Method and system for direction of arrival estimation of non-circular speech signals under impulsive noise

Abstract

The application discloses a method and system for direction of arrival estimation of non-circular speech signals under impulse noise. The method first receives multiple frames of non-circular QSS speech signals, calculates an adaptive index based on local entropy, and constructs a covariance matrix of each signal frame. Secondly, the covariance matrix is vectorized to obtain a single-snapshot vector, and a continuous and difference co-array SDCA equivalent single-snapshot vector containing an expanded virtual array aperture is extracted. Then, the equivalent single-snapshot vectors of all time frames are combined into a multi-frame joint equivalent received signal matrix, and the corresponding spatial covariance matrix is calculated. Finally, the spatial covariance matrix is constructed to form a reduced-dimension spectral function matrix, and the one-dimensional spatial spectrum of RD-MUSIC is calculated to obtain the DOA estimation value of the signal. The application effectively suppresses the negative impact of sudden large-amplitude noise, can estimate more sound source targets than the number of physical sensors, and accurately and efficiently completes the direction of arrival estimation.

Description

Technical Field

[0001] This invention belongs to the field of direction of arrival (DOA) estimation, specifically relating to a method for DOA estimation of quasi-stationary (QSS) non-circular speech signals based on flipped nested array (FNA) and enhanced adaptive step moment function (EAOMF) under impulse noise environment. Background Technology

[0002] DOA estimation is a key technology in array signal processing, widely used in radar, communication, sonar, and sound source localization. While subspace-based algorithms, such as Multiple Signal Classification (MUSIC) and the Rotationally Invariant Subspace (ESPRIT) method, can achieve high-precision estimation, their performance depends on the Gaussian noise assumption. In real-world environments, electromagnetic interference and industrial noise often exhibit impulse characteristics, leading to severe performance degradation of traditional algorithms. Therefore, research on robust DOA estimation under impulse noise environments has significant application value.

[0003] To suppress impulse noise, researchers have proposed various robust methods, such as fractional low-order moments (FLOM), signed covariance matrix (SCM), phase fractional low-order moments (PFLOM), infinity norm normalization (IN), and methods based on sparse representation and bounded nonlinear covariance (BNC). However, most of these methods are based on uniform linear arrays (ULA), which have limited degrees of freedom (DOFs) and suffer from mutual coupling effects. In contrast, sparse arrays can achieve higher DOFs with the same number of physical array elements and have been introduced into impulse noise scenarios in recent years. By extending FLOM, PFLOM, BNC, etc., to sparse arrays through virtualization techniques, estimation performance can be significantly improved.

[0004] However, existing methods face a key bottleneck when combining robust techniques with sparse arrays. The virtualization process generates coherent source models, and subspace-based methods need to use spatial smoothing (SS) to decoherentize them. However, SS reduces the effective aperture of the array, weakens the high DOF advantage of sparse arrays, and limits their performance under impulse noise. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a DOA estimation method for QSS non-circular speech signals based on FNA and EAOMF. This method jointly utilizes the QSS and non-circular characteristics of the speech signal. The QSS characteristics allow for the direct construction of a full-rank covariance matrix from multiple frames of data, enabling decoherence without SS. The non-circular characteristics are used to further expand the virtual array, increasing the number of identifiable sources, thereby achieving high DOFs and high-precision DOA estimation even in impulse noise environments.

[0006] To overcome the severe interference of impulse noise on sound source localization and the inherent complexity of QSS signals, this invention provides an EAOMF algorithm. This method combines an FNA structure, fully utilizing the non-circular characteristics of speech signals and QSS features, effectively extending DOFs and improving robustness to impulse noise. Simultaneously, it avoids computationally complex two-dimensional search through dimensionality reduction multiple signal classification (RD-MUSIC).

[0007] Technical solution: In one aspect, the present invention provides a method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise, comprising the following steps:

[0008] (1) Receive multi-frame non-circular QSS voice signals acquired based on FNA Adaptive exponent calculated based on local entropy Based on this, the EAOMF covariance matrix for each signal frame is constructed. .

[0009] (2) To Vectorization yields a single snapshot vector. Subsequently, through row transformation and redundancy removal operations, the equivalent single snapshot vector of the continuous sum-difference comatrix (SDCA) containing the expanded virtual array aperture is extracted. .

[0010] (3) Combine the equivalent single-shot vectors of all time frames into a multi-frame joint equivalent received signal matrix. And calculate its corresponding spatial covariance matrix. .

[0011] (4) Perform eigenvalue decomposition (EVD) on the above spatial covariance matrix to obtain the noise subspace. Utilize the structural characteristics of the SDCA direction vector to split the direction vector into the product of a matrix containing only DOA information and a vector containing only non-circular phase information. Based on this, construct a dimension-reduced spectral function matrix and combine it with the selected vector to calculate the one-dimensional spatial spectrum of RD-MUSIC. The DOA estimate of the signal can be directly obtained through one-dimensional spectral peak search.

[0012] In another aspect, the present invention also provides a direction-of-arrival estimation system for non-circular speech signals under impulse noise, for implementing the aforementioned direction-of-arrival estimation method, comprising the following modules:

[0013] The covariance matrix module is used to receive multi-frame non-circular QSS speech signals obtained based on a flipped nested array, calculate the adaptive exponent based on local entropy, and construct the EAOMF covariance matrix for each signal frame.

[0014] The equivalent single snapshot vector module is used to vectorize the covariance matrix to obtain a single snapshot vector and extract the equivalent single snapshot vector of the continuous sum-difference comatrix SDCA containing the expanded virtual array aperture.

[0015] The spatial covariance matrix module is used to combine the equivalent single-shot vectors of all time frames into a multi-frame joint equivalent received signal matrix and calculate the corresponding spatial covariance matrix.

[0016] The direction-of-arrival (DOA) estimation module performs eigenvalue decomposition on the spatial covariance matrix to obtain the noise subspace, constructs a dimension-reduced spectral function matrix, calculates the one-dimensional spatial spectrum of RD-MUSIC, and obtains the DOA estimate of the signal through the one-dimensional spectral peak.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] 1. Enhanced system robustness under impulse noise environments: This invention constructs an EAOMF matrix to address impulse noise interference in complex environments. By calculating local entropy and introducing an adaptive exponent, it can dynamically adapt to the statistical characteristics of impulse noise, effectively suppressing the negative impact of sudden large-amplitude noise and ensuring the boundedness of the covariance matrix and the consistency of the estimation results.

[0019] 2. Expanded Array DOFs and Virtual Aperture: This invention combines the non-circular characteristics of speech signals with the FNA structure, enabling the simultaneous use of differential co-array and additional sum co-array information when extracting virtual array information. By removing redundancy and reconstructing continuous SDCA, the number of virtual array elements and continuous physical aperture is significantly increased, allowing the system to estimate more sound source targets than the number of physical sensors.

[0020] 3. Successfully decoupled parameters and reduced computational complexity: Addressing the massive computational burden caused by the inherent non-circular phase and DOA two-dimensional joint search for non-circular signals, this invention designs the RD-MUSIC method. This method utilizes the algebraic structure of the continuous SDCA direction vector to separate the non-circular phase from the direction parameter, constructing a one-dimensional spatial spectral function independent of the non-circular phase. This not only avoids the complex two-dimensional joint spectral peak search but also retains the high-precision advantages of subspace algorithms, accurately and efficiently completing direction-of-arrival estimation, which is more conducive to real-time deployment in engineering applications. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the FNA structure involved in this invention;

[0022] Figure 2 This is the virtual array structure diagram corresponding to the FNA array;

[0023] 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;

[0024] Figure 4This is a performance comparison chart of the method of this invention with other algorithms under different snapshot numbers;

[0025] Figure 5 This is a performance comparison chart of the method of this invention with other algorithms under different impulse noise characteristic exponents. Detailed Implementation

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0027] I. Construction and Physical Configuration of FNA

[0028] To fully capture the additional spatial information of non-circular QSS speech signals and overcome the limitations of limited DOFs and severe mutual coupling effects in traditional ULAs, this invention employs a specially designed sparse array, namely a FNA, as the physical basis for signal reception. The specific structural configuration and virtual aperture generation process are as follows:

[0029] 1. Basic Components of a Physical Array

[0030] The array used in this invention is based on a traditional nested array, assuming it consists of two sub-arrays. and Composition, the total number of physical array elements is Subarray It is a dense linear array, composed of It consists of 1 array element, with a spacing between adjacent array elements of 1. The set of its array element positions can be represented as ,in , The carrier wavelength of the signal; subarray It is a sparse linear array, composed of It consists of 1 array element, with a spacing between adjacent array elements of 1. The set of its array element positions can be represented as .

[0031] 2. Subarray flipping operation

[0032] Building upon traditional nested arrays, this invention proposes a physical flipping and rearrangement of the two sub-arrays, swapping their structural positions. This results in a logic reversal from traditional nested arrays, moving from sparse to dense. Specifically, sparse array elements are placed starting from position 0, at which point the element spacing becomes... This section contains a total of Each array element, that is Then, immediately after the last element of the sparse subarray, at the basic spacing... Place the remaining dense array elements to ensure the total number of physical array elements. This part remains unchanged; it simply needs to be repositioned. Each array element, that is After flipping and arranging the positions of all physical array elements from smallest to largest, a completely new set of actual receiving array element positions is formed.

[0033] The fundamental purpose of this operation is not only to obtain the difference set containing the spatial characteristics of the signal, but also to fully acquire the additional information of its sum set, namely the "difference comatrix" and the "sum comatrix".

[0034] 3. Acquisition of virtual co-array information

[0035] Based on the rearranged physical element position set After receiving a non-circular QSS speech signal, the system can mathematically derive and obtain two key types of virtual array information through subsequent operations such as covariance vectorization: the difference comatrix, which is composed of the differences between the physical array element positions, is defined as follows: ; and the common array, consisting of the positive and the common array With negative and co-element Combining, and defined respectively and .

[0036] 4. Build a continuous SDCA

[0037] After obtaining the above information through FNA, the key implementation of this invention lies in combining and splicing the continuous segments in the difference comatrix and sum comatrix corresponding to the physical array to form a large-scale continuous SDCA. The spliced ​​virtual array elements are continuously distributed and located within the interval ,in and These represent the discrete set of integers and their union, respectively. The final range of the continuous virtual aperture is: The array structure parameters are as follows: and .

[0038] By employing the aforementioned FNA structure and continuous SDCA construction method, this invention significantly surpasses the performance of traditional co-array structures. Without increasing the number of actual physical sensors, it greatly expands the virtual aperture size, resulting in a greater number of spatial DOFs available for subsequent DOA estimation algorithms. This provides a sufficient spatial information basis for high resolution and multi-target estimation beyond the limit of the number of sensors.

[0039] II. Noise Model and Received Data Model

[0040] Traditional DOA estimation methods assume that the noise is Gaussian. However, in reality, noise consists of irregular impulses or spikes with short durations and large amplitudes, rendering traditional second-order statistics inapplicable. This type of impulse noise can typically be estimated using... Modeling with stable distributions has good applicability, and its characteristic function... It can be represented as:

[0041] (1)

[0042] (2)

[0043] (3)

[0044] in, These are the variables of the characteristic function. It is a characteristic index. The imaginary unit, 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 Stable distribution.

[0045] Assuming in the first Next snapshot time The DOAs are respectively narrowband signal Incident to Figure 1 The virtual array structure diagram corresponding to the FNA array shown is as follows: Figure 2 As shown, the array-received signal can be represented as:

[0046] (4)

[0047] in The direction matrix, As the guide vector, It is a non-circular phase matrix. Indicates the first The non-circular phase of the signal It obeys symmetry A stable distribution of impulse noise terms, and ; Let be a real signal vector, where Indicates the first One signal.

[0048] III. Angle Estimation Methods

[0049] 1. Parameter preprocessing and adaptive exponent calculation

[0050] In this invention, because the system is in an impulse noise environment, the traditional second-order statistical covariance matrix will fail under large-amplitude noise containing outliers. This impulse noise follows a characteristic exponent of... Complex symmetry -Stablize( The distribution is as follows. To effectively suppress impulse noise interference and ensure the boundedness of the covariance matrix, this invention utilizes local entropy characteristics to dynamically adjust the adaptive exponent. The specific calculation process is as follows:

[0051] First, the amplitude normalization process is performed on the speech signal received by the FNA. Let the amplitude be normalized at the 1st... Within the time frame of the speech signal, the first... Individual elements Percentage of received signal amplitude at any given time The calculation formula is:

[0052] (5)

[0053] Equation (5) calculates the first The proportion of the amplitude of the signal received by each array element to the norm of the entire array's received signal is used for subsequent evaluation of signal fluctuations. Indicates the first Individual elements The received signal at any time This represents the array receiving signal vector at this moment. Norm.

[0054] Based on the normalized sequence described above, the local entropy of the speech signal within the current time frame is calculated. This is used to quantify the intensity of impulse noise during that time period. Local entropy The expression is

[0055] (6)

[0056] Equation (6) calculates the local entropy using the normalized sequence. When sudden, large-amplitude pulse noise occurs, the distribution of the signal sequence will change drastically, and the local entropy will increase. This intensity can be effectively quantified, among which This indicates the number of snapshots contained within each signal frame. This is the index of the current time frame.

[0057] Finally, the comprehensive impulse noise characteristic index Amplitude adjustment factor and local entropy Calculate the adaptive exponent used to construct the subsequent matrix. Its expression is

[0058] (7)

[0059] Equation (7) Comprehensive Impulse Noise Characteristic Index and local entropy Dynamically adjusting the fractional moment ensures that while filtering out heavily tailed impulse noise, the effective information of the speech signal is preserved to the greatest extent. The design logic of this formula lies in the fact that when impulse noise exhibits strong impact, the local entropy... This will change; the adaptive mechanism can dynamically adjust the fractional moment. The size, so that it satisfies The boundedness condition is used to maximize the retention of effective information in the target speech signal while filtering out heavy tail noise.

[0060] 2. Construction of the EAOMF matrix

[0061] Having obtained the adaptive exponent dynamically calculated in the first step Subsequently, this invention extends the traditional received signal by introducing the non-circular characteristics of the speech signal, and constructs the EAOMF covariance matrix of the QSS speech signal by combining fractional moment theory. The specific operation is as follows:

[0062] First, based on the strictly non-circular nature of the target speech signal, equation (4) can be extended to:

[0063] (8)

[0064] Equation (8) utilizes the strictly non-circular property of the speech signal to concatenate the original signal with its conjugate signal, where the extended manifold matrix can be expressed as: The extended guide vector is The extended impulse noise vector is , This indicates a conjugate operation. The physical significance of this operation lies in increasing the dimensionality of the available data, providing a basis for subsequently expanding the aperture of the virtual array.

[0065] Subsequently, the first step regarding the QSS voice signal Time frames ( ), using signed exponentiation operator A nonlinear transformation is performed on the extended received signal to reduce large-amplitude impulse noise. In the EAOMF matrix of the nth time frame Sub-block matrix ( ) The formula for calculating each element is defined as follows:

[0066] (9)

[0067] Equation (9) calculates the elements of the EAOMF covariance matrix, where, This represents the operation of calculating mathematical expectation. For elements of extended non-circular speech signals, This indicates the application of an adaptive exponent to the extended signal components. The sign exponentiation operation is defined as follows:

[0068] (10)

[0069] Equation (10) can weaken the influence of large-amplitude impulse noise by applying signed nonlinear exponentiation to the extended signal.

[0070] Assemble all the elements obtained from the above calculations according to their corresponding indices to construct the complete first... The expression for the frame EAOMF block covariance matrix is ​​as follows:

[0071] (11)

[0072] Equation (11) represents the assembled EAOMF covariance matrix, where, to These are sub-matrix blocks corresponding to the four quadrants of the original signal autocorrelation, the cross-correlation between the original signal and the conjugate signal, respectively.

[0073] In terms of theoretical mechanism, the EAOMF covariance matrix after the above fractional nonlinear processing can be strictly equivalent to a linear superposition of the signal autocorrelation component and the variance component of the approximate Gaussian white noise:

[0074] (12)

[0075] Equation (13) proves that after nonlinear processing, the matrix is ​​theoretically equivalent to the standard structure of signal autocorrelation plus approximate Gaussian white noise variance, where, It is the first The diagonal matrix of a frame of real-valued signal. Representing the The equivalent power of a signal. This represents the approximate equivalent variance of the processed impulse noise. It is the identity matrix. This represents the conjugate transpose. This equivalent reconstruction transforms the impulse noise model, which cannot be directly calculated for its second-order covariance, into a standard Gaussian noise covariance structure, thus enabling the effective application of subspace-based DOA estimation algorithms.

[0076] 3. Array vectorization and extraction of continuous SDCA

[0077] After obtaining the second step of construction Frame EAOMF covariance matrix Subsequently, this invention extracts continuous SDCA information containing a large number of degrees of freedom from a finite number of physical array elements through matrix vectorization and redundancy removal operations. The specific operations are as follows:

[0078] First, regarding the covariance matrix Perform vectorization operations using the Khatri-Rao product ( Transform it into an equivalent single snapshot vector of a virtual array. :

[0079] (13)

[0080] Equation (13) vectorizes the matrix using the Khatri-Rao product to obtain the equivalent single-shot signal of the virtual array, where, This is the equivalent signal power vector. At this point, the direction matrix is ​​reduced to... It essentially contains the exponential terms of all the difference comatrixes and sum comatrixes of the physical array element positions.

[0081] To separate the structured difference comatrix and sum comatrix elements from the messy vectorization results, this invention constructs a row transformation matrix. ,in Represent a block diagonal matrix, multiply it by a vector on the left. The reconstructed single-speed vector is obtained. :

[0082] (14)

[0083] Equation (14) uses row transformation matrix The mixed virtual array elements are classified and integrated into structured difference co-arrays and positive-negative sum co-arrays, among which... .go through The linear transformation of the matrix divides the originally mixed virtual matrix elements into four parts, each corresponding to a continuous difference matrix element form. And positive, negative and co-array element forms with non-circular phases. and .

[0084] because The presence of virtual elements with numerous overlapping locations and discontinuous holes directly applied to DOA estimation leads to limited DOFs and phase ambiguity. This invention first introduces a selection matrix. Spatial averaging and redundancy removal are performed on the overlapping matrix elements to obtain the redundancy-removed vector. :

[0085] (15)

[0086] Equation (15) utilizes the selection matrix Spatial averaging is performed on redundant virtual array elements generated by physical array overlap to further reduce noise. This involves selecting a matrix... Its non-zero elements are arranged according to Values, For virtual array element positions The weight function at a given location (i.e., the number of physical element pairs that generate virtual elements at that location) is used to achieve spatial averaging noise reduction for overlapping elements.

[0087] Subsequently, by defining an index vector to remove discontinuous element positions, the final continuous SDCA equivalent single snapshot vector is extracted. , can be represented as:

[0088] (16)

[0089] in, This is the equivalent noise vector of the transformed continuous SDCA. The extracted continuous SDCA direction matrix has a form that strictly corresponds to the form from arrive Continuously arranged virtual array elements:

[0090] (17)

[0091] Equations (16) and (17) ultimately yield a large and completely continuous SDCA direction matrix by eliminating discontinuous voids. .

[0092] Through this step, the present invention maps the physical FNA to a virtual continuous SDCA. Unlike traditional methods that only utilize the difference comatrix, the present invention utilizes the unique "sum comatrix" information of non-circular signals, enabling the continuous virtual aperture range to reach... This significantly breaks through the Rayleigh diffraction limit of traditional arrays without increasing the cost of any physical antenna hardware, providing a rich reserve of space DOFs for resolving more coherent / incoherent sound source targets under strong impulse noise.

[0093] 4. Multi-frame joint and full-rank space covariance matrix calculation

[0094] In the traditional differential covariance matrix extraction process of sparse arrays, vectorization operations cause the signal to become a single-shot coherent source model, which usually requires the introduction of SS (Quick Spectrum Speech) technology for decoherence. However, this inevitably leads to loss of continuous virtual array aperture. This invention utilizes the QSS characteristics of speech signals to directly reconstruct the full-rank covariance matrix through multi-frame joint reconstruction. The specific steps are as follows:

[0095] First, the received total For each frame of the QSS audio signal, perform the above operations to obtain the corresponding continuous SDCA equivalent single snapshot vector for each frame. This The column vectors are concatenated column by column to form a multi-frame joint equivalent received signal matrix. :

[0096] (18)

[0097] in, It is a vector of all 1s. It is the equivalent signal power matrix composed of the equivalent signal power of each frame.

[0098] Then, using the above equivalent received signal matrix Calculate the spatial covariance matrix of continuous SDCA. :

[0099] (19)

[0100] Formula (18) combined For each data frame, the spatial covariance matrix is ​​directly calculated using equation (19). It is at full capacity.

[0101] Because the second-order statistics of the speech signal are time-varying (i.e., QSS characteristics) between different time frames, when processing the number of frames... Much greater than the target number of information sources At that time, the signal matrix composed of the power of each frame Naturally maintained in a state of full rank (rank is Therefore, the matrix It can be directly regarded as having The noncoherent SDCA received signal in one effective snapshot. This mechanism allows the present invention to completely eliminate its dependence on SS technology and retain all virtual arrays (DOFs) extracted in step three.

[0102] 5. DOA estimation and non-circular phase cancellation based on RD-MUSIC

[0103] Because this invention utilizes non-circular signals, the non-circular phase of the signal is inevitably coupled in the positive and negative and common arrays. Traditional MUSIC algorithms typically require two-dimensional peak search (2D-MUSIC), which is computationally extremely expensive. This invention proposes a dimension-reduced RD-MUSIC method, the specific solution process of which is as follows:

[0104] First, the continuous SDCA space covariance matrix obtained in the previous step... Perform EVD to separate the signal subspace and the corresponding noise subspace matrix. .

[0105] Secondly, in order to reduce the search dimensionality, the direction vector of the continuous SDCA is reconstructed. By utilizing its internal structural characteristics, it is decomposed into matrices that independently contain DOA information. With vectors containing non-circular phase The product form:

[0106] (20)

[0107] Equation (20) utilizes the algebraic structure of the SDCA direction vector to transform the matrix containing only DOA. With vectors containing only non-circular phases Separately, among them, .

[0108] Subsequently, leveraging the orthogonality between the noise subspace and the direction vector, the denominator term of the two-dimensional spectral function is defined and matrix algebraic transformations are performed to extract the core dimension reduction matrix. :

[0109] (twenty one)

[0110] Equation (21) combines the noise subspace Construct a dimension with only matrix The matrix The dimension is only And only with the angle to be determined related.

[0111] Finally, set the selection vector. Construct the one-dimensional spatial spectral function of RD-MUSIC:

[0112] (twenty two)

[0113] Equation (22), combined with the selection vector, allows for the direct calculation of the one-dimensional spatial spectrum. Within the defined spatial angular domain, the spatial spectrum function is searched through a one-dimensional traversal. The highest spectral peak. The angular position corresponding to the spectral peak is the accurate DOA estimate for each non-circular speech signal. .

[0114] By reconstructing the array vectors and performing algebraic dimension reduction transformation, this method completely eliminates the non-circular phase. Interference with the search process. The original The computational cost of the two-dimensional search at the level was reduced to The one-dimensional search at the level of precision significantly improves the execution efficiency of the algorithm while ensuring high accuracy.

[0115] IV. Experimental Simulation Analysis and Performance Analysis

[0116] To verify the effectiveness of the above method, multiple simulation experiments were conducted in this invention, and the experimental performance was analyzed. In an impulse noise environment, the generalized signal-to-noise ratio (GSNR) is defined as:

[0117] (twenty three)

[0118] The performance estimation standard is defined as the joint root mean square error (RMSE):

[0119] (twenty four)

[0120] in, For the first In the second MC test, the first The precise estimate of DOA for each source. This indicates the number of information sources, and MC represents the number of Monte Carlo trials.

[0121] This invention also provides a direction-of-arrival estimation system for non-circular speech signals under impulse noise, used to implement the aforementioned direction-of-arrival estimation method, comprising the following modules:

[0122] The covariance matrix module is used to receive multi-frame non-circular QSS speech signals obtained based on a flipped nested array, calculate the adaptive exponent based on local entropy, and construct the EAOMF covariance matrix for each signal frame.

[0123] The equivalent single snapshot vector module is used to vectorize the covariance matrix to obtain a single snapshot vector and extract the equivalent single snapshot vector of the continuous sum-difference comatrix SDCA containing the expanded virtual array aperture.

[0124] The spatial covariance matrix module is used to combine the equivalent single-shot vectors of all time frames into a multi-frame joint equivalent received signal matrix and calculate the corresponding spatial covariance matrix.

[0125] The direction-of-arrival (DOA) estimation module performs eigenvalue decomposition on the spatial covariance matrix to obtain the noise subspace, constructs a dimension-reduced spectral function matrix, calculates the one-dimensional spatial spectrum of RD-MUSIC, and obtains the DOA estimate of the signal through the one-dimensional spectral peak.

[0126] The method of this invention is compared with existing methods, including a non-circular enhanced bounded nonlinear covariance method based on nested arrays, a non-circular enhanced fractional low-order moment method based on coprime arrays, and an augmented phase fractional low-order moment method based on nested arrays. All of the above existing methods are based on non-circular signals and sparse array backgrounds.

[0127] Figure 3 In the impulse noise characteristic index The value is 0.5, the number of snapshots. The total number of signal frames is 500. Comparison of algorithm performance under different GSNR values ​​with a GSNR of 20. This figure represents the result of 1000 MC experiments, with the azimuth angles of the three sources being... The corresponding non-circular phase is It can be seen that the RMSE of all algorithms decreases with the increase of GSNR. Under the same GSNR conditions, the FNA-EAOMF algorithm proposed in this invention has the lowest RMSE and is closest to the Cramer-Rao lower bound (CRB).

[0128] Figure 4 In the impulse noise characteristic index The value is 0.5, and the generalized signal-to-noise ratio (GSNR) is... Total number of signal frames Comparison of algorithm performance under different snapshot numbers with a snapshot count of 20. This figure shows 1000 McAfee experiments run, with the azimuth angles of the three sources being... The corresponding non-circular phase is It can be seen that the performance of the present invention improves with the increase of the number of snapshots, and under the same snapshot conditions, the estimation performance of the present invention is consistently significantly better than other comparative methods.

[0129] Figure 5 At GSNR Quick shot number The total number of signal frames is 500. When the value is 20, different impulse noise characteristic indices Performance comparison of algorithms (with values ​​ranging from 0.2 to 1). This figure shows the results of 1000 MC experiments, with the azimuth angles of the three sources being... The corresponding non-circular phase is It can be seen that in strong impulse noise ( In environments where the RMSE is less than 1), the method of this invention consistently maintains the lowest and relatively stable RMSE, and its estimation performance is significantly better than that of existing comparative algorithms.

[0130] In summary, analysis of the simulation results shows that the proposed FNA-based DOA estimation method for QSS speech signals in impulse noise environments achieves accurate DOA estimation using FNA, improving the degrees of freedom. Compared with existing methods such as non-circular enhanced bounded nonlinear covariance based on nested arrays, non-circular enhanced fractional low-order moment based on coprime arrays, and augmented phase fractional low-order moment based on nested arrays, this invention fully utilizes quasi-stationary characteristics without sacrificing the virtual array aperture using spatial smoothing techniques, resulting in superior estimation performance. The DOA estimation method described in this invention can be executed using a computing device containing a processor and memory. In practical applications, the analog speech signal received by the FNA is sampled by an analog-to-digital converter and then fed into the processor to execute the digital signal processing algorithm described above, ultimately outputting the DOA estimation result of the sound source.

[0131] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise, characterized in that, Includes the following steps: S1. Receive multiple frames of non-circular QSS speech signals obtained based on a flipped nested array, calculate the adaptive exponent based on local entropy, and construct the EAOMF covariance matrix for each signal frame. The adaptive index is calculated as follows: Based on the virtual continuous sum-difference comatrix (SDCA), the received speech signal is amplitude normalized; based on the normalized sequence, the local entropy of the speech signal within the current time frame is calculated. Quantize the intensity of impulse noise during that period; Comprehensive Impulse Noise Characteristic Index Amplitude adjustment factor and local entropy ,pass and The ratio is used to calculate the adaptive exponent for constructing subsequent matrices. ,in Represents the natural logarithm; The covariance matrix is ​​calculated as follows: First, based on the non-circular characteristics of the target speech signal, the non-circular speech signal received by the extended array is represented as follows: ; Subsequently, the first step regarding the QSS voice signal A time frame, using the signed exponentiation operator Perform a nonlinear transformation on the extended received signal, the first... The covariance matrix of the i-th time frame in EAOMF The nth sub-block matrix The formula for calculating each element is defined as follows: ,in, This represents the operation of calculating mathematical expectation. For extended non-circular speech signals elements, This indicates the application of an adaptive exponent to the extended signal components. The sign exponentiation operation; All calculated elements Assemble according to the corresponding index to construct the complete first... Covariance matrix of frame EAOMF blocks: , to Sub-matrix blocks corresponding to the four quadrants; S2. Vectorize the covariance matrix to obtain a single snapshot vector, and extract the equivalent single snapshot vector of the continuous sum-difference comatrix SDCA containing the extended virtual array aperture. S3. Combine the equivalent single-shot vectors of all time frames into a multi-frame joint equivalent received signal matrix, and calculate the corresponding spatial covariance matrix. S4. Perform eigenvalue decomposition on the spatial covariance matrix to obtain the noise subspace, construct the dimension-reduced spectral function matrix, and calculate the one-dimensional spatial spectrum of RD-MUSIC. Obtain the DOA estimate of the signal through the one-dimensional spectral peak.

2. The method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise according to claim 1, characterized in that, The virtual continuous sum-difference comatrix SDCA is specifically implemented as follows: Assume the physical array consists of two subarrays and Composition, the total number of physical array elements is Subarray It is a dense linear array, composed of It consists of 1 array element, with the spacing between adjacent array elements being 1. subarray It is a sparse linear array, composed of Composed of individual array elements; By combining and splicing continuous segments from the difference comatrix and sum comatrix corresponding to the physical array, a continuous sum-difference comatrix (SDCA) is formed. The resulting virtual array elements are continuously distributed and located within the interval. ,in and These represent the discrete set of integers and their union, respectively; the final range of the continuous virtual aperture is... The array structure parameters are as follows: and .

3. The method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise according to claim 2, characterized in that, The specific implementation process of step S2 is as follows: First, for the covariance matrix Perform vectorization operations, using the Khatri-Rao product to... Equivalent single-snap vector converted to a virtual array ; Construct a row transformation matrix ,in Representing a block diagonal matrix, multiplying the row transformation matrix by a vector on the left. The reconstructed single snapshot vector is obtained. ; Introducing the selection matrix With single snapshot vector Multiplication is performed on the overlapping matrix elements, followed by spatial averaging and redundancy removal to obtain the redundancy-removed vector. , where the selection matrix , According to the zero element of China and Africa Values, For virtual array element positions Weight function at the location; Subsequently, by defining an index vector to remove discontinuous element positions, the final continuous SDCA equivalent single snapshot vector is extracted. .

4. The method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise according to claim 3, characterized in that, The specific implementation process of step S3 is as follows: For the received total From the QSS audio signal, obtain the equivalent single snapshot vector of continuous SDCA for each frame. , will this The column vectors are concatenated column by column to form a joint equivalent received signal matrix for multiple frames. ; Then, using the equivalent received signal matrix Calculate the spatial covariance matrix of continuous SDCA. .

5. The method for estimating the direction of arrival (DOA) of non-circular speech signals under impulse noise according to claim 4, characterized in that, The specific implementation process of step S4 is as follows: The spatial covariance matrix of the obtained continuous SDCA Eigenvalue decomposition (EVD) is performed to separate the signal subspace and the corresponding noise subspace matrix. ; Secondly, reconstruct the direction vector of continuous SDCA. , The DOAs are respectively It is decomposed into matrices that independently contain DOA information. With vectors containing non-circular phase The product form; Subsequently, leveraging the orthogonality between the noise subspace and the direction vector, the denominator term of the two-dimensional spectral function is defined and matrix algebraic transformations are performed to extract the dimension-reduced matrix. , Indicates conjugate transpose; Finally, set the selection vector. Based on the dimension reduction matrix, a one-dimensional spatial spectrum function of RD-MUSIC is constructed, and the one-dimensional spatial spectrum is calculated. Within the set spatial angle domain, the highest spectral peak of the one-dimensional spatial spectrum function is searched by one-dimensional traversal. The angle position corresponding to the spectral peak is the accurate DOA estimate of each non-circular speech signal.

6. A direction-of-arrival estimation system for non-circular speech signals under impulse noise, used to implement the direction-of-arrival estimation method according to any one of claims 1 to 5, characterized in that, Includes the following modules: The covariance matrix module is used to receive multi-frame non-circular QSS speech signals obtained based on a flipped nested array, calculate the adaptive exponent based on local entropy, and construct the EAOMF covariance matrix for each signal frame. The equivalent single snapshot vector module is used to vectorize the covariance matrix to obtain a single snapshot vector and extract the equivalent single snapshot vector of the continuous sum-difference comatrix SDCA containing the expanded virtual array aperture. The spatial covariance matrix module is used to combine the equivalent single-shot vectors of all time frames into a multi-frame joint equivalent received signal matrix and calculate the corresponding spatial covariance matrix. The direction-of-arrival (DOA) estimation module performs eigenvalue decomposition on the spatial covariance matrix to obtain the noise subspace, constructs a dimension-reduced spectral function matrix, calculates the one-dimensional spatial spectrum of RD-MUSIC, and obtains the DOA estimate of the signal through the one-dimensional spectral peak.

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