; meanwhile, on the basis of simultaneously extracting two orthogonal component quantum fluctuations of a quantum state as an entropy source, multiple high-frequency quantum sideband modes in a balanced homodyne detection bandwidth are extracted as sub-entropy sources in parallel for the two orthogonal components, so that the quantum random number generation rate is doubled in a double-parallel quantum entropy source extraction mode.

The invention discloses a single snapshot DOA (direction of arrival) estimation method based on weighted Toeplitz matrix reconstruction. The technology comprises a rank recovery technology for improving a Toeplitz covariance matrix and a DOA (Direction of Arrival) estimation technology. In order to solve the problem that a super-resolution DOA estimation algorithm fails under the conditions of single snapshot and low signal-to-noise ratio, a conventional Toeplitz matrix reconstruction technology is improved, a single snapshot algorithm based on weighted Toeplitz reconstruction is provided, and compared with the conventional Toeplitz reconstruction algorithm, the single snapshot algorithm has a better effect under the condition of a single target.

The invention provides a direction of arrival estimation method based on an accelerated near-end gradient method, and the method comprises the following steps: S1, based on the virtual domain characteristics of a received signal, in combination with the mathematical properties of a Kronecker product, carrying out vectorization processing, carrying out form transformation, and eliminating the aperture information of a redundant array by using a dimension reduction matrix; s2, constructing a corresponding atom set, determining an atom norm expression, converting the atom norm expression into a positive semidefinite programming problem by adopting a convex relaxation technology, introducing a regularization constraint mechanism, and solving by adopting an accelerated near-end gradient algorithm to obtain a receiving signal after sparse reconstruction and a corresponding Hermitian-toeplitz matrix; and S3, on the basis of the Hermitian-toeplitz matrix, performing eigenvalue decomposition operation, extracting a noise subspace, and applying a spectral peak search algorithm to realize accurate estimation of the direction of arrival. According to the method, the complete array aperture information of the received signal in the virtual domain is fully mined and utilized, so that the calculation complexity is remarkably reduced, and the better estimation precision performance is realized.

The present invention discloses a FDA-MIMO sonar fast gridless joint distance-angle estimation method and product based on a two-dimensional generalized fast interior point method, comprising: s1: performing frequency mixing and matched filtering on a received signal to obtain an extended virtual received signal model; s2: summarizing the estimation problem as an NsCP problem and initializing parameters related to the interior point method; s3: using a restricted memory BFGS algorithm and an augmented KKT condition to update the primal variable and the dual variable, performing a 2D-FFT fast feasible domain cone verification on the obtained variables, repeating this step until the result is within the feasible domain, and then going to s4; s4: performing a convergence check on the obtained variables, if converged, obtaining the optimal solution to the NsCP problem, and going to s5, otherwise going to step 3; s5: based on the optimal solution, retrieving sparse atoms through Vandermonde decomposition of a multi-level Toeplitz matrix, and extracting the distance and angle estimation of the target using linear correspondence.