CN116626646B - Radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling - Google Patents
Radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling Download PDFInfo
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Abstract
The invention discloses a radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling, which comprises the following steps: establishing a radar receiving echo signal model; vectorizing an echo signal data matrix and a target scattering coefficient matrix, and establishing a sparse reconstruction model according to the sparsity of the target in a distance-Doppler domain; initializing a priori information、Gridding error matrixAndthe method comprises the steps of carrying out a first treatment on the surface of the Sparse reconstruction mode based on establishmentType and currently available、、、Updating vectorized target scattering coefficient matrixPosterior estimated mean of (c)Sum of variancesThe method comprises the steps of carrying out a first treatment on the surface of the JudgingPosterior estimated mean of (c)Whether the precision requirement is met, if not, updating、Andandand update againPosterior estimated mean of (c)Sum of variancesThe method comprises the steps of carrying out a first treatment on the surface of the If yes, the current obtainedTargeted maximum a posteriori estimationOutputting and rearranging the target distance and Doppler information into a two-dimensional matrix form, wherein the index of the resolution grid corresponds to the target distance and Doppler information. The method has high reconstruction accuracy and can improve the efficiency of extracting the target parameters by the radar.
Description
Technical Field
The invention belongs to the field of radars, and particularly relates to a radar target gridding-free loss phase-coherent accumulation method based on time-frequency non-uniform sampling.
Background
Radar (Radar) is widely applied to the fields of strategic early warning, topographic mapping, target detection and the like according to the advantages of all-day, all-weather, long-distance, high-resolution imaging and the like. However, in the actual combat process, due to the influence of various interference signals and complex environmental information generated by electronic countermeasure, the radar is difficult to observe the same target for a long time, radar echo signals generally have the characteristics of undersampling and non-uniformity, the observation aperture is sparse, and the current method for accumulating the parameters of target distance, doppler and the like mainly comprises a two-dimensional FFT-based algorithm and a sparse reconstruction algorithm based on compressed sensing.
For example, D.A. Ausherman et al performs a two-dimensional discrete Fourier transform on the echo data range and azimuth of the target to achieve target range and Doppler information extraction (D.A. Ausherman, A. Kozma, J.L. Walker et al Developments in Radar Imaging [ J ]. IEEE Transacctions on Aerospace and Electronic Systems, 1984, 20 (4): 363-400.) the subsequent algorithms are optimized to varying degrees based on this core idea. In the field of sparse reconstruction, cheng Ping et al applied sparse Bayesian learning to ISAR imaging and corresponding coherent accumulation, (Cheng Ping, stannum, jiang Yicheng. Sparse signal representation ISAR imaging method based on sparse Bayesian learning [ J ]. E-newspaper, 2008,36 (3): 547-550.) solved the hyper-parameters using a desired maximum (Expectation Maximization, EM) criterion minimization cost function based on sparse modeling. The variances of the signals and noise to be recovered are modeled by introducing a Gamma-Gaussian hierarchical prior model on the basis of the variances, (H.C. Liu, H.W. Liu et al Superresolution ISAR Imaging Based on Sparse Bayesian Learning [ J ]. IEEE Transactions on Geoscience and Remote Sensing, 2014, 52 (8): 5005-5013 ]) and the maximum a posteriori estimation is used for realizing the finite impulse ISAR imaging. Zhang et al utilized a multiplier alternating method (Alternating Direction Method of Mul-multipliers, ADMM) to replace the matrix inversion step in sparse bayesian learning (Sparse Bayesian Learning, SBL), improving the algorithm sparse reconstruction speed. In addition, w.zhou proposes a sparse bayesian learning method based on Student's gaussian mixture prior (w.zhou, h. -t.zhang, and j. Wang, "An efficient sparse Bayesian learning algorithm based on Gaussian-scale minerals," IEEE trans, neural net, sparn, syst., early access, jan, 22, 2021.), which further improves the efficiency of the algorithm.
The traditional two-dimensional FFT method has a good coherent accumulation effect under the condition of complete time-frequency observation data, and can not well play a role in the under-sampling or non-uniform sampling of the echo, so that the result error of the traditional two-dimensional FFT algorithm is larger. In addition, the target accords with a scattering point model in an optical area, the scattering point model has sparse characteristics in a distance domain and a Doppler domain, a sparse reconstruction algorithm provides a new idea for solving the problems, however, when coherent accumulation is carried out, gridding errors exist between a frequency sampling point and actual parameters of the target, because the traditional sparse reconstruction algorithm is based on gridding division, the target is assumed to be distributed in the grid center, the reconstruction result of the algorithm is also a parameter value corresponding to a certain grid center or certain grid center, and for parameter values corresponding to other positions in the grid actually, the traditional sparse reconstruction method cannot eliminate the errors in the grid, namely gridding loss exists, and the actual reconstruction effect is influenced by the size of the grid.
Aiming at the problems, how to realize a novel radar target gridding-free loss coherent accumulation method is a technical problem to be solved in the field.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling. The technical problems to be solved by the invention are realized by the following technical scheme:
a radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling comprises the following steps:
step 1, establishing a radar receiving echo signal model;
step 2, vectorizing an echo signal data matrix and a target scattering coefficient matrix, and establishing a sparse reconstruction model according to the sparsity of the target in a distance-Doppler domain;
step 3, initializing prior information、/>Gridding error matrix-> and />；
Step 4, based on the established sparse reconstruction model and the current obtained sparse reconstruction model、/>、/>、/>Updating the vectorized target scattering coefficient matrix +.>Posterior estimated mean->Sum of variances->；
Step 5, judgingPosterior estimated mean->Whether the precision requirement is met or not, if not, executing the step 6; if yes, executing the step 7;
step 6, updating、/> and /> and />And executing the step 4;
step 7, the currently obtainedMaximum a posteriori estimation as target->Outputting and rearranging the target distance and Doppler information into a two-dimensional matrix form, wherein the index of the resolution unit corresponds to the target distance and Doppler information.
In one embodiment of the present invention, the establishing a radar receiving echo signal model includes:
the expression of using a chirp signal with a large time-wide bandwidth product as a radar transmission signal is determined as:
；
wherein ,representing a fast time; />Representing the transmit signal pulse width; />Representing imaginary units; />Representing the signal carrier frequency; />Is the frequency modulation slope; />Representing the signal bandwidth; />Representing a gate function;
assuming that the radar emits a multi-pulse chirp signal, then observing the scattering point of the targetThe secondary echo is as follows:
；
wherein ,representing the scattering coefficient; />Representing a transmit signal pulse repetition period; />Representing a slow time dimension;representing the corresponding pulse timeThe distance between the scattering point and the radar; />Representing the speed of light; />A natural number greater than 0;
setting the radial distance of the target at the starting moment of the radar transmitting pulse train asMixing and filtering the radar echo signals to obtain baseband signals:
；
wherein ,representing the radial velocity of the target relative to the radar line of sight.
In one embodiment of the present invention, the vectorizing the echo signal data matrix and the target scattering coefficient matrix, and establishing a sparse reconstruction model according to the sparsity of the target in the range-doppler domain includes:
step a1, constructing an initial sparse reconstruction model, wherein the initial sparse reconstruction model comprises the following steps:
；
wherein ,representing an echo signal data matrix,/->Indicating that it belongs to->Complex matrix of dimensions>Each column is fast time echo data, and each behavior slow time echo data; /> and />Respectively representing the number of sampling points in the pulse of the actually sampled received signal and the number of sampling points between pulses; />Representing a matrix of scattering coefficients of the object,indicating that it belongs to->Complex matrix of dimensions>The value of each element in (a) is the scattering coefficient of the target for the corresponding distance and speed,/a-> and />Are natural numbers greater than 0, +.> and />Search ranges representing the distance and speed of the object are divided into +.> and />A resolution grid; /> and />Fourier matrix inverse matrix representing fast time and slow time respectively,>，/>；/>representing a zero-mean complex gaussian white noise matrix; gridding error matrix->，/>；/>、/>Representing a sampling matrix after simulating intra-pulse and inter-pulse deletions; /> and />Representing the fast time sampling point number and the slow time sampling point number when the fast time and the slow time discretization sampling are carried out on the received echo signals respectively, < >>，/>、/>、 and />Are natural numbers greater than 0; />Hadamard product of the matrix is represented, +.>Representing a transpose of the matrix or vector;
step a2, vectorizing the initial sparse reconstruction model and recording、/> and />Vectorization is respectively、/> and />The obtained vectorized sparse reconstruction model is as follows:
；
wherein ,kronecker product representing a matrix; /> and />Representing the identity matrix with the dimension corresponding to the subscript;
step a3, record，And equivalently rewriting the vectorized sparse reconstruction model as:
；
the model after equivalent rewriting is a finally established sparse reconstruction model.
In one embodiment of the present invention, in step 4, the vectorized target scattering coefficient matrix is updatedPosterior estimated mean->Sum of variances->The formula adopted comprises:
；
；
；
wherein ,a priori information representing the variance of the noise; />Expressed as vector +.>A diagonal matrix with diagonal elements; />Representation->A priori information of the variance; />Representing the identity matrix with the dimension corresponding to the subscript; />Representing a conjugate transpose of the matrix or vector; />Representing intermediate variables.
In one embodiment of the present invention, in step 6, the update is performed、/>The formula adopted comprises:
；
；
wherein ,representation->Middle->An element; /> and />Representation->Shape parameters and scale parameters of the distribution;representation->Middle->Line->Elements of a column; />Representation->Middle->An element; /> and />Respectively representing a shape parameter and a scale parameter of noise variance distribution; />Represents the trace of the solution matrix,/->、/>、/> and />Are all greater than 0.
In one embodiment of the present invention, in step 6, the update is performed and />Comprises the following steps:
step b1, based on the current gridding error matrix and />By using the pre-derived +.>Gradient calculation formula and->Calculating a corresponding gradient by a gradient calculation formula;
step b2, judging whether the calculated gradients are smaller than a preset error judgment threshold; if yes, executing the step b3, and if not, executing the step b4;
step b3, ending the iteration, and carrying out current iteration and />Outputting as an optimal matrix;
step b4, calculating the search direction of the next iteration matrix, determining the optimal step length according to one-dimensional search, and obtaining an updated gridding error matrix by utilizing a gridding error matrix updating formula based on the obtained search direction of the next iteration matrix and the optimal step length and />And returns to step b1.
In one embodiment of the invention, the pre-derivedA gradient calculation formula comprising:
；
；
；
；
wherein ,representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />The representation dimension is +.>Is a conversion matrix of (a); />、/> and />Representing the identity matrix with the dimension corresponding to the subscript;representing vectorizing the matrix array; />Representing a diagonal matrix with vector elements in brackets as diagonal elements; /> and />Representing the conjugate of the corresponding matrix.
In one embodiment of the invention, the pre-derivedA gradient calculation formula comprising:
；
；
；
；
wherein ,representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />The representing dimension is the identity matrix corresponding to the subscript.
In one embodiment of the present invention, the formula used to calculate the next iteration matrix search direction includes:
；
the formula used for determining the optimal step size comprises the following steps:
；
wherein ,representing the next iteration matrix searching direction; />Is->The reference numbers corresponding to the gridding error matrix are respectively corresponding to +.2 when the values are 1 and 2> and />；/>Representing the iteration number; />Representing gridding error matrix->At iteration number +.>Time gradient; />Representing a solution target; />Representing a solution function; />Expressed in terms of iteration number +.>Gridding error matrix at time->；/>Representing a minimum value; />Indicate->The optimal step size corresponding to the iteration is obtained.
In one embodiment of the present invention, the meshing error matrix update formula includes:
；
wherein ,expressed in terms of iteration number +.>Gridding error matrix at time->。
The invention has the beneficial effects that:
according to the radar target non-meshing loss coherent accumulation method based on time-frequency non-uniform sampling, provided by the embodiment of the invention, a sparse Bayesian framework algorithm is applied to sparse reconstruction of the distance and Doppler characteristics of a target scattering point in the situation that the target scattering point is distributed sparsely in a distance domain and a Doppler domain, and the error in the same resolution unit, namely, meshing error, is corrected.
Drawings
Fig. 1 is a schematic flow chart of a radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling according to an embodiment of the present invention;
FIG. 2 is a two-dimensional FFT scatter intensity reconstruction result;
FIG. 3 shows the result of SBL scattering intensity reconstruction;
FIG. 4 is a graph showing the result of the scatter intensity reconstruction of the algorithm of the present invention;
fig. 5 is a graph of normalized mean square error change of recovery results of three algorithms at different signal-to-noise ratios.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The traditional two-dimensional FFT method has a good coherent accumulation effect under the condition of complete time-frequency observation data, and can not well play a role in undersampling or non-uniform sampling of echo; and a reconstruction algorithm based on sparse Bayesian learning divides the target parameter range into a plurality of resolution grids, and the reconstructed parameters are the central values of the resolution grids. When the target actual parameters are located at other positions in the same grid, the generated intra-grid errors and grid losses cannot be eliminated by iteration, and when the number of the resolution grids is too large, the calculation complexity of an algorithm is greatly improved, meanwhile, the incoherence of each resolution unit is possibly reduced due to the too dense grids, and the reconstruction effect is greatly reduced.
At present, a novel sparse Bayesian has become a new application direction, and when sparse reconstruction is performed, the novel sparse Bayesian utilizes the concept of no meshing, and errors can be regarded as variables to be continuously and iteratively optimized to be minimum, so that higher-precision signal reconstruction is possible.
As shown in fig. 1, the radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling provided by the embodiment of the invention adopts a sparse bayesian method to solve the problems of non-uniform sampling, undersampling and target parameter extraction under gridding errors, and can comprise the following steps:
step 1, establishing a radar receiving echo signal model;
specifically, step 1 may specifically include:
a Linear Frequency Modulation (LFM) signal with a large time-wide bandwidth product is used as a radar transmitting signal, and the expression is determined as follows:
(1)；
wherein ,representing a fast time; />Representing the transmit signal pulse width; />Representing imaginary units; />Representing the signal carrier frequency; />Is the frequency modulation slope; />Representing the signal bandwidth; />Representing a gate function;
assuming that the radar emits a multi-pulse chirp signal, then observing the scattering point of the targetThe secondary echo is as follows:
(2)；
wherein ,representing the scattering coefficient; />Representing a transmit signal pulse repetition period; />Representing a slow time dimension;representing the distance between the scattering point and the radar at the corresponding pulse time; />Representing the speed of light; />A natural number greater than 0;
setting the radial distance of the target at the starting moment of the radar transmitting pulse train asMixing and filtering the radar echo signals to obtain baseband signals:
(3)；
wherein ,representing the radial velocity of the target relative to the radar line of sight.
It will be appreciated that the conventional method performs fast and slow time-dimensional fast fourier transforms (Fast Fourier Transform, FFT) on equation (3) respectively to accumulate range and doppler (velocity) information of the target.
Step 2, vectorizing an echo signal data matrix and a target scattering coefficient matrix, and establishing a sparse reconstruction model according to the sparsity of the target in a distance-Doppler domain;
in an alternative embodiment, step 2 may specifically include:
step a1, constructing an initial sparse reconstruction model, wherein the initial sparse reconstruction model comprises the following steps:
(4)；
wherein the echo signal data received by the radar receiver comprises fast time data of scattering points in a single pulse and slow time data of scattering points among different pulses, the inventionEmbodiments perform fast and slow time discretized sampling of received echo signals, the number of (fast time) sampling points within a single pulse being recorded asThe pulse number (slow time sampling number) of the echo signal is. That is to say-> and />The fast time sampling point number and the slow time sampling point number when the fast time and the slow time discretization sampling are respectively carried out on the received echo signals are respectively represented.
Since radar has versatility, it can observe multiple targets and various interferences exist in space, in practice, echo data received by radar has partial deletions in and between pulses, and the sampling points in the pulse of the received signal sampled in practice can be recorded asThe inter-pulse sampling point is marked as +.>, wherein />，/>、/>、/> and />Are natural numbers greater than 0.
Will sampleIs arranged into a two-dimensional matrix form, namelyRepresenting an echo signal data matrix, wherein each column is fast time echo data; each behavioural slow time echo data, the matrix form of echo data may be expressed as +.>Indicating that it belongs to->A complex matrix of dimensions. Similarly, in the sparse reconstruction, the search range of the distance and speed of the target is divided into +.> and />A resolution grid, expressed as a two-dimensional matrix +.>Indicating that it belongs to->Complex matrix of dimensions>Representing a matrix of scattering coefficients of the target, each element value of which is the scattering coefficient of the target for the corresponding distance and speed,/for> and />Are natural numbers greater than 0; due to the limited number of targets and sparse distribution in the range-Doppler domain, +.>Most element values in the matrix are zero, and the distance and the speed corresponding to the non-zero element values in the matrix are realDistance and speed of the inter-target. Selecting a Fourier matrix inverse matrix taking a two-dimensional FFT as a core as a sensing matrix, wherein the Fourier matrix inverse matrix for recording fast time and slow time is +.> and />The corresponding gridding error matrix is +.> and />. Use +.>、/>Simulate the sampling matrix after intra-and inter-pulse deletions and record +.>Is a zero-mean complex gaussian white noise matrix. />Hadamard product of the matrix is represented, +.>Representing a transpose of the matrix or vector.
Step a2, vectorizing the initial sparse reconstruction model and recording、/> and />Vectorization is respectively、/> and />The obtained vectorized sparse reconstruction model is as follows:
(5)；
wherein ,kronecker product representing a matrix; /> and />Representing the identity matrix with the dimension corresponding to the subscript; such as->Is +.>。
Step a3, record，And equivalently rewriting the vectorized sparse reconstruction model as:
(6)；
the model after equivalent rewriting is a finally established sparse reconstruction model.
Step 3, initializing prior information、/>Gridding error matrix-> and />；
Because the target is sparsely distributed in the range-Doppler domain, the scatterer distribution is modeled in experiments by using a sampling layering model, wherein the first layer of assumed noise is zero-mean complex Gaussian white noise, and the variance isThe probability density function is:
(7)；
for the second layer in the hierarchical model, it is assumed that the noise variance obeys the Gamma distribution, i.e.:
(8)；
wherein ,respectively representing a shape parameter and a scale parameter of noise variance distribution; />Representing a Gamma function.
Similarly, assume that the sparse vector is to be reconstructedThe first layer meets the prior zero-mean complex Gaussian distribution, and the variance isIts probability distribution can be expressed as:
(9)；
wherein ,expressed as vector +.>The elements are diagonal matrices of diagonals. Assuming that the variances in the second layer are independent of each other and all follow the Gamma distribution, namely:
(10)；
step 4, based on the established sparse reconstruction model and the current obtained sparse reconstruction model、/>、/>、/>Updating the vectorized target scattering coefficient matrix +.>Posterior estimated mean->Sum of variances->；
Due toThe likelihood function of (2) is related to noise, and the likelihood function obtainable according to equation (7) is also subject to complex gaussian distribution, the probability density function of which is:
(11)；
from Bayes' formula, it can be obtainedThe posterior distribution of (2) is:
(12)；
wherein ,can be regarded as a constant in the coefficient reconstruction process, and can be obtained by using the maximum posterior criterion and Bayesian probability formula>The maximum a posteriori estimate (Maximum A Posterior, MAP) of (a) may be equivalent to +.>. From the nature of the complex Gaussian distribution, <' > the +.>The posterior estimates of (2) still obey complex Gaussian distribution, and the average value is recorded as +.>Variance isCombining the Woodbury equation, there are:
(13)；
(14)；
wherein Representing the conjugate transpose of the matrix or vector, the intermediate variables are: />
(15)；
The maximum posterior estimation of the output is obtained by sparse Bayesian algorithm。
Wherein, updating the vectorized target scattering coefficient matrixPosterior estimated mean->Sum of variances->The formulas used include the above formulas (13), (14) and (15), wherein ∈ ->A priori information representing the variance of the noise; />Representation->A priori information of the variance; />Expressed as vector +.>A diagonal matrix with diagonal elements; />Representing the identity matrix with the dimension corresponding to the subscript; />Representing a matrix or vectorIs a conjugate transpose of (2); />Representing intermediate variables.
Step 5, judgingPosterior estimated mean->Whether the precision requirement is met or not, if not, executing the step 6; if yes, executing the step 7;
the precision requirement can be set according to engineering requirements, and is not limited herein.
Step 6, updating、/> and /> and />And executing the step 4;
1) For updating、/>：
The core of the update of the superparameter is to select the proper and />So that->Max, for vectors to be reconstructed +.>Variance->Is equivalent to:
(16)；
wherein ,is->The%>The elements.
According to the maximum expected algorithm (Expectation-Maximization algorithm, EM), then equation (16) can be equivalently:
(17)；
pairing (17)Deriving, and enabling a derivative function to be equal to zero to obtain: />
(18)；
Similarly, for noise varianceThe estimation thereof can be equivalently:
(19)；
according to the EM algorithm, equation (19) can be equivalently written as:
(20)；
pairing (20)Deriving, and enabling a derivative function to be equal to zero to obtain:
(21)；
wherein the update、/>The formulas employed include formulas (18) and (21) described above. In the corresponding formula->Representation ofMiddle->An element; /> and />Representation->Shape parameters and scale parameters of the distribution; />Representation->Middle->Line->Elements of a column; />Representation->Middle->An element; /> and />Respectively representing a shape parameter and a scale parameter of noise variance distribution; />Represents the trace of the solution matrix,/->、/>、/> and />Are all greater than 0./>
2) For updating and />：
The update process may include the steps of:
step b1, based on the current gridding error matrix and />By using the pre-derived +.>Gradient calculation formula and->Calculating a corresponding gradient by a gradient calculation formula;
specifically, the error matrix is meshed and />Regarded as a variable, then->The posterior estimates and likelihood function distributions of (c) can be equivalently rewritten as:
(22)；
(23)；
combining EM algorithm and gradient descent method pair and />And (3) performing iterative estimation:
(24)；
equation (24) can be equated to:
(25)；
searching for optimum using gradient descent methodEliminating the constant term in formula (25), then p in formula (25)>The gradient can be equivalently:
(26)；
in the formula (26), the amino acid sequence of the compound,representing the matrix or number differential in brackets. Record->As a column vectorization function, then: />
(27)；
wherein ：
(28)；
in the formula Representing the transformation matrix, satisfying the equation->The method comprises the steps of carrying out a first treatment on the surface of the Substituting formula (28) into formula (24), and recording +.>Gradient of +.>Then:
(29)；
and the same applies to the second item:
(30)；
wherein ,substituting formula (28) into formula (30) for conjugate operator, and recording +.>Gradient of +.>Then:
(31)；
and also have equations, wherein />For the trace of the matrix, substituting equation (26) yields the third term: />
(32)；
Substituting formula (28) into formula (32) and recordingGradient of +.>Then:
(33)；
record (26) pairGradient of +.>The following steps are:
(34)；
similarly, record the pair of (26)Gradient of +.>The gradient corresponding to each term is +.>、/>、/>Then:
(35)；
(36)；
(37)；
(38)；
the formula involved in the derivation is:
(39)；
in conclusion, derived beforehandGradient calculation formulas including formulas (29), (31), (33) and (34); wherein,representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />Representing dimensions asIs a conversion matrix of (a); />、/> and />Representing the identity matrix with the dimension corresponding to the subscript;representing vectorizing the matrix array; />Representing a diagonal matrix with vector elements in brackets as diagonal elements; /> and />Representing the conjugate of the corresponding matrix.
Derived beforehandGradient calculation formula comprising formulas (35), (36), (37) and (38), wherein ∈10>Representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />The representing dimension is the identity matrix corresponding to the subscript.
Step b2, judging whether the calculated gradients are smaller than a preset error judgment threshold; if yes, executing the step b3, and if not, executing the step b4;
the embodiment of the invention selects the optimal gridding error matrix according to the gradient descent method, and when the optimal gridding error matrix is calculated and />Step b3 is executed when the error discrimination thresholds are smaller than the preset error discrimination threshold, otherwise, the step b3 is executedAnd step b4, wherein a preset error discrimination threshold can be set according to the needs, and the limitation is not limited.
Step b3, ending the iteration, and carrying out current iteration and />Outputting as an optimal matrix;
step b4, calculating the search direction of the next iteration matrix, determining the optimal step length according to one-dimensional search, and obtaining an updated gridding error matrix by utilizing a gridding error matrix updating formula based on the obtained search direction of the next iteration matrix and the optimal step length and />And returns to step b1.
Wherein the calculation of the next iteration matrix search direction represents the negative gradient direction. The formula used includes:
(40)；
wherein ,representing the next iteration matrix searching direction; />Is->The reference numbers corresponding to the gridding error matrix are respectively corresponding to +.2 when the values are 1 and 2> and />；/>Representing the iteration number; />Representing gridding error matrix->At iteration number +.>A gradient in time.
The formula used for determining the optimal step size comprises the following steps:
(41)；
wherein ,representing a solution target; />Representing a solution function; />Expressed in terms of iteration number +.>Gridding error matrix at time->；/>Representing a minimum value; />Indicate->The optimal step size corresponding to the iteration is obtained.
The meshing error matrix updating formula comprises the following steps:
(42)；
wherein ,expressed in terms of iteration number +.>Gridding error matrix at time->。
It will be appreciated that the above iterative steps are repeated until the calculated gradients are less than the predetermined error discrimination threshold, and updated and />。
Step 7, the currently obtainedMaximum a posteriori estimation as target->Outputting and rearranging the target distance and Doppler information into a two-dimensional matrix form, wherein the index of the resolution grid corresponds to the target distance and Doppler information.
According to the radar target non-meshing loss coherent accumulation method based on time-frequency non-uniform sampling, provided by the embodiment of the invention, a sparse Bayesian framework algorithm is applied to sparse reconstruction of the distance and Doppler characteristics of the scattering points of the target in the situation that the scattering points of the target are distributed sparsely in the distance domain and the Doppler domain, and the error in the same resolution grid, namely, meshing error, is corrected.
In order to verify the effectiveness of the method according to the embodiment of the present invention, experimental data are described below.
Experiments were performed on the device DESKTOP-CL80L4D, processor Inter (R) Core (TM) i7-9700 CPU @ 3.00GHz; baseband RAM 16.0GB; the operating system is windows10 (64-bit operating system, x 64-based processor); the simulation software is MATLAB2020a.
In the experiment, the radar emission wave is simulated by using a linear frequency modulation signal, and the signal carrier frequency isPulse width ofBandwidth is +.>The sampling rate is +.>. The observation station receives 50 pulse echo data. Assuming that five target scattering points exist in the space, the actual distance and the corresponding speed between the target scattering points and the radar are respectively +.>、、/>、/>、/>. The experiment compares the results of the two-dimensional FFT algorithm, SBL algorithm and the algorithm of the present invention. Meanwhile, the mean square error curve between the signal to noise ratio and the true value is given, and the robustness of the algorithm is verified.
FIG. 2 is a two-dimensional FFT scatter intensity reconstruction result; FIG. 3 shows the result of SBL scattering intensity reconstruction; FIG. 4 is the presentThe algorithm of the invention reconstructs a result of scattering intensity. Signal to noise ratio during the experiment isThe Monte Carlo number was 50. Distance and speed resolution unit length are +.> and />。
In the above result graph'"means the true scatterer scattering parameters. As can be seen from fig. 2, 3 and 4, for undersampling and sampling errors in the resolution grid, the three algorithms can well determine the vicinity of the resolution grid where the target is located, and the SBL algorithm effect is better than that of the two-dimensional FFT algorithm. When the signal to noise ratio is +.>When the two-dimensional FFT has partial false peaks, the SBL is less influenced by noise, the algorithm of the invention has almost no false peaks, and the imaging quality of the algorithm of the invention is higher.
FIG. 5 shows normalized mean square error curves of recovery results of three algorithms at different signal to noise ratios, as can be seen from the graph, when the signal to noise ratio is smaller thanAnd the algorithm error change speed is high. As the signal-to-noise ratio increases, the three algorithm errors decrease and the rate of change gradually flattens. Wherein, the error of the two-dimensional FFT algorithm is the largest in the whole course, the SBL algorithm is close to the normalized mean square error of the algorithm, and when the signal to noise ratio is +.>When the signal to noise ratio increases, the accuracy of the algorithm is higher than that of the SBL algorithm. The normalized mean square error is defined as:
(43)；
the normalized mean square error for the three algorithms at different signal-to-noise ratios is given in table 1:
table 1 normalized mean square error for three algorithms at different signal-to-noise ratios
Therefore, when solving the problem, the greedy algorithm is easy to fall into a local optimal solution, the sparse Bayesian assumption is that all recovery values are in the center of a resolution unit, and the influence of gridding errors cannot be eliminated when non-uniform sampling or sampling errors exist. According to the sparse Bayesian sparse reconstruction algorithm adopted by the embodiment of the invention, the scattering intensity is accurately estimated, and meanwhile, based on the gridding-free thought, the gridding error is regarded as a variable, and the influence of the gridding error is greatly reduced by using the EM criterion and the gradient descent algorithm for iterative updating. The embodiment of the invention can recover the accurate value of the scattering intensity under the conditions of undersampling and sampling errors, and can improve the resolution.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (9)
1. A radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling is characterized by comprising the following steps:
step 1, establishing a radar receiving echo signal model;
step 2, vectorizing an echo signal data matrix and a target scattering coefficient matrix, and establishing a sparse reconstruction model according to the sparsity of the target in a distance-Doppler domain;
step 3, initializing prior information、/>Gridding error matrix-> and />；
Step 4, based on the established sparse reconstruction model and the current obtained sparse reconstruction model、/>、/>、/>Updating the vectorized target scattering coefficient matrix +.>Posterior estimated mean->Sum of variances->；
Step 5, judgingPosterior estimated mean->Whether the precision requirement is met or not, if not, executing the step 6; if yes, executing the step 7;
step 6, updating、/> and /> and />And executing the step 4;
step 7, the currently obtainedMaximum a posteriori estimation as target->Outputting and rearranging the target distance and Doppler information into a two-dimensional matrix form, wherein the index of a resolution unit corresponds to the target distance and Doppler information;
the method for constructing the sparse reconstruction model according to the sparsity of the target in the distance-Doppler domain comprises the following steps of:
step a1, constructing an initial sparse reconstruction model, wherein the initial sparse reconstruction model comprises the following steps:
；
wherein ,representing an echo signal data matrix,/->Indicating that it belongs to->Complex matrix of dimensions>Each column is fast time echo data, and each behavior slow time echo data; /> and />Respectively representing the number of sampling points in the pulse of the actually sampled received signal and the number of sampling points between pulses; />Representing a matrix of scattering coefficients of the object, ">Indicating that it belongs toComplex matrix of dimensions>The value of each element in (a) is the scattering coefficient of the target for the corresponding distance and speed,/a-> and />Are natural numbers greater than 0, +.> and />Search range representing distance and speed of a targetThe circumference is divided into-> and />A resolution grid; /> and />Fourier matrix inverse matrix representing fast time and slow time respectively,>，；/>representing a zero-mean complex gaussian white noise matrix; gridding error matrix->，； />、/>Representing a sampling matrix after simulating intra-pulse and inter-pulse deletions; /> and />Respectively represent the fast time sum of the received echo signalsFast time sampling point number and slow time sampling point number when slow time discretization sampling is performed, +.>，/>、/>、/> and />Are natural numbers greater than 0; />Hadamard product of the matrix is represented, +.>Representing a transpose of the matrix or vector;
step a2, vectorizing the initial sparse reconstruction model and recording、/> and />Vectorization is respectively、/> and />The obtained vectorized sparse reconstruction model is as follows:
；
wherein ,kronecker product representing a matrix; /> and />Representing the identity matrix with the dimension corresponding to the subscript;
step a3, record，/>And equivalently rewriting the vectorized sparse reconstruction model as:
；
the model after equivalent rewriting is a finally established sparse reconstruction model.
2. The radar target non-gridding loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 1, wherein the establishing a radar receiving echo signal model comprises:
the expression of using a chirp signal with a large time-wide bandwidth product as a radar transmission signal is determined as:
；
wherein ,representing a fast time; />Representing the transmit signal pulse width; />Representing imaginary units; />Representing the signal carrier frequency;is the frequency modulation slope; />Representing the signal bandwidth; />Representing a gate function;
assuming that the radar emits a multi-pulse chirp signal, then observing the scattering point of the targetThe secondary echo is as follows:
；
wherein ,representing the scattering coefficient; />Representing a transmit signal pulse repetition period; />Representing a slow time dimension; />Representing the distance between the scattering point and the radar at the corresponding pulse time; />Representing the speed of light; />A natural number greater than 0;
setting the radial distance of the target at the starting moment of the radar transmitting pulse train asMixing and filtering the radar echo signals to obtain baseband signals:
；
wherein ,representing the radial velocity of the target relative to the radar line of sight.
3. The radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 2, wherein in step 4, the vectorized target scattering coefficient matrix is updatedPosterior estimated mean->Sum of variances->The formula adopted comprises:
；
；
；
wherein ,a priori information representing the variance of the noise; />Expressed as vector +.>A diagonal matrix with diagonal elements; />Representation->A priori information of the variance; />Representing the identity matrix with the dimension corresponding to the subscript; />Representing a conjugate transpose of the matrix or vector; />Representing intermediate variables.
4. The radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 3, wherein in step 6, updating is performed、/>The formula adopted comprises:
；
；
wherein ,representation->Middle->An element; /> and />Representation->Shape parameters and scale parameters of the distribution; />Representation->Middle->Line->Elements of a column; />Representation->Middle->An element; /> and />Respectively representing a shape parameter and a scale parameter of noise variance distribution; />Represents the trace of the solution matrix,/->、/>、/> and />Are all greater than 0.
5. The radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 4, wherein in step 6, updating is performed and />Comprises the following steps:
step b1, based on the current gridding error matrix and />By using the pre-derived +.>Gradient calculation formula and->Calculating a corresponding gradient by a gradient calculation formula;
step b2, judging whether the calculated gradients are smaller than a preset error judgment threshold; if yes, executing the step b3, and if not, executing the step b4;
step b3, ending the iteration, and carrying out current iteration and />Outputting as an optimal matrix;
step b4, calculating the search direction of the next iteration matrix, determining the optimal step length according to one-dimensional search, and obtaining an updated gridding error matrix by utilizing a gridding error matrix updating formula based on the obtained search direction of the next iteration matrix and the optimal step length and />And returns to step b1.
6. The time-frequency non-uniform sampling based radar target of claim 5The gridding-free loss phase-coherent accumulation method is characterized in that the method is obtained by deduction in advanceA gradient calculation formula comprising:
；
；
；
；
wherein ,representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />Representing dimensions asIs a conversion matrix of (a); />、/> and />Representing the identity matrix with the dimension corresponding to the subscript; />Representing vectorizing the matrix array; />Representing a diagonal matrix with vector elements in brackets as diagonal elements; /> and />Representing the conjugate of the corresponding matrix.
7. The radar target gridding-free loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 6, wherein the method is derived in advanceA gradient calculation formula comprising:
；
；
；
；
wherein ,representation->Is a gradient of (2); />、/>、/>Representation->Three of the gradients; />The representing dimension is the identity matrix corresponding to the subscript.
8. The radar target non-gridding loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 7, wherein the formula adopted for calculating the next iteration matrix search direction comprises the following steps:
；
the formula used for determining the optimal step size comprises the following steps:
；
wherein ,representing the next iteration matrix searching direction; />Is->The reference numbers corresponding to the gridding error matrix are respectively corresponding to +.2 when the values are 1 and 2> and />；/>Representing the iteration number; />Representing gridding error matrix->At iteration number +.>Time gradient; />Representing a solution target; />Representing a solution function; />Expressed in terms of iteration number +.>Gridding error matrix at time->；/>Representing a minimum value; />Indicate->The optimal step size corresponding to the iteration is obtained.
9. The radar target non-meshing loss coherent accumulation method based on time-frequency non-uniform sampling according to claim 8, wherein the meshing error matrix update formula comprises:
；
wherein ,expressed in terms of iteration number +.>Gridding error matrix at time->。
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