A lightweight deep neural network array direction finding method based on data deduplication

Abstract

This invention discloses a lightweight deep neural network array direction finding method based on data redundancy removal, which solves the problem that the traditional RDNN direction finding method has a large number of deep neural network nodes and cannot achieve network lightweighting. The method performs redundancy removal operation on the upper triangular elements of the covariance matrix, simplifies the number of subsequent hidden layer nodes, reduces the computational complexity of the model, and ensures that the direction finding accuracy of the model is not lost, thus realizing high-precision direction finding of lightweight deep neural networks.

Description

Technical Field

[0001] This invention belongs to the field of sensor technology, specifically relating to a lightweight deep neural network array direction finding method. Background Technology

[0002] The array direction finding estimation problem aims to estimate the input angle of a signal source by analyzing the correlation output of the array of received signals, and is a typical research topic in the field of signal processing. The MUSIC (Multiple Signal Classification) algorithm, proposed by ROSchmidt in 1979 in the paper "Multiple emitter location and signal parameter estimation[J].IEEE Transactions on Antennas and Propagation.1986,34(3),pp:276-280", divides the received data into two mutually orthogonal subspaces: a noise subspace and a signal subspace, by performing singular value decomposition on the covariance matrix data received by the array. A search space spectrum is constructed using the noise subspace, and the estimated angle value is obtained by searching for spectral peaks in the space spectrum. This method provides accurate estimation, but its computational complexity is high, and it does not meet the requirements for real-time processing. To reduce computational complexity, many studies in recent years have adopted machine learning techniques to solve the array direction finding estimation problem. In 2005, M. Pastorino and A. Randazzo used support vector regression to achieve array direction finding estimation in the paper "A smartantenna system for direction of arrival estimation based on a support vector regression. IEEE Trans. Antennas Propag., vol. 53, no. 7, pp. 2161–2168," which was more computationally efficient than subspace-based methods. In 2015, Xiao, Xiong, et al. used a classification-based single-layer neural network model to achieve array direction finding estimation in "A learning-based approach to direction of arrival estimation innoisy and reverberant environments. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2015): 2814-2818." However, due to the use of only one hidden layer, the neural network was trapped in local minima, resulting in poor direction finding performance. Subsequently, more and more improved neural networks have been proposed to solve the array direction finding estimation problem.In 2018, Z. Liu et al. proposed a method for direction finding of targets using classification-based deep neural networks (DNNs) in the paper "Direction-of-Arrival Estimation Based on Deep Neural Networks With Robustness to Array Imperfections[J], IEEE Transactions on Antennas and Propagation, 2018, 66(12), pp:7315-7327". The output dimension is the number of grids within the observation angle range, and the large output dimension leads to the complexity of the network model. In 2022, Y. Tao et al. proposed a regression-based deep neural network (RDNN) for array direction finding in the paper "DOAEstimation Using Deep Neural Network with Regression", which is called the traditional RDNN direction finding method. The output dimension of traditional RDNN direction finding methods is the number of targets, which significantly reduces the output dimension of classification-based deep neural network direction finding methods. However, this method uses the upper triangular elements of the covariance matrix as the input of the RDNN, without considering the redundant information in the elements of the covariance matrix, resulting in a large number of hidden layer nodes, making it difficult to achieve lightweight deep neural networks. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention provides a lightweight deep neural network array direction finding method based on data redundancy removal, which solves the problem that the traditional RDNN direction finding method has a large number of deep neural network nodes and cannot achieve network lightweighting. This method performs redundancy removal operation on the upper triangular elements of the covariance matrix, simplifies the number of subsequent hidden layer nodes, reduces the computational complexity of the model, and ensures that the direction finding accuracy of the model is not lost, thus achieving high-precision direction finding of lightweight deep neural networks.

[0004] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0005] Step 1: A uniform linear array is formed using M scalar sensors as array elements; K far-field, narrowband target signals are incident on the uniform linear array, with the angle of arrival of the k-th signal being θ. k The received signal of the m-th array element is r. m The observation data vector of M array elements is r(t) = [r1(t), r2(t), ..., r M (t)] H ,(·) HThis represents the conjugate transpose operation;

[0006] Step 2: Construct the covariance matrix N is the number of samples;

[0007] Step 3: [Regarding...] Performing a redundancy removal operation yields a one-dimensional vector of size M-1.

[0008] Step 4: According to Obtain a training data-label set consisting of I sets of data-label pairs {(x1,y1),(x2,y2),...,(x I ,y I )};

[0009] Step 5: Utilize the training data - label set {(x1,y1),(x2,y2),...,(x I ,y I Training deep neural networks;

[0010] Step 6: During the testing phase, obtain input data x that is not in the training dataset. t The values ​​are input into the deep neural network trained in step 5 to obtain the output angle estimate.

[0011] Preferably, in step 3:

[0012] Calculate a one-dimensional vector The values ​​of each element in the array are represented by b. m The value of the m-th element in the vector is calculated using the following formula: Among them, a i,(i-m) Represented as The element corresponding to index i, (im).

[0013] Preferably, step 4 specifically comprises:

[0014] Step 4-1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The real and imaginary parts of each element in the vector are concatenated, and then normalized to obtain a one-dimensional vector x of size 2M-2, denoted as . Where ||·||2 represents the 2-norm; the corresponding label data is a K-dimensional vector y, where the l-th element of y is the true input angle value of the l-th target signal, i.e., y(l) = θ. l Where l = 1, 2, ..., K;

[0015] Step 4-2: Obtain I sets of observation data {r} under different scenarios i (n), i = 1, 2, ..., I}, and according to steps 2 and 3, obtain group I. According to step 4-1, the training data-label set {(x1,y1),(x2,y2),...,(x1,y1),(x2,y2),...,(x2,y2),...,(x2,y1 ... I ,y I )}.

[0016] Preferably, step 5 specifically comprises:

[0017] Step 5-1: Input the training data obtained in step 4 into the input layer of the deep neural network;

[0018] Step 5-2: The input vector propagates from the input layer through the hidden layers to the output layer, and the output vector of the l-th layer is represented as net. l The calculation rule is: net l =W l,l-1 h l-1 +b l ,l=1,2,…,L-1, where L is the total number of layers in the network model excluding the input layer, W l,l-1 Let b be the fully connected feedforward weight matrix between layer (l-1) and layer l. l h is the bias vector of the l-th layer; l =g l (net l ), where g l Let g be the activation function for the l-th layer. Set the activation function to g. l =tanh, where α is any element in the output vector of the hidden layer;

[0019] Step 5-3: The output vector generated by the output layer of the deep neural network is represented as net. L =W L,L-1 h L-1 +b L During the training phase, the network model parameters are adjusted to make the output vector approximate the true label value.

[0020] Step 5-4: Update the network model parameters. Let Ω denote all parameters in the network model. Minimize the loss function to update the network parameters through backpropagation. The loss function is defined as follows: Among them net L,(i) Let y be the output vector corresponding to the i-th input vector. i Let be the true label value of the i-th input vector, and D be the number of input vectors.

[0021] The beneficial effects of this invention are as follows:

[0022] This invention, while maintaining the accuracy of array direction finding estimation, simplifies the input information by removing redundancy, thereby reducing the number of nodes in each layer of the deep neural network model and lowering the computational complexity, resulting in a lightweight deep neural network. The lightweighting effect of this invention is even more pronounced for array direction finding models with large amounts of input information. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention.

[0024] Figure 2 This is the curve showing the change of RMSE (Rating Root Mean Square) as a function of signal-to-noise ratio (SNR) in an embodiment of the present invention.

[0025] Figure 3 This is the curve showing the change of RMSE (Relative Root Meaning) with the number of snapshots in the embodiment of the present invention.

[0026] Figure 4 This is the curve showing the change of the RMSE of the angle estimation as a function of the estimated angle interval in an embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] The purpose of this invention is to provide a lightweight deep neural network model for array direction finding.

[0029] This invention discloses a lightweight deep neural network array direction finding method, wherein the array is a uniform linear array composed of M scalar sensors; the sensor array receives K far-field, narrowband target signals, and the angle of arrival of the k-th target is θ. k The specific implementation steps include:

[0030] (1) A uniform linear array consists of M array elements, and K far-field, narrowband target signals are incident on the array. The received signal of the m-th array element is r. m The observation data vector of M array elements is r(t) = [r1(t), r2(t), ..., r M (t)] H ,in,(·) H This represents the conjugate transpose operation;

[0031] (2) Construct the covariance matrix Where N is the number of samples;

[0032] (3) Performing a redundancy removal operation yields a one-dimensional vector of size M-1.

[0033] (4) According to Obtain a training data-label set consisting of I sets of data-label pairs {(x1,y1),(x2,y2),...,(x I ,y I )};

[0034] (5) Using the training data-label set {(x1,y1),(x2,y2),...,(x...} I ,y I Training deep neural networks;

[0035] (6) During the testing phase, obtain input data x that is not in the training dataset. t The input is fed into the deep neural network trained in step (5) to obtain the output angle estimate.

[0036] For a lightweight deep neural network array direction finding method based on data redundancy removal, the specific implementation steps of step (3) include:

[0037] Calculate a one-dimensional vector The values ​​of each element in the array are represented by b. m The m-th element in the vector is represented by the following formula: Among them, a i,(i-m) Represented as The element corresponding to index i, (im).

[0038] For a lightweight deep neural network array direction finding method based on data redundancy removal, the specific implementation steps of step (4) include:

[0039] (4.1) will The real and imaginary parts of each element in the vector are concatenated, and then normalized to obtain a one-dimensional vector x of size 2M-2, denoted as . Where ||·||2 represents the 2-norm; the corresponding label data is a K-dimensional vector y (where K is the number of target signals), and the l-th element of y is the true input angle value of the l-th target signal, i.e., y(l) = θ. l , where l = 1, 2, ..., K.

[0040] (4.2) Obtain I sets of observation data {r} under different scenarios i (n), i=1,2,…,I}, and according to steps 2-3, obtain group I. According to step (4.1), the training data-label set {(x1,y1),(x2,y2),...,(x1,y1),(x2,y2),...,(x2,y2),...,(x2,y1 ... I ,y I )}.

[0041] For a lightweight deep neural network array direction finding method based on data redundancy removal, the specific implementation steps of step (5) include:

[0042] (5.1) Input the training data obtained in step 4 into the input layer.

[0043] (5.2) The input vector propagates from the input layer through the hidden layers to the output layer. The output vector of the l-th layer is represented as net. l The calculation rule is: net l =W l,l-1 h l-1 +b l ,l=1,2,…,L-1, where L is the total number of layers in the network model excluding the input layer, W l,l-1 Let b be the fully connected feedforward weight matrix between layer (l-1) and layer l. l h is the bias vector of the l-th layer; l =g l (net l ), where g l Let g be the activation function for the l-th layer. Set the activation function to g. l =tanh, where α is any element in the output vector of the hidden layer.

[0044] (5.3) The output vector generated by the output layer is represented as net. L =W L,L-1 h L-1 +b L During the training phase, the network model parameters are adjusted to make the output vector approximate the true label value.

[0045] (5.4) Update the network model parameters. Let Ω denote all parameters in the network model. Minimize the loss function to update the network parameters through backpropagation. The loss function is defined as follows: Among them net L,(i) Let y be the output vector corresponding to the i-th input vector. i Let be the true label value of the i-th input vector, and D be the number of input vectors.

[0046] Example:

[0047] Combination Figure 1 The processing flow of the present invention includes the following steps:

[0048] The sensor array is a uniform linear array composed of M scalar sensors; the sensor array receives K far-field, narrowband target signals, and the angle of arrival of the k-th target is θ. k ;

[0049] A lightweight deep neural network array direction finding method based on data redundancy removal, the specific implementation steps of which include:

[0050] (1) The array consists of M elements, and K far-field, narrowband target signals are incident on the array. The received signal of the m-th element is r. m The observation data vector of M array elements is r(t) = [r1(t), r2(t), ..., r M (t)] H ,in,(·) H This represents the conjugate transpose operation;

[0051] (2) Construct the covariance matrix Where N is the number of samples;

[0052] (3) Performing a redundancy removal operation yields a one-dimensional vector of size M-1.

[0053] (3.1) Define a one-dimensional vector of size M-1. Initialize the size of the elements in the vector to 0.

[0054] (3.2) Calculate a one-dimensional vector The size of each element in the , expressed in b m The m-th element in the vector is represented by the following formula: Among them, a i,(i-m) Represented as The element corresponding to index i, (im).

[0055] (4) According to Obtain a training data-label set consisting of I sets of data-label pairs {(x1,y1),(x2,y2),...,(x I ,y I )};

[0056] (4.1) will The real and imaginary parts of each element in the vector are concatenated, and then normalized to obtain a one-dimensional vector x of size 2M-2, denoted as . Where ||·||2 represents the 2-norm; the corresponding label data is a K-dimensional vector y (where K is the number of target signals), and the l-th element of y is the true input angle value of the l-th target signal, i.e., y(l) = θ. l , where l = 1, 2, ..., K.

[0057] (4.2) Obtain I sets of observation data {r} under different scenarios i (n), i=1,2,…,I}, and according to steps 2-3, obtain group I. According to step (4.1), the training data-label set {(x1,y1),(x2,y2),...,(x1,y1),(x2,y2),...,(x2,y2),...,(x2,y1 ... I ,y I )}.

[0058] (5) Using the training data-label set {(x1,y1),(x2,y2),...,(x...} I ,y I Training deep neural networks;

[0059] (5.1) Input the training data obtained in step 4 into the input layer.

[0060] (5.2) The input vector propagates from the input layer through the hidden layers to the output layer. The output vector of the l-th layer is represented as net. l The calculation rule is: net l =W l,l-1 h l-1 +b l ,l=1,2,…,L-1, where L is the total number of layers in the network model excluding the input layer, W l,l-1 Let b be the fully connected feedforward weight matrix between layer (l-1) and layer l. l h is the bias vector of the l-th layer; l =g l (net l ), where g l Let g be the activation function for the l-th layer. Set the activation function to g. l =tanh, where α is any element in the output vector of the hidden layer.

[0061] (5.3) The output vector generated by the output layer is represented as net. L =W L,L-1 h L-1 +b L During the training phase, the network model parameters are adjusted to make the output vector approximate the true label value.

[0062] (5.4) Update the network model parameters. Let Ω denote all parameters in the network model. Minimize the loss function to update the network parameters through backpropagation. The loss function is defined as follows: Among them net L,(i) Let y be the output vector corresponding to the i-th input vector. i Let be the true label value of the i-th input vector.

[0063] (6) During the testing phase, obtain input data x that is not in the training dataset. tThe input is fed into the deep neural network trained in step (5) to obtain the output angle estimate.

[0064] The invention will be further described below with reference to simulation examples.

[0065] The sensor array consists of 11 array elements, which are uniformly and linearly arranged at intervals of λ / 2; the target signal is a far-field, narrow-band signal; the noise is Gaussian white noise, and the target signal is uncorrelated with the noise; the Monte Carlo degree is 100.

[0066] The deep neural network of this invention consists of an input layer, three hidden layers, and an output layer. The input layer has 2M-2 = 20 neurons, and the hidden layers have 26, 26, and 16 neurons respectively. Each hidden layer is followed by a tanh nonlinear activation function. The output layer has K neurons, where K is the number of target signals. Table 1 compares the network parameter count of this invention with that of a traditional RDNN. Note that the input of a traditional RDNN is a covariance matrix excluding the upper triangular elements of the diagonal, with a dimension of M(M-1) = 110, and the number of hidden layer neurons is 50, 50, and 30 respectively. Table 2 compares the number of multiplication and addition operations of this invention with that of a traditional RDNN, where the number of multiplication and addition operations is equal and represented by the same numerical value.

[0067] Training dataset construction: The target angle search interval is [-60°, 60°), and the search step size η = 0.1° is set. Consider two target signal scenarios, i.e., K = 2, and the set of these two target angle intervals is S = {2°, 4°, ..., 60°}, covering scenarios from close to far apart target signal intervals. The first target angle range θ1 ∈ [-60°, 60° - Δ s ), where Δ s This represents the angle between the two targets selected in S, with the second angle set as θ2 = θ1 + Δ. s Random noise was added to each set of target angles, and 10 sets of data were collected. Each set of data was labeled as x. i , where the subscript i is the data sequence number. x i Data label y i Let K be the true angle values ​​of the target signals. Additionally, consider training the network simultaneously using data from multiple signal-to-noise ratio scenarios, with multiple signal-to-noise ratios {-10dB, 10dB, 30dB}. The final dataset contains (118+116+...+60)×3=8010 covariance vectors and their labels, forming a data-label set {(x1,y1),(x2,y2),...,(x...}. I ,y I )}.

[0068] During the testing phase, the estimated angle accuracy was two decimal places. Three sets of experiments were conducted based on changes in experimental conditions:

[0069] (1) The root mean square error (RMSE) curve of angle estimation corresponding to the method of the present invention and the traditional RDNN deep neural network method using the upper triangular elements of the matrix varies with the signal-to-noise ratio (SNR) as follows: Figure 2 As shown, where, For the target signal power, This represents noise power. Estimated angle values ​​are -30.55° and -20.25°; the number of snapshots is set to 400.

[0070] (2) The root mean square error (RMSE) curves of angle estimation corresponding to the method of the present invention and the traditional RDNN deep neural network method using the upper triangular elements of the matrix change with the number of snapshots as follows: Figure 3 As shown. The estimated angle values ​​are -30.55° and -20.25°, and the signal-to-noise ratio (SNR) is set to 0dB.

[0071] (3) The root mean square error (RMSE) curves of angle estimation corresponding to the method of the present invention and the traditional RDNN deep neural network method using the upper triangular elements of the matrix change with the estimated angle interval as follows: Figure 4 As shown. The number of snapshots is set to 400, and the signal-to-noise ratio (SNR) is set to 0dB.

[0072] From Table 1, Table 2 and Figures 2-4 It can be seen that the method of the present invention can greatly reduce the amount of computation and parameters compared with the traditional RDNN deep neural network, while achieving similar performance to the traditional method. Therefore, it can realize lightweight target direction finding and serve the real-time embedded application of deep learning in target direction finding.

[0073] Table 1 Comparison of parameter counts for different deep neural network techniques

[0074] Parameters Hidden layer 1 Hidden layer 2 Hidden layer 3 Output layer total Method of the present invention 20×26+26＝546 26×26+26＝702 26×16+16＝432 16×2+2＝34 1714 Traditional RDNN 110×50+50＝5550 50×50+50＝2550 50×30+30＝1530 30×2+2＝62 9692

[0075] Table 2 Comparison of computational complexity for different deep neural network techniques

[0076] Number of multiplication / addition calculations Hidden layer 1 Hidden layer 2 Hidden layer 3 Output layer total Method of the present invention 20×26＝520 26×26＝676 26×16＝416 16×2＝32 1644 Traditional RDNN 110×50＝5500 50×50＝2500 50×30＝1500 30×2＝60 9560

Claims

1. A lightweight deep neural network array direction finding method based on data redundancy removal, characterized in that, Includes the following steps: Step 1: From M A scalar sensor is used as an array element to form a uniform linear array. K A far-field, narrowband target signal is incident on a uniform linear array, and the first... k The signal arrival angle is ; No. m The received signal of each array element is , M The observation data vector of each array element is , This represents the conjugate transpose operation; Step 2: Construct the covariance matrix , The number of samples; Step 3: [Regarding...] Perform a redundancy removal operation to obtain a size of M-1 a one-dimensional vector ; Step 4: According to , obtain by I Training data consisting of sets of data and label pairs - label set Step 4 specifically involves: Step 4-1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] The real and imaginary parts of each element in the equation are concatenated, and then normalized to obtain an integer of size 2. M-2 a one-dimensional vector , Represented as ,in Represents the 2-norm; the corresponding label data is K A vector y of dimension , the first dimension of y l The element is the first l The true input angle value of the target signal is ,in ; Step 4-2: Obtaining in different scenarios I Group observation data And based on steps 2 and 3, obtain I Group According to step 4-1, the result is obtained from... I Training data consisting of sets of data and label pairs - label set ; Step 5: Utilize the training data - label set Training a deep neural network; step 5 specifically involves: Step 5-1: Input the training data obtained in step 4 into the input layer of the deep neural network; Step 5-2: The input vector propagates from the input layer through the hidden layers to the output layer, thus... l The output vector of the layer is represented as The calculation rules are as follows: ,in L It is the total number of layers in the network model after removing the input layer. For the ( l -1) layer and the l Fully connected feedforward weight matrix between layers For the first l Layer bias vector; ,in For the first l The activation function of the layer; set the activation function to ,in , is any element in the output vector of the hidden layer; Step 5-3: The output vector generated by the output layer of the deep neural network is represented as follows: During the training phase, the network model parameters are adjusted to make the output vector approximate the true label value. Step 5-4: Update the network model parameters, and denote all parameters in the network model as follows: Minimize the loss function to update the network parameters through backpropagation. The loss function is defined as follows: ,in denoted as corresponding to the first i The output vector of an input vector. For the first i The true label values ​​of each input vector. D The number of input vectors; Step 6: Testing phase, obtaining input data not in the training dataset. The values ​​are input into the deep neural network trained in step 5 to obtain the output angle estimate.

2. The lightweight deep neural network array direction finding method based on data redundancy removal according to claim 1, characterized in that, In step 3: Calculate a one-dimensional vector The values ​​of each element in the middle are used Represents the first vector in the vector. m The value of each element is calculated using the following formula: ,in, Represented as The corresponding subscript is Element.

Images