A method for estimating DOA of absolute polynomial correlation entropy in pulse noise environment

Abstract

The application discloses a kind of absolute polynomial correlation entropy DOA estimation methods under pulse noise environment, receive signal by nested array structure antenna, according to received signal and absolute polynomial correlation entropy operator APCO calculate corresponding covariance matrix;With vectorization, ordering and redundancy are removed, obtain new virtual uniform linear array received signal;The continuous part of half wavelength between difference virtual array elements is spatially smoothed, and the spatially smoothed covariance matrix is constructed, and then the precise estimation of DOA is obtained by using the MUSIC method.The method uses absolute polynomial correlation entropy operator APCO to suppress pulse noise outliers, constructs APCO matrix, not only without relying on prior knowledge of noise, but also can get rid of the limitation of traditional correlation entropy algorithm, and can realize high-precision DOA estimation in strong pulse noise, low SNR, limited number of snapshots environment.

Description

Technical Field

[0001] This invention relates to the field of signal direction of arrival (DOA) estimation technology under impulse noise, specifically to an absolute polynomial correlation entropy (DOA) estimation method under impulse noise environment, which can be widely used in many fields such as radar, sonar, positioning and navigation, astronomy and medical diagnosis. Background Technology

[0002] Direction of arrival (DOA) estimation has become a key area in array signal processing, with wide applications in wireless communication, radar, sonar, seismic detection, and sound source localization. DOA estimation aims to determine the azimuth angle of multiple incident signals using algorithms. Classical methods include regression moving average, maximum likelihood entropy analysis, entropy spectrum decomposition, and subspace methods based on eigenvalue decomposition. Among these, subspace methods achieve super-resolution estimation through eigenvalue decomposition, breaking the traditional Rayleigh limit constraint, possessing unbiased characteristics, and achieving accuracy close to the Cramer-Rao bound. Traditional DOA estimation algorithms are generally based on Gaussian noise models. However, in environments with strong impulse noise, such as atmospheric noise caused by low-frequency and ultra-low-frequency radio waves, or noise generated by mechanical vibration, the Gaussian noise assumption is no longer applicable. In such cases, noise often exhibits impulse characteristics, and traditional Gaussian noise models are insufficient to effectively characterize its statistical properties. To address this issue, a new method is introduced... A stable distribution model, which belongs to a continuous probability distribution. Because... The probability density function of a stable distribution does not have a closed form, making it mathematically difficult to handle. However, it can be addressed using characteristic functions. This can be represented as:

[0003] ;

[0004] ;

[0005] ;

[0006] in, These are the variables of the characteristic function. It is a characteristic index, the magnitude of which can affect the impulse level of this distribution, ranging from... .when The time distribution follows a Gaussian distribution; j is an imaginary number. It is a dispersion parameter, and its meaning is consistent with the variance of the Gaussian distribution; It is a skewness parameter. It is a position parameter, when The distribution of time is symmetrical Stablize( )distributed; Different parameter choices represent different probability density functions. In distribution The smaller the pulse, the more pronounced it is; conversely... The larger the value, the closer the noise is to Gaussian noise. Based on this, a series of DOA estimation methods for impulse noise have been proposed, such as fractional low-order moments, robust covariance moments, and phase fractional low-order moments; however, these algorithms all have certain limitations. Gaussian distribution and The key difference between the Gaussian and Gaussian distributions is that the Gaussian distribution has second-order statistics, while... Distributed in If the second-order statistic does not exist, then the second-order covariance matrix does not exist either.

[0007] The invention disclosed in CN117518071A presents a broadband DOA estimation method based on correlation entropy under impulse noise, applying the concept of correlation entropy to broadband signal processing. However, the correlation entropy used is essentially still a single form of the exponential kernel. The invention disclosed in CN119024260A presents a robust low-order moment DOA estimation method under impulse noise conditions. Although it proposes an adaptive tuning parameter based on local information entropy, its core operator only utilizes the idea of ​​fractional low-order moments and does not essentially employ the kernel function structure of correlation entropy. Furthermore, the invention disclosed in CN116699508A presents a high-degree-of-freedom DOA estimation method based on a mirror coprime array (SCO algorithm) under impulse noise conditions, proposing a correlation entropy operator based on squared values. However, this method struggles when handling characteristic exponents. In such cases, the root mean square error is large, and it is also present in strong impulse noise. In some cases, the inability to handle outliers leads to ill-conditioned matrices, making it impossible to estimate the direction of arrival.

[0008] Therefore, there is an urgent need for a robust estimation algorithm that can effectively suppress impulse noise, requires no prior noise, and achieves stability. Summary of the Invention

[0009] To address the issues of traditional fractional low-order statistics relying on prior noise knowledge and the insufficient robustness of correlation entropy algorithms under strong impulse noise, this invention proposes an absolute polynomial correlation entropy (DOA) estimation method for impulse noise environments. It also proposes an absolute polynomial correlation entropy operator (APCO) that effectively suppresses outliers in impulse noise without requiring any prior noise knowledge. APCO is directly correlated with the data received by the array and is suitable for any impulse noise scenario and any sparse array.

[0010] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0011] An absolute polynomial correlation entropy (DOA) estimation method under impulse noise environment, the method comprising the following steps:

[0012] S1 receives signals through a nested array antenna structure, obtaining the received signal. According to the received signal Selecting the kernel length parameter , obtained the nuclear length ;

[0013] S2, based on the received signal And the absolute polynomial correlation entropy operator APCO is used to calculate the corresponding equivalent covariance matrix. The first of the matrix item It is expressed as follows:

[0014] ;

[0015] In the formula, , for The Line, representing the first The signal received by each array element for The line, indicating the first The signal received by each array element Indicates the conjugate operation;

[0016] S3, for the equivalent covariance matrix The vectorization process is performed, the data is sorted and redundancy is removed, and then spatial smoothing techniques are used to obtain the spatially smoothed covariance matrix. ;

[0017] S4, for spatially smoothed covariance matrix Eigenvalue decomposition is used to obtain the noise subspace, and the spatial spectral function is constructed; the noise subspace is then identified through MUSIC spectral peak search. Peak value, obtained The accurate estimation of DOA.

[0018] Step S1 further includes:

[0019] A two-level nested array is constructed using two uniform subarrays; the number of elements in the first-level subarray is... The spacing between array elements is The number of elements in the second-level subarray is The spacing between array elements is , The wavelength is λ; the distance between the two uniform subarrays is λ. The total number of array elements in the two-level nested array is The element positions of a two-level nested array are represented by a set as follows:

[0020] ;

[0021] make The second-level nested array received A far-field narrowband incoherent source signal with an incident angle of . The received signal is represented as:

[0022] ;

[0023] in It is a signal vector, where each element represents Signal sources from different directions, It is an impulse noise vector, where each element represents the noise signal in the signal received by each array element. Represent the complex vector space; Let be the direction matrix, the first... directional vectors for:

[0024] ;

[0025] Depend on Combine to obtain the received signal , for The first in A snapshot of the time zone.

[0026] Further, in step S1, the nuclear length is calculated using the following formula. :

[0027] ;

[0028] in, Signal vector The variance.

[0029] Step S3 further includes:

[0030] For equivalent covariance matrix Vectorize, sort, and remove redundancy to obtain a vector. ,vector This can be viewed as the received signal vector of a virtual array, where the total number of elements in the virtual array is... Using spatial smoothing technology, the virtual array is divided into Each subarray contains [number] subarrays. The first array element, then the second... The signals received by the subarrays of the virtual array are The obtained spatial smoothing covariance matrix as follows:

[0031] ;

[0032] In the formula, , , This indicates the conjugate transpose operation.

[0033] Step S4 further includes:

[0034] right Eigenvalue decomposition yields eigenvalues, of which The eigenvectors corresponding to the larger eigenvalues ​​form the signal subspace, and the rest... The eigenvectors corresponding to the smaller eigenvalues ​​form the noise subspace. :

[0035] ;

[0036] Based on noise subspace and signal direction vector Orthogonality relation, construct spatial spectral function:

[0037] ;

[0038] in, It is the incident angle of the signal source. For the corresponding direction vector, This represents the conjugate transpose operation;

[0039] Identify by MUSIC spectral peak search Peak value, obtained The accurate estimation of DOA.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] First, the absolute polynomial correlation entropy (DOA) estimation method under impulse noise environment of the present invention uses a nested array to receive signals emitted by the signal source. Based on the robustness of the algorithm used, it improves the DOA estimation accuracy under impulse environment and can be well combined with spatial smoothing technology to be applicable to various sparse array models.

[0042] Second, the absolute polynomial correlation entropy (APCO) estimation method for impulse noise environments proposed in this invention, compared with other DOA estimation algorithms for impulse noise environments, can perform polynomial fusion based on absolute values. When extreme outliers occur, the first-order term can play a dominant role to achieve robust suppression, thus it can be applied to strong impulse environments. At the same time, the polynomial structure under absolute values ​​can maintain sensitivity to impulse interference, so that the method can achieve accurate direction of arrival estimation without depending on specific signal types and array types. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the nested array structure involved in this invention;

[0044] Figure 2 This is a schematic diagram of the virtual array structure involved in this invention;

[0045] Figure 3 This is a performance comparison chart of the method of this invention with other algorithms under different generalized signal-to-noise ratio conditions;

[0046] Figure 4 This is a performance comparison chart of the method of this invention with other algorithms under different noise figure conditions;

[0047] Figure 5 This is a performance comparison chart of the method of this invention with other algorithms under different snapshot numbers;

[0048] Figure 6 This is a performance comparison chart of the method of the present invention under different sparse arrays as the generalized signal-to-noise ratio varies;

[0049] Figure 7 This is a performance comparison chart of the method of the present invention under different sparse arrays with varying snapshot numbers;

[0050] Figure 8 This is a flowchart of the absolute polynomial correlation entropy (DOA) estimation method under impulse noise environment according to the present invention. Detailed Implementation

[0051] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0052] See Figure 8 This invention discloses a method for estimating the absolute polynomial correlation entropy (DOA) under impulse noise conditions. The method includes the following steps:

[0053] S1 receives signals through a nested array antenna structure, obtaining the received signal. According to the received signal Selecting the kernel length parameter , obtained the nuclear length ;

[0054] S2, based on the received signal And the absolute polynomial correlation entropy operator APCO is used to calculate the corresponding equivalent covariance matrix. ;

[0055] S3, for the equivalent covariance matrix The data is vectorized, sorted, and redundancy removed. Spatial smoothing techniques are then used to obtain the spatially smoothed covariance matrix. ;

[0056] S4, for spatially smoothed covariance matrix Eigenvalue decomposition yields the noise subspace and constructs the spatial spectral function; peak search is then used to identify... Peak value, obtained The accurate estimation of DOA.

[0057] Depend on Figure 1 As shown, the two-level nested array consists of two uniform subarrays, where the first-level subarray has the following number of elements: The spacing between array elements is The number of elements in the second-level subarray is... The spacing between array elements is , Where is the signal wavelength. The distance between the two subarrays is... The total number of array elements in the two-level nested array is The element positions of a two-level nested array can be represented by a set as follows:

[0058] (1);

[0059] make The second-level nested array received A far-field narrowband incoherent source signal with an incident angle of . The received signal can then be expressed as:

[0060] (2);

[0061] in Let be the direction matrix, where the first... A directional vector can be written as:

[0062] (3);

[0063] It is a signal vector. It is the impulse noise vector. Received signal. Depend on Combining for The first in A snapshot of the time zone.

[0064] In impulse noise environments, outliers cause traditional DOA estimation methods to fail. The core problem lies in the fact that when the noise follows a characteristic exponent... of When the signal is distributed, the second-order statistics of the signal are absent, causing a sharp deterioration in the performance of traditional algorithms based on second-order moments. To address this, this invention proposes the Absolute Polynomial Correlation Entropy Operator (APCO) method. This method weakens the impact of outlier amplitudes of impulse noise through absolute value operations and polynomial forms, while also being independent of prior noise knowledge.

[0065] In this embodiment, the above-mentioned noise model and data model are applied to the DOA estimation algorithm of the present invention, namely the absolute polynomial correlation entropy MUSIC DOA estimation method, which specifically includes the following steps:

[0066] Step 1: Obtain signal reception through nested arrays .

[0067] The received signal can be obtained based on the data model. :

[0068] (4);

[0069] Received signal Depend on Combining for The first in A snapshot of the time zone.

[0070] Step 2: Select the core length parameter based on the received signal. After that, you can obtain the core. :

[0071] (5);

[0072] in, For signal The variance.

[0073] Step 3: Calculate the equivalent covariance matrix based on the received signal and the defined APCO operator. ;

[0074] (6);

[0075] Here, , for The OK, for The OK, Representative of the Nuclear Director.

[0076] Step 4, for Vectorize, sort, and remove redundancy to obtain ,make You can get ;

[0077] (7);

[0078] Step 5: Use the MUSIC estimation algorithm to obtain... Precise estimation of DOA: for Eigenvalue decomposition yields the noise subspace:

[0079] (8);

[0080] And construct the spatial spectral function:

[0081] (9);

[0082] Identify by MUSIC spectral peak search Peak value, thus obtaining Accurate estimation of DOA.

[0083] 1. Complexity Analysis

[0084] This invention uses the number of complex multiplications of real numbers (or complex numbers) as the standard for computational complexity. An equivalent covariance matrix is ​​constructed. The complexity is , Represents the number of time sampling points of the input data, vectorized. The complexity of sorting and removing redundancy is O(n). , build The complexity is ,right The complexity of eigenvalue decomposition is The total computational complexity of using the MUSIC algorithm is ,in This represents the number of searches. Therefore, the proposed... The total complexity of the algorithm is:

[0085] (10);

[0086] 2. Experimental Analysis

[0087] To verify the effectiveness of the above method, multiple simulation experiments were conducted in this embodiment, and the experimental performance was analyzed, as follows:

[0088] (1) Experimental performance evaluation indicators

[0089] In an impulse noise environment, the generalized signal-to-noise ratio is defined as:

[0090] (11);

[0091] The performance estimation criterion is the joint root mean square error (RMSE), defined as follows:

[0092] (12);

[0093] in, For the first The exact estimate of the DOA of the k-th source in the Monte Carlo process. This indicates the number of information sources, and MC represents the number of Monte Carlo trials.

[0094] (2) Experimental results diagram

[0095] Figure 1 A schematic diagram of the nested array structure involved in this invention is shown.

[0096] Figure 2 A schematic diagram of the virtual array structure involved in this invention is shown.

[0097] Figure 3 The impulse noise figure is given. Under the conditions, the three incident angles are respectively Incoherent signals arrive at a nested array consisting of 6 elements. The Monte Carlo loop count is set to 500, and the snapshot count is... The trends of RMSE with GSNR for different algorithms were analyzed. The algorithms compared included the Sign Covariance Matrix (SCM) method, the Phase Fractional Lower Order Moment (PFLOM) method, the Generalized Auto-Correntropy (GCO) method, the Correntropy Correlation (CRCO) method, the Square-based Correntropy Operator (SCO) method, and the Absolute Polynomial Correntropy Operator (APCO) method. It can be seen that the CRCO algorithm performs poorly, while the APCO algorithm consistently outperforms the GCO, SCM, PFLOM, and SCO algorithms, especially maintaining good performance under low generalized signal-to-noise ratio conditions.

[0098] Figure 4 The simulation shows the relationship between the RMSE of different algorithms and the characteristic exponent of impulse noise when GSNR = 0 dB. Other simulation conditions are compared with... Figure 3 Maintain consistency. From Figure 4 The results show that as the impulse noise intensity gradually decreases, the estimation performance of all algorithms improves, but the estimation accuracy of the algorithm in this invention is consistently significantly better than other algorithms. The SCO algorithm, in terms of feature index... of The performance of the distributed methods is generally poor, which is directly related to the inability of the operators used to handle outliers. When the characteristic exponent is less than a certain value, the matrix may even become ill-conditioned, making it impossible to estimate the direction of arrival (DOA). In contrast, the absolute polynomial correlation entropy operator APCO proposed in this invention performs polynomial fusion based on absolute values. When extreme outliers occur, the first-order term can play a dominant role to achieve robust suppression, thus making it suitable for strong impulse environments. In addition, practical verification shows that the DOA estimation performance of some existing algorithms depends on the incident signal being a non-circular signal (not satisfying rotational symmetry in a second-order statistical sense) and specific array structure assumptions. When the incident signal is circular, the performance drops sharply. However, the absolute polynomial correlation entropy operator APCO of this invention can maintain sensitivity to impulse interference, thus enabling the estimation method of this invention to achieve accurate DOA estimation without depending on specific signal types and array types. In this simulation example, a circular signal is used.

[0099] Figure 5 Shown in When GSNR = 0 dB, these algorithms are dependent on the number of snapshots. At this time, the performance of the CRCO algorithm is poor, and increasing the number of snapshots cannot improve the performance. However, the method of this invention has always had the best performance.

[0100] Figure 6 The trends of RMSE versus GSNR under different sparse array conditions were compared using the algorithm of this invention. The three sparse arrays were a traditional nested array (NA), an enhanced nested array (ENA), and a super nested array (SNA). Three incoherent narrowband signal sources were selected, with incident angles of [missing information]. These are applied to different types of sparse arrays, with the total number of array elements set to 6, and the noise follows a set rule. Distribution. From Figure 6 The results clearly show that the algorithm of this invention exhibits the best estimation accuracy under any sparse array structure, especially under the ENA array structure.

[0101] Figure 7 This further demonstrates that the method of the present invention is applied to different sparse arrays, and the RMSE varies with the number of snapshots. Trend analysis of changes. GSNR was set to 0 dB. The results show that the method of this invention maintains optimal performance consistently with increasing snapshot number, especially in ENA array structures.

[0102] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0103] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for estimating absolute polynomial correlation entropy (DOA) under impulse noise conditions, characterized in that, The method includes the following steps: S1 receives signals through a nested array antenna structure, obtaining the received signal. According to the received signal Selecting the kernel length parameter , obtained the nuclear length ; S2, based on the received signal And the absolute polynomial correlation entropy operator APCO is used to calculate the corresponding equivalent covariance matrix. The first of the matrix item It is expressed as follows: ； In the formula, , for The Line, representing the first The signal received by each array element for The line, indicating the first The signal received by each array element Indicates the conjugate operation; S3, for the equivalent covariance matrix The vectorization process is performed, the data is sorted and redundancy is removed, and then spatial smoothing techniques are used to obtain the spatially smoothed covariance matrix. ; S4, for spatially smoothed covariance matrix Eigenvalue decomposition is used to obtain the noise subspace, and the spatial spectral function is constructed; the noise subspace is then identified through MUSIC spectral peak search. Peak value, obtained The accurate estimation of DOA.

2. The method for estimating absolute polynomial correlation entropy (DOA) under impulse noise environment according to claim 1, characterized in that, Step S1 further includes: A two-level nested array is constructed using two uniform subarrays; the number of elements in the first-level subarray is... The spacing between array elements is The number of elements in the second-level subarray is The spacing between array elements is , The wavelength is λ; the distance between the two uniform subarrays is λ. The total number of array elements in the two-level nested array is The element positions of a two-level nested array are represented by a set as follows: ； make The second-level nested array received A far-field narrowband incoherent source signal with an incident angle of . The received signal is represented as: ； in It is a signal vector, where each element represents Signal sources from different directions, It is an impulse noise vector, where each element represents the noise signal in the signal received by each array element. Represent the complex vector space; Let be the direction matrix, the first... directional vectors for: ； Depend on Combine to obtain the received signal , for The first in A snapshot of the time zone.

3. The method for estimating absolute polynomial correlation entropy (DOA) under impulse noise environment according to claim 2, characterized in that, In step S1, the nuclear length is calculated using the following formula. : ； in, Signal vector The variance.

4. The method for estimating absolute polynomial correlation entropy (DOA) under impulse noise environment according to claim 1, characterized in that, Step S3 further includes: For equivalent covariance matrix Vectorize, sort, and remove redundancy to obtain a vector. ,vector This can be viewed as the received signal vector of a virtual array, where the total number of elements in the virtual array is... Using spatial smoothing technology, the virtual array is divided into Each subarray contains [number] subarrays. The first array element, then the second... The signals received by the subarrays of the virtual array are The obtained spatial smoothing covariance matrix as follows: ； In the formula, , , This indicates the conjugate transpose operation.

5. The method for estimating absolute polynomial correlation entropy (DOA) under impulse noise environment according to claim 2, characterized in that, Step S4 further includes: right Eigenvalue decomposition yields eigenvalues, of which The eigenvectors corresponding to the larger eigenvalues ​​form the signal subspace, and the rest... The eigenvectors corresponding to the smaller eigenvalues ​​form the noise subspace. : ； Based on noise subspace and signal direction vector Orthogonality relation, construct spatial spectral function: ； in, It is the incident angle of the signal source. For the corresponding direction vector, This represents the conjugate transpose operation; Identify by MUSIC spectral peak search Peak value, obtained The accurate estimation of DOA.

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