Array signal robust positioning method for impulse noise environment

Abstract

The invention discloses an array signal robust positioning method for an impulse noise environment, and the method comprises the following steps: a co-prime array receives a far-field narrowband signal source signal, and initializes related parameters; estimating a covariance matrix Rx by using a limited number of data sampling snapshots; vectorizing the covariance matrix Rx, and reconstructing a covariance matrix Rss through spatial smoothing; and constructing an information source orientation dictionary, and realizing multi-information-source positioning based on sparse representation signal reconstruction.

Description

Technical Field

[0001] The invention relates to the technical field of array signal processing, and in particular to an array signal robust positioning method for an impulse noise environment. Background Art

[0002] Wireless positioning is an important research branch in array signal processing and is widely used in many fields such as radar, wireless communication and sonar. In the field of wireless positioning research in recent years, sparse reconstruction algorithms and coprime arrays have gradually become the research hotspots of scholars. In traditional uniform regular arrays, the degree of freedom is closely related to the number of array elements, that is, when the number of sources is greater than the number of array elements, the wireless positioning estimation algorithm will fail. Compared with traditional uniform arrays, coprime arrays (CA) have broken through the limitation of array element spacing less than half a wavelength, simple structure, systematic configuration, and high degree of freedom. It has attracted widespread attention at home and abroad, as described by Vaidyanathan PP et al. (2011). Based on the central limit theorem, in the decades of development of signal processing theory, most sparse reconstruction algorithms are based on Gaussian white noise model analysis, and signal processing methods and theories based on Gaussian distribution assumptions are becoming increasingly mature. However, researchers have observed that in many real-world environments, electromagnetic noise, ground clutter, sea clutter, etc. in mobile wireless communication channels often deviate from Gaussian distribution, showing thick tail characteristics on the probability density function (PDF), and short-time pulse characteristics in the time domain. This noise that has a significant deviation from Gaussian distribution noise is called impulse noise or pulse noise. Alpha stable distribution can better describe pulse noise, as described by Nikias CL et al. (1995). Although the sparse reconstruction algorithm has significant performance compared to traditional high-resolution positioning algorithms, the algorithm performance is bound to degrade or even fail in an impulse noise environment.

[0003] In summary, in order to overcome the problems and defects of the prior art, the present invention discloses a high-degree-of-freedom sparse representation target robust positioning method based on correlation entropy in an impulse noise environment. Specifically, in view of the performance degradation of the traditional sparse representation positioning algorithm in an impulse noise environment, inspired by the characteristics of the maximum correlation entropy criterion (MCC) approximating the 0 norm, as described by Liu W et al. (2007), the present invention proposes a new method of resilient positioning based on sparse representation. The multi-measurement vector underdetermined system focusing solution algorithm (MFOCUSS) (described by Cotter SF et al. (2005)) is combined with the maximum correlation entropy accurate MCC to propose the MCC-MFOCUSS algorithm. Secondly, the coprime array is introduced into the MCC-MFOCUSS algorithm. The coprime array can obtain higher resolution and degree of freedom, and realizes the positioning of the source, the number of sources, and the joint estimation of the source power in the full impulse noise environment, which has higher resolution and estimation accuracy than the existing algorithms. Moreover, the signal processing algorithm based on coprime arrays can also reduce the cost and complexity of software and hardware, and has important research value and significance in practical applications. Summary of the invention

[0004] The purpose of the present invention is to provide an array signal robust positioning method for an impulse noise environment in view of the technical defects existing in the prior art.

[0005] The technical solution adopted to achieve the purpose of the present invention is:

[0006] A robust positioning method for array signals in an impulse noise environment comprises the following steps:

[0007] Step 1: The coprime array receives P signal sources to obtain a far-field narrowband signal x(n) and initializes related parameters;

[0008] Step 2: Use the far-field narrowband signal x(n) obtained in step 1 to estimate the covariance matrix R x ;

[0009] Step 3, vectorize the covariance matrix R x The equivalent virtual array signal y of the coprime array is obtained, and the equivalent virtual array signal y is reconstructed by spatial smoothing to obtain a new covariance matrix R ss ;

[0010] Step 4: Construct the signal sparse representation dictionary A and input the covariance matrix R ss , reconstruct the signal and realize multi-source positioning.

[0011] In the above technical solution, in step 1, the far-field narrowband signal x(n) is:

[0012]

[0013] in, It is M 1 +2M 2 coprime arrays to obtain data vectors, n∈N represents the nth sampling, N is the number of snapshots, M 1 and M 2 are the number of array elements of coprime arrays, is the array direction vector, and the first array element is taken as the reference element, f p is the pth signal carrier frequency, j is a complex operator, and d is the array element spacing, which is half the carrier wavelength 0.5λ max , c is the medium propagation speed, θ p represents the incident angle of the pth signal, [·] T represents transpose, C is the field of complex numbers, s[n]=[s 1 ,s 2 ,···,s p ]∈C P×1 is the source vector, s p [·] is the pth source vector, and v[n] represents the impulse noise.

[0014] In the above technical solution, in step 2, the covariance matrix R x :

[0015]

[0016] Where N is the number of snapshots (number of samples), [·] H represents the conjugate transpose.

[0017] In the above technical solution, in step 3, the covariance matrix is ​​vectorized: R x Arrange the columns to form a vector to obtain the equivalent virtual array signal of the coprime array:

[0018]

[0019] in, is equivalent to the expanded array direction vector, represents the Kronecker product, [·]* represents conjugation, p=diag(σ 1 2 , σ 2 2 , …, σ p 2 ) represents the power of P incident signals, σ p 2is the power of the pth signal, diag(·) represents a diagonal matrix, i = vec(I), vec(·) represents arranging the elements in the matrix column by column into a vector, I is the unit matrix, σ n 2 represents the power of the noise;

[0020] The vector y after vectorization is similar to the far-field narrowband signal x(n) obtained in step 1. Therefore, the vector y can be regarded as the second-order equivalent virtual receiving signal corresponding to the virtual domain array, which is equivalent to 2M 1 M 2 +1 virtual array element receives the signal, which greatly improves the degree of freedom and is not limited to the number of physical array elements. 1 +2M 2 The array element can effectively identify 2M 1 M 2 +1 signal.

[0021] In the above technical solution, in step 3, the covariance matrix R is reconstructed SS : y is equivalent to a single snapshot of the received signal, which is deduplicated and then arranged by distance:

[0022]

[0023] in, is the element vector of the corresponding position in y, ii = 1, 2, ..., M 1 M 2 +1, R ss It is M 1 M 2 The spatial smoothing matrix is ​​obtained by averaging the covariance matrices of the +1 subarrays. The covariance matrix R is restored through the spatial smoothing operation. ss rank.

[0024] In the above technical solution, in step 4, multi-target azimuth positioning: grid the entire spatial orientation, construct a signal sparse representation dictionary A, A = B, set the number of iterations mIts, error threshold ε, regularization parameter λ, input the covariance matrix R ss , initialize the number of iterations mIts = 0, reconstruct the signal S 0 is a zero matrix, a weight matrix W=1, and the reconstructed signal S is:

[0025] S=WA H (AWA H +λΙ) -1 R ss (7)

[0026] Update the weight matrix:

[0027]

[0028] Repeat formulas (7) and (8) until the number of iterations is mIts or ∥SS 0 ∥ F <ε, update S 0 =S, the final output is S,κ δ (0) is the kernel function, δ represents the kernel length, ∥·∥ F Represents the Frobenius norm, and the final output is S, where the position of the non-zero item represents the position of the incident signal, and the non-zero item represents the power of the signal.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. The positioning method of the present invention comprises the following steps: a coprime array receives a far-field narrowband source signal and initializes relevant parameters; a covariance matrix R is estimated using a limited number of data sampling snapshots; x ; Vectorized covariance matrix R x , reconstruct the covariance matrix R by spatial smoothing ss ; Build a source orientation dictionary and realize multi-source positioning based on sparse representation signal reconstruction.

[0031] 2. The present invention realizes the effective estimation of the location of the signal source, the number of signal sources, and the power of the signal source in the full pulse noise environment, and has higher resolution and estimation accuracy than the existing algorithms. In addition, the signal processing algorithm based on the coprime array can also reduce the cost and complexity of software and hardware, and has important research value and significance in practical applications.

[0032] 3. In view of the performance degradation of traditional sparse representation positioning algorithms in pulse noise environments, inspired by the characteristics of the maximum correlation entropy criterion (MCC) approximating the 0 norm, the present invention proposes a resilient positioning method based on sparse representation. The multi-measurement vector underdetermined system focusing solution (MFOCUSS) algorithm is combined with the maximum correlation entropy accurate measurement MCC to propose the MCC-MFOCUSS algorithm. Secondly, the coprime array is introduced into the MCC-MFOCUSS algorithm. The coprime array can obtain higher resolution and degrees of freedom, and realizes the positioning of the source, the number of sources, and the effective estimation of the source power in the full pulse noise environment, with higher resolution and estimation accuracy than the existing algorithms. And the signal processing algorithm based on the coprime array can also reduce the cost and complexity of software and hardware, and has important research value and significance in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the array signal robust positioning method in an impulse noise environment of the present invention;

[0034] Figure 2 It is the topological diagram of the coprime array structure;

[0035] Figure 3 is the noise time domain waveform, where a, b, c, and d are noises of different impact strengths (characteristic indexes) respectively;

[0036] Figure 4 This is a comparison chart of mean square error of different algorithms under different generalized signal-to-noise ratios;

[0037] Figure 5 This is a comparison chart of the mean square error of different algorithms under noise of different impact strengths. DETAILED DESCRIPTION

[0038] The present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0039] Example 1

[0040] like Figure 1-Figure 3 As shown, a robust positioning method for array signals in an impulse noise environment comprises the following steps:

[0041] Step 1: The coprime array receives P signal sources to obtain the far-field narrowband signal x(n) and initializes the relevant parameters:

[0042]

[0043] in, It is M 1 +2M 2 coprime arrays to obtain data vectors, n∈N is the nth sampling, N is the number of snapshots, M 1 and M 2 The number of array elements is coprime (such as Figure 2 shown), is the array direction vector, and the first array element is taken as the reference element, f p is the pth signal carrier frequency, j is a complex operator, and d is the array element spacing, which is half the carrier wavelength 0.5λ max , c is the medium propagation speed, θ p represents the incident angle of the pth signal, [·] T represents transpose, C is the field of complex numbers, s[n]=[s 1 ,s 2 ,···,s p ]∈C P×1 is the source vector, and v[n] represents the impulse noise.

[0044] Step 2: Use the far-field narrowband signal x(n) obtained in step 1 to estimate the covariance matrix R x :

[0045]

[0046] Where N is the number of snapshots (number of samples), [·] H represents the conjugate transpose.

[0047] Step 3: Reconstruct the covariance matrix R SS :

[0048] Vectorize the covariance matrix: Convert R x Arrange the columns to form a vector to obtain the equivalent virtual array signal of the coprime array:

[0049]

[0050] in, is equivalent to the expanded array direction vector, represents the Kronecker product, [·]* represents conjugation, p=diag(σ 1 2 , σ 2 2 , …, σ p 2 ) represents the power of P incident signals, σ p is the power of the pth signal, diag(·) represents a diagonal matrix, i = vec(I), vec(·) represents arranging the elements in the matrix column by column into a vector, I is the unit matrix, σ n 2 represents the power of the noise;

[0051] The vector y after vectorization is similar to the far-field narrowband signal x(n) obtained in step 1. Therefore, the vector y can be regarded as the second-order equivalent virtual receiving signal corresponding to the virtual domain array, which is equivalent to 2M 1 M 2 +1 virtual array element receives the signal, which greatly improves the degree of freedom and is not limited to the number of physical array elements. 1 +2M 2 The array element can effectively identify 2M 1 M 2 +1 signal.

[0052] Reconstruct the covariance matrix R SS : y is equivalent to a single snapshot of the received signal, which is deduplicated and then arranged by distance:

[0053]

[0054]

[0055] in, vector, ii = 1, 2, ..., M 1 M 2 +1, R ss It is M 1 M 2 The spatial smoothing matrix is ​​obtained by averaging the covariance matrices of the +1 subarrays. The covariance matrix R is restored through the spatial smoothing operation. ss rank.

[0056] Step 4, multi-target orientation positioning: divide the entire spatial orientation into grids, construct a signal sparse representation dictionary A, A = B, set the number of iterations mIts, error threshold ε, regularization parameter λ, and input the covariance matrix R ss , initialize the number of iterations mIts = 0, reconstruct the signal S 0 is a zero matrix, a weight matrix W=Ι, I is the identity matrix, and the reconstructed signal S is:

[0057] S=WA H (AWA H +λΙ) -1 R ss (7)

[0058] Update the weight matrix:

[0059]

[0060] Repeat formulas (7) and (8) until the number of iterations is mIts or ∥SS 0 ∥ F <ε, update S 0 =S, the final output is S,κ δ (0) is the kernel function, δ represents the kernel length, ∥·∥ F represents the Frobenius norm, where the corresponding grid position of the non-zero term represents the position of the incident signal, and the non-zero term represents the power of the signal.

[0061] Figure 2 This is the layout of the array elements in the coprime array of this embodiment. Figure 3 are different forms of impulse noise in this embodiment, Figure 3 The d in is Gaussian noise.

[0062] Test Example 1

[0063] In order to verify the effectiveness of the positioning method of Example 1, the following two experiments are used to evaluate it. Since the impulse noise obeys the symmetric Alpha stable distribution, the generalized signal-to-noise ratio GSNR is used to measure the strength of the signal and noise. At the same time, the root mean square error RMSE E[(XY) 2 ]=E[X 2 ]+E[Y 2 ]-2E[XY], the performance of the SBL algorithm, SOMP-LS algorithm, regularized MFOCUSS algorithm, RxPenalty algorithm, DS algorithm and the MCC-MFOCUSS positioning method (algorithm) proposed in Example 1 were compared and studied, wherein the parameters,

[0064] Generalized Signal-to-Noise Ratio (GSNR) measures the strength of signal and noise.

[0065]

[0066] Where N is the number of snapshots and γ is the dispersion coefficient of the impulse noise distribution.

[0067] In order to evaluate the performance of the algorithm, the root mean square error (RMSE) is used as the evaluation indicator. The root mean square error is defined as:

[0068]

[0069] Among them, θ p is the incident angle of the pth source, θ^ i,p represents the effect of the ith MC experiment on θ p The estimated value of , T represents the number of trials.

[0070] Test Example 2

[0071] The influence of generalized signal-to-noise ratio GSNR on the positioning method (algorithm). The characteristic index of impulse noise α = 1.4, GSNR = 5dB, the number of snapshots N = 256, the grid division range [-90°, 90°], the number of divisions 180, 12 Gaussian sources incident on the coprime array (M1 = 3, M 2 =4), kernel function σ=5, regularization parameter λ=0.25, iteration number mIts=1000, error threshold ε=0.0001. Monte Carlo experiment T=200 times, GSNR∈[-1020]dB. Figure 4 The RMSE results of six algorithms when the GSNR changes are given. In a low signal-to-noise ratio environment, the MCC-MFOCUSS algorithm provided in Example 1 can still obtain a relatively low error. After the signal-to-noise ratio reaches 10dB, the performance of the DS algorithm, the MFOCUSS algorithm, and the RxPenalty algorithm are comparable.

[0072] Test Example 3

[0073] The influence of characteristic index α on the algorithm. α represents the strength of noise impact in the time domain. The simulation conditions are the same as those in test case 1, α∈[0.52]. The experiment simulates the estimated root mean square error of several algorithms when the characteristic index α changes. The results are shown in Figure 5 As shown in the figure, the estimation errors of the SBL algorithm and the SOMP-LS algorithm are relatively large. The smaller the characteristic index α, the higher the RMSE of all algorithms, and the performance decreases. However, the algorithm proposed in Example 1 still maintains a high estimation accuracy under impulse noise with any characteristic index (0.5<α<2), achieves impulse noise suppression, and has higher resolution and wider practicability.

[0074] The above is only a preferred embodiment of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A robust positioning method for array signals in an impulse noise environment, characterized in that: The following steps are involved: Step 1: The coprime array receives P signal sources to obtain a far-field narrowband signal x(n) and initializes related parameters; Step 2: Use the far-field narrowband signal x(n) obtained in step 1 to estimate the covariance matrix R x ; Step 3, vectorize the covariance matrix R x The equivalent virtual array signal y of the coprime array is obtained, and the equivalent virtual array signal y is reconstructed by spatial smoothing to obtain a new covariance matrix R ss ; Step 4: Construct the signal sparse representation dictionary A and input the covariance matrix R ss , reconstruct the signal and realize multi-source positioning.

2. The positioning method according to claim 1, characterized in that: In step 1, the far-field narrowband signal x(n) is: in, The data vector is obtained by M1+2M2 coprime arrays, n∈N represents the nth sampling, N is the number of snapshots, M1 and M2 are the number of array elements of the coprime array, is the array direction vector, and the first array element is taken as the reference element, f p is the pth signal carrier frequency, j is a complex operator, and d is the array element spacing, which is half the carrier wavelength 0.5λ max , c is the medium propagation speed, θ p represents the incident angle of the pth signal, [·] T represents transpose, C is the field of complex numbers, s[n]=[s1,s2,···,s p ]∈C P×1 is the source vector, s p [·] is the pth source vector, and v[n] represents the impulse noise.

3. The positioning method according to claim 2, characterized in that: In step 2, the covariance matrix R x : Where N is the number of snapshots (number of samples), [·] H represents the conjugate transpose.

4. The positioning method according to claim 3, characterized in that: In step 3, vectorize the covariance matrix: x Arrange the columns to form a vector to obtain the equivalent virtual array signal of the coprime array: in, is equivalent to the expanded array direction vector, represents the Kronecker product, [·]* represents conjugation, p=diag(σ1 2 ,σ2 2 , …, σ p 2 ) represents the power of P incident signals, σ p 2 is the power of the pth signal, diag(·) represents a diagonal matrix, i = vec(I), vec(·) represents arranging the elements in the matrix column by column into a vector, I is the unit matrix, σ n 2 Represents the power of the noise.

5. The positioning method according to claim 4, characterized in that: B in formula (3) is:

6. The positioning method according to claim 5, characterized in that: In step 3, the covariance matrix R is reconstructed SS : y is equivalent to a single snapshot of the received signal, which is deduplicated and then arranged by distance: in, is the element vector of the corresponding position in y, ii = 1, 2, ..., M1M2+1, R ss The spatial smoothing matrix is ​​obtained by averaging the covariance matrices of the M1M2+1 subarrays. The covariance matrix R is restored through spatial smoothing operation. ss rank.

7. The positioning method according to claim 6, characterized in that: y in formula (5) ii for:

8. The positioning method according to claim 7, characterized in that: In step 4, multiple targets are positioned, the signal S is reconstructed, and the weight matrix is ​​updated.

9. The positioning method according to claim 8, characterized in that: Divide the entire spatial orientation into grids, construct the signal sparse representation dictionary A, A = B, set the number of iterations mIts, error threshold ε, regularization parameter λ, and input the covariance matrix R ss , initialize the number of iterations mIts = 0, reconstruct the signal S0 as a zero matrix, the weight matrix W = 1, and the reconstructed signal S is: S=WA H (AWA H +λΙ) -1 R ss (7)。 10. The positioning method according to claim 9, characterized in that: Update the weight matrix: Repeat formulas (7) and (8) until the number of iterations is mIts or ∥S-S0∥ F <ε, update S0=S, and finally output S,κ δ (0) is the kernel function, δ represents the kernel length, ∥·∥ F Represents the Frobenius norm, and the final output is S, where the position of the non-zero item represents the position of the incident signal, and the non-zero item represents the power of the signal.

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