CN116879862A - Single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration - Google Patents
Single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration Download PDFInfo
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Abstract
The invention discloses a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration, which comprises the following steps: obtaining an initial spatial angle resolution result based on the single snapshot data, and estimating a noise variance; grid division is carried out on the space angle, and a sparse constraint coefficient is calculated; establishing an angle super-resolution compressed sensing model according to the single snapshot data and the initial overcomplete space angle sparse base matrix, and acquiring a cost function of the sensing model; calculating a hierarchical iteration weighting coefficient and a hierarchical iteration sparse base matrix; and carrying out iterative solution on the cost function according to the hierarchical iteration weighting coefficient, the hierarchical iteration sparse base matrix and the sparse constraint coefficient to obtain a space angle estimation value. The method can effectively utilize single snapshot data, break through the Rayleigh limit of the system and realize the super resolution of the space angle under single snapshot; and in addition, the influence of noise is considered in the layering sparse solving process, so that the high-performance spatial angle super-resolution under the condition of low signal-to-noise ratio is realized, and the radar detection and recognition performance is improved.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration.
Background
The main function of spatial signal angle estimation is parameter estimation and target positioning, which play an important role in multiple fields of radar, geophysics, satellite communication, military and the like. The detection and recognition capability of the radar can be enhanced by combining the spatial angle information of the target signal with other parameters of the target (such as the target distance and the target speed).
With the development of radar technology, radar performance is continuously improved, but insufficient resolution is unavoidable in the process of processing multiple targets. Modern radars typically employ high range resolution and high angular resolution to improve the target spatial resolution of the radar. The high resolution capability allows for the detection and identification of objects from a strong ground object background, as compared to conventional radar systems.
The spatial angular resolution of the radar is related to the array aperture, the larger the aperture, the higher its resolution. Conventional approaches generally increase the spatial angular resolution of the array by increasing the array aperture. In order to obtain a large-aperture high-resolution array, and only the number of array elements can be increased under the condition that the spacing of the array elements meets the requirement of a space sampling theorem, the method can cause the system to be too complex, and the system cost is increased. Another way to effectively increase the aperture of the array is to increase the spacing of the array elements under the condition of keeping the number of the array elements unchanged, or to extract some array elements from the original ideal array plane to form a sparse array. Compared with an ideal array, when the number of the array elements is the same, the sparse array can obtain larger aperture, improve the spatial angle resolution capability of the radar, and reduce the system cost.
At present, the research for improving the spatial angle resolution performance of a sparse array is mainly divided into two aspects, namely, the theoretical angle resolution of a system is improved by methods of increasing the aperture of the array, reducing the noise coefficient of a receiver and the like. But this method is not only too costly to develop, but is also limited by the practical circumstances. On the other hand, a signal processing algorithm is adopted to improve the spatial angle resolution capability of the radar.
For example, in the paper "an improved DOA estimation method for orthogonal matching pursuit" published by the Japanese plum, et al, aiming at the problem that the angular resolution of a conventional orthogonal matching pursuit DOA estimation algorithm is limited by a Rayleigh limit and cannot meet the requirement of high resolution, an orthogonal matching pursuit DOA estimation method combined with local optimization is provided. However, the method has two defects, namely, under the condition of single snapshot observation data, the space angle value estimated by the method has larger phase difference with the actual target position, and the angle super-resolution performance is poor; secondly, the influence of noise on the model is not considered in the model establishing and solving process, and the super-resolution performance of the target difference angle smaller than the Rayleigh time-limited space angle under the low signal-to-noise ratio cannot be ensured.
For another example, any clouds et al in the paper published by any clouds et al in the paper of forward-looking imaging based on airborne multichannel radar iterative super-resolution estimation, aiming at the problems that a conventional spatial angle super-resolution algorithm needs a large number of snapshots, the resolution of azimuth angle is limited to be improved, the influence of noise is large and the like, provide a multichannel radar forward-looking imaging algorithm based on single-snapshot iterative super-resolution processing. However, the method has two defects, namely, the method uses multi-channel data in a single snapshot, and the method is similar to a multi-snapshot single-channel data acquisition mode, has large data storage capacity and occupies large hardware resources; secondly, the method has limited noise suppression capability in iterative solution, and cannot guarantee the spatial angle super-resolution performance under low signal-to-noise ratio.
In conclusion, most of the existing methods are carried out under the condition of multi-snapshot observation data, so that the occupied hardware resources are large, and the required cost is high; and the influence of the signal-to-noise ratio is large, and under the condition of low signal-to-noise ratio, the error of the existing spatial angle super-resolution method is large, so that the high-precision spatial angle information of the target can not be obtained, and the estimation performance is poor. In addition, the existing sparse array is easy to generate high side lobes when performing angle super resolution, so that false target points are introduced, and the detection and recognition performance of the radar are affected.
Disclosure of Invention
The invention provides a single snapshot sparse array space angle super-resolution method based on layering sparse iteration, which aims to solve the problems that the angle super-resolution performance is poor under low signal to noise ratio in the existing space angle super-resolution technology, high side lobes can be generated during sparse array angle super-resolution, the angle super-resolution data size is large and the occupied hardware resources are large under the multi-snapshot condition. The technical problems to be solved by the invention are realized by the following technical scheme:
a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration comprises the following steps:
acquiring an initial spatial angle resolution result based on single snapshot data of the radar echo;
estimating a noise variance according to the initial spatial angle resolution result;
grid division is carried out on the space angle, and a sparse constraint coefficient is calculated according to a grid division result and the noise variance;
constructing an initial overcomplete space angle sparse base matrix based on the grid division result and the sparse array element position;
establishing an angle super-resolution compressed sensing model according to the single snapshot data and the initial overcomplete space angle sparse base matrix, and obtaining a cost function of the sensing model according to a Lagrangian multiplier method;
calculating a hierarchical iteration weighting coefficient, and calculating a hierarchical iteration sparse base matrix according to the hierarchical iteration weighting coefficient;
and carrying out iterative solution on the cost function according to the hierarchical iteration weighting coefficient, the hierarchical iteration sparse base matrix and the sparse constraint coefficient to obtain a space angle estimation value.
The invention has the beneficial effects that:
1. according to the single snapshot sparse array space angle super-resolution method based on layered sparse iteration, on one hand, a sparse array space angle super-resolution perception model is established by utilizing single snapshot observation data, and the system Rayleigh limit is broken through by iteration solution of the model, so that the sparse array space angle super-resolution under single snapshot is realized; the problems of large data volume, large occupied hardware resources and high required cost under the condition of multiple snapshots are avoided; on the other hand, the influence of noise on the spatial angle super-resolution is considered, the noise variance is estimated by utilizing single-snapshot observation data, the sparse constraint coefficient of the single-snapshot sparse array spatial angle super-resolution is obtained according to the noise variance, the influence of the noise is considered in the sparse solving process, and the high-performance spatial angle super-resolution of the target under the low signal-to-noise ratio is realized.
2. The method and the device also continuously carry out iterative contraction on the target area and the non-target area through layered sparse iteration, effectively solve the problem of high side lobe when the sparse array carries out spatial angle super resolution, improve radar detection and identification performance, and have higher application value.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flow chart of a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration provided by the embodiment of the invention;
fig. 2 is another flow chart of a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a specific arrangement of sparse array masks used in simulation experiments;
FIG. 4 is an initial angular resolution result when the target angular interval exceeds the Rayleigh limit;
FIG. 5 is a graph showing the super-resolution of angles obtained by OMP algorithm when the target angle interval exceeds the Rayleigh limit;
FIG. 6 is a graph of the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention when the target angular interval exceeds the Rayleigh limit;
FIG. 7 is an initial angular resolution result when the target angular interval is less than the Rayleigh limit;
FIG. 8 is a graph showing the super-resolution of angles obtained by OMP algorithm when the target angle interval is smaller than Rayleigh;
FIG. 9 is a graph showing the super-resolution result of the angle obtained by the hierarchical sparse iteration using the method of the present invention when the target angle interval is smaller than the Rayleigh limit;
FIG. 10 shows the result of angle super resolution obtained by OMP algorithm under 20dB signal-to-noise ratio;
FIG. 11 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 20dB signal-to-noise ratio;
FIG. 12 is a graph showing the result of angle super resolution obtained by OMP algorithm at 15dB SNR;
FIG. 13 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at 15dB signal-to-noise ratio;
FIG. 14 is a graph showing the result of angle super resolution obtained by OMP algorithm at 10dB SNR;
FIG. 15 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 10dB signal-to-noise ratio;
FIG. 16 is a graph showing the angle super-resolution result obtained by OMP algorithm under 5dB signal-to-noise ratio;
fig. 17 shows an angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 5dB signal-to-noise ratio.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
Example 1
Referring to fig. 1 and fig. 2 in combination, fig. 1 is a schematic flow chart of a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration according to an embodiment of the present invention, and fig. 2 is another schematic flow chart of a single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration according to an embodiment of the present invention. The single snapshot sparse array space angle super-resolution method based on layered sparse iteration mainly comprises the following steps:
step 1: and obtaining an initial spatial angle resolution result based on the single snapshot data of the radar echo.
Specifically, the present inventionThe embodiment is an improvement scheme provided for the radar sparse array space angle super-resolution technology, so before the algorithm starts, firstly, the electromagnetic parameters of the radar and the structural parameters of the sparse array surface are required to be set, and the method comprises the carrier frequency of the radarWavelength->Pulse width->Signal bandwidth->The sparse array plane structure parameter comprises the number of array elements of the sparse array plane>Array element position arrangement and array face sparsity +.>Etc.
Then, using single snapshot dataCalculating the initial spatial angle resolution result +.>. For specific procedures, reference is made to the related art, and this embodiment is not described in detail here.
Step 2: and estimating the noise variance according to the initial spatial angle resolution result.
First, the results are resolved from the initial spatial angleDistinguishing the target region from the noise region, extracting noise units corresponding to the noise region, vectorizing, and adding +.>And (3) representing.
In particular, the results may be resolved by initial spatial angleWhether or not the element in (c) is 0 to distinguish the target region from the noise region. The position of the element 0 is marked as a noise area, namely a non-target area, and the position of the element non-0 is marked as a target area.
Based on the actual situation, a threshold value can be set according to the sceneAs a basis for differentiation, the threshold +.>Much smaller than the average of the scene elements. When->The elements in (2) are greater than a threshold +.>When the element is considered to be a non-0 element, the position corresponding to the element is defined as the target area. When->The elements in (2) are less than or equal to a threshold value->When this element is considered to be 0 element, the position corresponding to this element is divided into noise regions. The unit corresponding to the noise region is the noise unit, and the noise unit is vectorized and then usedAnd (3) representing.
Then, the noise variance is estimated using the noise unit, expressed as:
；
in the formula ,representing noise variance->Representing the averaging operation, +.>Representing noise unit->Is a conjugate transpose of (a).
Step 3: and performing grid division on the space angle, and calculating a sparse constraint coefficient according to a grid division result and the noise variance.
31 Dividing the angular grid of the spatial pitch angle and the azimuth angle intoAnd a spatial angle.
Specifically, the size of the space angle grid is set according to the requirement, and the angle grid division of the space pitch angle and the azimuth angle is performed, and the embodiment is divided intoThe number of spatial angles, namely the number of spatial angle sampling points after the subsequent super resolution is +.>And each.
32 A laplace scale factor is calculated according to the mesh division result.
Specifically, assuming that the target angle after spatial angle super-resolution obeys the same distribution, and assuming that each point has the same laplace factor, the calculation formula of the laplace scale factor is:
；
in the formula ,representing the Laplace scale factor,/->Representing the number of spatial angle sampling points after super resolution, < + >>Representation->Norms.
33 Calculating a sparse constraint coefficient according to the Laplace scale factor and the noise variance, wherein the calculation formula is as follows:
；
in the formula ,and represents the sparse constraint coefficients.
According to the embodiment, the influence of scene noise on spatial angle super-resolution is considered, the sparse constraint coefficient is calculated and used for subsequent angle estimation, and high-performance spatial angle super-resolution under low signal-to-noise ratio is realized.
Step 4: and constructing an initial overcomplete space angle sparse base matrix based on the grid division result and the sparse array element positions.
Specifically, the constructed initial overcomplete space angle sparse base moment matrix is recorded asThe matrix dimension isThen->Is>The individual elements are expressed as:
；
in the formula ,、/> and />Respectively represent +.>The array elements are in space->、/> and />The position on the shaft is such that,；/>、/>respectively represent +.>Pitch angle and azimuth angle corresponding to each spatial angle, +.>，/>Representing wavelength.
Step 5: and establishing an angle super-resolution compressed sensing model according to the single snapshot data and the initial overcomplete space angle sparse base matrix, and obtaining a cost function of the sensing model according to a Lagrangian multiplier method.
51 And (3) establishing an angle super-resolution compressed sensing model.
In particular, the method comprises the steps of,using single snapshot dataAnd an initial overcomplete spatial angle sparse basis matrix +.>According to the compressed sensing theory, an angle super-resolution compressed sensing model is established and expressed as:
；
wherein ,representing spatial angle super-resolution results,/->Representation->Norms (F/F)>Representation->Norms (F/F)>Representing the noise level.
52 Obtaining the cost function of the perception model according to the Langerhans multiplier method.
In particular, constructionAn optimization model, which is solved by nonlinear optimization and adopts iteration +.> Norm optimized approximation ++>In the norm mode, the angle super-resolution compressed sensing model established in the step 51) can be written as follows:
；
wherein ,，/>representation->Middle->Values corresponding to the individual elements->Representing the absolute value of the elementTo the power of (I)>。
The cost function of the perceptual model can be written in the form of:
；
in the formula ,representing a cost function->Is Lagrangian multiplier vector, +.>Representing the transpose operation.
Step 6: and calculating a hierarchical iteration weighting coefficient, and calculating a hierarchical iteration sparse base matrix according to the hierarchical iteration weighting coefficient.
61 A hierarchical iteration weighting coefficient is calculated.
It can be appreciated that when the number of iterations is 0, the result can be resolved directly from the initial spatial angleConstructing a diagonal matrix for representing the initial hierarchical iterative weighting coefficients +.>The expression is:
；
in the formula ,representing the +.sup.th in the initial spatial angle resolution result>The value corresponding to the individual element is used,representing construction of a diagonal matrix function, < >>I.e. the use of the parameter +.>And->。
The present embodiment focuses on the case where the number of iterations is greater than 0.
When the iteration number is greater than 0, after each iteration, distinguishing a target area from a non-target area in the current spatial angle super-resolution result, and eliminating the position with the element of 0.
It should be noted that the number of the substrates,here, regarding the distinction between the target area and the non-target area, the method of distinguishing the target area from the noise area from the initial spatial angle resolution result in step 2 may be performed by setting a threshold value far smaller than the average value of the scene elementsTo realize the method. Super-resolving the current spatial angle by more than threshold value +.>Is identified as a non-0 element, and the positions corresponding to these elements are marked as target areas. The current spatial angle super-resolution result is less than or equal to a threshold value +.>Is identified as a non-0 element and the locations corresponding to these elements are delineated as target areas.
Optionally, after the target area and the non-target area are distinguished, marking the position with the element being 0, and then calculating the position without considering the position with the element being 0, and marking the calculated position as。
Super-resolution result of current space anglePerforming layered matrix compression operation to obtain layered compression matrix. The specific method for hierarchical matrix compression operation can be implemented with reference to the related art, and this embodiment is not described in detail herein.
Finally, based on layered compression matrixConstructing a diagonal matrix for representing hierarchical iteration weighting coefficients +.>Which is provided withThe expression is:
；
in the formula ,representing a hierarchical compression matrix->Middle->The value corresponding to the individual elements is 1 to less than or equal to%>The number of the compressed positions is less than or equal to the number of the compressed positions.
62 A hierarchical iterative sparse basis matrix is calculated.
First, construct a compressed basis matrix。
It will be appreciated that when the number of iterations is 0, the base matrix is compressedSparse base matrix equal to initial overcomplete space angle>。
The present embodiment focuses on the case where the number of iterations is greater than 0.
When the iteration number is greater than 0, after each iteration, distinguishing a target area from a non-target area in the current spatial angle super-resolution result, and eliminating the position with the element of 0.
With respect to the distinction between target and non-target areas, it is still possible to implement the method according to step 61). Setting a threshold value far smaller than the average value of scene elementsThe current space angle super-resolution result is addedGreater than threshold->Is identified as a non-0 element, and the positions corresponding to these elements are marked as target areas. The current spatial angle super-resolution result is less than or equal to a threshold value +.>Is identified as a non-0 element and the locations corresponding to these elements are delineated as target areas.
Optionally, after the target area and the non-target area are distinguished, marking the position with the element being 0, and then calculating the position without considering the position with the element being 0, and marking the calculated position as。
Super-resolution result of current space anglePerforming layered matrix compression operation to obtain layered compression matrix. The specific method for hierarchical matrix compression operation can be implemented with reference to the related art, and this embodiment is not described in detail herein.
Finally, the layered compression matrix is utilizedAn initial overcomplete spatial angle sparse basis matrix corresponding to the vector in (1)>Related columns of (a) constitute a layered compressed basis matrix +.>。
Specifically, a hierarchical compression matrixTarget area in (a)Position information in the uncompressed matrix corresponds to the initial overcomplete spatial angle sparse basis matrix +.>Is included in the column.
Second, constructing a layered iterative sparse base matrix。
Specifically, weighting weight coefficients according to hierarchical iterationAnd layered compressed base matrix->Constructing a layered iterative sparse base matrix, wherein the expression is as follows:
；
in the symbol'"means matrix multiplication.
Step 7: and carrying out iterative solution on the cost function according to the hierarchical iteration weighting coefficient, the hierarchical iteration sparse base matrix and the sparse constraint coefficient to obtain a space angle estimation value.
71 Using Lagrangian multiplier method to solve cost function, and obtaining space angle estimated valueThe solution expression of (2) is:
；
in the formula ,weight diagonal matrix representing weight coefficients not subjected to iterative compression, < ->Representing spatial angle super resolution result->The%>The value corresponding to the individual element; base matrix->，/>Representation and->Identity matrix with the same dimension ∈>Represents the conjugate transpose->Representing matrix inversion, < >>And represents the sparse constraint coefficients.
72 Weighting weight coefficients according to hierarchical iterationLayered iterative sparse basis matrix> and />The solution expression of (2) can be expressed as a space angle estimated value after layered sparse iteration solution:
；
in the formula ,representation and->Identity matrix with the same dimension.
According to the embodiment, the sparse array space angle super-resolution perception model is established by utilizing the single-snapshot observation data, the Rayleigh limit of the system is broken through by means of iterative solution of the model, and the sparse array space angle super-resolution under the single snapshot is realized.
It should be noted that, after obtaining the spatial angle estimation value, the method further includes:
step 8: judging whether the space angle estimated value meets the requirement or not based on a preset threshold, and if so, outputting the current space angle estimated value as a final space angle super-resolution result;
if the current space angle estimation value does not meet the target area, returning to the step of calculating the hierarchical iteration weighting coefficient and the hierarchical iteration sparse base matrix, and updating the hierarchical iteration weighting coefficient and the hierarchical iteration sparse base matrix and re-solving the cost function after distinguishing the target area from the non-target area according to the current space angle estimation value.
Specifically, the spatial angle estimation value obtained by iterationJudging +.>Whether the requirements are satisfied:
；
in the formula ,representing a spatial angle estimate; if the number of iterations is 0, then +.>Resolving results for initial spatial anglesIf the number of iterations is greater than 0, +.>The spatial angle estimated value obtained for the last iteration; />Representation->Norms (F/F)>Representing a preset threshold, the value of which is a smaller threshold discrimination constant.
If the above formula is true, the iteratively determined spatial angle estimates are describedMeeting the requirements, the currently found +.>And outputting as a final spatial angle super-resolution result.
If the above formula is not satisfied, indicating that iteration solution needs to be continued, returning to the step 5, and modifying and updating the hierarchical iteration weighting coefficient according to the condition that the iteration number is greater than 0And hierarchical iterative sparse basis matrix->And (5) repeating the calculation process of the step 6 until the requirement is met.
It can be appreciated that other judging conditions can be set in this embodiment as the judging basis of whether the space angle estimated value meets the requirement, for exampleEtc. Alternatively, a maximum number of iterations may be provided, and when a preset maximum number of iterations is reached,and outputting a spatial angle super-resolution result.
According to the single snapshot sparse array space angle super-resolution method based on layered sparse iteration, on one hand, a sparse array space angle super-resolution perception model is established by utilizing single snapshot observation data, and the system Rayleigh limit is broken through by iteration solution of the model, so that the sparse array space angle super-resolution under single snapshot is realized; the problems of large data volume, large occupied hardware resources and high required cost under the condition of multiple snapshots are avoided; on the other hand, the influence of noise on the spatial angle super-resolution is considered, the noise variance is estimated by utilizing single-snapshot observation data, the sparse constraint coefficient of the single-snapshot sparse array spatial angle super-resolution is obtained according to the noise variance, the influence of the noise is considered in the sparse solving process, and the high-performance spatial angle super-resolution of the target under the low signal-to-noise ratio is realized.
In addition, the method and the device continuously carry out iterative contraction on the target area and the non-target area through layered sparse iteration, effectively solve the problem of high side lobe when the sparse array carries out spatial angle super resolution, improve radar detection and recognition performance, and have higher application value.
Example two
The method of the invention is compared with the existing method through simulation experiments, and the beneficial effects of the invention are verified.
1. Experimental conditions
The simulation experiment uses the center frequencyIs->Wavelength->Is->Bandwidth is->Pulse width->Is->Distance resolution of->Spatial angular resolution is +.>For example, specific parameters are shown in table 1.
Table 1 radar basic parameters
The sparse array surface structure parameters are shown in Table 2, wherein the ideal array element spacingThe aperture size of the sparse array area array surface is as follows: length x width =>Sparsity of array surface->0.5, sparse array area array element number +.>50, a sparse mask specific arrangement is shown in fig. 3.
TABLE 2 sparse array surface Structure parameters
In addition, the performance of the angle super-resolution algorithm is measured through the Root Mean Square Error (RMSE) in the simulation experiment, and the root mean square error of the target angle after angle super-resolution and the ideal target angle value is calculated and expressed as:
；
wherein ,representing the number of scene experiments>Representing the number of target signals> and />Represents the estimated azimuth and pitch angles, respectively, +.> and />Representing the true azimuth and pitch angles, respectively. The smaller the root mean square error RMSE, the closer the target angle estimate is to the ideal target position.
2. Experimental content and results analysis
Experiment one:
aiming at the situation that the target angle interval exceeds the Rayleigh limit in a single snapshot scene, the hierarchical sparse iteration method and the existing deterministic maximum likelihood algorithm (Deterministic Maximum Likelihood, DML) and the orthogonal matching pursuit algorithm (Orthogonal Matching Pursuit, OMP) are adopted to conduct angle super-resolution, and the results are shown in figures 4-6 and table 3. FIG. 4 is an initial angular resolution result when the target angular interval exceeds the Rayleigh limit; FIG. 5 is a graph showing the super-resolution of angles obtained by OMP algorithm when the target angle interval exceeds the Rayleigh limit; fig. 6 is an angular super-resolution result obtained by adopting the method of the invention through hierarchical sparse iteration when the target angle interval exceeds the rayleigh limit. In FIGS. 4-6, theta)、phi(/>) Representing pitch and azimuth, respectively.
TABLE 3 comparison of angle super-resolution results for target angle intervals exceeding Rayleigh time limits
From the results of fig. 4-6 and table 3, it can be seen that when the target angle interval exceeds the rayleigh limit, both the hierarchical sparse iteration method and the DML algorithm provided by the present invention can obtain a better spatial angle estimation result, but the time of the DML algorithm is much longer than that of the hierarchical sparse iteration algorithm of the present invention.
Experiment II:
aiming at the situation that the target angle interval is smaller than the Rayleigh limit in a single snapshot scene, the hierarchical sparse iteration method and the existing DML and OMP methods are respectively adopted to conduct angle super-resolution, and the results are shown in figures 7-9 and table 4. Wherein, fig. 7 is an initial angle resolution result when the target angle interval is smaller than the rayleigh limit, fig. 8 is an angle super resolution result obtained by adopting an OMP algorithm when the target angle interval is smaller than the rayleigh limit, and fig. 9 is an angle super resolution result obtained by adopting the method of the invention through layering sparse iteration when the target angle interval is smaller than the rayleigh limit. In FIGS. 7-9, theta)、phi(/>) Representing pitch and azimuth, respectively.
TABLE 4 super-resolution results vs. Table for angles for which the target angular separation is less than Rayleigh time limit
From the results of fig. 7-9 and table 4, it can be seen that, when the target angle interval is smaller than the rayleigh limit, both the hierarchical sparse iteration method and the DML algorithm provided by the present invention can obtain a better spatial angle estimation result, the performance of the OMP algorithm is greatly reduced, but the time of the DML algorithm is far longer than that of the hierarchical sparse iteration algorithm of the present invention.
Experiment III:
aiming at the condition that the target angle interval is smaller than the Rayleigh limit under the condition that noise exists, the layered sparse iteration method and the existing DML and OMP methods are adopted to conduct angle super-resolution under different signal to noise ratios, and the results are shown in figures 10-17 and table 5. Wherein, FIG. 10 is the angle super-resolution result obtained by OMP algorithm under 20dB signal-to-noise ratio; FIG. 11 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 20dB signal-to-noise ratio; FIG. 12 is a graph showing the result of angle super resolution obtained by OMP algorithm at 15dB SNR; FIG. 13 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at 15dB signal-to-noise ratio; FIG. 14 is a graph showing the result of angle super resolution obtained by OMP algorithm at 10dB SNR; FIG. 15 is a graph showing the angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 10dB signal-to-noise ratio; FIG. 16 is a graph showing the angle super-resolution result obtained by OMP algorithm under 5dB signal-to-noise ratio; fig. 17 shows an angular super-resolution result obtained by hierarchical sparse iteration using the method of the present invention at a 5dB signal-to-noise ratio. In FIGS. 10-17, theta)、phi(/>) Representing pitch and azimuth, respectively.
TABLE 5 comparison of angle super resolution results for target angle intervals less than Rayleigh time limit at different signal-to-noise ratios
As can be seen from the results of fig. 10 to 17 and table 5, when the DML algorithm is used to perform spatial angle super resolution in the presence of noise, the calculation amount is large, the algorithm operation time is long, the consumed resources are more, the required cost is high, and the angle estimation performance is obviously reduced along with the reduction of the signal-to-noise ratio; when the OMP algorithm is used for spatial angle super-resolution, noise is greatly affected, estimation performance is also worse and worse along with the reduction of signal-to-noise ratio, the obtained spatial angle position is greatly different from an ideal position, a false target position can be obtained, and the radar detection recognition capability is greatly affected. In contrast, the single snapshot sparse array space angle super-resolution method based on layered sparse iteration provided by the invention not only can effectively utilize single snapshot observation data and break through the Rayleigh limit of a system to realize space angle super-resolution, but also can continuously carry out iterative contraction on a target area and a non-target area through layered sparse iteration, thereby effectively solving the problem of high side lobe when the sparse array carries out space angle super-resolution, reducing the operation time of an algorithm, simultaneously having good noise suppression capability and being capable of realizing high-performance space angle super-resolution under low signal to noise ratio.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (10)
1. A single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration is characterized by comprising the following steps:
acquiring an initial spatial angle resolution result based on single snapshot data of the radar echo;
estimating a noise variance according to the initial spatial angle resolution result;
grid division is carried out on the space angle, and a sparse constraint coefficient is calculated according to a grid division result and the noise variance;
constructing an initial overcomplete space angle sparse base matrix based on the grid division result and the sparse array element position;
establishing an angle super-resolution compressed sensing model according to the single snapshot data and the initial overcomplete space angle sparse base matrix, and obtaining a cost function of the sensing model according to a Lagrangian multiplier method;
calculating a hierarchical iteration weighting coefficient, and calculating a hierarchical iteration sparse base matrix according to the hierarchical iteration weighting coefficient;
and carrying out iterative solution on the cost function according to the hierarchical iteration weighting coefficient, the hierarchical iteration sparse base matrix and the sparse constraint coefficient to obtain a space angle estimation value.
2. The single snapshot sparse array spatial angle super-resolution method of claim 1, wherein estimating noise variance from the initial spatial angle resolution result comprises:
distinguishing a target area and a noise area from the initial spatial angle resolution result, taking out a noise unit corresponding to the noise area, and vectorizing the noise unitA representation;
estimating a noise variance using the noise unit, the formula being:
；
in the formula ,representing noise variance->Representing the averaging operation, +.>Representing noise unit->Is a conjugate transpose of (a).
3. The hierarchical sparse iteration-based single snapshot sparse array spatial angle super-resolution method of claim 1, wherein meshing a spatial angle and calculating a sparse constraint coefficient according to a meshing result and the noise variance comprises:
dividing the angular grid of the spatial pitch angle and the azimuth angle intoA plurality of spatial angles;
and calculating the Laplace scale factor according to the grid division result, wherein the calculation formula is as follows:
；
in the formula ,representing the Laplace scale factor,/->Representing the total number of space angles after grid division, +.>Representing the initial spatial angle resolution result,/->Representation->A norm;
and calculating a sparse constraint coefficient according to the Laplace scale factor and the noise variance, wherein the calculation formula is as follows:
；
in the formula ,representing sparse constraint coefficients, ++>Representing the noise variance.
4. The single snapshot sparse array spatial angle super-resolution method based on hierarchical sparse iteration of claim 1, wherein the angle super-resolution compressed sensing model is expressed as:
；
wherein ,representing spatial angle super-resolution results,/->Representation->Norms (F/F)>Representing single snapshot data, +.>Representing an initial overcomplete spatial angle sparse basis matrix, < >>Representation->Norms (F/F)>Representing the noise level.
5. The single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration of claim 1, wherein the cost function is expressed as:
；
in the formula ,
；
representing a cost function->Representing spatial angle super-resolution results,/->Representing the number of spatial angle sampling points after super resolution, < + >>Representation->Middle->Values corresponding to the individual elements->，/>Representing the absolute value of the elementTo the power of (I)>，/>Representing the Lagrangian multiplier vector, +.>Representing a transpose operation->Representing an initial overcomplete spatial angle sparse basis matrix, < >>Representing single snapshot data.
6. The single snapshot sparse array spatial angle super-resolution method based on hierarchical sparse iteration of claim 1, wherein the calculating the hierarchical iteration weighting coefficients comprises:
when the iteration times are greater than 0, after each iteration, distinguishing a target area from a non-target area in the current spatial angle super-resolution result, and eliminating the position with the element of 0;
super-resolution result for current space anglePerforming hierarchical matrix compression operation to obtain a hierarchical compression matrix +.>；
Based on the layered compression matrixConstructing hierarchical iterative weighting coefficients->Expressed as:
；
in the formula ,representing construction of a diagonal matrix function, < >>Representing a hierarchical compression matrix->Middle->The value corresponding to the individual elements is 1 to less than or equal to%>The number of positions after compression is less than or equal to the number of positions after compression>。
7. The single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration of claim 1, wherein calculating a hierarchical iterative sparse basis matrix according to the hierarchical iterative weighting coefficients comprises:
when the iteration times are greater than 0, after each iteration, distinguishing a target area from a non-target area in the current spatial angle super-resolution result, and eliminating the position with the element of 0;
super-resolution result for current space anglePerforming hierarchical matrix compression operation to obtain a hierarchical compression matrix +.>；
Compressing a matrix using the hierarchyAn initial overcomplete spatial angle sparse basis matrix corresponding to the vector in (1)>Related columns of (a) constitute a layered compressed basis matrix +.>；
Weighting weight coefficients according to the hierarchical iterationAnd said layered compressed base matrix->Constructing a layered iterative sparse base matrix, wherein the expression is as follows:
；
in the formula ,representing a hierarchical iterative sparse basis matrix, symbol ">"means matrix multiplication.
8. The single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration of claim 1, wherein solving the cost function according to the hierarchical iteration weighting weight coefficient, the hierarchical iteration sparse base matrix and the sparse constraint coefficient to obtain a space angle estimation value comprises:
solving the cost function by utilizing Lagrangian multiplier method to obtain a space angle estimated valueThe solution expression of (2) is:
；
in the formula ,weight diagonal matrix representing weight coefficients not subjected to iterative compression, < ->Representing spatial angle super-resolution resultsThe%>Values corresponding to the individual elements->Base matrix->，/>Representing an initial overcomplete spatial angle sparse basis matrix; />Representation and->Identity matrix with the same dimension ∈>Represents the conjugate transpose->The matrix inversion is represented by a matrix inversion,representing the sparse constraint coefficients;
weighting weight coefficients according to the hierarchical iterationThe hierarchical iterative sparse basis matrix +.> and />The solution expression of (2) can be expressed as a space angle estimated value after layered sparse iteration solution:
；
in the formula ,representation and->Identity matrix with the same dimension.
9. The single snapshot sparse array spatial angle super-resolution method based on hierarchical sparse iteration of claim 1, further comprising, after obtaining the spatial angle estimate:
judging whether the space angle estimated value meets the requirement or not based on a preset threshold, and if so, outputting the current space angle estimated value as a final space angle super-resolution result;
if the current space angle estimation value does not meet the target area, returning to the step of calculating the hierarchical iteration weighting coefficient and the hierarchical iteration sparse base matrix, and after distinguishing the target area from the non-target area according to the current space angle estimation value, updating the hierarchical iteration weighting coefficient and the hierarchical iteration sparse base matrix, and re-solving the cost function.
10. The single snapshot sparse array space angle super-resolution method based on hierarchical sparse iteration of claim 9, wherein the condition for judging whether the space angle estimated value meets the requirement based on a preset threshold is:
；
in the formula ,representing a spatial angle estimate; if the number of iterations is 0, then +.>For the initial spatial angle resolution result +.>If the number of iterations is greater than 0, +.>The spatial angle estimated value obtained for the last iteration; />Representation->Norms (F/F)>Representing a preset threshold.
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Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120133779A1 (en) * | 2010-11-29 | 2012-05-31 | Microsoft Corporation | Robust recovery of transform invariant low-rank textures |
| US20140111372A1 (en) * | 2012-10-22 | 2014-04-24 | Saab-Sensis Corporation | Sensor system and method for determining target location using sparsity-based processing |
| US20180225807A1 (en) * | 2016-12-28 | 2018-08-09 | Shenzhen China Star Optoelectronics Technology Co., Ltd. | Single-frame super-resolution reconstruction method and device based on sparse domain reconstruction |
| CN110261841A (en) * | 2019-07-26 | 2019-09-20 | 南京信息工程大学 | MIMO radar list based on iteration weighting proximal end projection measures vector DOA estimation method |
| CN110349160A (en) * | 2019-06-25 | 2019-10-18 | 电子科技大学 | One kind is based on super-pixel and fuzzy C-means clustering SAR image segmentation method |
| CN111175692A (en) * | 2020-01-17 | 2020-05-19 | 西北工业大学 | Discrete sparse Bayesian DOA estimation method based on layered synthesis Lasso prior model |
| CN111257845A (en) * | 2020-02-11 | 2020-06-09 | 中国人民解放军国防科技大学 | Approximate message transfer-based non-grid target angle estimation method |
| CN111538007A (en) * | 2020-05-22 | 2020-08-14 | 电子科技大学 | Sparse super-resolution imaging method based on two-step acceleration |
| US20230274139A1 (en) * | 2021-03-24 | 2023-08-31 | Samsung Electronics Co., Ltd. | Method for super-resolution |
-
2023
- 2023-09-08 CN CN202311152930.4A patent/CN116879862B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20120133779A1 (en) * | 2010-11-29 | 2012-05-31 | Microsoft Corporation | Robust recovery of transform invariant low-rank textures |
| US20140111372A1 (en) * | 2012-10-22 | 2014-04-24 | Saab-Sensis Corporation | Sensor system and method for determining target location using sparsity-based processing |
| US20180225807A1 (en) * | 2016-12-28 | 2018-08-09 | Shenzhen China Star Optoelectronics Technology Co., Ltd. | Single-frame super-resolution reconstruction method and device based on sparse domain reconstruction |
| CN110349160A (en) * | 2019-06-25 | 2019-10-18 | 电子科技大学 | One kind is based on super-pixel and fuzzy C-means clustering SAR image segmentation method |
| CN110261841A (en) * | 2019-07-26 | 2019-09-20 | 南京信息工程大学 | MIMO radar list based on iteration weighting proximal end projection measures vector DOA estimation method |
| CN111175692A (en) * | 2020-01-17 | 2020-05-19 | 西北工业大学 | Discrete sparse Bayesian DOA estimation method based on layered synthesis Lasso prior model |
| CN111257845A (en) * | 2020-02-11 | 2020-06-09 | 中国人民解放军国防科技大学 | Approximate message transfer-based non-grid target angle estimation method |
| CN111538007A (en) * | 2020-05-22 | 2020-08-14 | 电子科技大学 | Sparse super-resolution imaging method based on two-step acceleration |
| US20230274139A1 (en) * | 2021-03-24 | 2023-08-31 | Samsung Electronics Co., Ltd. | Method for super-resolution |
Non-Patent Citations (4)
| Title |
|---|
| MINGYUAN JIU ET AL.: "A Deep Primal-Dual Proximal Network for Image Restoration", 《IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING》, vol. 15, no. 2, pages 190 - 203, XP011839762, DOI: 10.1109/JSTSP.2021.3054506 * |
| YINGHUI QUAN ET AL.: "Microwave Correlation Forward-Looking Super-Resolution Imaging Based on Compressed Sensing", 《IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING》, vol. 59, no. 10, pages 8326 - 8337, XP011879567, DOI: 10.1109/TGRS.2020.3047018 * |
| 任凌云等: "基于机载多通道雷达迭代超分辨估计的前视成像", 《雷达学报》, pages 1 - 14 * |
| 范剑超等: "高分三号SAR影像在国家海域使用动态监测中的应用", 《雷达学报》, vol. 6, no. 5, pages 456 - 472 * |
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