A method, device and electronic equipment for direction of arrival estimation based on a two-stage denoising neural network

Abstract

The application provides a two-stage denoising neural network-based direction of arrival estimation method, device and electronic equipment. The method comprises the following steps: constructing an array receiving signal matrix and extracting an amplitude matrix and a phase matrix according to the receiving signal of a linear uniform array; extracting the median of all elements in the amplitude matrix and performing range compression to obtain an amplitude statistical feature; inputting the amplitude statistical feature into an adaptive threshold subnetwork to generate a compression coefficient; performing amplitude limiting processing on the amplitude matrix by using the compression coefficient, combining the new amplitude matrix and the phase matrix into a limited amplitude signal matrix; constructing a bounded covariance matrix with a second-order statistical form based on the limited amplitude signal matrix; inputting the bounded covariance matrix into a complex residual convolution subnetwork to generate a noise residual matrix; obtaining an equivalent covariance matrix based on the bounded covariance matrix and the noise residual matrix; and performing spatial spectrum search on the equivalent covariance matrix by using a MUSIC method to obtain a direction of arrival estimation result of a signal source.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and more specifically to a method, apparatus, and electronic device for direction-of-arrival estimation based on a two-stage denoising neural network. Background Technology

[0002] Direction of Arrival (DOA) estimation, as the core of array signal processing, has extremely high application value in fields such as radar, wireless communication, and seismic detection. Its goal is to accurately determine the azimuth angles of multiple incident signals. Subspace-based methods based on eigenvalue decomposition, with their super-resolution characteristics, were once considered classic approaches in this field. However, these methods heavily rely on the Gaussian noise assumption. In practical engineering, transient electromagnetic interference and sudden interference from mechanical and electrical equipment often cause array received signals to be affected by non-Gaussian impulse noise. Since impulse noise lacks second-order statistics, the physical description of the array received signal covariance matrix fails, leading to the failure of traditional subspace-based algorithms, such as MUSIC. Although researchers have proposed methods to suppress impulse noise, such as fractional low-order statistics and correlation entropy operators, significant shortcomings remain. First, some methods rely on prior knowledge of noise, manually preset thresholds, or fixed empirical parameters, making it difficult to achieve stable performance when the noise intensity is unknown. Second, when the spatial angles of multiple targets are extremely close and in a low signal-to-noise ratio environment, existing robust algorithms struggle to extract the true signal phase features from strong interference.

[0003] In recent years, deep learning methods have been introduced into the field of direction-of-arrival (DOA) estimation. These methods typically input received snapshot data, the covariance matrix, or their derived features into a neural network, and then estimate the angle through classification, regression, or spatial spectrum reconstruction. These methods have shown certain advantages in scenarios with low signal-to-noise ratios, array errors, and insufficient snapshot numbers. However, most existing deep learning-based ODA methods still rely on Gaussian white noise or slightly perturbed environments, and their input features usually depend on the original snapshots or sample covariance matrices. When the received signal is contaminated by strong impulse noise, abnormal amplitude points severely disrupt the covariance structure before feature extraction, making it difficult for the network to simultaneously achieve impulse noise suppression, inter-element phase information preservation, and high-resolution spatial spectrum reconstruction. Summary of the Invention

[0004] In view of this, the present invention proposes a direction-of-arrival estimation method, device and electronic device based on a two-stage denoising neural network, which can adaptively suppress abnormal pulse components in the received signal without relying on manual thresholds or fixed empirical parameters, while maintaining the spatial phase relationship in the array signal, and improving the accuracy and resolution of direction-of-arrival estimation under low snapshot, low generalized signal-to-noise ratio and close-range multi-source conditions.

[0005] Specifically, the present invention is achieved through the following technical solution:

[0006] According to a first aspect of the embodiments of this specification, a direction-of-arrival estimation method based on a two-stage denoising neural network is provided. The two-stage denoising neural network includes an adaptive thresholding subnetwork and a complex residual convolutional subnetwork. The direction-of-arrival estimation method includes the following steps:

[0007] Step S1: Receive signals from each signal source within the target area using a uniform linear array; construct an array received signal matrix based on the received signals; and perform amplitude-phase decomposition on the array received signal matrix to obtain the amplitude matrix and phase matrix.

[0008] Step S2: Extract the median of the amplitude matrix and perform range compression to obtain amplitude statistical features;

[0009] Step S3: Input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity;

[0010] Step S4: The amplitude matrix is ​​limited using the compression coefficient, and the new amplitude matrix after limiting is combined with the phase matrix to construct a limited signal matrix;

[0011] Step S5: Construct a bounded covariance matrix based on the amplitude-limited signal matrix;

[0012] Step S6: Input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix.

[0013] Step S7: Subtract the bounded covariance matrix from the noise residual matrix to obtain the equivalent covariance matrix;

[0014] Step S8: Perform eigenvalue decomposition on the equivalent covariance matrix to obtain the noise subspace, construct a spatial spectrum function using the noise subspace, and determine the estimated direction of arrival (DOA) of each source by searching for spectral peaks.

[0015] According to a second aspect of the embodiments of this specification, a direction-of-arrival estimation device based on a two-stage denoising neural network is provided, the two-stage denoising neural network including an adaptive threshold subnetwork and a complex residual convolution subnetwork, the direction-of-arrival estimation device comprising:

[0016] The data acquisition unit is used to receive signals emitted by various signal sources within the target area through a uniform linear array, construct an array received signal matrix based on the received signals, and perform amplitude-phase decomposition on the array received signal matrix to obtain an amplitude matrix and a phase matrix.

[0017] The feature statistics unit is used to extract the median of the amplitude matrix and perform range compression to obtain amplitude statistical features;

[0018] An adaptive mapping unit is used to input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity.

[0019] The signal reconstruction unit uses the compression coefficient to perform amplitude limiting on the amplitude matrix, and combines the new amplitude matrix with the phase matrix to construct a limited signal matrix.

[0020] A covariance construction unit is used to construct a bounded covariance matrix based on the amplitude-limited signal matrix.

[0021] The noise estimation unit is used to input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix.

[0022] The noise removal unit subtracts the bounded covariance matrix from the noise residual matrix to obtain an equivalent covariance matrix;

[0023] The direction-of-arrival (DOA) estimation unit is used to perform eigenvalue decomposition on the equivalent covariance matrix to obtain a noise subspace, construct a spatial spectrum function using the noise subspace, and determine the DOA estimates of each source by searching for spectral peaks.

[0024] According to a third aspect of the embodiments of this specification, an electronic device is provided, comprising: a processor; and a computer-readable storage medium storing computer program instructions that, when executed by the processor, cause the processor to perform the method as described in the first aspect.

[0025] The embodiments of the present invention have at least the following technical effects:

[0026] (1) It can adaptively adjust the compression degree of pulse anomaly values ​​according to the current array received signal;

[0027] (2) It can retain the spatial phase information required for DOA estimation while suppressing abnormal pulse amplitude, thereby improving the accuracy of DOA estimation and the ability to distinguish adjacent information sources;

[0028] (3) Further improve the covariance matrix purification effect through residual learning;

[0029] (4) It does not rely on prior knowledge of noise or other fixed empirical parameters. Attached Figure Description

[0030] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Some specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings in an exemplary and non-limiting manner. The same reference numerals in the drawings indicate the same or similar parts or components. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings:

[0031] Figure 1 This is a schematic diagram illustrating the overall process of direction-of-arrival estimation according to an exemplary embodiment of the present invention;

[0032] Figure 2 This is a flowchart illustrating an exemplary embodiment of the present invention of a direction-of-arrival estimation method based on a two-stage denoising neural network;

[0033] Figure 3 This is a schematic diagram of the structure of an adaptive threshold subnetwork shown in an exemplary embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the structure of a complex residual convolutional subnetwork shown in an exemplary embodiment of the present invention;

[0035] Figure 5 This is a comparison chart of the root mean square error of the method of the present invention and the comparative method under different generalized signal-to-noise ratio conditions, as shown in an exemplary embodiment of the present invention.

[0036] Figure 6 This is a comparison chart of the root mean square error of the method of the present invention and the comparative method under different snapshot numbers, as shown in an exemplary embodiment of the present invention.

[0037] Figure 7 This is a comparison chart of the root mean square error of the method of the present invention and the comparative method under different characteristic index conditions, as shown in an exemplary embodiment of the present invention.

[0038] Figure 8 This is a block diagram illustrating an electronic device according to an exemplary embodiment of the present invention;

[0039] Figure 9 This is a block diagram illustrating a direction-of-arrival estimation device based on a two-stage denoising neural network, as shown in an exemplary embodiment of the present invention. Detailed Implementation

[0040] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the invention as detailed in the appended claims.

[0041] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The singular forms “a,” “the,” and “the” used in this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0042] Traditional direction-of-arrival (DOA) estimation algorithms are generally based on Gaussian noise models. However, in real-world radar, wireless communication, sonar, and industrial sensing environments, transient electromagnetic interference, mechanical and electrical equipment start-up and shutdown interference, and intermittent co-channel interference may exist. These types of noise typically exhibit obvious spikes and heavy tails, making them difficult to accurately describe using a Gaussian distribution with finite variance.

[0043] To solve the above problems, a method was introduced. Stable distribution model. Because... The probability density function of a stable distribution typically does not have a uniform closed-form probability density function; therefore, auxiliary characteristic functions are used. Describe its statistical properties:

[0044] (1)

[0045] in, , , The imaginary unit, The variable is the characteristic function;

[0046] It is a characteristic index used to characterize the impulse level of noise, ranging from... ,when The time distribution is a Gaussian distribution;

[0047] It is a dispersion parameter, and its meaning is consistent with the variance of the Gaussian distribution;

[0048] It is a skewness parameter. It is a position parameter, when The distribution of time is symmetrical Stable distribution, also known as distributed; The distribution represents different probability density functions depending on the choice of parameters; In distribution The smaller the pulse, the more pronounced it is; conversely... The larger the value, the closer the noise is to Gaussian noise;

[0049] 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 is ​​inaccurate.

[0050] This embodiment employs a uniform linear array composed of M omnidirectional array elements, with a spacing of d between adjacent elements. Assume there are K independent far-field narrowband incoherent sources within the target region, with directions of arrival of [missing information]. The signal received by the i-th element in the l-th time snapshot is represented as:

[0051] (2)

[0052] in, This represents the signal of the k-th source at the l-th time snapshot.

[0053] The pulse noise received by the i-th array element;

[0054] Let be the steering coefficient of the k-th source relative to the i-th array element. The signal wavelength corresponds to the direction. The array steering vector is .

[0055] By writing the received signals of each array element in a snapshot at the same time into vector form, we can obtain:

[0056] (3)

[0057] in, , , .

[0058] By acquiring L consecutive time snapshots, an array receiving signal matrix can be formed. .

[0059] In an ideal Gaussian noise environment, the covariance matrix is ​​usually expressed as:

[0060] (4)

[0061] However, under impulse noise conditions, there are no second-order statistics, so it is necessary to construct an equivalent covariance matrix. In this example, the equivalent covariance matrix is ​​obtained through a two-stage denoising neural network.

[0062] like Figure 1 As shown, the design principle of this invention is as follows:

[0063] 1. By receiving signals from a signal source using a uniform linear array, the received signal matrix is ​​first decomposed into amplitude and phase matrices. Then, the amplitude statistical characteristics representing the overall amplitude of the received signal matrix are obtained from the amplitude matrix and input into an adaptive threshold sub-network to obtain adaptive compression coefficients. These compression coefficients are then used to perform soft amplitude limiting on the received signal matrix. Simultaneously, this is combined with the phase matrix of the original received signal to obtain a limited array signal matrix that preserves the phase relationship between array elements. Therefore, this invention can adaptively determine the degree of amplitude compression based on the statistical characteristics of the currently received data, without the need to pre-set thresholds, fractional low-order moment parameters, or related entropy kernel width parameters.

[0064] 2. A bounded covariance matrix is ​​constructed based on the amplitude-limited array signal matrix and input into a complex residual convolutional subnetwork. This subnetwork jointly processes the real and imaginary parts of the covariance matrix in the complex domain. Through multi-layer complex-valued convolution, complex-valued batch normalization, and complex-valued nonlinear activation operations, it extracts the spatial correlation features between different array elements and outputs a noise residual matrix. Then, the equivalent clean covariance matrix is ​​obtained by subtracting the noise residual matrix from the bounded covariance matrix. Finally, the accurate direction-of-arrival (DOA) estimate can be obtained through the MUSIC method. By using residual learning, this subnetwork mainly learns the perturbation of the bounded covariance matrix caused by impulse noise, without needing to relearn the complete bounded covariance matrix. This helps reduce the learning difficulty of the network and improves the stability of the bounded covariance matrix purification.

[0065] 3. During the network training phase, this invention employs a joint loss function to jointly optimize the adaptive threshold sub-network and the complex residual convolution sub-network. The joint loss function includes off-diagonal covariance reconstruction loss and spatial spectrum alignment loss. The off-diagonal covariance reconstruction loss masks the element autocorrelation terms on the main diagonal of the covariance matrix, allowing the network to focus on learning off-diagonal elements containing phase differences and spatial cross-correlation information between elements, thus reducing the dominant role of high-amplitude diagonal elements in the network training process. The spatial spectrum alignment loss constrains the difference between the spatial spectrum obtained from the reconstructed covariance matrix and the reference spatial spectrum constructed from the true source direction, ensuring that the reconstructed spatial spectrum forms more accurate, clear, and distinguishable spectral peaks near the true source direction.

[0066] 4. After completing network training, the actual array received signal matrix is ​​sequentially input into the adaptive dynamic threshold network and the complex residual convolutional network to obtain the reconstructed equivalent pure covariance matrix; the equivalent pure covariance matrix is ​​decomposed into eigenvalues ​​to obtain the signal subspace and noise subspace, and the spatial spectrum is constructed using the MUSIC algorithm. The direction of arrival estimation result of the signal source is obtained by searching for the spectral peak position in the spatial spectrum.

[0067] The following detailed explanation of each step is provided in conjunction with the accompanying drawings.

[0068] This invention provides a direction-of-arrival estimation method based on a two-stage denoising neural network, wherein the two-stage denoising neural network includes an adaptive threshold sub-network and a complex residual convolution sub-network. Figure 2 This is a flowchart illustrating an exemplary embodiment of the present invention of a direction-of-arrival estimation method based on a two-stage denoising neural network, as shown below. Figure 2 As shown, the direction-of-arrival estimation method includes the following steps:

[0069] Step S1: Receive signals from various signal sources within the target area using a uniform linear array. Construct an array received signal matrix based on the received signals and perform amplitude-phase decomposition on the array received signal matrix to obtain the amplitude matrix and phase matrix.

[0070] This step constructs an array received signal matrix based on the complex domain received signals of each array element in the uniform linear array under multiple time snapshots. Each complex element in the array received signal matrix is ​​decomposed into amplitude and phase to obtain an amplitude matrix that characterizes the signal amplitude distribution characteristics and a phase matrix that characterizes the signal phase distribution characteristics.

[0071] Step S2: Extract the median of the amplitude matrix and compress its range to obtain amplitude statistical features.

[0072] This step extracts the median of all elements in the amplitude matrix and compresses the range of the median to obtain amplitude statistical features that reflect the overall amplitude level of the current array received signal.

[0073] Step S3: Input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity.

[0074] This step inputs the amplitude statistical features into the adaptive threshold subnetwork, which is used to perform adaptive mapping based on the amplitude statistical features to generate compression coefficients for controlling the amplitude compression intensity.

[0075] Step S4: The amplitude matrix is ​​limited using the compression coefficient, and the new amplitude matrix after limiting is combined with the phase matrix to construct a limited signal matrix.

[0076] This step uses the compression coefficient to limit the amplitude of each element in the amplitude matrix, and combines the new amplitude matrix after the limiting process with the phase matrix to construct a limited signal matrix.

[0077] Step S5: Construct a bounded covariance matrix based on the amplitude-limited signal matrix.

[0078] This step involves performing a conjugate transpose multiplication operation on the amplitude-limited signal matrix to construct a bounded covariance matrix in the form of second-order statistics.

[0079] Step S6: Input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix.

[0080] This step inputs the bounded covariance matrix into the complex residual convolutional subnetwork, which is used to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and output the corresponding noise residual matrix.

[0081] Step S7: Perform a subtraction operation between the bounded covariance matrix and the noise residual matrix to obtain an equivalent covariance matrix.

[0082] Step S8: Perform eigenvalue decomposition on the equivalent covariance matrix to obtain the noise subspace, construct a spatial spectrum function using the noise subspace, and determine the estimated direction of arrival (DOA) of each source by searching for spectral peaks.

[0083] This step performs eigenvalue decomposition on the equivalent covariance matrix to obtain a noise subspace. A spatial spectrum function is constructed using the noise subspace. By performing a spectral peak search on the spatial spectrum function, the estimated direction of arrival (DOA) of each signal source is determined based on the searched peak positions.

[0084] Figure 2The proposed direction-of-arrival (DOA) estimation method extracts the median amplitude and inputs it into an adaptive threshold subnetwork, allowing the compression coefficients to be entirely driven by the currently received data. This eliminates reliance on manually preset thresholds, fractional low-order moment parameters, or kernel width parameters, enabling adaptive adjustment of the limiting force under various impulse noise intensities. By soft-limiting the amplitude matrix and directly reusing the phase matrix of the original signal for signal reconstruction, it ensures that the spatial phase difference relationship between array elements is preserved while suppressing abnormal impulse amplitudes, retaining crucial phase features for subsequent high-precision DOA estimation. Furthermore, by utilizing a complex residual convolution subnetwork combined with global skip connections, the network only needs to learn the noise residuals in the bounded covariance matrix instead of reconstructing the complete covariance from scratch. This reduces the learning difficulty of the network and effectively stabilizes the covariance matrix cleanup process, avoiding distortion of input features. Thus, the method of this invention can operate stably under extreme conditions such as strong impulse noise, low generalized signal-to-noise ratio, and a very small number of snapshots, where second-order statistics should be invalid.

[0085] Next, combined Figures 3 to 4 The direction of arrival estimation process of this invention is described in detail.

[0086] The direction-of-arrival (DOA) estimation method provided by this invention can be deployed and executed in one or more signal processing devices within an array signal processing system. These signal processing devices include, but are not limited to, general-purpose computers, embedded signal processing platforms, digital signal processors (DSPs), field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), or combinations thereof. Each signal processing device includes at least a processor and a memory, wherein the memory stores computer program instructions. When the processor executes these computer program instructions, the signal processing device performs the method described in this invention.

[0087] The first step of this system is to execute step T1, which obtains the received signal matrix through a uniform linear array.

[0088] As described above, a uniform linear array is used to receive signals from a signal source, and L time frames are collected to form an array-received signal matrix. .

[0089] Then, perform step T2 to extract the amplitude matrix and phase matrix.

[0090] This system receives signals from an array matrix. Perform amplitude-phase decomposition, the amplitude matrix is The m-th row and the first row of the matrix Column elements are The phase matrix is .

[0091] Next, proceed to step T3 to construct amplitude statistical features.

[0092] Abnormal amplitudes in impulse noise can be much larger than normal signal amplitudes. Directly inputting these abnormal amplitudes into a neural network can easily lead to gradient instability or neuron saturation. Therefore, this embodiment extracts the amplitude matrix. The median of all elements is obtained, and the dynamic range is compressed using a logarithmic function to obtain the amplitude statistics. :

[0093] (5)

[0094] in, It is the median operator.

[0095] Next, step T4 is executed to generate the adaptive compression coefficient.

[0096] Amplitude statistical characteristics The compression coefficient is obtained by inputting an adaptive threshold subnetwork. .

[0097] like Figure 3 As shown, the adaptive threshold subnetwork includes a first fully connected layer, an activation layer, a second fully connected layer, and a positive constraint layer connected in sequence. The first fully connected layer is used to map the input amplitude statistical features into hidden layer feature vectors. The activation layer uses the ReLU activation function to perform a nonlinear transformation on the hidden layer feature vectors. The second fully connected layer is used to map the nonlinearly transformed hidden layer feature vectors into a one-dimensional scalar. The positive constraint layer is used to perform positive value processing on the one-dimensional scalar to generate a compression coefficient greater than zero. The positive value processing uses the Softplus function or the absolute value function.

[0098] The compression coefficient of this embodiment Represented as:

[0099] (6)

[0100] in, and For trainable weights, and This is a trainable bias.

[0101] In this embodiment, the compression coefficient The amplitude is determined by the statistical characteristics of the signal received by the current array, rather than by a pre-fixed amplitude limiting threshold.

[0102] Next, step T5 is executed to perform amplitude soft limiting and phase recombination.

[0103] This embodiment utilizes the compression coefficient. For the amplitude matrix Parametric hyperbolic tangent limiting is applied. The hyperbolic tangent function allows large anomalous amplitudes to gradually enter the saturation region, thereby reducing the amplitude differences between pulse anomalies and avoiding discontinuous changes caused by hard truncation. The new amplitude matrix after limiting is then applied. Phase matrix of the original array received signal Recombining them yields a phase-preserving, amplitude-limited signal matrix. :

[0104] (7)

[0105] in, This indicates an element-wise addition operation.

[0106] This embodiment only compresses the amplitude portion, while the phase matrix comes from the original array received signal, which is beneficial for preserving the spatial phase relationship between different array elements.

[0107] Next, proceed to step T6 to construct the bounded covariance matrix.

[0108] According to the amplitude limiting signal matrix Construct a bounded covariance matrix :

[0109] (8)

[0110] in, This indicates the conjugate transpose operation.

[0111] Next, step T7 is performed to further denoise using a complex residual convolutional subnetwork.

[0112] In some embodiments, the complex residual convolutional subnetwork includes a first complex convolutional block, an intermediate complex convolutional block group, and an output complex convolutional layer arranged sequentially.

[0113] The first complex convolutional block includes a first complex convolutional layer and a first complex activation layer. The first complex convolutional layer is used to map the input bounded covariance matrix into a complex feature map, and the first complex activation layer uses a complex ReLU activation function to perform nonlinear activation on the complex feature map.

[0114] The intermediate complex convolutional block group includes a plurality of complex convolutional blocks connected in sequence. Each complex convolutional block includes a complex convolutional layer, a complex batch normalization layer and a second complex activation layer connected in sequence. Each complex convolutional layer uses the same complex convolutional kernel, and each second complex activation layer uses the complex ReLU activation function.

[0115] The output complex convolutional layer uses a 1×1 complex convolutional kernel to map the complex feature map into a single-channel noise residual matrix.

[0116] by Figure 4 As shown in the example, the complex residual convolutional subnetwork consists of 9 complex convolutional layers: the first layer uses 64 pixels of size 1.5. The complex convolution kernel will convert the input bounded covariance matrix... The map is mapped to a 64-channel complex feature map and connected to a complex ReLU activation layer; the middle 7 layers consist of complex convolutional layers, complex batch normalization layers, and complex ReLU activation layers, with each layer's output maintaining a 64-channel complex feature map; the last layer uses a single image with a size of... The complex convolution kernel maps the complex feature map to a single-channel noise residual matrix, and no activation function is applied after the last layer. The output of this sub-network is a noise residual matrix. Then, through a global jump connection, the bounded covariance matrix is... Subtracting the noise residual matrix Further denoising yields the equivalent covariance matrix. Instead of directly generating the complete equivalent covariance matrix, this network learns the noise residuals that need to be removed from the bounded covariance matrix, which helps to preserve the existing spatial correlation structure in the input matrix.

[0117] Next, proceed to step T8 to perform a MUSIC spatial spectrum search.

[0118] This embodiment is... Perform eigenvalue decomposition to obtain the noise subspace. And construct the spatial spectral function:

[0119] (9)

[0120] By searching the MUSIC spectrum peaks, the K largest peaks are identified, thus obtaining an accurate estimate of the DOA.

[0121] To verify the direction-of-arrival (DOA) estimation performance of the method of the present invention under impulse noise conditions, this embodiment of the invention also uses simulation data for network training and performance testing. For example, the number of elements in the uniform linear array is set to 16, the spacing between adjacent elements is half a wavelength, and the training data includes 30,000 training samples and 1,024 validation samples. In each training sample, one to three independent far-field narrowband sources are randomly selected, with the source directions located at... Within the specified range, the angular range is divided into 10,000 angular grids to construct a high-resolution reference spatial spectrum. The minimum angular interval between adjacent sources is 3°. During training, online dynamic data generation is employed, resampling the generalized signal-to-noise ratio, feature index, number of sources, and direction of arrival for each training batch, thereby increasing the diversity of noise conditions and spatial locations in the training samples. This invention is implemented using PyTorch and trained using a graphics processing unit.

[0122] This embodiment employs a joint loss function to jointly optimize the two-stage denoising neural network. The joint loss function includes off-diagonal covariance reconstruction loss and spatial spectrum alignment loss. First, based on the noise-free reference array signal matrix... Construct the reference covariance matrix :

[0123] (10)

[0124] Construct a mask matrix , It is a matrix of all ones. It is the identity matrix. A mask matrix with 0s on the main diagonal and 1s for the rest.

[0125] Then the non-diagonal covariance reconstruction loss Represented as:

[0126] (11)

[0127] in, This represents the Ferrobenius norm.

[0128] The off-diagonal covariance reconstruction loss masks the main diagonal autocorrelation terms in the covariance matrix, allowing the network to focus on learning the cross-correlation structure and phase relationship between different matrix elements.

[0129] Based on the equivalent covariance matrix Calculate the MUSIC spatial spectrum, denoted as A reference space spectrum is constructed based on the actual direction-of-arrival (DOA) labels, denoted as . The reference spatial spectrum is obtained by superimposing Gaussian kernels centered on each true direction of arrival, and the spatial spectrum alignment loss... Represented as:

[0130] (12)

[0131] The joint loss function Represented as:

[0132] (13)

[0133] Through the joint loss function A two-stage denoising neural network was trained to balance covariance matrix structure recovery and spatial spectral resolution.

[0134] To improve the training stability of the network in a strong impulse noise environment, this embodiment adopts a progressive training strategy.

[0135] For example, in the first 10 training epochs, the generalized signal-to-noise ratio (SNR) is randomly sampled from a relatively mild range of [0, 20] dB, allowing the network to first learn the basic mapping relationship between the array received signal and the spatial covariance structure. In subsequent training epochs, the SNR is adjusted to [-12, 5] dB, enabling the network to further learn the ability to suppress anomalous amplitudes and recover the covariance structure under conditions of low SNR and strong impulse noise. Throughout the training process, the characteristic exponent of symmetric α-stabilized noise is randomly sampled in the range of [1, 2]. By dynamically changing the SNR and characteristic exponent during training, the network is exposed to impulse interference of different intensities, reducing overfitting for single noise conditions.

[0136] To verify the effectiveness of the above methods, multiple simulation experiments were conducted in this embodiment. The comparison methods included the phase fractional low-order moment method PFLOM, the sign covariance matrix method SCM, and the improved squared correlation entropy method ISCO. Those skilled in the art can refer to the relevant technical solutions for the specific implementation schemes of these three comparison methods. The embodiments of this invention will not be described in detail here.

[0137] The performance evaluation metrics used in this experiment.

[0138] In an impulse noise environment, the generalized signal-to-noise ratio Defined as:

[0139] (14)

[0140] in, It is the mathematical expectation operator. It is a dispersion parameter.

[0141] The performance estimation standard is the root mean square error (RMSE), which is defined as follows:

[0142] (15)

[0143] in, For the first The exact estimate of the DOA of the k-th source in the second Monte Carlo process. This indicates the number of information sources, and MC represents the number of Monte Carlo trials.

[0144] Figure 5 This paper demonstrates the direction-of-arrival (DOA) estimation errors of the method of this invention and different comparative methods under various generalized signal-to-noise ratio (SNR) conditions. In this experiment, three independent far-field narrowband sources were set up, with DOAs of [missing information]. Two adjacent signal sources are spaced at a minimum angle of 4° to test the resolution capability of small-angle-spaced signal sources. An impulse noise characteristic index is set. The number of snapshots L=100, the number of Monte Carlo simulations is 500, and the generalized signal-to-noise ratio varies from -10dB to 8dB.

[0145] Experimental results show that as the generalized signal-to-noise ratio (SNR) increases, the root mean square (RMS) error of each method generally decreases. However, under low SNR conditions, the comparative methods are significantly affected by pulse anomalies, resulting in relatively high errors. The method of this invention can enter the low-error region more quickly as the SNR increases, and reduces the RMS error to below approximately 2° when the SNR reaches around -2dB.

[0146] Figure 6 The method of this invention and different comparative methods are shown to have different directions of arrival (DOA) estimation errors at different snapshot numbers. In this experiment, the source direction and... Figure 5 The comparison experiment was the same, and the impulse noise characteristic index was set. The generalized signal-to-noise ratio is 2dB, and the number of snapshots L varies from 25 to 200.

[0147] Experimental results show that the comparison method tends to have large estimation errors when the number of snapshots is small, while the method of this invention can still achieve a relatively low root mean square error with only 25 snapshots and maintains relatively stable estimation performance throughout the entire snapshot test range. These results indicate that the method of this invention is suitable for array signal processing scenarios with a limited number of snapshots.

[0148] Figure 7 The diagram illustrates the direction-of-arrival (DOA) estimation errors of the method of this invention and different comparative methods under various impulse noise characteristic exponents. (Source direction and...) Figure 5 The comparison experiment was the same, with the number of snapshots L=100, the generalized signal-to-noise ratio of 2dB, and the feature index ranging from 0.2 to 2.

[0149] Experimental results show that when the characteristic exponent is small, the noise is more impulsive, and the estimation error of various robust methods increases significantly. The method of this invention can still maintain stable direction-of-arrival estimation results under strong impulse noise conditions. Under extremely strong impulse test conditions with a characteristic exponent of approximately 0.8, the root mean square error of the method of this invention is less than 1°.

[0150] Figure 8 This is a schematic diagram of an electronic device illustrated in this specification according to an exemplary embodiment. Please refer to... Figure 8At the hardware level, the device includes a processor 810, an internal bus 820, a network interface 830, memory 840, a hardware acceleration device 850, and non-volatile memory 860, and may also include other hardware required for its functions. One or more embodiments of the present invention can be implemented in software, for example, the processor 810 reads the corresponding computer program from the non-volatile memory 860 into the memory 840 and then runs it. Of course, in addition to software implementation, one or more embodiments of the present invention do not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the above processing flow is not limited to each logic unit, but can also be hardware or logic devices.

[0151] Figure 9 This is a structural block diagram of a direction-of-arrival (DOA) estimation device based on a two-stage denoising neural network, as illustrated in an exemplary embodiment of the present invention. The DOA estimation device can be applied to applications such as... Figure 8 The electronic device shown implements the technical solution of the present invention. The direction-of-arrival estimation device includes:

[0152] The data acquisition unit 910 is used to receive signals emitted by various signal sources within the target area through a uniform linear array, construct an array received signal matrix based on the received signals, and perform amplitude-phase decomposition on the array received signal matrix to obtain an amplitude matrix and a phase matrix.

[0153] The feature statistics unit 920 is used to extract the median of the amplitude matrix and perform range compression to obtain amplitude statistical features;

[0154] The adaptive mapping unit 930 is used to input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity.

[0155] The signal reconstruction unit 940 is used to perform amplitude limiting processing on the amplitude matrix using the compression coefficient, and combine the new amplitude matrix after amplitude limiting with the phase matrix to construct an amplitude-limited signal matrix;

[0156] Covariance construction unit 950 is used to construct a bounded covariance matrix based on the amplitude-limiting signal matrix;

[0157] The noise estimation unit 960 is used to input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix.

[0158] The noise removal unit 970 is used to subtract the bounded covariance matrix from the noise residual matrix to obtain an equivalent covariance matrix;

[0159] The direction-of-arrival estimation unit 980 is used to perform eigenvalue decomposition on the equivalent covariance matrix to obtain a noise subspace, construct a spatial spectrum function using the noise subspace, and determine the direction-of-arrival estimate of each source by searching for spectral peaks.

[0160] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0161] Accordingly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any of the above embodiments.

[0162] Accordingly, embodiments of the present invention also provide a computer program product configured to perform the methods described in any of the above embodiments.

[0163] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer, which can take the form of a personal computer, laptop computer, cellular phone, camera phone, smartphone, personal digital assistant, media player, navigation device, email sending and receiving device, game console, tablet computer, wearable device, or any combination of these devices.

[0164] In a typical configuration, a computer includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0165] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0166] Computer-readable media, including both permanent and non-permanent, removable and non-removable media, can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random-access memory (SRAM), dynamic random-access memory (DRAM), other types of random-access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, disk storage, quantum memory, graphene-based storage media or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0167] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather are primarily intended to describe features of specific embodiments of a particular invention. Certain features described in the various embodiments herein may also be implemented in combination in a single embodiment. Conversely, various features described in a single embodiment may also be implemented separately in various embodiments or in any suitable sub-combination. Furthermore, while features may function in certain combinations as described above and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and a claimed combination may refer to a sub-combination or a variation thereof.

[0168] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or requiring all illustrated operations to be performed to achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system modules and components in the above embodiments should not be construed as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0169] Thus, specific embodiments of the subject matter have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings are not necessarily shown in a specific order or sequence to achieve the desired result. In some implementations, multitasking and parallel processing may be advantageous.

[0170] It should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A direction-of-arrival estimation method based on a two-stage denoising neural network, characterized in that, The two-stage denoising neural network includes an adaptive thresholding subnetwork and a complex residual convolutional subnetwork, and the direction-of-arrival estimation method includes the following steps: Step S1: Receive signals from each signal source within the target area using a uniform linear array; construct an array received signal matrix based on the received signals; and perform amplitude-phase decomposition on the array received signal matrix to obtain the amplitude matrix and phase matrix. Step S2: Extract the median of the amplitude matrix and compress its range to obtain amplitude statistical features; Step S3: Input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity; Step S4: The amplitude matrix is ​​limited using the compression coefficient, and the new amplitude matrix after limiting is combined with the phase matrix to construct a limited signal matrix; Step S5: Construct a bounded covariance matrix based on the amplitude-limited signal matrix; Step S6: Input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix. Step S7: Subtract the bounded covariance matrix from the noise residual matrix to obtain the equivalent covariance matrix; Step S8: Perform eigenvalue decomposition on the equivalent covariance matrix to obtain the noise subspace, construct a spatial spectrum function using the noise subspace, and determine the estimated direction of arrival (DOA) of each source by searching for spectral peaks.

2. The method according to claim 1, characterized in that, The expression for the amplitude statistical characteristics in step S2 is: ； in, For amplitude statistical characteristics, Let be the amplitude matrix.

3. The method according to claim 1, characterized in that, The adaptive threshold subnetwork comprises a first fully connected layer, an activation layer, a second fully connected layer, and a positive constraint layer connected in sequence. The first fully connected layer is used to map the input amplitude statistical features into hidden layer feature vectors; The activation layer uses the ReLU activation function to perform a nonlinear transformation on the feature vector of the hidden layer. The second fully connected layer is used to map the hidden layer feature vectors after nonlinear transformation into one-dimensional scalars; The positive constraint layer is used to perform positive value processing on the one-dimensional scalar to generate a compression coefficient greater than zero.

4. The method according to claim 1, characterized in that, The expression for the amplitude-limiting signal matrix in step S4 is: ； in, For the amplitude-limited signal matrix, The compression factor is 1. The phase matrix is... The imaginary unit, The new amplitude matrix after amplitude limiting .

5. The method according to claim 1, characterized in that, The expression for the bounded covariance matrix in step S5 is: ； in, It is a bounded covariance matrix. For the amplitude-limited signal matrix, The number of snapshots.

6. The method according to claim 1, characterized in that, The complex residual convolutional subnetwork includes a first complex convolutional block, an intermediate complex convolutional block group, and an output complex convolutional layer arranged sequentially. The first complex convolutional block includes a first complex convolutional layer and a first complex activation layer. The first complex convolutional layer is used to map the input bounded covariance matrix into a complex feature map, and the first complex activation layer uses a complex ReLU activation function to perform nonlinear activation on the complex feature map. The intermediate complex convolutional block group includes a plurality of complex convolutional blocks connected in sequence. Each complex convolutional block includes a complex convolutional layer, a complex batch normalization layer and a second complex activation layer connected in sequence. Each complex convolutional layer uses the same complex convolutional kernel, and each second complex activation layer uses the complex ReLU activation function. The output complex convolutional layer uses a 1×1 complex convolutional kernel to map the complex feature map into a single-channel noise residual matrix.

7. The method according to any one of claims 1 to 6, characterized in that, The two-stage denoising neural network is jointly optimized and trained using a joint loss function, which includes off-diagonal covariance reconstruction loss and spatial spectrum alignment loss. The off-diagonal covariance reconstruction loss is ; The spatial spectrum alignment loss is ; in, , It is a matrix of all ones. It is the identity matrix. A mask matrix with 0s on the main diagonal and 1s for all other elements. The equivalent covariance matrix is ​​constructed based on the output of a two-stage denoising neural network. The reference covariance matrix is ​​a tag constructed from a noise-free reference array signal matrix; For based on Calculated spatial spectrum This is a reference space spectrum constructed based on real direction-of-arrival (DOA) labels.

8. A direction-of-arrival estimation device based on a two-stage denoising neural network, characterized in that, The two-stage denoising neural network includes an adaptive thresholding subnetwork and a complex residual convolutional subnetwork, and the device includes: The data acquisition unit is used to receive signals emitted by various signal sources within the target area through a uniform linear array, construct an array received signal matrix based on the received signals, and perform amplitude-phase decomposition on the array received signal matrix to obtain an amplitude matrix and a phase matrix. The feature statistics unit is used to extract the median of the amplitude matrix and perform range compression to obtain amplitude statistical features; An adaptive mapping unit is used to input the amplitude statistical features into the adaptive threshold sub-network to generate compression coefficients for controlling the amplitude compression intensity. The signal reconstruction unit is used to perform amplitude limiting processing on the amplitude matrix using the compression coefficient, and combine the new amplitude matrix after limiting with the phase matrix to construct a limited signal matrix; A covariance construction unit is used to construct a bounded covariance matrix based on the amplitude-limited signal matrix. The noise estimation unit is used to input the bounded covariance matrix into the complex residual convolutional subnetwork to extract the residual impulse noise interference features in the bounded covariance matrix in the complex domain and generate a noise residual matrix. The noise removal unit is used to subtract the bounded covariance matrix from the noise residual matrix to obtain an equivalent covariance matrix; The direction-of-arrival (DOA) estimation unit is used to perform eigenvalue decomposition on the equivalent covariance matrix to obtain a noise subspace, construct a spatial spectrum function using the noise subspace, and determine the DOA estimates of each source by searching for spectral peaks.

9. An electronic device, characterized in that, include: processor; as well as A computer-readable storage medium storing computer program instructions that, when executed by the processor, cause the processor to perform the method as described in any one of claims 1 to 7.

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