102 results about "Hankel matrix" patented technology

The invention discloses a multi-modal fusion lithium iron phosphate battery thermal runaway early warning method and system, and the method comprises the steps: collecting multi-source heterogeneous data, such as temperature, voltage, gas concentration and shell strain pressure, in real time through deploying a heterogeneous sensor network, and carrying out the noise reduction and time sequence feature extraction through employing a sub-linear time low-rank approximation algorithm of a Hankel matrix; constructing a cross-modal feature association network by applying a secondary time algorithm of a maximum weight sparse subgraph problem, inputting a fused feature vector into a Bayesian network health degree evaluation model for probabilistic reasoning calculation to obtain a battery health degree score and a thermal runaway risk level, generating a graded early warning signal through multi-level early warning threshold comparison, and performing early warning on the battery health degree score and the thermal runaway risk level. And corresponding prevention and control suggestions are matched. The method solves the technical problems that single physical quantity monitoring is difficult to comprehensively reflect the complex change in the battery and the response delay of a centralized processing architecture causes the early warning lag, and achieves the timely capture and accurate early warning of the early weak characteristics of thermal runaway.

The invention provides a bearing fault diagnosis method based on a one-dimensional local binary pattern and a Hankel matrix. The bearing fault diagnosis method comprises the following steps: acquiring a discrete vibration signal; performing first-order differential operation on the discrete vibration signal to obtain a differential signal; performing inherent time scale decomposition on the differential signal to obtain an inherent rotation component signal; performing quantization and signal reconstruction on each inherent rotation component signal by taking a root mean square as a quantization criterion of a one-dimensional local binary mode method to obtain a decimal feature signal; constructing a Hankel matrix of the decimal characteristic signal and performing signal reconstruction according to a covariance matrix of the Hankel matrix; performing spectral analysis on the reconstructed signal, calculating the fault characteristic frequency of the bearing, and then judging the state and the fault type of the bearing through a frequency component obtained through spectral analysis and the fault characteristic frequency of the bearing obtained through calculation. According to the bearing fault diagnosis method, noise can be effectively suppressed, the bearing fault feature information can be effectively extracted, and the bearing state and the fault type can be accurately identified.

The invention discloses a PRFI suppression method based on a Hankel structure and truncation nuclear norm regularization. The method comprises the following steps: acquiring an SAR echo signal interfered by a PRFI signal; the SAR echo signals are constructed into a Hankel matrix, and the Hankel matrix comprises a low-rank PRFI signal interference component matrix and a sparse SAR useful signal component matrix; constructing a low-rank sparse decomposition model based on a Hankel matrix, wherein an objective function of the low-rank sparse decomposition model comprises a truncation nuclear norm regular term used for constraining a PRFI signal component and a sparse regular term used for constraining an SAR useful signal component; performing iterative solution on the low-rank sparse decomposition model by adopting an alternating direction multiplier method to obtain a PRFI signal interference component matrix and an SAR useful signal component matrix after separation; and carrying out inverse transformation on the SAR useful signal component matrix to obtain an SAR useful signal from which the PRFI signal is removed. According to the method, the loss of the SAR useful signal can be reduced while the PRFI signal interference is efficiently suppressed, so that the fidelity of the SAR useful signal is improved.

The invention relates to the field of seismic data reconstruction, in particular to a seismic data low-rank reconstruction method fusing double-domain transformation, and the method comprises the steps: obtaining original incomplete seismic data, and initializing to-be-reconstructed seismic data and other model variables and parameters under an alternating direction multiplier method frame; performing fractional order gradient transformation on seismic data to be reconstructed along different directions, and mapping to obtain fractional order gradient domain data; performing space-time Hankel tensor expansion transformation on each piece of fractional order gradient domain data, and converting the data into a space-time Hankel matrix; performing low-rank constraint on each space-time Hankel matrix by adopting a Schatten norm to obtain a seismic data low-rank reconstruction model fused with double-domain transformation; and carrying out iterative solution on the model by using an ADMM framework until the model is stable, and obtaining a final seismic data reconstruction result. The method provided by the invention can effectively reconstruct the seismic data with the missing trace, and has a reconstruction effect with strong robustness and relatively good precision for incomplete seismic data with different missing degrees.

The invention discloses a hydroelectric generating set vibration signal noise reduction method based on SW-EEMD (Single Wave-Ensemble Empirical Mode Decomposition) and Hansel-SVD (Hanker-Singular Value Decomposition). The method comprises the following steps: processing an original noisy signal by adopting an SW-EEMD method; screening effective IMF components through correlation coefficients; respectively constructing Hankel matrixes for the screened IMF components and residual components; respectively carrying out singular value decomposition on the constructed Hankel matrix; carrying out soft threshold processing on the obtained singular value; the method aims at restraining the end effect of EEMD, noise in the vibration signals can be effectively filtered out, signal features are enhanced, more real and effective signal components can be obtained easily, and more reliable data are provided for state operation and maintenance of the hydroelectric generating set.

The invention relates to the technical field of electrostatic dust collection and discloses an accurate frequency adjustment method for an intelligent frequency modulation high-voltage power supply of an electrostatic dust collector. The method comprises the steps of collecting voltage signals with frequency fluctuation in operation of a high-voltage power supply to form a voltage sequence; dividing period segments by using wave crest distribution in the voltage sequence, and clustering to obtain adjustment subsequences; obtaining a trend fluctuation index based on local signal change trend fluctuation and signal differences of the adjustment subsequences, and obtaining an amplitude drop difference and an amplitude interval difference according to an amplitude change trend difference and an amplitude bit sequence change trend difference; obtaining a period stability coefficient by combining the difference, the average condition of the trend fluctuation index and the average condition of the sub-sequence similarity; constructing a Hankel matrix and performing singular value decomposition, and obtaining a main component proportion and a difference index based on a singular value condition; and according to the Hankel matrix line data correlation, the period stability coefficient, the main component proportion and the difference index, obtaining a signal stability index, and according to the signal stability index, accurately adjusting the high-voltage power supply frequency.

The invention belongs to the technical field of partial discharge detection, particularly relates to a partial discharge signal denoising method based on SVDTQWT, and aims to effectively remove periodic narrow-band interference and white noise in partial discharge signals. Comprising the following steps: performing Fourier transform on a noisy partial discharge signal to obtain a frequency spectrum, determining the number of periodic narrowband interferences through singular value decomposition, constructing a Hankel matrix to eliminate the periodic narrowband interferences, and obtaining a preliminary de-noised signal; and decomposing the preliminarily denoised signal by adopting adjustable quality factor wavelet transform to obtain a plurality of sub-bands. And dividing the plurality of sub-bands into high-frequency sub-bands and low-frequency sub-bands through sample entropy. Wherein the sample entropy indicates measurement of the complexity of the time series. And de-noising the high-frequency sub-band by using a group sparse total variation de-noising algorithm, de-noising the low-frequency sub-band by using an improved wavelet threshold de-noising algorithm, and reconstructing by using adjustable quality factor wavelet transform to obtain a pure partial discharge signal.

The invention discloses a noise reduction and rub-impact fault identification method based on information entropy and eigenvalue decomposition, and relates to the technical field of rotating machinery fault diagnosis, and the method comprises the following steps: obtaining an original discrete vibration signal through a sensor and a data collection card; according to the original discrete vibration signal, constructing a Hankel matrix, and through eigenvalue decomposition, obtaining an eigenvector of the Hankel matrix and an eigenvalue matrix; performing signal reconstruction according to different feature values in the feature value matrix and feature vectors corresponding to the feature values to obtain a reconstructed signal set; and selecting the reconstructed signal with the minimum information entropy in the reconstructed signal set as an optimal reconstructed signal, performing spectrum analysis on the optimal reconstructed signal, and judging the rub-impact fault according to the frequency component. Rub-impact fault recognition is realized through the optimal reconstruction signal determined by the feature value and the feature vector corresponding to the minimum information entropy, the influence of noise interference is reduced, the fault feature information is relatively prominent, and the fault recognition result is more accurate.

The invention relates to a damage prediction method and device for a tunnel lining structure, equipment, a medium and a program product. The method comprises the following steps: acquiring a strain monitoring data set of a plurality of lining structure monitoring points of a tunnel; the strain detection data set is composed of strain monitoring sub-data sets corresponding to load action times of each lining structure monitoring point at a plurality of historical moments; constructing a Hankel matrix of each lining structure monitoring point under the action of each load based on the strain monitoring sub-data set, so as to obtain the strain modal frequency of each lining structure monitoring point; determining a damage early warning index of each lining structure monitoring point based on the strain modal frequency; training and verifying a pre-constructed tunnel lining damage prediction model based on the plurality of damage early warning indexes to obtain a trained tunnel lining damage prediction model; and inputting the damage early-warning index set to be subjected to damage prediction into the trained tunnel lining damage prediction model to obtain an output damage prediction result, namely a predicted damage early-warning index.

The invention discloses a high-resolution tomographic SAR four-dimensional imaging method for space-time baseline decoupling processing, and the method comprises the following steps: 1, reconstructing original satellite data into uniform baseline observation data, and solving the noise-free estimation of the uniform baseline observation data through the low-rank characteristic of a Hankel matrix; step 2, inverting elevation information based on noise-free estimation, taking the elevation information as priori, constructing a deformation spectrum estimation dictionary through space-time decoupling, and performing deformation information estimation; and step 3, matching the estimated elevation and deformation quantity by using a maximum likelihood method so as to realize four-dimensional imaging. According to the method, the algorithm complexity of four-dimensional imaging is reduced exponentially while high-precision imaging is realized, and differential tomography SAR four-dimensional imaging result verification is carried out based on domestic land exploration No.1 satellite data.

The application discloses a kind of high-resolution tomography SAR four-dimensional imaging methods of space-time baseline decoupling processing, which comprises the following steps: step 1, reconstruct original satellite data into uniform baseline observation data, and utilize the low rank characteristic of Hankel matrix, solve its noiseless estimation;Step 2, elevation information is inverted based on noiseless estimation, and elevation information is used as priori, deformation spectrum estimation dictionary is constructed by space-time decoupling, and deformation information estimation is carried out;Step 3, the elevation and deformation variable estimated are matched using maximum likelihood method to realize four-dimensional imaging.The method realizes high-precision imaging while exponentially reducing the algorithm complexity of four-dimensional imaging, and the differential tomography SAR four-dimensional imaging result verification is carried out based on domestic land exploration No.1 satellite data.

The application discloses a frequency-space domain alternating iteration seismic random noise suppression method and system, transforms a seismic signal from a time-space domain to a frequency-space domain, and obtains a frequency slice by taking data of a fixed frequency domain index; arranges the frequency slice into a Hankel matrix and performs singular value decomposition, selects singular values and corresponding singular vectors to perform rank reduction reconstruction on the Hankel matrix; obtains the reconstructed frequency slice, and takes the next frequency slice to complete spatial direction denoising; takes single seismic trace data of a fixed space domain index in the frequency-space domain data, arranges the single seismic trace data into a Hankel matrix and performs singular value decomposition, selects singular values and corresponding singular vectors to perform rank reduction reconstruction on the Hankel matrix; then, the reconstructed single seismic trace data is obtained through anti-diagonal average, the next seismic trace data is taken, the obtained frequency-space domain data after denoising is transformed back to the time-space domain, and a signal after noise suppression is obtained.

The invention discloses a signal delay estimation method based on block processing. The signal delay estimation method comprises the following steps: acquiring CSI (Channel State Information) data and pre-processing (validity check, noise filtering and effective index selection); blocking according to a preset block number and an overlapping proportion to obtain overlapped data blocks; a Hankel matrix and an enhancement matrix are established for each block, and a delay estimation value is obtained through singular value decomposition, subspace separation and characteristic polynomial solution; distributing weights for each estimated value in combination with signal quality evaluation; and determining a final result based on the delay estimation value and the weight information. According to the method, the large matrix is disassembled through block overlapping, the singular value decomposition complexity and storage occupation are reduced, and lightweight hardware is adapted; processing time consumption is shortened, multi-scene real-time requirements are met, the method can be operated on common equipment, and positioning deviation caused by delay is avoided.

The application discloses a ground microseismic event signal enhancement method, comprising the following steps: 1) obtaining a ground microseismic signal after dynamic correction containing noise according to a ground microseismic event signal; 2) obtaining time slice data at a given time point t1; 3) constructing a hankel matrix of each trace for the time slice data; 4) performing random singular value decomposition on the rearranged Hankel matrix of each time slice; 5) adding a damping operator to suppress the random noise of the residual error; 6) using Hankel matrix inverse transformation to transform the reconstructed matrix after truncation of singular values back to time slice data, and obtaining signal data after noise suppression; 7) repeating steps 2) to 6) until all time slices are processed, and obtaining an enhanced signal of the original ground microseismic event signal. The application can highlight the effective signal energy of the ground microseismic event, suppress noise interference, improve the ground microseismic event signal energy ratio, and enhance the effective signal identification capability.

The invention provides a bearing fault identification method based on singular value decomposition. The method comprises the following steps: acquiring a discrete vibration signal of a bearing; a Hankel matrix of the vibration signals is constructed, the dimension of the matrix is smaller than < and is the length of the vibration signals, and the column number is determined based on the minimum characteristic frequency of typical components of the equipment; performing singular value decomposition on the matrix; selecting an effective row vector of the matrix by taking high periodicity, high cyclic stability and low complexity of the signal as targets, determining an effective singular value based on the effective row vector, and performing signal reconstruction based on the effective singular value; and carrying out spectrum analysis on the reconstructed signal and carrying out bearing fault identification according to a relation between a prominent frequency component in a spectrum and a bearing fault characteristic frequency. According to the bearing fault identification method, the features of the signals can be enhanced while noise reduction is carried out on the signals, and accurate judgment of bearing faults is facilitated.

The application discloses a two-dimensional sparse array single-shot DOA estimation method based on a deep unfolding convolutional network, and belongs to the technical field of cross array signal processing and deep learning. First, a two-dimensional uniform planar array is constructed, and sparse observation data are constructed. Then, an isomorphic tensor mapping mode of separating real parts and imaginary parts is adopted to decompose the sparse observation signals and splice them along the channel dimension, so that a three-dimensional input tensor containing real part channels and imaginary part channels is constructed to maintain the two-dimensional spatial topological structure of the array. Then, the overall structure of the deep unfolding network is unfolded, and a sliding window rule with a predetermined size is used to rearrange the two-dimensional array data into a block Hankel matrix. Finally, network training is performed to realize DOA estimation. The application maintains the two-dimensional spatial structure, improves the reconstruction accuracy, reduces the computational complexity, improves the robustness under a low signal-to-noise ratio condition, realizes high-precision DOA estimation under a single-shot condition, and has good engineering application value.

The invention discloses a series fault arc identification method and system based on singular spectrum statistical characteristics, and the method comprises the steps: S1, collecting the current waveform of a series AC fault arc, and obtaining a current sampling sequence; s2, constructing a Hankel matrix Y based on the current sampling sequence, and then performing singular value decomposition on the Hankel matrix Y to obtain a singular spectrum; s3, statistical features are calculated based on singular spectrums, and feature vectors are formed; and S4, inputting the feature vector into a trained XGBoost classifier to obtain a category label of the series AC fault arc, and realizing real-time identification of the fault arc. According to the method, the singular spectrum of the current waveform is constructed through Hankel matrix decomposition, and the high-frequency harmonic and amplitude characteristics of the fault arc are efficiently captured through the singular spectrum, so that the recognition precision is improved; and the hyper-parameters of the classifier are optimized in combination with a differential evolution algorithm, so that the recognition efficiency of the series alternating-current fault arc is improved.

The present disclosure provides an unknown unmanned system data-driven multi-step kernel prediction control method and system. The method is aimed at the problem of unknown non-parametric unmanned system model. Only the off-line collected system input and output noise data are used. The Hankel matrix is constructed to extract the time sequence characteristics. The kernel matrix is constructed by combining the renewable kernel function. The nonlinear system rule is converted into high-dimensional linear representable data rule. The multi-step kernel prediction optimization problem based on the kernel matrix is solved on-line and rolling. The optimal control input is output to realize closed-loop control. The present invention does not need to construct an accurate mathematical model and does not need the full-dimensional state of the system. The problem of poor adaptability and long scene error accumulation of the traditional method is solved. The robustness and engineering landing performance are strong.

The invention discloses an anti-transition resistance semi-decoupling multi-terminal differential line fault positioning and distance measuring method, belongs to the field of power system relay protection, and solves the problems of complex calculation, weak anti-transition resistance and difficult equipment upgrading caused by multi-terminal data coupling in the existing method. The method comprises the following steps: S1, calculating a distance ratio based on local side voltage and current, and preliminarily positioning a fault branch; s2, constructing an equation containing transition resistance R and fault impedance ZL-1, and generating a transition resistance matrix r and a fault impedance matrix z (dimensionality is adaptive to CPU computing power); s3, denoising through a Hankel matrix and singular value decomposition to obtain an accurate sequence; and S4, verifying the sequence consistency within 20-40ms after the fault, and outputting a result or repositioning. The method is free of iteration and high in transition resistance resistance, the complexity is linearly improved along with the number of T-connection terminals, hardware computing power and old equipment upgrading are adapted, and the method is suitable for a new energy T-connection multi-terminal network.

The application discloses a signal separation method for harmonic signals and impact signals, comprising the following steps: step 1, constructing a first Hankel matrix; step 2, iterative operation, updating the first Hankel matrix; step 3, calculating the estimated value of the time-domain harmonic signal according to the first Hankel matrix after alpha iteration update; step 4, subtracting the estimated value of the time-domain harmonic signal from the time-domain total signal to obtain the first estimated value of the time-domain impact signal; step 5, constructing a second Hankel matrix; step 6, iterative operation, updating the second Hankel matrix; step 7, calculating the second estimated value of the time-domain impact signal according to the first Hankel matrix after alpha iteration update, and performing inverse Fourier transform on the second estimated value of the time-domain impact signal to obtain the third estimated value of the time-domain impact signal; and step 8, subtracting the third estimated value of the time-domain impact signal from the time-domain total signal and returning to step 1.

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 invention discloses a singular value decomposition sub-signal selection method for rotating machine fault diagnosis, and belongs to the technical field of rotating machine state monitoring and fault diagnosis. The method comprises the following steps: receiving an original vibration signal of the rotating machine, and adaptively determining the optimal decomposition times of singular value decomposition through exhaustion search by taking the number of periodic pulse quantized values as an optimization target; constructing a Hankel matrix for the original vibration signal and performing singular value decomposition to obtain a group of sub-signals; the square envelope of each sub-signal is calculated, the periodic pulse performance of each sub-signal is quantized, a clustering guide line is drawn, and key sub-signals are screened out; continuously adjacent key sub-signals are classified into one class for reconstruction mixing, fault components are formed for envelope spectrum analysis, and rotating machine fault diagnosis is achieved. According to the invention, periodic impact components related to faults in the signals can be effectively highlighted, and the accuracy and reliability of composite fault diagnosis of the rotating machinery under complex working conditions are remarkably improved.

The application relates to the technical field of array signal processing, in particular to a distributed single-shot direction of arrival estimation method based on two-dimensional Hankel matrix completion, which comprises the following steps: acquiring signals received by each sensor of each subarray and stacking the signals into a global data matrix, obtaining an under-sampling observation signal containing additive noise based on an element sampling operator and the global data matrix; constructing a two-dimensional Hankel matrix based on the global data matrix; calculating a local cost function based on the under-sampling observation signal, converting the completion problem of the two-dimensional Hankel matrix into a distributed consistency optimization problem, realizing consistency iteration through a DHEX algorithm, obtaining a global low-rank solution, and then obtaining a reconstructed signal; and processing the reconstructed signal by using a two-dimensional subspace method to obtain a direction of arrival estimation value. The method can realize high-precision and scalable direction of arrival estimation under the condition of only local incomplete observation.

This invention discloses a high-precision FMCW laser ranging method based on the ESPRIT algorithm, belonging to the field of laser ranging technology. First, the laser beam is split into two beams by an optical beam splitter. One beam serves as the local oscillator beam, and the other as the signal beam. The signal beam hits the target object and returns, carrying the distance information of the target. The local oscillator beam and the signal beam are coupled in an optical coupler to obtain a difference frequency signal, which is then acquired by a photodetector and a digital acquisition card. A Hankel matrix is ​​constructed from the difference frequency signal. The Hankel matrix is ​​decomposed using singular value decomposition (SVD) to extract the signal subspace. Based on the decomposition of the signal subspace, an invertible matrix rotation operator is obtained and optimized to obtain the signal frequency, thereby calculating the distance to the target object. This invention is not only simple to implement and easy to operate, but also highly practical and suitable for widespread use.

The invention discloses a high-speed rail seismic source seismic data wave field separation method and system using random Cadzow filtering, and belongs to the technical field of exploration geophysics. The method comprises the following steps: acquiring seismic data when a high-speed rail passes; estimating the seismic wave propagation speed through Radon transformation; performing time difference correction on the same-direction wave field event to obtain aligned data; blocking the aligned data and randomly rearranging the aligned data; fourier transform is carried out on the rearranged data, and a Hankel matrix is constructed; carrying out SVD (Singular Value Decomposition) decomposition and low-rank reconstruction on the Hankel matrix; reconstructing a frequency domain data block through an anti-Hankel operation; inverse Fourier transform is carried out, and a trace sequence is recovered; and extracting and averaging a central channel to obtain unidirectional wave field data. The system comprises modules with corresponding functions. The method can effectively separate the high-speed rail seismic source mixed wave field, improves the signal-to-noise ratio of data, and provides a reliable data basis for underground imaging.

The present application relates to the technical field of data processing, more particularly, the present application relates to a kind of power supply monitoring method for atmosphere light bar production, the method comprises: obtaining and preprocessing power supply signal in current time window, obtain current estimated noise sequence;Power supply signal is converted into Hankel matrix and is carried out singular value decomposition, the cumulative energy ratio of each truncation order is calculated;According to current noise level and the degree of aggregation of data in current estimated noise sequence, calculate adaptive energy threshold;Select the minimum truncation order of cumulative energy ratio greater than the threshold as target truncation order, reconstruct Hankel matrix and restore to obtain target power supply signal;Through abnormal detection to target power supply signal, identify power supply anomaly.The present application can improve the filtering effect of SVD filtering to power supply signal, realize the accurate monitoring of power supply anomaly in light bar production process.

The application relates to the field of power distribution system simulation, in particular to a distributed power distribution system unified scale load modeling simulation method and system, which comprises the following steps: denoising and fitting a wideband signal to obtain a multiscale signal; obtaining a Hankel matrix time-varying extended model based on the multiscale signal and historical modal parameters and solving to obtain real-time modal parameters; constructing a coupling matrix based on the real-time modal parameters, fitting a fast action layer state equation and a slow action layer state equation by using the coupling matrix to obtain a unified coupling equation; transforming and decoupling the unified coupling equation to obtain a mixed differential-algebraic equation group; and solving the mixed differential-algebraic equation group by using a preset step length switching rule based on a dominant dynamic type to obtain full-time domain simulation results of the distributed power distribution system. The application can effectively solve the problems of time scale fragmentation and insufficient parameter identification accuracy in traditional load modeling.

The application belongs to the technical field of target positioning, and particularly relates to a 2D-DOA estimation method of a reconfigurable intelligent surface assisted MISO system. The method establishes a far-field signal model of the RIS assisted MISO system, and the far-field signal model is composed of M RIS panels, K target signals and a receiving end. According to the far-field signal model, a receiving data expression is constructed, a meshless sparse reconstruction is performed by using an atomic norm, and a sparse reconstruction signal is obtained. The obtained sparse reconstruction signal is expressed in the form of a Hankel matrix, singular value decomposition is performed on the Hankel matrix, and a signal subspace and a noise subspace are obtained. In combination with a MUSIC algorithm, the azimuth and the elevation of the target are obtained by using spectral peak search.

The invention discloses a subspace joint parameter estimation algorithm for constructing an analytic signal based on Hilbert transform in high-precision multi-surface phase-shift interference, belongs to the technical field of high-precision optical interference measurement, and aims to solve the problems of inaccurate frequency estimation caused by spectrum leakage and a fence effect in a traditional algorithm. And the problem that a modern spectrum estimation algorithm cannot directly process real-value light intensity signals is solved. The method comprises the following steps: firstly, performing Hilbert transform on a real-value light intensity sequence to construct an analysis signal; then, a Hankel matrix is constructed based on the analysis signal, and subspace decomposition is carried out; further, taking the obtained high-precision frequency as prior information, and performing joint correction on the amplitude and the phase by using a double-section phase difference correction method; and finally, reconstructing the surface topography according to the corrected phase. According to the invention, the limitation of spectrum leakage and the like is overcome, the joint fine positioning of frequency, amplitude and phase is realized, and the precision, robustness and measurement repeatability of interference parameter demodulation are obviously improved.