CN109709547A - A kind of reality beam scanning radar acceleration super-resolution imaging method - Google Patents
A kind of reality beam scanning radar acceleration super-resolution imaging method Download PDFInfo
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Abstract
The present invention provides a kind of real beam scanning radars to accelerate super-resolution imaging method, belongs to radar imaging technology field.The present invention problem slower for iteration threshold contraction algorithm convergence rate, in conjunction with Taylor expansion principle, before each iterative operation, by history is iterative vectorized and its preceding two order differences information structuring predicted vector, reduce the number of iterations, algorithm the convergence speed is improved, the time needed for shortening super-resolution imaging, achievees the purpose that acceleration.
Description
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to an accelerated super-resolution imaging method for a real beam scanning radar.
Background
Real-beam scanning radar imaging plays an important role in the fields of ground attack, terrain matching, ocean detection, military reconnaissance and the like, but the azimuth resolution is always limited by the size and the distance of an antenna aperture. In order to improve the imaging quality, it is urgent to improve the azimuth resolution of the real beam scanning radar.
Because in the azimuth direction, the radar echo can be regarded as a convolution form of an antenna directional diagram and target distribution characteristics, and an iterative deconvolution method can be adopted to realize scanning radar super-resolution imaging. Iterative threshold shrinkage algorithms stand out in these approaches due to their own simplicity and stability. However, the iterative threshold shrinkage algorithm approaches to sub-linear convergence, and the convergence speed is known to be slow, which seriously affects the real-time performance of data processing.
In order to improve the convergence rate of the algorithm, an iteration threshold contraction algorithm and an iteration weighted compression algorithm are combined, a two-step iteration threshold contraction algorithm is provided, the next iteration vector is obtained by linearly combining the first two iteration vectors, the iteration mode is changed, the iteration times are reduced, the convergence rate of the algorithm is improved to a certain extent, and the convergence performance of the algorithm cannot be effectively guaranteed when the ill-conditioned problem is processed.
And a rapid iteration threshold contraction algorithm is also provided, which adopts a Nesterov acceleration gradient method idea on the basis of the iteration threshold contraction algorithm, and before each iteration operation, constructs an iteration vector by using historical iteration information, reduces the iteration times and achieves the acceleration purpose. But since the prediction step tends to 1 in a short time, the iterative process enters an underdamped state, so that the target function oscillates, and the acceleration performance is influenced.
And based on the idea of constructing a prediction vector according to the linear combination of the historical iteration vectors before the iteration operation, an accelerated iteration threshold shrinkage algorithm is provided, and before each iteration operation is executed, one prediction vector is extrapolated by two historical iteration vectors to realize the acceleration of the algorithm. But only the first order difference information of the iterative sequence is used in the process of constructing the prediction vector, and the acceleration effect is not obvious.
Disclosure of Invention
The invention aims to provide a real beam scanning radar acceleration super-resolution imaging method aiming at the defects in the prior art, and an iterative prediction vector is constructed according to first-order and second-order difference information of an iterative sequence by combining the Taylor expansion principle, so that the iteration times are reduced, and the algorithm convergence speed is improved.
A real beam scanning radar accelerated super-resolution imaging method comprises the following steps:
s1, obtaining radar echo signals, and performing range direction pulse compression processing on the echo signals to obtain an echo signal matrix S;
s2, obtaining an antenna directional diagram H, and constructing a convolution matrix H according to the antenna directional diagram;
s3, extracting the jth row of data in the echo signal matrix S as an echo data vector S to be processed, and setting an initial iteration vector x0Is 0;
s4, determining an iterative model;
S5、x is to be0Substituting the iteration model to obtain an iteration result x1X is to be1Substituting the iteration model to obtain an iteration result x2；
S6, according to the iteration result x2、x1And x0Constructing a prediction vector y based on the Taylor expansion principle, and substituting the prediction vector y into the iterative model to obtain an iterative result x3；
S7, judging whether the iteration result meets a preset iteration termination condition, and if so, entering the step S8; if the condition is not satisfied, x is3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to said step S6;
s8, judging whether all the data in the echo signal matrix S are processed completely, and if the processing is finished, outputting a super-resolution imaging result; if the processing is not completed, let j equal to j +1, and the flow returns to step S3.
Further, the step S2 includes:
obtaining antenna directional diagram h ═ h0h1... hl-1]L is the number of antenna directional diagram points; constructing a convolution matrix H from H
Further, the step S4 includes:
calculating the gradient measured out in the current direction
Wherein,x represents a target scattererCoefficient, (.)TRepresenting a transpose operation on a matrix;
according to the steepest descent method, substituting the current vector into the direction with the fastest descending negative gradient
Where t is the iteration step size, is determined byIs determined by the inverse of the Lipschitz constant of (1), i.e.eigmax(HTH) Representation matrix (H)TH) The maximum eigenvalue of (d);
to zkPerforming threshold shrinkage operation to obtain an iterative model
Wherein x iskAs a result of the k-th iteration, (T)λt(z))i＝(zi-λt)+sgn(zi) Sgn (·) is a sign function.
Further, the step S5 includes:
will initial iteration vector x0Substituting the iteration model to obtain a first iteration result x1The result x of the first iteration is then used1Substituting the iteration model to obtain a second iteration result x2。
Further, the step S6 includes:
according to the iteration result x2、x1And x0Constructing a prediction vector y based on the Taylor expansion principle
Wherein α is the prediction step size;
substituting the obtained prediction vector y as an iteration vector into the iteration model to obtain an iteration result x3。
Further, the step S7 includes:
s71, judging whether the iteration result meets a preset iteration termination condition;
s72, if the condition is satisfied, the flow proceeds to step S8;
s73, if the condition is not met, dividing x3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to the step S6.
Further, the preset iteration termination condition is as follows:
||x3-x2||2＜T
wherein T is a termination threshold.
Further, the step S8 includes:
s81, judging whether all the data in the echo signal matrix S are processed, namely whether the J-th row processed currently exceeds the total row number J;
s82, outputting a super-resolution imaging result if the processing is finished;
s83, if the processing is not completed, let j equal to j +1, and the flow returns to step S3.
The invention has the beneficial effects that: the invention provides a real beam scanning radar acceleration super-resolution imaging method, which aims at the problem of low convergence speed of an iterative threshold contraction algorithm, combines the Taylor expansion principle, constructs a prediction vector by a historical iteration vector and previous two-order difference information before each iteration operation, reduces iteration times, improves the convergence speed of the algorithm, shortens the time required by super-resolution imaging, and achieves the purpose of acceleration.
Drawings
Fig. 1 is a flow chart provided by an embodiment of the present invention.
Fig. 2 is a scene diagram adopted in the embodiment of the present invention.
FIG. 3 is a cross-sectional view of a radar echo generated by an embodiment of the present invention.
Fig. 4 is an antenna pattern employed by an embodiment of the present invention.
FIG. 5 is a graph of super-resolution results from 1500 iterations of the prior art algorithm.
Fig. 6 is a graph of super-resolution results obtained from 1500 iterations according to an embodiment of the present invention.
Detailed Description
In this embodiment, MATLAB is used for simulation verification. The embodiments of the present invention will be further described with reference to the accompanying drawings.
Table 1 below is a table of parameters used in examples of the present invention.
| Parameter(s) | Symbol | Numerical value |
| Pulse repetition frequency | prf | 2000Hz |
| Width of antenna main lobe | θ | 3o |
| Scanning speed | ω | 60°/s |
| Scanning range | θmin～θmax | -15°～15° |
TABLE 1 parameter table
Referring to fig. 1, the method for accelerated super-resolution imaging of real beam scanning radar according to the present invention is implemented by the following steps:
and S1, acquiring radar echo signals, and performing range direction pulse compression processing on the echo signals to obtain an echo signal matrix S.
Referring to fig. 2, fig. 2 is a scene graph adopted by the embodiment of the present invention, and x is a scatterer coefficient of the extended target scene in fig. 2.
In this embodiment, a radar echo signal R is obtained, and range direction pulse compression processing is performed on the echo signal, so as to obtain an echo signal matrix S, as shown in fig. 3.
And S2, obtaining an antenna directional diagram H, and constructing a convolution matrix H according to the antenna directional diagram.
In this embodiment, an antenna pattern h ═ h shown in fig. 4 is obtained0h1... h266]L is the number of points of antenna directional diagram267; constructing a convolution matrix H from H
S3, extracting jth row of data in an echo signal matrix S, setting j initial value as 1, using the j initial value as an echo data vector S to be processed, and setting an initial iteration vector x0Is 0.
And S4, determining an iterative model.
In this embodiment, s may be modeled as a convolution form of an antenna directional diagram h and a target scatterer coefficient x, and expressed as s in a form of an antenna directional diagram convolution matrix
s＝Hx+n (2)
Where n is a noise vector.
Since the radar echo signal is a convolution model, a deconvolution method can be used to find the distribution characteristics of the target in the original scene. However, the direct deconvolution method requires an inversion operation on the matrix, and due to the low-pass effect of the convolution matrix H itself, at the cut-off frequency, noise is amplified infinitely, which greatly affects the imaging quality.
Aiming at the problem of noise sensitivity, a regularization method is adopted, and the method is characterized in that1The norm controls the sparsity of the solution to reduce the sensitivity to noise, standardizes the solution of the linear inverse problem, and determines a solution model as follows:
wherein,the optimal solution of the target is represented, lambda is a regularization parameter and is used for balancing the relation between the confidence coefficient of the observation data and the confidence coefficient of the prior information, and the value can be 0.001; | x | non-conducting phosphor1L being x1Norm, the sum of the absolute values of all elements in x.
The model is solved by adopting a gradient descent method or a steepest descent method, and an iterative formula is
Due to the norm term l in the objective function F (x)1Not inconsiderable, the gradient descent method cannot solve this problem. Order to
f(x)＝||s-Hx||2(5)
Approximation by gradient descent methodThe iterative equation (4) can be equivalent to:
neglecting the constant term in equation (6), there are
Due to l1The linearly separable nature of the norm, iterative equation (7) can be reduced to a one-dimensional minimization problem for each component of the iterative vector, i.e.
Wherein x iskIs the result of the k-th iteration;
t is the iteration step size, is composed ofIs determined by the inverse of the Lipschitz constant of (1), i.e.
eigmax(HTH) Representation matrix (H)TH) Maximum eigenvalue of (c) (. 1)TRepresenting a transpose operation on a matrix;
equation (10) represents the least squares term f (x) in the objective function over the iteration vector xk-1The gradient of (d);
(Tλt(x))i＝(xi-λt)+sgn(xi) (11)
equation (11) is a threshold puncturing operation, sgn (·) is a sign function, and its threshold λ t is 5.083 × 10-4The regularization parameter λ is 0.001 and the iteration step t is 5.083 × 10-2And (4) jointly determining.
S5, mixing x0Substituting into the iterative model to obtain an iterative result x1X is to be1Substituting into the iterative model to obtain an iterative result x2。
In this embodiment, an initial iteration vector x with a value of 0 is used0Substituting into the iterative model (8), and calculating to obtain a first iterative result x1. The first iteration result x is processed again1Substituting into the iterative model (8) to obtain a second iterative result x2。
S6, according to the iteration result x2、x1And x0Constructing a prediction vector y based on the Taylor expansion principle, and substituting the prediction vector y into an iterative model to obtain an iterative result x3。
In this embodiment, assuming that y is any vector in the iteration path, the vector y isVector xkThe taylor expansion formula of (a) is:
wherein α denotes the iteration vectors y and xkInformation of the distance between them, i.e. the predicted step length, ΔnxkRepresenting the iterative sequence at xkThe n-order differential information of (1). According to Taylor expansion equation (12), the iteration vector y can be represented by xkAnd the iterative sequence is in vector xkThe difference information at (a) is approximately indicative that the more high order terms that remain, the smaller the error. However, as the order increases, the information of the high-order term is less and less, the influence on the error is negligible, and the high-order term is retained, so that a large storage space is consumed, and unnecessary resource waste is caused. Therefore, the vector y is approximated by selecting the first three terms that retain the Taylor expansion formula:
according to equation (13), from the iteration result x2、x1And x0Constructing a prediction vector y, i.e.
Wherein α is the prediction step size:
to ensure convergence of the algorithm, the prediction step size range is set to 0 < α < 1, when α > 1, let α > 1.
Using the obtained prediction vector y as iterationSubstituting the vector into an iterative model (8), and calculating to obtain an iterative result x3。
S7, judging whether the iteration result meets a preset iteration termination condition, and if so, entering the step S8; if the condition is not satisfied, x is3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to step S6.
S71, judging whether the iteration result meets a preset iteration termination condition, wherein the preset iteration termination condition is as follows:
||x3-x2||2＜T
wherein T is a termination threshold value which can be 1 × 10-5；
S72, if the condition is satisfied, the flow proceeds to step S8;
s73, if the condition is not met, dividing x3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to step S6.
S8, judging whether all the data in the echo signal matrix S are processed completely, and if the processing is finished, outputting a super-resolution imaging result; if the processing is not completed, let j equal to j +1, and the flow returns to step S3.
S81, judging whether all data in the echo signal matrix S are processed, namely whether the J-th row processed currently exceeds the total number of rows J;
s82, outputting a super-resolution imaging result if the processing is finished;
s83, if the process is not completed, let j equal to j +1, and the flow returns to step S3.
Fig. 5 is a super-resolution result obtained by 1500 iterations of the prior art algorithm, and fig. 6 is a super-resolution result obtained by 1500 iterations of the present invention.
It will be appreciated by those of ordinary skill in the art that the examples provided herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited examples and embodiments. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (8)
1. A real beam scanning radar accelerated super-resolution imaging method is characterized by comprising the following steps:
s1, obtaining radar echo signals, and performing range direction pulse compression processing on the echo signals to obtain an echo signal matrix S;
s2, obtaining an antenna directional diagram H, and constructing a convolution matrix H according to the antenna directional diagram;
s3, extracting the jth row of data in the echo signal matrix S as an echo data vector S to be processed, and setting an initial iteration vector x0Is 0;
s4, determining an iterative model;
s5, mixing x0Substituting the iteration model to obtain an iteration result x1X is to be1Substituting the iteration model to obtain an iteration result x2；
S6, according to the iteration result x2、x1And x0Constructing a prediction vector y based on the Taylor expansion principle, and substituting the prediction vector y into the iterative model to obtain an iterative result x3；
S7, judging whether the iteration result meets a preset iteration termination condition, and if so, entering the step S8; if the condition is not satisfied, x is3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to said step S6;
s8, judging whether all the data in the echo signal matrix S are processed completely, and if the processing is finished, outputting a super-resolution imaging result; if the processing is not completed, let j equal to j +1, and the flow returns to step S3.
2. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S2 includes:
obtaining antenna directional diagram h ═ h0h1...hl-1]L is the number of antenna directional diagram points; constructing a convolution matrix H from H
3. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S4 includes:
calculating the gradient measured out in the current direction
Wherein,x represents the target scatterer coefficient, (. C)TRepresenting a transpose operation on a matrix;
according to the steepest descent method, substituting the current vector into the direction with the fastest descending negative gradient
Where t is the iteration step size, is determined byIs determined by the inverse of the Lipschitz constant of (1), i.e.eigmax(HTH) Representation matrix (H)TH) The maximum eigenvalue of (d);
to zkPerforming threshold shrinkage operation to obtain an iterative model
Wherein x iskAs a result of the k-th iteration, (T)λt(z))i＝(zi-λt)+sgn(zi) Sgn (·) is a sign function.
4. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S5 includes:
will initial iteration vector x0Substituting the iteration model to obtain a first iteration result x1The result x of the first iteration is then used1Substituting the iteration model to obtain a second iteration result x2。
5. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S6 includes:
according to the iteration result x2、x1And x0Constructing a prediction vector y based on the Taylor expansion principle
Wherein α is the prediction step size;
substituting the obtained prediction vector y as an iteration vector into the iteration model to obtain an iteration result x3。
6. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S7 includes:
s71, judging whether the iteration result meets a preset iteration termination condition;
s72, if the condition is satisfied, the flow proceeds to step S8;
s73, if the condition is not met, dividing x3、x2、x1Are respectively assigned to x2、x1、x0The flow returns to the step S6.
7. The real beam scanning radar accelerated super resolution imaging method according to claim 6, wherein the preset iteration termination condition is:
||x3-x2||2＜T
wherein T is a termination threshold.
8. The real beam scanning radar accelerated super resolution imaging method according to claim 1, wherein the step S8 includes:
s81, judging whether all the data in the echo signal matrix S are processed, namely whether the J-th row processed currently exceeds the total row number J;
s82, outputting a super-resolution imaging result if the processing is finished;
s83, if the processing is not completed, let j equal to j +1, and the flow returns to step S3.
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