DOA estimation method based on INCK in impulse noise environment

Abstract

The present invention discloses an INCK-based Direction of Arrival (DOA) estimation method in an impulse noise environment. The method receives signals using a uniform linear array antenna to obtain received signal information #imgabs0#. Based on the received signal information, the local information entropy #imgabs1# for a single snapshot is calculated using a local entropy calculation formula. The infinite norm for a single snapshot is calculated using the infinite norm calculation formula. A semi-infinite norm Cauchy kernel and a full infinite norm Cauchy kernel are then constructed. The effects of the two Cauchy kernels are adjusted by the magnitude of the local information entropy #imgabs2#, and a weight #imgabs3# corresponding to each received signal information is established accordingly. #imgabs4# is weighted to obtain #imgabs5#, and a covariance matrix #imgabs7# is constructed for #imgabs6#. Finally, a rotationally invariant subspace algorithm is used to perform DOA estimation. The method uses the local information entropy #imgabs8# to adjust the effect of the infinite norm Cauchy kernel, suppress outliers in the received signal, and effectively estimate the DOA of the signal in the presence of alpha-stable distributed impulse noise.

Description

Technical Field

[0001] The present invention belongs to the field of Direction of Arrival (DOA) estimation, and in particular relates to an INCK-based DOA estimation method in an impulse noise environment. Background Art

[0002] In recent years, the innovative application of information entropy theory in array signal processing has attracted widespread attention in academia. By quantifying the uncertainty characteristics of the signal space, it provides a novel theoretical framework for DOA estimation. Traditional DOA estimation methods generally construct the covariance matrix based on second-order statistics. These methods are based on the strong assumption that the ambient noise follows a Gaussian distribution. However, in real-world engineering scenarios, the noise statistics often exhibit significant non-Gaussian characteristics due to complex electromagnetic interference, multipath effects, and sudden noise sources. In such high-impulse noise environments, the high-order statistics of the received signal exhibit significant divergence, causing the covariance matrix relied upon by traditional methods to exhibit ill-conditioned characteristics, leading to a sharp drop in DOA estimation accuracy and even algorithm failure. Further research has shown that existing robustness improvement schemes based on second-order moments (such as the fractional low-order moment method) can mitigate the impact of impulse noise under certain conditions, but their performance is limited by the identifiability of the noise prior parameters and lacks the ability to adaptively adjust to the non-stationary random processes of the noise statistics. Therefore, achieving robust DOA estimation without prior noise information in the presence of strong impulse noise has become a core challenge in array signal processing that needs to be overcome. Summary of the Invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a DOA estimation method based on INCK in an impulse noise environment. Specifically, INCK refers to Infinity Norm Cauchy Kernel based on local entropy, that is, the infinite norm Cauchy kernel of local entropy.

[0004] The present invention provides a DOA estimation method based on INCK in an impulse noise environment, comprising the following steps:

[0005] Step (1): Receive the signal through the uniform linear array antenna to obtain the received signal information. ;

[0006] Step (2): Calculate the local information entropy of a single snapshot using the local entropy calculation formula based on the received signal information. ;

[0007] Step (3), according to the received signal information, the infinite norm of a single snapshot is calculated by the infinite norm calculation formula, and a semi-infinite norm Cauchy kernel and a full infinite norm Cauchy kernel are constructed;

[0008] Step (4), based on the obtained local information entropy , semi-infinite norm Cauchy kernel and full infinite norm Cauchy kernel, construct each received signal information Corresponding weight ;

[0009] Step (5): According to the obtained weight, the received signal information Perform weighted processing to obtain , and Constructing the covariance matrix , and then use the ESPRIT / MUSIC algorithm to estimate DOA.

[0010] Furthermore, the array antenna of the uniform linear array structure in step (1) is composed of M The array elements are composed of array elements, and the array element spacing is ,in , is the carrier wavelength.

[0011] Furthermore, the received signal information in step (1) for:

[0012]

[0013] in, is the direction matrix, is the direction vector, j is the imaginary unit, M is the number of array elements, For the k The angles at which the signal sources are located, is an impulse noise term that obeys a stable distribution with symmetric characteristic exponent α, and ; is the signal vector, where Indicates the k A signal, t For Snapshot ( ).

[0014] Furthermore, the local information entropy in step (2) For the t The local information entropy of a snapshot:

[0015]

[0016]

[0017] in, For the i The first tA quick shot of the signal information; To take the absolute value.

[0018] Furthermore, the step (3) includes the following steps:

[0019] 3-1. Calculate the infinity norm for each snapshot:

[0020]

[0021] in To take the maximum value among them.

[0022] 3-2. Construct the Cauchy kernel based on the infinite norm of each snapshot:

[0023]

[0024] in is the semi-infinite norm Cauchy kernel; is the Cauchy kernel of full infinite norm.

[0025] Furthermore, the weight W in step (4) is:

[0026]

[0027] in is the hyperbolic tangent function.

[0028] Furthermore, the signal information after weighted processing in step (5) for:

[0029]

[0030] Among them, the size of the signal information Y is the same as the size of the received signal information x; construct the signal information after weighted processing The covariance matrix of :

[0031]

[0032] in, represents the conjugate transpose.

[0033] The beneficial effects of the present invention are as follows:

[0034] Compared with the prior art, the present invention uses the Local Entropy-Infinite Norm Cauchy Kernel (INCK) based on local entropy to improve the accuracy of DOA estimation in harsh environments; in step (4), the weights are constructed using local entropy and the Cauchy kernel. , the received signal is weighted After processing, the impulse noise in the received signal is suppressed without requiring prior information about the noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the uniform linear array structure of the present invention.

[0036] Figure 2 When 5 signal sources are incident on the array, =1.5. Schematic diagram of the peak search obtained from a single MC experiment.

[0037] Figure 3 When two signal sources are incident on the array, =1.5. Schematic diagram of the peak search obtained from a single MC experiment.

[0038] Figure 4 When three signal sources are incident on a uniform linear array, where M=10, 1000 MC experiments are run using the method of the present invention and other algorithms. =1.5, RMSE performance diagram under different generalized signal-to-noise ratio conditions.

[0039] Figure 5 When three signal sources are incident on a uniform linear array, =0.8, M=10, and running M=101000 MC experiments. Schematic diagram of RMSE performance of the method of the present invention and other algorithms under different snapshot numbers.

[0040] Figure 6 When three signal sources are incident on a uniform linear array, =1.2, M=10, and 1000 MC experiments are run. Schematic diagram of the RMSE performance of the method of the present invention and other algorithms under different snapshot numbers.

[0041] Figure 7 When three signal sources are incident on a uniform linear array, where M=10, 1000 MC experiments are run using the method of the present invention and other algorithms at different characteristic indices. Schematic diagram of RMSE performance under different conditions. DETAILED DESCRIPTION

[0042] The present invention will be further described in detail below with reference to the accompanying drawings.

[0043] Most DOA estimation methods use the second-order statistics of the Gaussian noise model. However, in practical situations (such as radar echoes, low-frequency atmospheric noise, and underwater acoustic signal research), the noise is composed of irregular pulses or spikes with short duration and large amplitude, and the traditional second-order statistics are no longer applicable. This kind of impulse noise can usually be modeled using the α-stable distribution, which has good applicability and its characteristic function is It can be expressed as:

[0044] ;

[0045] ;

[0046] ;

[0047] in, is the variable of the characteristic function, is the characteristic index, j is the imaginary unit, is the dispersion parameter, which has the same meaning as the variance of the Gaussian distribution; is the skewness parameter, is a positional parameter, when The distribution is symmetrical when Stable distributed noise ( , Symmetric Alpha-Stable Distribution Noise).

[0048] The present invention provides a DOA estimation method based on INCK in an impulse noise environment, which specifically includes the following steps:

[0049] Step (1): Receive the signal through the uniform linear array antenna to obtain the received signal information. .

[0050] like Figure 1 The array antenna structure shown is composed of M The uniform linear array of array elements is composed of the first sensor as the reference element, and the array element spacing is ,in , is the carrier wavelength. Assume K The DOAs are Narrowband signal Incident on Figure 1 On the nested linear array shown, the array receiving signal can be expressed as:

[0051]

[0052] in, is the direction matrix, is the direction vector, j is the imaginary unit, M is the number of array elements, For the k The angles at which the signal sources are located, Is subject to the symmetric characteristic index Stable distribution of impulse noise terms, and ; is the signal vector, where Indicates the k A signal, t For Snapshot ( ).

[0053] Step (2): Calculate the local information entropy of a single snapshot using the local entropy calculation formula based on the received signal information. .

[0054] Local information entropy Calculated by the following formula:

[0055] ;

[0056] ;

[0057] in, For the i The first t A quick shot of the signal information; To take the absolute value.

[0058] Step (3): According to the received signal information, the infinite norm of a single snapshot is calculated by the infinite norm calculation formula, and a semi-infinite norm Cauchy kernel and a full infinite norm Cauchy kernel are constructed.

[0059] Compute the infinity norm for each snapshot:

[0060] ;

[0061] Construct the Cauchy kernel based on the infinite norm obtained for each snapshot:

[0062] ;

[0063] in is the semi-infinite norm Cauchy kernel; is the Cauchy kernel of full infinite norm.

[0064] Step (4), according to the obtained And the Cauchy kernel, construct the weight W corresponding to each received signal information.

[0065] According to the local information entropy obtained in steps (2) and (3) and infinite norm Cauchy kernel, the local information entropy Through the hyperbolic tangent function, the weight of the semi-infinite norm Cauchy kernel is obtained a , construct the weight corresponding to each received signal information :

[0066] ;

[0067] in is the hyperbolic tangent function.

[0068] Step (5): According to the obtained weight information, Perform weighted processing to obtain , and Constructing the covariance matrix , and then use the ESPRIT algorithm to estimate DOA.

[0069] The weighted signal information for:

[0070] ;

[0071] Among them, the size of Y is the same as that of x; construct the signal information after weighted processing The covariance matrix of :

[0072] ;

[0073] in, represents the conjugate transpose.

[0074] right Perform eigenvalue decomposition:

[0075] ;

[0076] in, , , is the noise variance; .Pick The characteristic value of K The larger eigenvalues constitute the signal subspace estimation and are divided into and Two parts, constructing the matrix And perform eigenvalue decomposition, and then Decompose into Submatrix of :

[0077] ;

[0078] ;

[0079] ;

[0080] in, Indicates the inverse matrix. Then calculate The eigenvalue of , and then calculate the DOA estimate by the formula Value:

[0081] ;

[0082] in To invert the trigonometric function, Indicates calculating the angle corresponding to the complex number.

[0083] In order to verify the effect of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed. In an impulse noise environment, the generalized signal-to-noise ratio is defined as:

[0084] ;

[0085] in is the signal vector, is the dispersion parameter, is the expectation operator.

[0086] The performance estimation criterion is the joint root mean square error (RMSE) defined as:

[0087] ;

[0088] in, For the The Monte Carlo process k The accurate estimate of the DOA of each source, For the k is the angle at which the signal sources are located, represents the number of information sources, and MC represents the number of Monte Carlo trials.

[0089] The present invention (INCK-ESPRIT) is compared with existing methods, including the phase fractional lower-order moment ESPRIT (PFLOM-ESPRIT) method, the signed covariance matrix ESPRIT (SCM-ESPRIT) method, the infinity norm normalized ESPRIT (IN-ESPRIT) method, and the correlation entropy-based infinity norm ESPRIT (Co-IN-ESPRIT) method.

[0090] Figure 2 When A signal source is incident on the array, and the DOA is ,exist , Snap , Schematic diagram of the spectrum peak search obtained by running only one MC experiment using the present invention. Figure 2 It can be seen that the present invention can obtain accurate DOA estimation.

[0091] Figure 3 When A signal source is incident on the array, and the DOA is ,exist , Snap , Schematic diagram of the spectrum peak search obtained by running only one MC experiment using the present invention. Figure 3 It can be seen that the present invention can accurately perform DOA estimation for two signal sources that are very close to each other.

[0092] Figure 4 is , Snap In the case of , the performance of the algorithms under different GSNRs is compared. 1000 MC experiments are run. The azimuth angles of the three signal sources are .from Figure 4 It can be seen that under the condition of lower generalized signal-to-noise ratio, the present invention has better DOA estimation performance.

[0093] Figure 5 is , In the case of , the algorithm performance comparison under different snapshot numbers, running 1000 MC experiments, the azimuth angles of the three signal sources are .from Figure 5 It can be seen that the performance of the present invention improves with the increase of the number of snapshots. Under high pulse conditions, the estimation performance of the present invention is better than other estimation methods for the same snapshot.

[0094] Figure 6 is , In the case of , the algorithm performance comparison under different snapshot numbers, running 1000 MC experiments, the azimuth angles of the three signal sources are .from Figure 6 It can be seen that the performance of the present invention improves with the increase of the number of snapshots. Under the same snapshot conditions, the estimation performance of the present invention is better than other estimation methods.

[0095] Figure 7 is , Snap In the case of , the performance of the algorithms under different characteristic index conditions is compared. 1000 MC experiments are run. The azimuth angles of the three signal sources are .from Figure 7 It can be seen that the performance of the present invention increases with the characteristic index The same Under these conditions, the method of the present invention has better estimation performance.

[0096] In summary, from the analysis of the simulation effect diagram, it can be seen that the DOA estimation method based on INCK in an impulse noise environment proposed in the present invention realizes accurate DOA estimation in an impulse noise environment.

[0097] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. The DOA estimation method based on INCK in impulse noise environment is characterized by: INCK represents the infinite norm Cauchy kernel of local entropy, which specifically includes the following steps: Step (1), receiving a signal through a uniform linear array antenna to obtain received signal information x(t); Step (2): Calculate the local information entropy H under a single snapshot using the local entropy calculation formula based on the received signal information. t ; Step (3), according to the received signal information, the infinite norm of a single snapshot is calculated by the infinite norm calculation formula, and a semi-infinite norm Cauchy kernel and a full infinite norm Cauchy kernel are constructed; 3-1. Calculate the infinity norm for each snapshot: ||x(t)|| ∞ =max{x1(t),x2(t),...,x M (t)} Where max{} is the maximum value; x i (t) is the signal information of the t-th snapshot of the i-th array element; 3-2. Construct the Cauchy kernel based on the infinite norm of each snapshot: Where ω1(i,t) is the semi-infinite norm Cauchy kernel; ω2(i,t) is the full infinite norm Cauchy kernel; Step (4): Based on the obtained local information entropy H t , semi-infinite norm Cauchy kernel and full infinite norm Cauchy kernel, construct the weight W corresponding to each received signal information x(t); The weight W in step (4) is: W(i,t)=aω1(i,t)+(1-a)ω2(i,t) a=tanh(H t ) Where tanh(·) is the hyperbolic tangent function; Step (5): According to the obtained weights, the received signal information x(t) is weighted to obtain Y, and the covariance matrix R is constructed for Y. INCK , and then use the ESPRIT / MUSIC algorithm to estimate DOA.

2. The DOA estimation method based on INCK in an impulse noise environment according to claim 1, characterized in that: The array antenna of the uniform linear array structure in step (1) is composed of M array elements, and the array element spacing is d0, where d0 = λ / 2, λ is the carrier wavelength.

3. The DOA estimation method based on INCK in an impulse noise environment according to claim 1 or 2, characterized in that: The received signal information x(t) in step (1) is: x(t)=A(θ)s(t)+n(t), Where A=[a(θ1),…,a(θ k ),…a(θ K )] is the direction matrix, is the direction vector, j is the imaginary unit, M is the number of array elements, θ k is the angle at which the kth signal source is located, n(t) is an impulse noise term that obeys a stable distribution with a symmetric characteristic index α, and 0<α≤2; s(t)=[s1(t),…,s k (t),…s K (t)] T is the signal vector, where s k (t) represents the kth signal, t is a snapshot, t=1,2,…,T s .

4. The DOA estimation method based on INCK in an impulse noise environment according to claim 3, characterized in that: The local information entropy H in step (2) t is the local entropy of the t-th snapshot: Among them, x i (t) is the signal information of the t-th snapshot of the i-th array element; |·| is the absolute value.

5. The DOA estimation method based on INCK in an impulse noise environment according to claim 4, characterized in that: The signal information Y after weighted processing in step (5) is: Y it =W(i,t)x i (t) Among them, the size of the signal information Y is the same as the size of the received signal information x; construct the covariance matrix R of the signal information Y after weighted processing INCK : R INCK =YY H / T s in,[] H represents the conjugate transpose.

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