Maximum likelihood direction of arrival estimation method based on unsupervised machine learning

Abstract

The application discloses a maximum likelihood direction of arrival estimation method based on unsupervised machine learning, comprising the following steps: building an unsupervised regression type full connection neural network, setting a loss function of the full connection neural network according to a traditional maximum likelihood method, fitting a mapping relationship between a sample complex covariance matrix and a direction of arrival angle by using the regression type full connection neural network, and directly outputting a direction of arrival estimation result of a signal by an output layer. The application has the characteristics of combining the traditional maximum likelihood method, keeping the estimation accuracy of the maximum likelihood method in a low signal-to-noise ratio scene, and being lower in complexity. The estimation performance of the unsupervised regression type neural network is not limited by grid accuracy and grid mismatch problems, real angle labels are not needed, and the application is suitable for scenes in which real angle labels are difficult to obtain. The application shows good estimation performance in a simulation data test scene and is effectively applied to the field of direction of arrival estimation.

Description

Technical Field

[0001] This invention relates to the fields of array signal processing direction-of-arrival estimation and deep learning technology, specifically to a maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning. Background Technology

[0002] Direction of arrival (DOA) estimation methods are widely used in underwater acoustic communication, radar, detection, and mobile positioning. Traditional DOA estimation methods include multiple signal classification algorithms, rotation-invariant subspace methods, and maximum likelihood methods, each with its own limitations. Multiple signal classification methods require spectral peak search and have high complexity. Rotation-invariant subspace methods sacrifice array aperture. For maximum likelihood estimation, its performance is theoretically optimal, but its complexity increases exponentially with the number of signals, and its estimation performance in low signal-to-noise ratio scenarios cannot approach the theoretical limit, making it more suitable for low snapshot and coherent signal scenarios.

[0003] To address the high complexity of traditional DOA estimation methods, some works have utilized deep learning techniques. A key feature of deep learning is its ability to train networks offline, transferring complexity to the offline training phase and significantly reducing the complexity of online estimation. However, ordinary deep learning algorithms are data-driven, essentially functioning as a "black box," with limited interpretability and requiring a large amount of data with real angle labels to train the neural network. To address this issue, Ye Yuan et al. proposed an unsupervised learning strategy based on sparse power spectrum and the l1 norm (Y. Yuan, S. Wu, M. Wu and N. Yuan. Unsupervised learning strategy for direction-of-arrival estimation Network[J]. IEEE Signal Processing Letters,2021, 28:1450-1454.). This strategy uses the l1 norm to approximate the l0 norm to simplify the NP-hard optimization problem, deriving an expression for the angle spectrum. This expression is then directly used as the loss function of the neural network, and the network training process involves finding the minimum value of this expression. Finally, the network output is the sparse power spectrum of the signal. However, the neural network proposed in this method is a classification network, and its estimation accuracy is limited by grid accuracy and grid mismatch. In addition, the network output is not a direct DOA estimation result, but a sparse power spectrum of the signal, which needs to be Gaussian weighted averaged to obtain a spectrum with clear peaks.

[0004] In summary, existing traditional DOA estimation methods and deep learning DOA estimation methods have the following main problems:

[0005] 1. Traditional maximum likelihood DOA estimation algorithm has the best theoretical performance, but it has high complexity and room for improvement in low signal-to-noise ratio scenarios.

[0006] 2. Neural networks are entirely data-driven and lack strong interpretability.

[0007] 3. The main method used in deep learning DOA estimation research is to train neural networks using real angle labels, but in real-world scenarios, it is difficult to obtain real angles.

[0008] 4. The mainstream neural network structure in deep learning DOA estimation methods is a classification network, and the estimation accuracy is limited by grid accuracy and grid mismatch problems. Summary of the Invention

[0009] The purpose of this invention is to address the aforementioned deficiencies in the prior art and provide a maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning.

[0010] The objective of this invention can be achieved by adopting the following technical solutions:

[0011] A maximum likelihood direction-of-arrival (DOA) estimation method based on unsupervised machine learning, the DOA estimation method comprising the following steps:

[0012] S1. Set the number of array elements M, the number of signal sources K, and the array observation space range in the signal receiving array. Array response matrix ;

[0013] S2. Generate a dataset D for training a machine learning neural network. Each data sample in dataset D includes a complex covariance matrix. And the corresponding number of signals K;

[0014] S3. Extract the complex covariance matrix of the samples from dataset D. Convert it into a two-channel real matrix and then vectorize it to obtain the real covariance matrix. ;

[0015] S4. Construct an unsupervised machine learning regression fully connected neural network;

[0016] S5. Set the loss function for the fully connected neural network to achieve unsupervised learning without needing to set real angle labels. The expression for the loss function is as follows:

[0017] ,

[0018] Where [ ]* denotes the conjugate transpose operation on the matrix. The expression indicates that the matrix is ​​inverted, and tr{} indicates that the trace of the matrix is ​​found, which is the sum of the elements on the main diagonal of the matrix.

[0019] S6. Using the dataset obtained in step S3, iteratively train the fully connected neural network until the loss function converges to its minimum value, thus obtaining the model parameter set ζ. * ;

[0020] S7. Using the model parameter set ζ * Initialize a fully connected neural network to generate a covariance matrix of K test signal samples. After normalization and vectorization, the matrix is ​​input into the fully connected neural network. The estimated direction of arrival (DOA) of the signal is directly obtained through the output neurons of the fully connected neural network. ,in, These represent the directions of arrival of the 1st, ..., Kth sources, respectively.

[0021] Furthermore, the process of generating the dataset D for training the neural network in step S2 is as follows:

[0022] Assuming K independent far-field narrowband signal incident signal receiving arrays, the signal receiving arrays are uniform linear arrays with M array elements, then the sample complex covariance matrix R Y for: ,

[0023] in, It is the array output of the signal receiving array at time t, N is the number of snapshots, and [ ]* indicates the number of snapshots. The conjugate transpose operation, the d-th sample is defined as D is the total number of samples, and the dataset is... , Let represent the samples in group 1, group 2, ..., group D, respectively. The signal incident angles in dataset D are randomly generated within a preset range, with an interval of 1°. It also includes scenes with different signal-to-noise ratios or different numbers of snapshots, allowing the fully connected neural network to learn general features during training. This enhances the robustness of the fully connected neural network to signal-to-noise ratios and signal incident angles, making it more widely applicable.

[0024] Furthermore, in step S3, the complex covariance matrix of the samples is... Decomposed into a two-channel real matrix ,in It is a four-dimensional matrix, with its second dimension carrying the real and imaginary parts respectively. , , and These represent the operations of extracting the real part and the imaginary part, respectively. Finally, the operations are performed on... Vectorization. The initially generated sample covariance matrix. It is a complex number, but neural networks can only process real numbers, so the complex covariance matrix of the samples needs to be... Decompose to generate a two-channel real matrix Then it is fed into the input layer of the fully connected neural network to complete the subsequent steps.

[0025] Furthermore, the fully connected neural network consists of an input layer, several hidden layers, a dropout layer, and an output layer connected sequentially. The input layer is the first layer of the fully connected neural network, importing the sample covariance matrix. The number of hidden layers and neurons varies depending on the application scenario and simulation performance. The dropout layer is used to suppress overfitting. The output layer is the last layer of the fully connected neural network, outputting the mapping relationship between the fitted sample covariance matrix and the DOA estimation result. The number of output neurons in the output layer equals the number of information sources, and the output value of each neuron is the DOA estimation result. The fully connected neural network adopts the output structure of a regression network, where the output value of the output neuron is directly the DOA estimation result, effectively avoiding the problems of improper grid precision settings and grid mismatch that exist in classification networks.

[0026] Furthermore, the process of determining the loss function in step S5 is as follows:

[0027] The problem of direction-of-arrival estimation for narrowband source sensor arrays in the field of signal processing is reduced to parameter estimation based on the following model:

[0028] ,

[0029] in, It is the array output of the signal receiving array at time t, corresponding to the observed vector of the signal. It is the observation vector of the signal. It is the complex amplitude vector of the signal. It is additive noise, where N represents the number of snapshots, and the array response matrix is... abbreviated as , Is the i-th signal and The turning vector between them Indicates the direction of arrival of the signal. It is a real parameter. These represent the directions of arrival of the 1st, ..., i-th, ..., Kth signals, respectively.

[0030] Maximum likelihood estimation of the signal's direction of arrival (DOA) is performed. The above model satisfies the following conditions: the number of array elements M is greater than the number of sources K, and the number of snapshots N is greater than the number of array elements M; noise signals at different snapshot numbers are uncorrelated, and the noise received by each array element is normally distributed; the sample complex covariance matrix... It is positive definite, yes. Taking the likelihood function, we get:

[0031] ,

[0032] In the formula, M is the number of array elements. Let V be the variance of the noise received by each array element; then, taking the log-likelihood function, the expression is as follows:

[0033] ,

[0034] The calculation and derivation yielded the following: , ,

[0035] ,

[0036] In the formula, yes Maximum likelihood estimation, yes Maximum likelihood estimation, yes Maximum likelihood estimation, yes Maximum likelihood estimation, It is a common constant, Substitution , Undetermined, by By substitution, we obtain the likelihood function as , ;

[0037] At this point, the solution is needed. Find the minimum value, and obtain The maximum likelihood estimate is to Set as the loss function for a fully connected neural network.

[0038] The training of a fully connected neural network aims to minimize the loss function by continuously updating and iterating the network parameters until the most suitable set of parameters is found. Therefore, The loss function is set as the full-connected neural network. The network training process is based on the maximum likelihood DOA estimation method so that the network can estimate the direction of arrival of the signal. The value of the output layer neuron is the estimate of the signal direction of arrival by the full-connected neural network method.

[0039] The present invention has the following advantages and effects compared with the prior art:

[0040] 1. This invention combines the traditional maximum likelihood method with lower complexity. While the traditional maximum likelihood DOA estimation method theoretically offers the best performance, it is highly complex. This invention leverages the offline training and online estimation capabilities of deep learning, transferring the complexity to the training portion of the fully connected neural network. The fully connected neural network is trained using a large training dataset, continuously adjusting its parameters to obtain and save a parameter set that demonstrates good performance on the training dataset. Subsequently, the fully connected neural network constructed using this parameter set is used for online estimation of the signal's direction of arrival, resulting in lower complexity than the maximum likelihood method.

[0041] 2. The fully connected neural network proposed in this invention is unsupervised. The expression solved by the maximum likelihood method is used as the loss function of the fully connected neural network. Compared to existing supervised deep learning DOA estimation methods, it can complete signal direction-of-arrival estimation without a training dataset containing real angle labels, making it more suitable for scenarios where real angle labels are unavailable. The training dataset of this invention is the complex covariance matrix of samples generated from signals received by the array. Since the loss function of the fully connected neural network is the maximum likelihood expression, the training process of the fully connected neural network is essentially solving for the minimum value of the loss function. Therefore, the output neurons of the network can directly obtain the signal direction-of-arrival estimation result of this invention.

[0042] 3. The fully connected neural network proposed in this invention is regressive, and its estimation accuracy is not limited by grid precision or grid mismatch issues. Existing classification-based deep learning DOA estimation methods use an output neuron count equal to the predetermined grid count. If the grid precision is not set properly, the estimation results are prone to large errors. Furthermore, grid mismatch issues cause a decrease in the accuracy of classification-based deep learning DOA estimation methods. This invention employs a regressive fully connected neural network where the output neurons directly output the DOA estimation results, effectively avoiding the grid problem.

[0043] 4. The method disclosed in this invention exhibits superior performance in low signal-to-noise ratio (SNR) and low snapshot speed scenarios. Its performance in low snapshot speed scenarios aligns with the characteristic that traditional maximum likelihood DOA estimation methods are more suitable for such scenarios. This invention effectively solves the problem of poor performance of traditional maximum likelihood DOA estimation methods in low SNR scenarios. Attached Figure Description

[0044] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0045] Figure 1This is a flowchart of the maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning disclosed in this invention;

[0046] Figure 2 This is a network structure block diagram of an embodiment of the maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning disclosed in this invention;

[0047] Figure 3 This is a test result diagram using simulated data from the present invention. The simulation scenario involves an incident array of signals with 1-3 fixed snapshots but different signal-to-noise ratios. Figure 3 (a) Figure 3 (b) Figure 3 (c) is a performance comparison chart of deep learning methods and traditional maximum likelihood methods in a 200-shot scenario. Figure 3 (d) is a performance comparison chart of deep learning methods and traditional maximum likelihood methods in the 10-shot scenario;

[0048] Figure 4 This is a diagram showing the test results using simulated data from this invention. The simulation scenario involves 1-2 signal incident arrays with a fixed signal-to-noise ratio but different snapshot numbers. Figure 4 (a) is a graph comparing the impact of different snapshot numbers on the performance of the method of the present invention with other traditional methods in a signal scenario. Figure 4 (b) is a comparison graph showing the impact of different snapshot numbers on the performance of the method of the present invention under two signal scenarios, as well as with other traditional methods. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages 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 some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Example 1

[0051] This embodiment discloses a maximum likelihood direction-of-arrival (DOA) estimation method based on unsupervised machine learning. This method uses a large amount of training data with different signal-to-noise ratios and different snapshot numbers to fit the mapping relationship between the complex covariance matrix of the samples and the DOA of the signal. The theoretically optimal maximum likelihood method in traditional methods is used as the loss function to build a regression-type fully connected network. The network directly outputs the DOA estimation result of the signal.

[0052] As attached Figure 1 This is a flowchart of the maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning disclosed in this invention. Figure 2This is a network structure diagram of an embodiment of the maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning disclosed in this invention. This invention includes the following steps:

[0053] S1. Set the array signal processing model as follows: .in, It is the array output of the signal receiving array at time t, corresponding to the observed vector of the signal. It is the complex amplitude vector of the signal. It is additive noise, where N represents the number of snapshots, and the array response matrix is... abbreviated as , Is the i-th signal and The turning vector between them Indicates the direction of arrival of the signal. It is a real parameter. These represent the directions of arrival of the 1st, ..., i-th, ..., Kth signals, respectively.

[0054] S2, Set the array observation space range The signal-to-noise ratio (SNR) ranges from -17.5dB to 2.5dB. The number of snapshots N = {N1, N2}, where N1 = 200 and N2 = 10. The number of signals K = {K1, K2, K3}, where K1 = 1, K2 = 2, and K3 = 3. Given K independent, uniform linear arrays with N snapshots and M = 10 incident far-field narrowband signals, according to the formula... Generate datasets D for training fully connected neural networks, where [ ]* denotes the conjugate transpose operation, and the d-th sample is defined as D is the total number of samples, and the dataset is... , Let D represent the samples in group 1, group 2, ..., group D respectively. D = {D1, D2, D3, D4}, where D1 represents the dataset under one source with 200 snapshots, where K = K1 and N = N1; D2 represents the dataset under two sources with 200 snapshots, where K = K2 and N = N1; D3 represents the dataset under three sources with 200 snapshots, where K = K3 and N = N1; and D4 represents the dataset under two sources with 10 snapshots, where K = K2 and N = N2.

[0055] S3. Convert the sample covariance matrices of datasets D1, D2, D3, and D4 into two-channel real number matrices and then vectorize them.

[0056] S4. Construct an unsupervised machine learning fully connected regression neural network, corresponding to... Figure 1The regression-type fully connected network consists of nine neural network layers. The first layer is the input layer, containing the covariance matrix of the samples. The second layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The third layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The fourth layer includes a fully connected layer with 1280 neurons and a ReLU activation layer. The fifth layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The sixth layer includes a fully connected layer with 640 neurons and a ReLU activation layer. The seventh layer includes a fully connected layer with 320 neurons and a ReLU activation layer. The eighth layer includes a fully connected layer with 160 neurons and a ReLU activation layer. The ninth layer is the output layer with 2 neurons.

[0057] S5. Determine the loss function of the neural network. The theoretically optimal maximum likelihood method in traditional approaches is used to solve this. The minimum value of is used as the loss function of the neural network.

[0058] S6. Using the datasets D1, D2, D3, and D4 obtained after step S3, iteratively train the neural network until the loss function converges to its minimum value, thus obtaining the model parameter set. , , , , This represents the set of model parameters obtained from training dataset D1. This represents the set of model parameters obtained from training dataset D2. This represents the set of model parameters obtained from training on dataset D3. This represents the set of model parameters obtained from training on dataset D4;

[0059] S7. Using the model parameter set , , , The neural network is initialized separately, and the complex covariance matrix of the test signal samples with signal-to-noise ratio (SNR) = {-17.5, 15, -12.5, -10, -7.5, -5, -2.5, 0, 2.5} dB and angles of -10.55° and 5.25° is input into the neural network. The output neurons of the neural network directly obtain the estimated result of the signal direction of arrival.

[0060] The test results of this embodiment are as follows: Figure 3 As shown, where Figure 3(a) is the root mean square error curve of the direction angle in a signal scene with 200 snapshots. Figure 3 (b) shows the root mean square error curves of the direction angle for two signal scenarios with 200 snapshots. Figure 3 (c) shows the root mean square error curves of the direction angle for three signal scenarios with 200 snapshots. Figure 3 (d) shows the root mean square error curves of the direction angle for two signal scenarios with 10 snapshots. In the figure, "DL" represents the method proposed in this invention, "ML" represents the traditional maximum likelihood method, and "alternating projection ML" represents the alternating projection maximum likelihood method. Figure 3 (a) Figure 3 (b) Figure 3 (c) As can be seen, in low signal-to-noise ratio scenarios, the method disclosed in this invention performs better than or no worse than the traditional maximum likelihood method and its complexity-improved algorithm, alternating projection maximum likelihood method, for the estimation of direction of arrival for one or more signals. However, taking two signal simulation scenarios as an example, the alternating projection method takes 682.11s, while the method proposed in this invention takes only 0.170s, reducing the complexity by three orders of magnitude. Figure 3 (b) Figure 3 (d) It can be seen that the performance of the method proposed in this invention conforms to the theoretical characteristics of the maximum likelihood method, which is more suitable for low-speed shooting scenarios, and the estimation performance is superior in 10-speed shooting scenarios.

[0061] Example 2

[0062] This embodiment discloses a maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning. The present invention uses a large number of sample data with different snapshot numbers to fit the mapping relationship between the sample covariance matrix and the direction of arrival of the signal, which proves that the simulation results of the present invention are consistent with the traditional theoretical results.

[0063] The embodiments disclose the specific implementation steps of a maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning under different snapshot numbers.

[0064] S1. Set the array signal processing model as follows: .in, It is the array output of the signal receiving array at time t, corresponding to the observed vector of the signal. It is the complex amplitude vector of the signal. It is additive noise, where N represents the number of snapshots, and the array response matrix is... abbreviated as , Is the i-th signal and The turning vector between them Indicates the direction of arrival of the signal. It is a real parameter. These represent the directions of arrival of the 1st, ..., i-th, ..., Kth signals, respectively.

[0065] S2, Set the array observation space range The signal-to-noise ratio (SNR) is set to -10dB, the number of snapshots N is randomly generated between 10 and 190 snapshots, and the number of signals K = {K1, K2}. A uniform linear array of K independent far-field narrowband signal incident arrays M = 10 is used, according to the formula... Generate a dataset D for training a machine learning neural network. Here, [ ]* denotes the conjugate transpose operation, and the d-th sample group is defined as... D is the total number of samples, and the dataset is... , Let K represent the first group, the second group, ..., the Dth group of samples. D = {D1, D2}, where D1 represents the dataset under one source scenario, and K = K1. D2 represents the dataset under two source scenarios, and K = K2.

[0066] S3. Convert the sample covariance matrices of datasets D1 and D2 into two-channel real matrices and then vectorize them.

[0067] S4. Construct an unsupervised machine learning fully connected regression neural network, corresponding to... Figure 2 The regression-type fully connected network consists of nine neural network layers. The first layer is the input layer, containing the covariance matrix of the samples. The second layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The third layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The fourth layer includes a fully connected layer with 1280 neurons and a ReLU activation layer. The fifth layer includes a fully connected layer with 1280 neurons, a ReLU activation layer, and a Dropout layer with a dropout rate of p=0.03. The sixth layer includes a fully connected layer with 640 neurons and a ReLU activation layer. The seventh layer includes a fully connected layer with 320 neurons and a ReLU activation layer. The eighth layer includes a fully connected layer with 160 neurons and a ReLU activation layer. The ninth layer is the output layer with 2 neurons.

[0068] S5. Determine the loss function of the neural network. The theoretically optimal maximum likelihood method in traditional approaches is used to solve this. The minimum value of is used as the loss function of the neural network.

[0069] S6. Using the datasets D1 and D2 obtained in step S3, iteratively train the neural network until the loss function converges to its minimum value, thus obtaining the model parameter set. , , This represents the set of model parameters obtained from training dataset D1. This represents the set of model parameters obtained from training dataset D2;

[0070] S7. Using the model parameter set , The neural network is initialized to generate a number of snapshots N={10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190}, a signal-to-noise ratio SNR=-10dB, and complex covariance matrices of test signal samples with angles of -10.55° and 5.25°. The output neurons of the neural network directly obtain the estimated result of the signal direction of arrival.

[0071] The test results of this embodiment are as follows: Figure 4 As shown, Figure 4 (a) shows the impact of different snapshot numbers on DOA estimation results in a scenario with a fixed signal-to-noise ratio. Figure 4 (b) shows the impact of different snapshot numbers on DOA estimation results under two scenarios with fixed signal-to-noise ratios. In the figure, "DL" represents the method proposed in this invention, and "alternating projection ML" represents the alternating projection maximum likelihood method.

[0072] The test results of this embodiment are as follows: Regardless of whether it is a single-source or multi-source estimation scenario, the method proposed in this invention has better performance in low snapshot scenarios, which is consistent with the theoretical analysis results of the traditional alternating projection algorithm and the maximum likelihood algorithm being applicable to low signal-to-noise ratio and low snapshot scenarios, and indirectly verifies the theoretical interpretability of the proposed model.

[0073] In summary, this invention proposes a maximum likelihood direction-of-arrival (DOA) estimation method based on unsupervised machine learning. By leveraging the custom loss function characteristic of unsupervised learning, it combines the theoretically optimal maximum likelihood method with deep learning techniques, shifting the algorithmic complexity to the offline training stage of the network. This simultaneously addresses the high complexity of the maximum likelihood method and the difficulty in obtaining true angle labels in deep learning methods. A regression-type fully connected network structure is chosen, ensuring that the estimation accuracy is not limited by grid precision or grid mismatch issues. Simulation results show that the proposed method is more suitable for low-speed-capture scenarios, conforms to the theoretical characteristics of the traditional maximum likelihood method, and solves the problem of poor performance of the maximum likelihood method in low signal-to-noise ratio scenarios. Compared to traditional maximum likelihood DOA estimation methods and mainstream deep learning DOA estimation methods, the proposed method has lower complexity, does not require true angle labels, and is suitable for scenarios where true angle labels are difficult to obtain, making it effectively applicable to the field of DOA estimation.

[0074] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning, characterized in that, The direction-of-arrival estimation method includes the following steps: S1. Set the number of array elements M, the number of signal sources K, and the array observation space range in the signal receiving array. Array response matrix ; S2. Generate a dataset D for training a machine learning neural network. Each data sample in dataset D includes a complex covariance matrix. And the corresponding number of signals K; S3. Extract the complex covariance matrix of the samples from dataset D. Convert it into a two-channel real matrix and then vectorize it to obtain the real covariance matrix. ; S4. Construct an unsupervised machine learning regression fully connected neural network; S5. Set the loss function for the fully connected neural network to achieve unsupervised learning without needing to set real angle labels. The expression for the loss function is as follows: ， Where [ ]* denotes the conjugate transpose operation on the matrix. The expression indicates that the matrix is ​​inverted, and tr{} indicates that the trace of the matrix is ​​found, which is the sum of the elements on the main diagonal of the matrix. S6. Using the dataset obtained in step S3, iteratively train the fully connected neural network until the loss function converges to its minimum value, thus obtaining the model parameter set ζ. * ; S7. Using the model parameter set ζ * Initialize a fully connected neural network to generate a covariance matrix of K test signal samples. After normalization and vectorization, the matrix is ​​input into the fully connected neural network. The estimated direction of arrival (DOA) of the signal is directly obtained through the output neurons of the fully connected neural network. ,in, These represent the directions of arrival of the 1st, ..., Kth sources, respectively.

2. The maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning according to claim 1, characterized in that, The process of generating the dataset D for training the neural network in step S2 is as follows: Assuming K independent far-field narrowband signal incident signal receiving arrays, the signal receiving arrays are uniform linear arrays with M array elements, then the sample complex covariance matrix R Y for: , in, It is the array output of the signal receiving array at time t, N is the number of snapshots, and [ ]* indicates the number of snapshots. The conjugate transpose operation, the d-th sample is defined as D is the total number of samples, and the dataset is... , Let them represent the samples in group 1, group 2, ..., group D, respectively.

3. The maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning according to claim 1, characterized in that, In step S3, the complex covariance matrix of the samples is... Decomposed into a two-channel real matrix ,in It is a four-dimensional matrix, with its second dimension carrying the real and imaginary parts respectively. , , and These represent the operations of extracting the real part and the imaginary part, respectively. Finally, the operations are performed on... Vectorization.

4. The maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning according to claim 1, characterized in that, The fully connected neural network consists of an input layer, several hidden layers, a Dropout layer, and an output layer connected sequentially. The input layer is the first layer of the fully connected neural network, which imports the covariance matrix of the samples. The number of hidden layers and neurons varies depending on the application scenario and simulation performance. The Dropout layer is used to suppress overfitting. The output layer is the last layer of the fully connected neural network, which outputs the mapping relationship between the sample covariance matrix fitted in the fully connected neural network and the DOA estimation result. The number of output neurons in the output layer is equal to the number of information sources, and the output value of the output neurons is the DOA estimation result.

5. The maximum likelihood direction-of-arrival estimation method based on unsupervised machine learning according to claim 1, characterized in that, The process of determining the loss function in step S5 is as follows: The problem of direction-of-arrival estimation for narrowband source sensor arrays in the field of signal processing is reduced to parameter estimation based on the following model: ， in, It is the array output of the signal receiving array at time t, corresponding to the observed vector of the signal. It is the observation vector of the signal. It is the complex amplitude vector of the signal. It is additive noise, where N represents the number of snapshots, and the array response matrix is... abbreviated as , Is the i-th signal and The turning vector between them Indicates the direction of arrival of the signal. It is a real parameter. These represent the directions of arrival of the 1st, ..., i-th, ..., Kth signals, respectively. Maximum likelihood estimation of the signal's direction of arrival (DOA) is performed. The above model satisfies the following conditions: the number of array elements M is greater than the number of sources K, and the number of snapshots N is greater than the number of array elements M; noise signals at different snapshot numbers are uncorrelated, and the noise received by each array element is normally distributed; the sample complex covariance matrix... It is positive definite, yes. Taking the likelihood function, we get: ， In the formula, M is the number of array elements. Let V be the variance of the noise received by each array element; then, taking the log-likelihood function, the expression is as follows: ， The calculation and derivation yielded the following: , , ， In the formula, yes Maximum likelihood estimation, yes Maximum likelihood estimation, yes Maximum likelihood estimation, yes Maximum likelihood estimation, It is a common constant, Substitution , Undetermined, by By substitution, we obtain the likelihood function as , ； At this point, the solution is needed. Find the minimum value, and obtain The maximum likelihood estimate is to Set as the loss function for a fully connected neural network.

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