Near-field signal source localization method based on deep residual learning under unknown colored noise

Abstract

This invention discloses a near-field signal source localization method based on deep residual learning under unknown colored noise. The method involves acquiring or simulating near-field signal data to be located, and obtaining a feature extraction matrix from the near-field signal data. The feature extraction matrix is ​​then input into an optimized deep residual neural network model, which outputs the direction of arrival (DOA) and incident distance (AR) of the near-field signal, thus achieving near-field signal source localization. This invention introduces a deep residual neural network model, which improves the estimation accuracy of DOA and AR by ten times compared to other baseline algorithms when the signal-to-noise ratio (SNR) is below 5 dB, and by more than five times when the angular separation is less than 5°. Furthermore, it demonstrates high estimation accuracy and strong real-time localization capability under various harsh environments.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, and specifically relates to a near-field signal source localization method based on deep residual learning under unknown colored noise. Background Technology

[0002] Near-field signal source localization plays a crucial role in fields such as radar, sonar, wireless communication, speech processing, and radio astronomy. Over the past few decades, numerous model-driven algorithms with near-field assumptions have emerged. Among these, mainstream algorithms include methods based on maximum likelihood estimation, methods based on two-dimensional multi-signal classification, and methods based on generalized rotation invariance. The performance of these model-driven algorithms heavily relies on the accuracy of the pre-built model. However, due to the complexities of application environments, signal models are difficult to construct accurately, leading to a significant performance degradation in existing model-driven algorithms.

[0003] In contrast, thanks to its data-driven structure, deep learning algorithms can more accurately learn the complex nonlinear relationship between the location parameters of a signal source and the array output data, exhibiting significant advantages in localization problems, including the absence of prior knowledge requiring statistical assumptions about the signal source and robustness to complex application environments. Currently, deep learning-based localization algorithms can be broadly categorized into three types. The first type of algorithm discretizes the potential location regions of signal sources, transforming the localization problem into a classification problem. However, due to the large quantization resolution of the localization parameters, the algorithm cannot achieve high-precision localization performance. The second type of algorithm estimates the discrete signal spectrum using a regressive neural network, then combines the various spectral peaks of the signal spectrum to ultimately determine the signal source location. However, this type of algorithm struggles to extend to solve near-field signal source localization problems because it requires estimating a highly refined two-dimensional signal spectrum. Additionally, another type of algorithm uses a regressive neural network to directly predict the localization parameters. It is important to note that the algorithms mentioned above study source localization in simple Gaussian noise environments. Currently, in the literature on array signal processing, the localization of near-field signal sources in unknown colored noise environments has not been well studied.

[0004] Furthermore, traditional model-based near-field signal source localization methods have poor localization accuracy in scenarios with small angular and distance separation. Summary of the Invention

[0005] The purpose of this invention is to provide a near-field signal source localization method based on deep residual learning under unknown colored noise. This method improves the estimation accuracy of direction of arrival and incident distance by ten times when the signal-to-noise ratio is less than 5dB, and has high estimation accuracy.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A near-field signal source localization method based on deep residual learning under unknown colored noise includes the following steps:

[0008] Acquire or simulate near-field signal data to be located, and obtain the feature extraction matrix based on the near-field signal data;

[0009] The feature extraction matrix is ​​input into the optimized deep residual neural network model, and the model outputs the direction of arrival and incident distance of the near-field signal to achieve near-field signal source localization.

[0010] Furthermore, acquiring or simulating near-field signal data to be located, and obtaining the feature extraction matrix based on the near-field signal data includes the following steps:

[0011] The covariance matrix of the array received data is calculated based on the near-field signal data, and the feature extraction matrix is ​​calculated based on the covariance matrix.

[0012] Furthermore, the covariance matrix R of the array received data is:

[0013] R = E{x(n)x(n)} H} = AR s A H +Q

[0014] Where A is the manifold matrix of a uniform linear array, R s Let R be the covariance matrix of the incident signal, Q be the covariance matrix of the colored noise, and R be the covariance matrix of the incident signal. s =E{s(n)s(n) H}, where s(n) is the incident signal vector, and Q = E{ω(n)ω(n)} H}, where ω(n) is the additive noise vector, and E{·} denotes the expectation, (·) H Let x(n) represent the Hermitian transpose, and x(n) be the near-field signal data. x1(n), x2(n) and x M (n) represent the data received on the 1st, 2nd and Mth array elements, respectively.

[0015] Furthermore, the incident signal vector s(n) is calculated using the following formula:

[0016]

[0017] In the formula, s1(n), s2(n), and s K (n) represent the signals emitted by the 1st, 2nd and Kth near-field signal sources, respectively.

[0018] Furthermore, the additive noise vector ω(n) is calculated using the following formula:

[0019]

[0020] In the formula, w1(n), w2(n), and w M (n) represents the unknown colored noise received on the 1st, 2nd and Mth sensor array elements, respectively.

[0021] Furthermore, the feature extraction matrix X has a size of M×M×3, where M is the total number of matrix elements, including the first two-dimensional matrix. Second two-dimensional matrix and the third two-dimensional matrix in, and Let represent the real part, imaginary part, and complex angle of the matrix complex values, respectively; R is the covariance matrix of the array received data.

[0022] Furthermore, the deep residual neural network model includes an input layer, a convolutional layer, a normalization layer, a ReLU activation function layer, a residual learning layer, a Flatten layer, a fully connected layer, and an output layer.

[0023] Furthermore, the convolutional layer has 1 layer and uses 128 filters with a dimension of 3×3 and a stride of 1.

[0024] The number of residual learning layers is 2. In the first residual learning layer, the number of kernels in the inner convolutional layer is 64. In the shortcut connection structure, the dimension of the filter is 1×1, and the dimension of the other filters is 3×3, with a stride of 1. In the second residual learning layer, the number of kernels in the inner convolutional layer is 32, and the parameter settings are the same as those in the first residual learning layer.

[0025] Furthermore, the loss function of the deep residual neural network model Where T is the total number of training samples; i is the training sample index; y i It is the true location parameter value of the i-th sample; It is the predicted output of the deep residual neural network model for the position parameters of the i-th sample.

[0026] Furthermore, the optimized deep residual neural network model is obtained by training a deep residual neural network model on the training set and then optimizing it. The training set is obtained through the following process:

[0027] Two signal sources are incident on the array from a distance of 2λ to 4λ, within the range of [-30°, 30°], and both are located in the Fresnel region of the array aperture. For the simulation settings of the direction of arrival, the angular separation of the two signal sources is selected as {1°, 2°, ..., 18°}. For any angular separation Δψ, the direction of arrival angles of the two signal sources are discretized in the ranges of [-30°, 30°-Δψ] and [-30°+Δψ, 30°] at 1° intervals, respectively. For the simulation settings of the incident distance, the distance separation of the two signal sources is selected as {0.2λ, 0.4λ, ..., 1.0λ}. For any distance separation Δζ, the incident distances of the two signal sources are discretized in the ranges of [2.0λ, 4.0λ-Δζ] and [2.0λ+Δζ, 4.0λ] at 0.2λ intervals, respectively.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention provides a near-field signal source localization method based on deep residual learning under unknown colored noise. Compared with traditional model-based near-field signal source localization algorithms, which suffer from poor localization performance in harsh environments, this method improves the estimation accuracy of direction of arrival (DOA) and incident distance by tenfold when the signal-to-noise ratio (SNR) is below 5dB. Under various snapshot counts and signal correlation levels in experiments, the estimation accuracy of DOA and incident distance is higher than that of traditional model-based algorithms, demonstrating the localization potential of the deep residual neural network model. Furthermore, compared to traditional model-based near-field signal source localization algorithms, which perform poorly in scenarios with low angle and distance separation, this invention, by introducing a deep residual neural network model, improves the estimation accuracy of DOA and incident distance by more than five times when the angle separation is less than 5°. Under various distance separation levels in experiments, the estimation accuracy of DOA and incident distance is improved by approximately four times and two times, respectively, and the network exhibits good robustness.

[0030] Furthermore, this invention experimentally determined an optimal training loss function and residual learning layer number, which can simultaneously achieve high positioning accuracy and low computational cost, thus reducing unnecessary time costs. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; obviously, the drawings described below are some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0032] Figure 1This is a schematic diagram of the deep residual neural network model structure according to an embodiment of the present invention;

[0033] Figure 2 These are schematic diagrams illustrating the variation of root mean square error (RMSE) for near-field signal direction-of-arrival (DOA) and range estimation with signal-to-noise ratio (SNR). The horizontal axis of each diagram represents SNR, and the vertical axis represents the root mean square error (RMSE) of the estimated parameters. Specifically, (a) is a schematic diagram illustrating the variation of root mean square error (RMSE) for near-field signal DOA estimation with SNR; and (b) is a schematic diagram illustrating the variation of root mean square error (RMSE) for near-field signal range estimation with SNR.

[0034] Figure 3 These are schematic diagrams illustrating the variation of the root mean square error (RMSE) of near-field signal direction of arrival (DOA) and range estimation with the number of snapshots. The horizontal axis of each graph represents the number of snapshots, and the vertical axis represents the root mean square error (RMSE) of the estimated parameters. Specifically, (a) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal DOA estimation with the number of snapshots; and (b) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal range estimation with the number of snapshots.

[0035] Figure 4 These are schematic diagrams illustrating the variation of the root mean square error (RMSE) of near-field signal direction of arrival (DOA) and range estimation with the signal angular separation. The horizontal axis of each figure represents the angular separation, and the vertical axis represents the root mean square error (RMSE) of the estimation parameters. Specifically, (a) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal DOA estimation with the signal angular separation; and (b) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal range estimation with the signal angular separation.

[0036] Figure 5 These are schematic diagrams illustrating the variation of the root mean square error (RMSE) of near-field signal direction of arrival (DOA) and range estimation with the signal incident distance separation. The horizontal axis of each figure represents the signal incident distance separation, and the vertical axis represents the root mean square error (RMSE) of the estimation parameters. Specifically, (a) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal DOA estimation with the signal incident distance separation; and (b) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal range estimation with the signal incident distance separation.

[0037] Figure 6This is a schematic diagram illustrating the variation of the estimation performance of the neural network with different training loss functions and the number of residual learning layers in an embodiment of the present invention. Specifically, (a) is a schematic diagram illustrating the variation of the root mean square error (RMSE) of near-field signal distance estimation with the signal-to-noise ratio (SNR) under different training loss functions, where the horizontal axis represents the SNR and the vertical axis represents the RMSE; (b) is a schematic diagram illustrating the variation of the test error of the neural network with the number of training iterations under different numbers of residual learning layers, where the horizontal axis represents the number of training iterations (Epoch) and the vertical axis represents the test error (Test Loss). Detailed Implementation

[0038] To make the objectives, technical effects, and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention. Based on the embodiments disclosed in the present invention, other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0039] Consider K near-field narrowband incoherent signals {s} k (n)} impacts a uniform linear array of M sensor elements spaced d apart, and it is assumed that these sensors are fully calibrated.

[0040] If we define the first element of the array as the phase reference point, then the noisy signal x received by the m-th sensor... m (n) can be represented as:

[0041]

[0042] Where m = 1, ..., M, s k (n) represents the k-th signal, w m (n) represents additive noise, t m,k The phase delay of the k-th signal between the reference sensor and the m-th sensor is caused by the time delay.

[0043]

[0044] Where, θ k and r k Here, λ represents the direction of arrival and incident distance of the k-th signal, respectively, and λ is the wavelength. When the k-th signal is within the Fresnel region (e.g., r...),... k ∈(0.62(D 3 / λ) 1 / 2 2D 2 λ), where D is the array aperture, equation (1) is reformulated as:

[0045]

[0046] in,(·) T denoted as transpose, s(n) and ω(n) are given by the incident signal vector and the additive noise vector, respectively.

[0047]

[0048]

[0049] Wherein, s1(n), s2(n) and s K (n) represent the signals emitted by the 1st, 2nd, and Kth near-field signal sources, respectively; w1(n), w2(n), and w M (n) represents the unknown colored noise received on the 1st, 2nd and Mth sensor array elements, respectively.

[0050] A is the manifold matrix of a calibrated uniform linear array, denoted as... a(θ k ,r k ) is the direction vector of a uniform linear array, which can be represented as:

[0051]

[0052] In the formula, τ m,k It is the phase delay of the k-th signal between the reference sensor element and the m-th sensor element caused by the time delay, expressed as:

[0053]

[0054] Where, θ k and r k λ represents the direction of arrival and incident distance of the k-th signal, respectively, and λ is the wavelength.

[0055] In this invention, it is assumed that the incident signal {s} k {(n)} is a generalized, zero-mean static random process with additive noise {w} m {(n)} is unknown colored noise in the spacetime complex domain, and is related to the signal {s} k (n)} is irrelevant.

[0056] An embodiment of the present invention provides a near-field signal source localization method based on deep residual learning under unknown colored noise, which is a near-field multi-signal source localization method, comprising the following steps:

[0057] (1) Collect or simulate near-field signal data to be located, calculate the covariance matrix R of the array received data based on the near-field signal data, and calculate the feature extraction matrix X based on the covariance matrix R.

[0058] In step (1), the feature extraction matrix X of the network input is calculated:

[0059] From near-field signal data First, the covariance matrix R of the array received data is calculated;

[0060] R = E{x(n)x(n)} H} = AR s A H +Q

[0061] Where A is the manifold matrix of a uniform linear array, R s Let R be the covariance matrix of the incident signal. s =E{s(n)s(n) H}, where Q is the covariance matrix of the colored noise, s(n) is the incident signal vector, and Q = E{ω(n)ω(n)} H}, where ω(n) is the additive noise vector, and E{·} denotes the expectation, (·) H Denotes the Hermitian transpose, x1(n), x2(n), and x M (n) represent the data received on the 1st, 2nd and Mth array elements, respectively.

[0062] Generally, the covariance matrix R of the array received data can be approximated by averaging the time term n. This invention preserves all information of the covariance matrix, including its real, imaginary, and complex angle information. This processing method provides the network with superior feature extraction performance and achieves satisfactory estimation accuracy. The specific content of the feature extraction matrix X proposed in this invention is described as follows:

[0063] The feature extraction matrix X is a three-dimensional matrix of size M×M×3. M represents the total number of matrix elements, and it consists of three two-dimensional matrices, each with dimensions consistent with the covariance matrix. and in, and These represent the real part, imaginary part, and complex angle of the complex value of the matrix, respectively.

[0064] (2) Construct a deep residual neural network model; the deep residual neural network model takes the feature extraction matrix X obtained in step (1) as input, and maps the output of the deep residual neural network model to the direction of arrival and incident distance of the near field signal through convolutional layers, residual learning layers and regression structures;

[0065] For details, see Figure 1The deep residual neural network model constructed in this invention includes an input layer, a convolutional layer, a normalization layer, a ReLU activation function layer, two residual learning layers (Conv2D Residual Block_1 / 2), a flatten layer, a fully connected layer, and an output layer.

[0066] The feature extraction matrix X obtained in step (1) is the input layer of the deep residual neural network, with dimensions of M×M×3, indicating that the length and width are M pixels and there are three channels;

[0067] Next is a Conv2D layer, which is used to initially extract local features of the input signal. It uses 128 3×3 filters with a stride of 1 to perform convolution operations on the input signal. Then there is a batch normalization layer (BN layer), which is used to normalize the activation and gradient functions transmitted in the network, making the network training easier to optimize. Then there is a ReLU layer, which enhances the expressive power of the network through non-linear mapping.

[0068] To improve the estimation accuracy of the network and address the gradient vanishing problem caused by deep networks, this invention incorporates two residual learning layers (Conv2D Residual Block_1 / 2): In the first residual learning layer, the number of filters in each inner convolutional layer is 64, i.e., k1_1 = k1_2 = k1_3 = 64, where k1_1, k1_2, and k1_3 represent the number of filters in the three different inner convolutional layers within the first residual learning layer. Except for the 1×1 dimension of the filters in the shortcut connection structure, the dimensions of the other filters are 3×3, and the stride is 1. In the second residual learning layer, the number of filters in each inner convolutional layer is 32, i.e., k2_1 = k2_2 = k2_3 = 32, where k2_1, k2_2, and k2_3 represent the number of filters in the three different inner convolutional layers within the second residual learning layer. Other parameter settings are the same as in the first residual learning layer, and the signal input to the residual learning layer is processed.

[0069] Next is the Flatten Layer, which is used to simplify multi-dimensional data into one dimension.

[0070] Then comes the fully connected (Dense Layer), which receives the one-dimensional data output from the Flatten layer to enable the network's regression prediction capability and complete the localization of near-field signals;

[0071] Finally, there is the output layer, which outputs the position parameters of the near-field signal sources, namely the direction of arrival and the incident distance; for the position estimation of K near-field signal sources, the network outputs 2K position parameters.

[0072] (3) A training set is generated through simulation, the deep residual neural network model is trained using the training set, and the parameters required for training the deep residual neural network model are determined.

[0073] Specifically, the parameters required for training a deep residual neural network model should be set according to the following conditions:

[0074] 1) The training loss function of a deep residual neural network model is represented by the mean absolute error. Where T is the total number of training samples; i is the training sample index; y i It is the true location parameter value of the i-th sample; It is the predicted output of the deep residual neural network model for the position parameters of the i-th sample, including the direction of arrival and incident distance of the near-field signal source;

[0075] 2) The deep residual neural network model was trained using an Adaptive Moment Estimation Optimizer with an initial rate of 0.001;

[0076] 3) To prevent training from getting stuck in local optimization or diverging, the learning rate is set to 0.2 times the current rate every 10 epochs;

[0077] 4) The maximum number of training cycles is set to 30;

[0078] 5) The mini-batch size used in the training iterations is 128;

[0079] 6) Shuffle the order of the training set data before each training iteration.

[0080] (4) Train the deep residual neural network model constructed in step (2) using the parameters obtained in step (3) to obtain the trained deep residual neural network model;

[0081] (5) Optimize the loss function of the trained deep residual neural network model to obtain the optimized training loss function; in addition, specifically, optimize the number of residual learning layers of the trained deep residual neural network model obtained in step (4) to obtain the optimized deep residual neural network model.

[0082] Input the feature extraction matrix X obtained in step (1) into the deep residual neural network model that has been trained in step (5). The deep residual neural network model outputs the direction of arrival and incident distance of the near-field signal to realize the localization of the near-field signal source.

[0083] To provide a reference for improving neural network models, this invention designed experiments to investigate the impact of the training loss function and the number of residual learning layers on network performance. With a snapshot count of 200, the Range estimation performance of networks trained with both mean absolute error and mean squared error loss functions was compared as a function of signal-to-noise ratio. With a fixed loss function, the test error of networks with 1 to 3 residual learning layers was compared as a function of training cycles. By comparing these results, the optimal training loss function and the number of residual learning layers corresponding to the best-performing estimate were determined.

[0084] The effectiveness of the method of the present invention is verified by numerical simulation below:

[0085] The method proposed in this embodiment of the invention is verified on a uniform linear array consisting of 9 sensor elements, with the spacing between the sensors being one-quarter of the wavelength. The covariance matrix of the spatially unknown colored noise is in the form of... in This represents the noise variance. Theoretically, this network can simultaneously train multiple near-field signal sources and estimate their direction of arrival (DOA) and range. However, for simplicity, this invention only provides an example with two near-field signal sources. To generate the training dataset, two signal sources are incident on the array from range element 2λ to 4λ, within the range [-30°, 30°], both located in the Fresnel region of the array aperture. For the simulation settings of the DOA, the angular separation of the two signal sources is chosen to be {1°, 2°, ..., 18°}. For any angular separation Δψ, the DOA angles of the two signal sources are discretized in the ranges [-30°, 30°-Δψ] and [-30°+Δψ, 30°] at 1° intervals, respectively. For the simulation settings of the incident distance, the distance separation of the two signal sources was selected as {0.2λ, 0.4λ, ..., 1.0λ}. For any distance separation Δζ, the incident distances of the two signal sources were discretized in the ranges [2.0λ, 4.0λ-Δζ] and [2.0λ+Δζ, 4.0λ] at intervals of 0.2λ. At each of the discretized grid points, 50 signals were incident on the array. For each position parameter setting, there were 50 samples, resulting in a total of 1.854 million samples, two-tenths of which were used as the validation dataset. The experiments for snapshot count and signal-to-noise ratio had the same training and validation set sizes. The experimental results were compared with three algorithms: 2D multi-signal classification (2DMUSIC), generalized rotation-invariant localization (GESPRIT), and weighted linear localization (WLPM).

[0086] Figure 2 Figures (a) and (b) illustrate the root mean square error (RMSE) of the direction of arrival (DOA) and the distance of incidence (Range) as a function of the signal-to-noise ratio (SNR). Two near-field sources are located at (8.1°, 2.19λ) and (13.5°, 2.66λ), respectively. The number of snapshots is set to 200, and the SNR varies from -10 dB to 20 dB. It can be seen that the estimation error of most algorithms decreases as the SNR increases. Notably, the method proposed in this invention outperforms the baseline scheme, especially at lower SNRs. Furthermore, if the SNR level is used as the evaluation criterion, for the same estimation error, the method proposed in this invention requires an SNR level at least 15 dB and 5 dB lower than the baseline method for the estimated DOA and distance of incidence, respectively.

[0087] Figure 3Figures (a) and (b) illustrate the root mean square error of the direction of arrival and incident distance as a function of the number of snapshots. Two near-field sources are located at (8.1°, 2.19λ) and (19.8°, 2.66λ), respectively. The signal-to-noise ratio is set to 10 dB, and the number of snapshots varies from 10 to 1000. Figure 3 As shown in Figures (a) and (b), the proposed method outperforms other algorithms regardless of the number of snapshots. In particular, the performance of the proposed algorithm does not "saturate" with increasing snapshot count, demonstrating the network's localization potential. These two figures demonstrate that the proposed method can overcome the shortcomings of model-driven algorithms in localization performance under low signal-to-noise ratio and small snapshot environments.

[0088] The near-field signal source localization method in this invention improves the estimation accuracy of direction of arrival and incident distance by ten times compared with other baseline algorithms when the signal-to-noise ratio is less than 5dB. Under various snapshot counts in the experimental settings, the estimation accuracy of direction of arrival and incident distance is higher than that of other baseline algorithms.

[0089] Figure 4 Figures (a) and (b) illustrate the root mean square error (RMSE) of the direction of arrival (DOA) and incident distance (ORA) as a function of the signal direction angle separation. Two near-field sources are located at (6.4°, 2.19λ) and (6.4° + Δθ, 2.19λ), respectively, with the angle separation Δθ ranging from 1° to 18° and a step size of 1°. The signal-to-noise ratio (SNR) is set to 10 dB, and the number of snapshots is set to 200. As can be observed from the figures, the proposed method exhibits better robustness to different angular intervals than other algorithms. Specifically, regardless of the angular interval variation, the estimation accuracy of the proposed algorithm remains within a very small fluctuation range. Notably, compared to existing model-driven algorithms, the proposed method performs better in scenarios with small angular intervals.

[0090] Figure 5 Figures (a) and (b) illustrate the variation of the root mean square error of the direction of arrival and incident distance with the signal incident distance separation. Two near-field sources are located at (6.5°, 2.36λ) and (6.4°, 2.36λ + Δλ), respectively, with a distance separation Δλ ranging from 0.1λ to 1.0λ in step size of 0.1λ. Other external conditions are... Figure 4 The settings are the same. As can be seen from the figure, compared with other algorithms, the proposed method has better localization performance in different distance separation intervals.

[0091] This invention introduces a deep residual neural network model, which improves the estimation accuracy of direction of arrival and incident distance by more than five times compared with other baseline algorithms when the angular separation is less than 5°. Under various distance separation conditions set in the experiment, the estimation accuracy of direction of arrival and incident distance is improved by approximately four times and two times, respectively.

[0092] Please see Figure 6 In (a) and (b), through Figure 6 As shown in (a), with the increase of signal-to-noise ratio, the estimation performance of networks based on mean squared error loss deteriorates compared to those based on mean absolute error loss. This is because mean absolute error loss is more sensitive to small errors than mean squared error loss, thus providing better estimation performance. Figure 6 As shown in (b), the estimation performance improves as the number of residual learning layers increases from 1 to 3, because theoretically, deeper networks have stronger expressive power. However, it is worth noting that although the localization performance of a deep neural network consisting of 2 residual learning layers is slightly worse than that of a network consisting of 3 layers, it has lower computational cost. Therefore, this invention chooses two residual learning layers as a balance between localization accuracy and real-time performance.

[0093] Furthermore, to evaluate the computational cost of the localization method in this invention, Table 1 records the running time of various methods (averaged over 1000 test runs). As can be seen from the table, the method in this invention has the shortest test time compared to other baseline methods. Although the running time of the Weighted Linear Localization (WLPM) algorithm is close to that of the method in this invention, its estimation performance is the worst. These results demonstrate the superior real-time and precise localization capabilities of the localization method in this invention.

[0094] Table 1. Comparison of training time and running time for various algorithms

[0095] The algorithm of this invention GESPRIT 2DMUSIC WLPM Training time 2h 4min 35s \ \ \ Test time 0.29ms 2.03ms 227.11ms 0.43ms

[0096] This invention proposes a deep residual neural network model to solve the problem of near-field signal source localization under unknown colored noise. Unlike previous methods that mainly focused on near-field signal source localization under Gaussian noise, this invention primarily addresses signal source localization under unknown colored noise. This invention fully utilizes the multidimensional information of the array covariance and inputs it into the neural network in matrix form, rather than vector form. This allows for better utilization of the structural advantages of the neural network. Simultaneously, this invention designs a residual learning structure to improve estimation accuracy and real-time localization performance. Simulation results show that the proposed method outperforms traditional model-based methods in harsher environments. Compared to existing traditional near-field signal source localization algorithms, the proposed method maintains high performance under various conditions, including low snapshot number, poor signal-to-noise ratio, small direction-of-arrival separation angles (DOA) of multiple signal sources, and low incident distance separation. Furthermore, it exhibits strong robustness to different DOA and incident distance separations. Moreover, since network training is conducted offline, the trained network can be directly used online, resulting in no unnecessary computational load and high efficiency.

[0097] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still make modifications or equivalent substitutions to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention are within the protection scope of the claims of the present invention pending approval.

Claims

1. A near-field signal source localization method based on deep residual learning under unknown colored noise, characterized in that, Includes the following steps: Acquire or simulate near-field signal data to be located, and obtain the feature extraction matrix based on the near-field signal data; The covariance matrix of the array received data is calculated based on the near-field signal data, and the feature extraction matrix is ​​calculated based on the covariance matrix. Covariance matrix of array received data for: in, The manifold matrix of a uniform linear array, Let be the covariance matrix of the incident signal. The covariance matrix of the colored noise is , Let be the incident signal vector. , It is an additive noise vector. Indicates the expectation. Indicates Hermite transpose. Near-field signal data, near-field signal data , , and They represent the 1st, 2nd and 3rd respectively. Data received by each array element; The feature extraction matrix is ​​input into the optimized deep residual neural network model, and the deep residual neural network model outputs the direction of arrival and incident distance of the near-field signal to realize the localization of the near-field signal source. The optimized deep residual neural network model is obtained by training a deep residual neural network model on a training set and then optimizing it. The training set is obtained through the following process: Two signal sources from the range array element arrive , The signals incident on the array within the range are all located in the Fresnel region of the array aperture; for the simulation settings in the direction of arrival, the angular separation of the two signal sources is selected as [value missing]. Separation at any angle The direction of arrival angles of the two signal sources are according to The intervals are respectively at and Discretize within the range; for the simulation settings of the incident distance, the distance separation between the two signal sources is selected as [value missing]. For any distance separation degree The incident distance between the two signal sources is according to The intervals are respectively at and Discretize within the range.

2. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 1, characterized in that, Incident signal vector Calculated using the following formula: （4） In the formula, , and They represent the 1st, 2nd and... K The signal is emitted by a near-field signal source.

3. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 1, characterized in that, Additive noise vector Calculated using the following formula: （5） In the formula, , and They represent the 1st, 2nd and... M Unknown colored noise received on each sensor element.

4. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 1, characterized in that, Feature extraction matrix Size is , The total number of array elements, including the first two-dimensional matrix. Second two-dimensional matrix and the third two-dimensional matrix ,in, , and These represent the real part, imaginary part, and complex angle of the complex value of the matrix, respectively; This is the covariance matrix of the data received by the array.

5. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 1, characterized in that, A deep residual neural network model includes an input layer, a convolutional layer, a normalization layer, a ReLU activation function layer, a residual learning layer, a Flatten layer, a fully connected layer, and an output layer.

6. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 5, characterized in that, The convolutional layer has 1 layer and uses 128 dimensions. The filter has a step size of 1; The residual learning layer has 2 layers. In the first residual learning layer, the inner convolutional layer has 64 kernels. The filter dimension in the shortcut connection structure is... In addition, the dimensions of other filters are The stride is 1 for all layers; in the second residual learning layer, the number of kernels in the inner convolutional layer is 32, and the parameter settings are the same as those in the first residual learning layer.

7. The near-field signal source localization method based on deep residual learning under unknown colored noise according to claim 1, characterized in that, Loss function of deep residual neural network model ,in, This represents the total number of training samples; i is the training sample index. It is the first The true location parameter values ​​of each sample; It is a deep residual neural network model for the first The predicted output of the location parameters of each sample.

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