CN109031239B - Compressed sensing external radiation source radar target detection method based on information fusion - Google Patents

Abstract

The invention belongs to the technical field of signal processing, and relates to a target detection method of an external radiation source radar based on compressed sensing. According to the method, firstly, a sparse vector is obtained according to the projection of a sparse signal on a dictionary base, then a new measurement matrix is designed by combining a Gaussian random matrix and the dictionary base matrix, and for the condition that the time delay of echoes under different paths is different, a group of optimized weight coefficients are designed by utilizing different distribution characteristics of compression sampling values, so that an information fusion detection method based on compressed sensing is provided. And finally, completing the detection of the target. The method directly processes the compressed sampling value without signal reconstruction, reduces the data operation amount and can normally work under the condition of low signal-to-noise ratio. The method has good reference and practical application in the detection direction to be detected.

Description

Compressed sensing external radiation source radar target detection method based on information fusion

Technical Field

The invention belongs to the technical field of signal processing, and relates to a target detection method of an external radiation source radar based on compressed sensing.

Background

In recent years, the compressive sensing theory has become more and more mature in radar signal processing and wireless communication, such as signal detection, signal identification, and parameter estimation. Unlike the traditional Nyquist sampling theorem, after compressed sensing is introduced, the characteristics of the signal before compression are not substantially lost under the condition that the analysis of the sample data volume is obviously reduced. The compressed sensing technology adopted in the existing radar system generally needs to reconstruct signals by utilizing a reconstruction algorithm so as to realize target detection and parameter estimation. However, the reconstruction algorithm generally requires a high signal-to-noise ratio to obtain a reconstructed signal satisfying target detection and parameter estimation. For radar like external radiation source, which is a bistatic non-cooperative radar in nature, the target echo power is low, and the signal-to-noise ratio requirement of signal reconstruction is not usually met. Therefore, a new method is needed for realizing weak signal detection by adopting a compressed sensing technology.

The signal detection is to analyze and judge whether the target signal exists or not by the received signal, and after the compressed sensing technology is adopted, the mathematical model of the target detection is as follows,

wherein phi ∈ R ^M×N Is a measurement matrix, n ∈ R ^N×1 Is white Gaussian noise, x ∈ R ^N×1 Is the signal to be detected, let H ₀ Is the absence of a signal to be detected, assume H ₁ Is the case in the presence of a signal to be detected. The detection algorithms currently exist mainly in the following ways: (1) liu Bing et al in 2010 propose a mean comparison algorithm, the core idea of which is that the noise is white noise with a mean of 0, then H ₀ In the case where E (y) ═ E (Φ n) ═ 0, H ₁ In the case of E (y) ═ E (Φ (x + n)) ═ Φ x, the variance does not change in both cases. Therefore, the method adopted by the user is to take the deviation between the actual sampling value and the mathematical expectation under the two assumption conditions as the judgment basis to finish the detection; (2) in 2015, Alireza Hariri et al propose a maximum likelihood ratio algorithm, which has a core idea that a signal to be detected is not reconstructed to obtain likelihood functions of two conditions, then a ratio is made, a threshold formula is obtained through likelihood ratio function probability density characteristics, and judgment is performed. However, the above three detection algorithms cannot achieve target detection at a signal-to-noise ratio below-5 dB. This limits the range of applications of the detector and in order to detect a larger range, the detection of the signal to be detected at a lower signal-to-noise ratio needs to be addressed. (3) In 2017, Majunhu et al propose a weak signal detection algorithm based on sparse domain accumulation according to the property of non-zero position fixation of a sparse vector. The algorithm solves the problem of low signal-to-noise ratio. However, this algorithm requires that the sparse element positions of each set of data be the same. For a distributed external radiation source radar scene, the time delay and Doppler information corresponding to each receiver are different, so that target echoes generated by different receiversSparse representation under dictionary base has different sparse positions. The above method based on element position accumulation fails. Therefore, it is necessary to further study the detection of signals when the positions of the non-zero elements of the sparse vectors are different without increasing the data amount.

Disclosure of Invention

The invention aims to solve the technical problem of directly detecting a compressed signal without signal reconstruction when the positions of non-zero elements of sparse vectors are different.

For ease of understanding, the techniques employed in the present invention are described as follows:

according to the formula (1), the following signal detection model is established

Wherein y is _n ∈R ^M×1 Signal N representing the nth compressed sample is 1,2, …, N _b ，n _n Is white gaussian noise, and its distribution is:

the signal sparsity is represented as: x is the number of _n ＝Ψα _n ，Ψ∈R ^N×N Is a unit dictionary basis matrix. The sparse vector alpha is obtained by projecting the sparse signal on the basis of the dictionary _n ＝Ψ ^H x _n ，

The number of the non-zero elements is far less than that of the sparse vector elements, and for different observation times alpha _n Are different from each other namely

And therefore cannot employ sparse element position accumulation. For a single observation x _n When the signal is determined, the sparse vector is determined, and the value corresponding to the non-zero position of the sparse vector can be regarded as a constant. Therefore, the projection of the sparse vector under the gaussian matrix still follows a gaussian distribution. Is sparse in Gaussian white noiseSparse domains have no sparsity, and the projection of the sparse domains on the basis of a dictionary follows Gaussian distribution. And the projection of white gaussian noise under a random gaussian matrix also follows a gaussian distribution. The measurement matrix designed by combining the random Gaussian matrix and the dictionary basis matrix is as follows:

at H ₀ Under the signal detection model, y _n The distribution of (A) is as follows:

at H ₁ Under the detection model, y _n The distribution of (A) is as follows:

comparing the two gaussian distributions shows that the mean values are the same and the variance is different, so the detector is designed according to the variance. However, for multiple observation situations, because the signal-to-noise ratio of each path is different, the detector is designed by using the idea of information fusion, so that the detection probability is effectively improved, the specific method is to design a group of weight coefficients to a fusion center, obtain optimized data and further design the detector, and the specific scheme is shown in fig. 1.

At H ₀ This distribution is a standard normal distribution, under the assumption:

then pass through N _b Second observation y _n Variance T of _n ＝D(y _n ) The vector consisting of the mean values of (a) is: m is ₀ ＝[1，1，…，1] ^T Further analysis gave T _n The variance of (c) is:

and at H ₁ Under the detection model:

let y _n Variance T of _n The vector consisting of the mean values of (a) is:

wherein

As shown in FIG. 1, a statistic is defined

Wherein the weight coefficient

And is

Wherein

So as to make

A diagonal matrix composed of diagonal elements.

In order to solve the problems, the technical scheme of the invention is as follows:

a method for detecting a target by an external radiation source radar based on compressed sensing is used for directly detecting a compressed signal without signal reconstruction, and is characterized by comprising the following steps:

s1, establishing a signal detection model:

wherein y is _n ∈R ^M×1 Signal N representing the nth compressed sample is 1,2, …, N _b ，n _n Is white gaussian noise, and its distribution is:

phi is a Gaussian matrix, psi is a unit dictionary basis matrix, N _b The number of target echoes is taken;

s2, determining a detection threshold, specifically comprising:

s21, generating a random Gaussian matrix phi and a dictionary basis matrix psi, and designing a measurement matrix

N is the signal length, σ _n Noise power received for the nth receiver;

s22, measuring matrix phi _n Compressive sampling of a signal containing noise to obtain y _n ＝Φ _n (x _n +n _n )，x _n Is a signal to be detected;

s23, finding y _n Variance of (d) is denoted as e _n ；

S24, definition

Wherein w _n Is a weight coefficient, and

wherein the content of the first and second substances,

so as to make

Diagonal matrix composed of diagonal elements, m ₀ ＝[1，1，…，1] ^T Is in step S1H ₀ Under the detection model, passing through N _b Second observation y _n A vector of the mean of the variances of (a),

is in step S1H ₁ Y under test model _n A vector of the mean of the variances of (a);

s3, judging whether T > gamma is true or not according to the threshold value gamma of the detector, and if yes, judging that a signal exists; otherwise, judging that the signal does not exist, and determining the value of gamma according to the noise distribution.

The method has the advantages that firstly, a sparse vector is obtained according to the projection of a sparse signal on a dictionary base, then a new measurement matrix is designed by combining the Gaussian random matrix and the dictionary base matrix, and for the condition that the time delays of echoes under different paths are different, a group of optimized weight coefficients are designed by utilizing different distribution characteristics of compression sampling values, so that the information fusion detection method based on the compression sensing is provided. And finally, completing the detection of the target. The method directly processes the compressed sampling value without signal reconstruction, reduces the data operation amount and can normally work under the condition of low signal-to-noise ratio. The method has good reference and practical application in the detection direction to be detected.

Drawings

FIG. 1 is a schematic diagram of the method of the present invention;

FIG. 2 is a flow chart of the method for detecting a signal to be detected;

fig. 3 shows the variation of the detection performance of the detector when the compression ratio is M/N-0.5 and the false alarm probability is different.

Detailed Description

The technical solution of the present invention will be further explained with reference to the accompanying drawings and examples.

Examples

The detection implementation method of the embodiment is shown in the attached figures 1 and 2. The specific steps are as follows:

the signal to be detected is known as a single-frequency sinusoidal signal x _n ＝A _n *exp(1j*2πf _n (0: N-1)), wherein

For the amplitude, SNR, of the signal received by the nth receiver _n To the signal-to-noise ratio, f _n ＝[0.12 0.25 0.34 0.43 0.52 0.60]，n＝1,...,N _b ，N _b 6, N1000. Let the sparse dictionary base Ψ ∈ R ^N×N Is a unit Fourier transform matrix, phi _n ∈R ^M×N Is a random gaussian matrix, where M is 500. n is _n ∈R ^N×1 The signal-to-noise ratio corresponding to each receiver is SNR respectively for white Gaussian noise _n ＝[-5,-7,-9,-8.5,-6,-9.5]。

The method comprises the following steps: generating a random Gaussian matrix phi and a dictionary basis matrix psi, and designing a measurement matrix

N is the signal length, σ _n Noise power received for the nth receiver;

step two: measurement matrix phi _n Compressive sampling of a signal containing noise to obtain y _n ＝Φ _n (x _n +n _n )，x _n Is a signal to be detected;

step three: y is obtained _n Variance of (d) is denoted as e _n ；

Step four: definition of

Wherein w _n Is a weight coefficient, and

wherein m is ₀ ＝[1，1，…，1] ^T ，

Step five: if T is more than gamma, judging that a signal exists; otherwise, judging that the signal does not exist, wherein gamma is a threshold value of the detector and is determined according to the noise distribution.

Fig. 3 is a simulation of the embodiment, and fig. 3 shows the detection performance of the detector under different false alarm probabilities when the compression ratio M/N is 0.5, and it can be seen from fig. 3 that when the signal-to-noise ratio of the receiver is low, the method can still detect the target with a high probability and does not need signal reconstruction, so that the present invention has good detection performance.

Claims (1)

1. The external radiation source radar target detection method based on compressed sensing is used for directly detecting a compressed signal without signal reconstruction, and is characterized by comprising the following steps of:

s1, establishing a signal detection model:

wherein y is _n ∈R ^M×1 Signal N representing the nth compressed sample is 1,2, …, N _b ，n _n Is white gaussian noise, and its distribution is:

phi is Gaussian matrix, psi is unit dictionary base matrix, N _b The number of target echoes is taken;

s2, determining statistics, specifically comprising:

s21, generating a random Gaussian matrix phi and a dictionary basis matrix psi, and designing a measurement matrix

N is the signal length, σ _n Noise power received for the nth receiver;

s22, measuring matrix phi _n Compressive sampling of a signal containing noise to obtain y _n ＝Φ _n (x _n +n _n )，x _n Is a signal to be detected;

s23, finding y _n Variance of (d) is denoted as e _n ；

S24, defining statistics

Wherein w _n Is a weight coefficient, and

wherein the content of the first and second substances,

so as to make

A diagonal matrix composed of diagonal elements,

m ₀ ＝[1，1，…，1] ^T is in step S1H ₀ Under the detection model, passing through N _b Second observation y _n A vector of the mean of the variances of (a),

is in step S1H ₁ Y under test model _n A vector of the mean of the variances of (a);

s3, judging whether T > gamma is true or not according to the threshold value gamma of the detector, and if yes, judging that a signal exists; otherwise, judging that the signal does not exist, and determining the value of gamma according to the noise distribution.

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