CN113640762B - Radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing - Google Patents
Radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing Download PDFInfo
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Abstract
The radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing provided by the invention can be independent of priori knowledge and has good robustness under low signal-to-noise ratio. According to the invention, through performing traversal search on the number, the azimuth and the amplitude of the targets, corresponding azimuth signals of the targets are obtained; and the optimal target azimuth information is obtained based on the least square criterion by utilizing each target azimuth signal, so that the azimuth super-resolution is realized, priori knowledge is not relied on, and the method has good robustness under the condition of low signal-to-noise ratio. According to the invention, the Fourier transform is multiplied by the frequency domain to replace the convolution operation of the time domain, so that the time domain calculation is converted into the frequency domain, the convolution calculation is avoided, the complexity is reduced, and the calculation efficiency is improved. The invention adopts particle swarm algorithm to accelerate solving speed.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing.
Background
Radar azimuth super-resolution is to resolve multiple equidistant targets within the same radar beam using digital signal processing techniques without increasing antenna aperture or transmit signal frequency. The radar azimuth super-resolution is a research hotspot in the radar detection field, and has important significance for development and application of radar high-resolution imaging, target detection, identification, tracking and other related technologies.
The prior art comprises the following steps: a wiener filtering method, a maximum posterior probability method, a constraint optimization method and the like. Deconvolution azimuth super-resolution is mainly based on target echo signals received by a radar and is obtained by convolving target azimuth signals with an antenna pattern, and target azimuth signal reconstruction is achieved by adopting a convolution inversion mode. However, radar azimuth super-resolution is an ill-posed problem, because noise has unknown characteristics, and system noise and echo signals are mutually independent, even if the noise is very small, the azimuth information of the reconstructed signal obtained by the deconvolution method has a large deviation from an actual value, and thus the system noise and the echo signals are ill-posed. The existing algorithm has poor adaptive capacity to noise, parameter setting depends on echo characteristics, and has certain limitations.
Disclosure of Invention
In view of the above, the invention provides a radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing, which can not depend on priori knowledge and has good robustness under low signal-to-noise ratio.
In order to achieve the above purpose, the radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing of the invention comprises the following steps:
constructing an azimuth super-resolution objective function:
wherein,for the optimal target azimuth signal, argmin { } represents the minimum value of the self-variable, N is the target number, A n For the n-th target amplitude, θ n N=1, 2,3 … N for the azimuth of the nth target; />Is the square of the vector 2-norm; y is the known radar azimuth echo; h is an (M+L-1) x M-dimensional antenna pattern matrix constructed by an antenna pattern H (θ), where M is a target azimuth signal and L is a radar antenna pattern data length; x is a target azimuth signal, satisfying the following formula:
wherein θ is a point on the azimuth axis, and δ () is an impact function;
setting the maximum value N of the target number N according to the real radar azimuth echo and the antenna directional diagram max Target maximum amplitude A max And the azimuth range of each target; wherein the nth target amplitude A n ∈[0,A max -A 1 -…-A n-1 ]The method comprises the steps of carrying out a first treatment on the surface of the Nth target azimuth θ n ∈[θ min ,θ max ]；
Traversing search within set scope N, A n θ n Thereby constructing x (θ);
traversing all x (theta) of the construction, solving the azimuth super-resolution objective function based on least square calculation to obtain an optimal solution of the azimuth super-resolution objective functionAnd (5) finishing estimation.
The time domain expression of the azimuth super-resolution objective function is as follows:
wherein ω is a signal frequency sampling point, Y (ω) is a frequency domain expression of a known radar azimuth echo Y, X (ω) is a frequency domain expression obtained by fourier transforming the target azimuth signal X (θ), and H (ω) is a frequency domain expression of a radar antenna pattern H (θ);
the current estimation error err is calculated using the following equation:
obtaining X (omega) which enables err to be minimum through least square calculation, and further obtaining an optimal solution
Setting an error threshold, terminating operation when the current estimation error is smaller than the error threshold, replacing least square calculation with the error threshold, taking the current estimation error as X (omega) which enables err to be minimum, and further obtaining an optimal solution
The azimuth search interval is an azimuth sampling interval delta theta, the amplitude search interval is p.delta a, wherein delta a is the quantization precision of the receiver, p is a positive integer, and the size depends on the required amplitude precision.
And performing global optimization by adopting a particle swarm optimization algorithm instead of traversal search to obtain an optimal solution of the azimuth super-resolution objective function.
Wherein the maximum value N of the number of targets max No more than 10.
Wherein the target maximum amplitude A max Not greater than the true echo peak.
Wherein the azimuth range of the target does not exceed one beamwidth.
Wherein the maximum value N of the number of targets max No more than 10; target maximum amplitude A max Not greater than the true echo peak; the azimuth range of the target does not exceed one beamwidth.
Wherein the maximum value N of the number of targets max No more than 10; target maximum amplitude A max Not greater than the true echo peak; the azimuth range of the target does not exceed one beamwidth.
The beneficial effects are that:
the invention carries out traversal search on the number, the azimuth and the amplitude of the targets to obtain corresponding azimuth signals of each target; and the optimal target azimuth information is obtained based on the least square criterion by utilizing each target azimuth signal, so that the azimuth super-resolution is realized, priori knowledge is not relied on, and the method has good robustness under the condition of low signal-to-noise ratio.
According to the invention, the Fourier transform is multiplied by the frequency domain to replace the convolution operation of the time domain, so that the time domain calculation is converted into the frequency domain, the convolution calculation is avoided, the complexity is reduced, and the calculation efficiency is improved.
The invention adopts particle swarm algorithm to accelerate solving speed.
Drawings
FIG. 1 is a flow chart of a radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing.
FIG. 2 shows the result of the azimuthal super-resolution at different signal-to-noise ratios according to an embodiment of the present invention.
FIG. 3 is a graph of SNR versus accuracy at different azimuthal resolution intervals according to an embodiment of the present invention.
FIG. 4 shows the azimuth error under different SNR conditions according to an embodiment of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The invention discloses a radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing, which is shown in a flow chart in figure 1 and comprises the following steps:
step one, constructing a radar target azimuth echo model:
assuming that a conventional radar scans a certain azimuth, the change of pitch angle is ignored, and only radar azimuth resolution is considered. If there are several point targets in the area, the azimuth echo signal of the radar can be expressed as a convolution of the antenna pattern and the target azimuth signal. The radar target azimuth echo model may be defined as
Wherein: x (theta) is a target azimuth signal, and the data length is M; h (theta) is a radar antenna pattern, and the data length is L; n (θ) is the receiver noise and only additive noise is considered by the present invention. y (θ) is radar azimuth echo, and the length thereof is (M+L-1) according to convolution operation.
From the formula, the azimuth resolution can be regarded as a process of knowing the radar azimuth echo y and the antenna pattern h and solving x.
Formula (1) is rewritten as a matrix-vector form:
y＝Hx+n (2)
wherein:
x＝[x(1) x(2) … x(M)] T (3)
y＝[y(1) y(2) … y(M+L-1)] T (5)
h is an (M+L-1) x M-dimensional antenna pattern matrix constructed from the antenna patterns.
Considering that the target azimuth signal can be represented by an impulse signal under ideal conditions, the azimuth signals of a plurality of targets can be regarded as superposition of a plurality of impulse signals, namely:
wherein n=1, 2,3 … N, N is the target number, a n For the n-th target amplitude, θ n Azimuth for the nth target; delta () is the impact function,
formula (6) is rewritten as a matrix-vector form:
wherein,is a 1 x L dimensional vector.
Constructing an azimuth super-resolution objective function:
wherein arg min { } represents the argument that takes the minimum value,is the square of the vector 2-norm.
Step three, setting the maximum value N of the target number N according to the real radar azimuth echo and the antenna directional diagram max Target maximum amplitude A max And the azimuth range of each target; wherein the nth target amplitude A n ∈[0,A max -A 1 -…-A n-1 ]N=1, 2, …, N; nth target azimuth θ n ∈[θ min ,θ max ],n＝1,2,…,N。
In general, the maximum value N of the target number max No more than 10, target maximum amplitude A max Not greater than the true echo peak, the azimuth range of the target does not exceed one beam width.
Step four, traversing the search N, A within the range set in step three n θ n Thereby constructing x (θ);
solving the azimuth super-resolution objective function based on a least square criterion by utilizing all x (theta) constructed to obtain an optimal solution of the azimuth super-resolution objective functionAnd (5) finishing estimation.
The azimuth search interval is an azimuth sampling interval delta theta, the amplitude search interval is p.delta a, wherein delta a is the quantization precision of the receiver, p is a positive integer, and the size depends on the required amplitude precision.
Further, to simplify the calculation, the radar target azimuth echo model may be calculated by fourier transform with multiplication of the frequency domain instead of convolution of the time domain. Obtaining a frequency domain expression of a radar target azimuth echo model through Fourier transformation:
Y(ω)＝X(ω)*H(ω)+N(ω) (9)
where ω is a signal frequency sampling point, X (ω) is a frequency domain expression obtained by fourier transforming the target azimuth signal X (θ), and similarly H (ω) is a frequency domain expression of the radar antenna pattern H (θ), N (ω) is a frequency domain expression of the receiver noise N (θ), then the formula (8) may be rewritten as follows:
the current estimation error can be calculated using the following equation:
wherein err is the current estimation error, and X (omega) which enables err to be minimum is obtained through least square calculation, so that the optimal solution is obtainedThe time domain calculation is converted into the frequency domain, so that convolution calculation is avoided, the complexity is reduced, and the calculation efficiency is improved.
In addition, in order to reduce the operation times, avoid the huge operation amount caused by traversal search and ensure the precision of the search result, an error threshold can be set, when the current estimation error is smaller than the error threshold, the operation is stopped, the least square calculation is replaced, the current estimation error is taken as X (omega) which enables err to be minimum, and then the optimal solution is obtained
Further, as the calculation amount of the traversal search increases sharply along with the increase of the target number N, the search time is long, so that an optimization algorithm (Particle Swarm Optimization, PSO) such as a particle swarm and the like can be adopted to replace the traversal search to perform global optimization, an optimal solution is obtained, and the calculation time can be greatly shortened.
In the embodiment, the radar azimuth scanning range is assumed to be-15 degrees, and the azimuth sampling interval is assumed to be 0.1 degreesThe pulse repetition frequency is 1KHz, the scanning speed is 100 DEG/s, the antenna pattern is a Sinc function, the half-power beam width is 2.5 DEG, two equal-amplitude targets are respectively positioned at-0.1 DEG and 0.1 DEG, and the number of targets is maximum N max =3, target maximum amplitude a max ＝max[y(θ)]Target azimuth range [ theta ] min ,θ max ]＝[-2.5°,2.5°]Azimuth sampling interval Δθ=0.1°, and amplitude search interval p·Δa=1. 100 Monte Carlo tests are carried out, and the accuracy and the azimuth error under different signal-to-noise ratios are calculated for the target intervals of 0.2 degrees and 0.3 degrees (two equal-amplitude targets are respectively positioned at-0.1 degrees and 0.2 degrees). And when the number of the resolution targets is correct and the azimuth error is not larger than the resolution interval, the identification result is considered to be correct.
Fig. 2 shows the result of the super-resolution of the azimuth under different signal-to-noise ratios, wherein blue lines (solid lines) represent the target azimuth information, and red lines (dashed lines) represent the radar target azimuth echoes. When the signal-to-noise ratio is 20dB and 30dB respectively, the resolution result is basically consistent with the actual position of the target. But at a lower signal-to-noise ratio (0 dB), the azimuth error gradually increases and the method performance is less stable. Fig. 3 is a signal-to-noise ratio-accuracy curve of different azimuth resolution intervals, and fig. 4 is an azimuth error at different signal-to-noise ratios. As the signal-to-noise ratio increases, the accuracy increases and the average bearing error decreases. Compared with the traversal search method, the particle swarm algorithm is adopted, the accuracy is reduced, and the average azimuth error is slightly increased under the same azimuth resolution interval. However, as the signal-to-noise ratio increases, the accuracy of the particle swarm optimization algorithm gradually approaches the accuracy of the traversal search.
In summary, the above embodiments are only preferred embodiments of the present invention, and are 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 should be included in the protection scope of the present invention.
Claims (10)
1. A radar target azimuth super-resolution estimation method based on multidimensional parameter space self-focusing is characterized by comprising the following steps:
constructing an azimuth super-resolution objective function:
wherein,for the optimal target azimuth signal, argmin { } represents the minimum value of the self-variable, N is the target number, A n For the n-th target amplitude, θ n N=1, 2,3 … N for the azimuth of the nth target; />Is the square of the vector 2-norm; y is the known radar azimuth echo; h is an (M+L-1) x M-dimensional antenna pattern matrix constructed by an antenna pattern H (θ), where M is a target azimuth signal and L is a radar antenna pattern data length; x is a target azimuth signal, satisfying the following formula:
wherein θ is a point on the azimuth axis, and δ () is an impact function;
setting the maximum value N of the target number N according to the real radar azimuth echo and the antenna directional diagram max Target maximum amplitude A max And the azimuth range of each target; wherein the nth target amplitude A n ∈[0,A max -A 1 -…-A n-1 ]The method comprises the steps of carrying out a first treatment on the surface of the Nth target azimuth θ n ∈[θ min ,θ max ]；
Traversing search within set scope N, A n θ n Thereby constructing x (θ);
traversing all x (theta) of the construction, solving the azimuth super-resolution objective function based on least square calculation to obtain an optimal solution of the azimuth super-resolution objective functionAnd (5) finishing estimation.
2. The estimation method of claim 1, wherein the time domain expression of the azimuth super-resolution objective function is:
wherein ω is a signal frequency sampling point, Y (ω) is a frequency domain expression of a known radar azimuth echo Y, X (ω) is a frequency domain expression obtained by fourier transforming the target azimuth signal X (θ), and H (ω) is a frequency domain expression of a radar antenna pattern H (θ);
the current estimation error err is calculated using the following equation:
obtaining X (omega) which enables err to be minimum through least square calculation, and further obtaining an optimal solution
3. The estimation method as set forth in claim 2, wherein an error threshold is set, and when the current estimation error is smaller than the error threshold, the operation is terminated, thereby replacing least square calculation, taking the current estimation error as X (ω) for minimizing err, and further obtaining an optimal solution
4. The estimation method of claim 1, wherein the azimuth search interval is an azimuth sampling interval Δθ, and the amplitude search interval is p·Δa, where Δa is a quantization accuracy of the receiver, and p is a positive integer, and the magnitude depends on a required amplitude accuracy.
5. The estimation method according to any one of claims 1 to 4, wherein a particle swarm optimization algorithm is adopted to replace traversal search to perform global optimization, so as to obtain an optimal solution of the azimuth super-resolution objective function.
6. The estimation method according to any one of claims 1-4, wherein the target number maximum N max No more than 10.
7. The estimation method according to any one of claims 1-4, wherein the target maximum amplitude a max Not greater than the true echo peak.
8. The estimation method according to any one of claims 1-4, wherein the azimuth range of the target does not exceed one beam width.
9. The estimation method according to any one of claims 1-4, wherein the target number maximum N max No more than 10; target maximum amplitude A max Not greater than the true echo peak; the azimuth range of the target does not exceed one beamwidth.
10. The estimation method according to claim 5, wherein the target number maximum value N max No more than 10; target maximum amplitude A max Not greater than the true echo peak; the azimuth range of the target does not exceed one beamwidth.
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