A method for direction of arrival estimation based on pulse neural convolution network

Abstract

The present application relates to the technical field of radar target signal direction finding, and proposes a wave direction estimation method based on a pulse neural convolutional network.The pulse neural network used by the present application is a neural network model most similar to the brain, which is derived from biological inspiration, has biological interpretation and learning mechanism, and is applied to a convolutional neural network to create a pulse neural-convolutional network, i.e., an SNC type network.The SNC type network model uses a leaky integrate-and-fire neuron in the pulse neuron model, and can realize the updating of weights and hyperparameters by using a back propagation algorithm.The simulation shows that the SNC network has the effect of obviously improving the estimation accuracy.

Description

Technical Field

[0001] This invention relates to the field of radar target signal direction finding technology, and uses deep learning methods to estimate the direction of arrival of echo signals. Background Technology

[0002] Direction of Arrival (DOA) estimation is a broad research area with applications in wireless communication, astronomical observation, radar, and sonar. In radar target signal direction finding, DOA estimation is achieved through model-driven methods. These methods first establish a forward parametric model from the signal direction to the array output, and then use the properties of pre-assumed formulas to estimate the direction. The performance of these model-driven methods largely depends on the accuracy of the pre-defined model. However, in practical applications, limitations such as cost, physical constraints, or site constraints make it difficult to obtain arrays with sufficiently high resolution, thus affecting the accuracy of DOA estimation. Furthermore, in complex signal propagation environments, multipath effects and noise can interfere with DOA estimation, potentially reducing its accuracy. Some applications require high real-time performance for DOA estimation, while traditional subspace-based techniques typically require significant computation time to complete the estimation process, limiting the accuracy of the direction of arrival under non-ideal conditions. This may limit the availability of these methods in real-time applications. Summary of the Invention

[0003] To address the limitation of DOA estimation accuracy caused by traditional uniform linear arrays, this invention proposes a DOA estimation method based on a spiking neural-convolutional network (SNC) within the field of deep learning. This technique combines convolutional layers and spiking neurons to create a type of spiking neural-convolutional network (SNC). First, for the received DOA data, the sparse spatial spectrum of the received signal is expanded and imported into the SNC network model of this invention for training and validation to obtain the corresponding parameters. Then, test data is imported, and the corresponding spectral peak is found based on the output spectral peak value; this peak represents the DOA to be estimated.

[0004] Technical solution:

[0005] A DOA estimation method based on spiking neural convolutional networks specifically includes the following steps:

[0006] S1: Narrowband far-field wave signals are received through an array antenna with a uniform array structure, and the received signal information for each snapshot is y0(t); the covariance matrix is ​​calculated based on the received signal information.

[0007] S2: For the covariance matrix Vectorization is performed to obtain the virtual array received signal. Calculate the sparse spatial spectrum of the received signal;

[0008] S3: Based on the sparse spatial spectrum of the received signal Create a dataset and its corresponding labels. The dataset is a collection of sparse spatial spectra of the signal after traversing a certain range, and the corresponding labels are set to 1 for the position of the corresponding direction of arrival and 0 for the rest, and are divided into training set and validation set.

[0009] S4: Construct an improved spiking neural convolutional network and set up the SNC-type network in this invention;

[0010] S5: Import the training data into the network, perform forward propagation, minimize the loss function, and then perform back propagation to calculate the weights. and deviation Update;

[0011] S6: Based on the trained network, input the spatial sparse spectrum of the test signal. Estimate the direction of arrival of the target signal source.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] This invention combines deep learning methods with the problem of DOA estimation for array radar echo signals. It leverages the advantage of spiking neurons using pulse signals to transmit and process information, combining it with convolutional neural networks to improve the estimation accuracy during training and validation. Furthermore, it employs the Adam optimizer to dynamically update the learning rate, reducing the loss function in the network. In angle testing experiments, the proposed SNC-type network effectively estimates the DOA of the target signal, exhibiting superior network performance. Attached Figure Description

[0014] Figure 1 Schematic diagram of the method flow of this invention;

[0015] Figure 2 A schematic diagram illustrating the principle of the spiking neuron of this invention;

[0016] Figure 3 A schematic diagram of the SNC neural network framework of this invention;

[0017] Figure 4 Comparison of training set loss functions of the network of the present invention when the number of signals is 2;

[0018] Figure 5 Comparison of training set accuracy of the network of the present invention when the number of signals is 2;

[0019] Figure 6Comparison of validation set loss functions of the network of the present invention when the number of signals is 2;

[0020] Figure 7 Comparison of validation set accuracy of the network of the present invention when the number of signals is 2 (Example);

[0021] Figure 8 Example: Comparison of test set errors of the network of the present invention at different signal-to-noise ratios when the number of signals is 2;

[0022] Figure 9 Example: Comparison of test set errors when the number of signals is 2 and the network of the present invention is separated at different angles;

[0023] Figure 10 Example: Comparison of spectral peaks of the network of the present invention at different angles when the number of signals is 2. Detailed Implementation

[0024] Neural networks are a crucial technology in machine learning and artificial intelligence, having made significant progress and possessing powerful learning capabilities. Trained on massive amounts of data, they can learn complex patterns and relationships. Neural networks can also automatically extract and represent features from data, enabling highly accurate classification, regression, and prediction tasks. Furthermore, neural networks can handle nonlinear relationships, and their computational processes can be highly parallelized, giving them high computational efficiency and processing power for large-scale data and complex tasks. The rise of deep learning has enabled neural networks to excel in image, speech, and natural language processing, encompassing fields such as medical diagnosis, intelligent transportation, financial analysis, and recommender systems. However, their application in radar signal processing is currently limited; therefore, using neural networks to solve the DOA estimation problem requires further research and exploration.

[0025] Spiking Neural Networks (SNNs) are neural network models that simulate the transmission of pulse signals in a nervous system. They mimic the pulse transmission mechanism in biological neural systems, where information is transmitted in the form of discrete pulses. Compared to traditional continuous-value neural networks, spiking neural networks achieve higher energy efficiency in processing and transmitting information. However, the application of spiking neural networks in array signal processing is relatively limited; therefore, exploring the use of spiking neurons in signal processing is worthwhile.

[0026] This invention combines convolutional layers and spiking neurons to create a Spiking Neural-Convolutional Network (SNC), also known as an SNC-type network. First, for the received data of the DOA (Depth of Allocation), the sparse spatial spectrum of the received signal is expanded and imported into the SNC network model of this invention for training and validation to obtain the corresponding parameters. Then, test data is imported, and the corresponding spectral peak is found based on the output spectral peak value, which is the DOA to be estimated.

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

[0028] Example

[0029] The flowchart of the method of this invention is shown below. Figure 1 As shown, the process is as follows:

[0030] S1: Narrowband far-field wave signals are received through an array antenna with a uniform array structure, and the received signal information for each snapshot is y0(t); the covariance matrix is ​​calculated based on the received signal information. Specifically:

[0031] Consider K narrowband far-field sources θ k Let k = 1, 2, ..., K be incident on a uniform linear array, which consists of M sensors. λ is the element spacing, and λ is the wavelength of the signal carrier. The signal information received by the sensor at the t-th snapshot (t = 1, 2, ..., T) is represented as...

[0032]

[0033] The data mentioned is received at time t. θ is the signal reception steering vector. k Let be the DOA of the k-th signal, and n(t) be the noise term following a Gaussian distribution. Here, j is the imaginary unit, and s... k (t) represents the k-th signal, and t represents a time-domain snapshot. Let... Let A be a discrete set of directions sampled from the latent space of the incident signal. Let L represent the sampling interval, and L be the number of discrete directions to be divided. The true source direction θ is included in Φ, resulting in a smaller quantization error. Therefore, the received signal can be reformulated in an overcomplete form as follows:

[0034]

[0035] Here Sometimes, otherwise Using the statistical properties of the signal, the covariance matrix is ​​calculated as follows:

[0036]

[0037] in This represents the signal strength on the l-th grid. A space spectrum is a non-zero element if and only if it is located at the true source location; therefore, the spatial spectrum... It is sparse. The symbol (·) represents this. T For transpose, (·) H This is the conjugate transpose. Let V be the variance of the Gaussian noise, and I represent the identity matrix.

[0038] S2: For the covariance matrix Vectorization is performed to obtain the virtual array received signal. Calculate the sparse spatial spectrum of the received signal; specifically:

[0039] The m-th column of the covariance matrix obtained from the received data can be re-represented as follows:

[0040]

[0041] here e m It is an M×1 vector, where the m-th element is 1 and all other elements are 0. Therefore, it can be vectorized. To define a new measurement vector,

[0042]

[0043] in However, in actual calculations, the sample covariance matrix is ​​calculated as follows: If there is an error between the sample covariance matrix and the statistical covariance matrix, then the corresponding estimated measurement vector value is...

[0044]

[0045] Where Δy is the estimation error. The DOA estimation problem then becomes a typical sparse linear inverse problem, i.e., from measurement... The spatial spectrum μ is recovered in the middle.

[0046] S3: Based on the sparse spatial spectrum of the received signal Create a dataset and its corresponding labels. The dataset is a collection of sparse spatial spectra of the signal after traversing a certain range, and the corresponding labels are set to 1 for the position of the corresponding direction of arrival and 0 for the rest, and are divided into training set and validation set.

[0047] The spatial domain is divided into a certain range; in this invention, the spatial domain [-60°, -59°] is used. First, the sparse signal covariance matrix of the adopted space is calculated, and then it is vectorized to become a sparse spatial spectrum.

[0048] Generating the training dataset: Consider 8 array elements receiving signals, with a snapshot of T=256. Based on the assumed spatial domain, the signal-to-noise ratio is set to -10dB. Considering two incident signals, the interval between the two signals is set to [2°, 40°] within the range [-60°, -59°]. 19800 data samples are generated at 2° intervals. Each data sample has 120-dimensional features. Based on the real and imaginary parts of the features, the features representing each data sample are listed. Simultaneously, labels are set for the corresponding angles within the 120 angle range, with the position corresponding to the angle set to 1 and the remaining positions set to 0.

[0049] Generate a test signal-to-noise ratio (SNR) dataset: Based on the sparse spatial spectrum, consider two incident angles: the first incident angle is around -10°, and the second is around 5°. Consider 8 array elements receiving the signal, with a snapshot of T = 256. The SNR varies between [-15dB, 15dB] in 1dB intervals, generating 1000 samples, each with 120×2 features. The corresponding labels are set identically: within the 120 angle range, labels are set for the corresponding angle positions, with 1 for those positions and 0 for the rest.

[0050] Generate a dataset with test angle intervals: Based on the sparse spatial spectrum, consider two incident angles, one of which is around -1°, and the other incident angle with an increasing interval from the first angle, ranging from [2°, 15°], with 1° intervals. The signal-to-noise ratio is 0dB, generating 1000 samples. Each sample also has 120×2 features, and the corresponding labels are set in the same way, that is, within the range of 120 angles, the labels for the corresponding angles are set, with the position of the corresponding angle set to 1 and the other positions set to 0.

[0051] The dataset for generating test angles is as follows: Based on the sparse spatial spectrum, consider two incident angles. One incident angle varies with θ1 = -1: -2: -10, and the other has an incident angle of θ2 = 1: 2: 10. It is easy to obtain data for 5 pairs of angles with a signal-to-noise ratio of 0dB. Each pair of samples also has 120×2 features, and the corresponding labels are set identically. That is, within the range of 120 angles, labels are set for the corresponding angles, with the corresponding position set to 1 and the rest set to 0.

[0052] S4: Construct an improved spiking neural convolutional network and set up the SNC-type network in this invention;

[0053] The SNC network utilizes convolutional layers and spiking neural networks to learn spectral features and reconstructs them in the output layer. As the network deepens, to avoid excessive increases in network parameters and overfitting risk, five hidden layers are selected to achieve the network's non-linear expression.

[0054] The SNC-type network consists of five overall modules, each composed of a one-dimensional convolution, an activation function, and a LIFNode layer. The kernel size and convolution dimension vary in each convolution layer, with kernel sizes of 24, 12, 6, 3, and 1, and convolution dimensions of 35, 25, 15, 5, and 3, respectively. After convolution, each module passes through a ReLU activation function, then through spiking neurons, and finally to the next module. This process constructs the SNC-type network.

[0055] S5: Import the training data into the network, perform forward propagation, minimize the loss function, and then perform back propagation to calculate the weights. and deviation The update is as follows:

[0056] The training data is imported into the network to perform forward propagation. For an input μ, the output of the k-th layer SNC can be expressed as:

[0057]

[0058] When i = 1, k = 1, 2, 3, 4, 5; when i = 2, k = 1, 2, 3, 4. The initial value is h. 0 =μ, the output value is The meaning of the representation and the index k are related to i, representing the input value of each layer. Additionally, and , where represents the weights and bias of the convolution in the k-th layer, * represents the convolution operation, ReLU(·) represents the activation function, the padding operator P(·) fills the output of ReLU(·) with zeros to get the original input size, and L(·) represents the process of entering the spiking neural network after the convolution operation.

[0059] The working principle of the Leaky Integra-And-Fire (LIF) neuron model is as follows:

[0060] Assuming each spiking neuron has a voltage v, when the neuron receives no pulse signal input, the voltage v will exponentially stabilize over time to an equilibrium voltage b. v This process can be represented using the LIF model as follows:

[0061]

[0062] When a neuron is surrounded by a cell membrane, the cell membrane acts as a good insulator. When a driving current is injected into the neuron, the cell membrane acts like a capacitor, allowing the added charge to enter the neuron; however, over time, the charge gradually leaks out of the cell membrane, at which point the cell membrane acts like a finite resistor. Based on this principle, the LIF model can be modeled as a loop circuit formed by a capacitor C and a resistor R in parallel. Using the law of conservation of current, the driving current can be divided into two parts.

[0063] I(τ)=I R (τ)+I C (τ)

[0064] Among them, I R For the circuit with resistor R, I is the current. C The current in the capacitor C circuit is denoted as .

[0065] Assuming the initial voltage of the neuron is U, when the driving current is stopped being injected into the neuron, the voltage of the capacitor changes from U. rest This means that, within time τ, the driving current can be rewritten as...

[0066]

[0067] Further simplification

[0068]

[0069] Introducing the leaky integrator time parameter ζ = CR, which also controls the exponential descent rate, transforms the above equation into the standard passive membrane equation:

[0070]

[0071] Assuming the membrane voltage is U at time τ = 0. rest +Δu. Therefore, if the incident current duration is long enough, the membrane voltage will inevitably return to its resting state, i.e., U. rest +Δu;As the incident current continues, the membrane voltage will gradually increase to the voltage of the capacitor, reaching U(∞)=U rest +RI(τ). From these analyses, the solution to the passive membrane equation is:

[0072]

[0073] Where τ>τ0. When the current input causes the membrane voltage to reach the voltage that triggers action at a certain moment, the action potential will immediately release a pulse voltage U. r ,Right now

[0074]

[0075] At this point, for the i-th neuron, this pulse sequence can be represented as:

[0076]

[0077] Where f is the pulse label and δ(x) is the Dirac function. Therefore, the LIF model consists of two parts: the leakage formula and the adjustment formula. The voltage of the i-th neuron at any time can be expressed as...

[0078]

[0079] At this point, the forward propagation is complete. The goal of network training is to minimize the reconstructed spectrum on the training dataset. The mean square error (MSE) between the original spectrum μ and the training dataset can be represented as... Where T represents the batch number.

[0080]

[0081] MSE (Minimum Score) is a suitable criterion for minimizing the error between the learning objective and the true objective. To continuously reduce the loss function, backpropagation of variables is needed to update the weight matrix and weights. The update process is as follows:

[0082]

[0083]

[0084] Wherein, the loss function is and Let be the partial derivative of the parameter with respect to the neurons in the k-th layer, using These parameters reflect the sensitivity of the final loss to neurons in the k-th layer, where ξ represents the learning rate. By training these network parameters, the network can be used to predict the corresponding output spatial spectrum in near real-time upon completion of training. This invention employs an adaptive moment estimation (Adam) update algorithm to optimize the parameters of a neural network. Since the learning rate is a crucial parameter in neural network optimization, if the learning rate is too large, the loss function will not converge; if the learning rate is too small, the convergence speed of the loss function will be too slow. Therefore, this invention selects a dynamically changing learning rate to adaptively adjust the convergence of the loss function.

[0085] Assumption The first moment, representing the partial derivative, The second moment, representing the partial derivative, is used in the Adam algorithm, which combines the RMSprop algorithm and momentum-based algorithms. To ensure that each update is related to historical values, the gradient is first processed. and the square of the gradient Perform the gliding operation separately, that is

[0086]

[0087]

[0088] Where β1 and β2 are the decay rates of the two moving averages, respectively; in this paper, β1 = 0.9 and β2 = 0.999 are chosen. Next, the initial coasting value is corrected, i.e.

[0089]

[0090]

[0091] Finally, update the parameters.

[0092]

[0093]

[0094] in Let ξ be the dynamic learning rate, and set ξ = 0.001.

[0095] S6: Based on the trained network, input the spatial sparse spectrum of the test signal. Estimate the direction of arrival of the target signal source.

[0096] Based on the trained network, input test data sets, namely test signal-to-noise ratio dataset, test angle interval dataset, and test angle dataset, import these datasets into the trained network, output the corresponding sparse spatial spectrum, perform angle search on the spatial spectrum, and estimate the direction of arrival of the target source based on the grid peak values.

[0097] Simulation verification

[0098] Simulations were performed on signals with two elements, and the sampling frequency was set to 300kHz. The specific parameters for the simulation were as follows:

[0099] When the number of signals is 2, consider 8 physical array elements and 256 snapshots. Assume two independent narrowband signals of equal power collide with a uniform linear array. Set the training and validation batch size to 64 and the number of rounds to 150. Simultaneously, the performance estimation metric is the joint root mean square error (RMSE), defined as:

[0100]

[0101] in θ is the precise estimate of the DOA of the k-th signal. kThis represents the true value of the k-th signal DOA.

[0102] First, the generated training dataset is divided. 80% of the data features and corresponding labels are randomly selected for training, and the remaining 20% ​​of the data features and corresponding labels are used for validation. The loss function and training accuracy of the proposed SNC network are compared with those of traditional Deep Convolutional Networks (DCN). Figure 4 and Figure 5 As shown, the SNC network proposed in this invention has a lower loss function in its training set, falling below 0.01 after 50 rounds. Furthermore, the training accuracy of the SNC network in this invention reaches over 98.5%, which verifies that the proposed network has high accuracy.

[0103] In the validation set, the loss function and training accuracy of the SNC-type network proposed in this invention and the traditional DCN network are compared. Figure 6 and Figure 7 As shown, the SNC network proposed in this invention has a lower loss function in its training set, and the validation accuracy of the SNC network reaches over 98.5%, which also verifies that the network of this invention has high accuracy.

[0104] Next, the SNC network model of this invention is tested. First, the error estimation results of two targets under different signal-to-noise ratios are considered, such as... Figure 8 As shown, after the test signal-to-noise ratio dataset is fed into the proposed SNC network, the true angle is calculated using spectral peaks, and the error is estimated by comparing it with the true angle. Figure 8 The results show that when SNR < -10dB, the estimation results of the traditional DCN network have higher errors, but as the signal-to-noise ratio increases, the error values ​​of the two algorithms are almost the same.

[0105] Figure 9 The results show the target signal error estimation results at two different angular intervals. Figure 9 The results show that as the angle interval increases, the error estimation of the SNC-type network in this invention decreases.

[0106] Figure 10 The paper lists four sets of signals at different angular intervals, comparing their spectral peak diagrams with those of the traditional DCN method and the Sparse Bayesian learning (SBL) method. Figure 10 As shown in (a) and 10(b), when the angular interval is less than 10°, although the algorithm proposed in this invention can estimate the spectral peak, there are some interfering values. Figure 10As shown in (a) and 10(b), when the angular interval between the two signals is large, the algorithm of the SNC network proposed in this invention can estimate the accurate spectral peak value.

[0107] Simulation results on radar echo signal estimation demonstrate that the proposed DOA estimation algorithm based on a spiking neural convolutional network can effectively estimate the true DOA. This method extends the application of spiking neurons to general convolutional layer networks, offering a new approach to network structure construction. Furthermore, this invention introduces array signal processing problems into the field of deep learning, exploring new perspectives for solving array signal processing issues.

Claims

1. A direction-of-arrival estimation method based on a spiking neural convolutional network, specifically including the following steps: S1: Narrowband far-field wave signals are received through an array antenna with a uniform array structure. The signal information received by each snapshot is as follows: Based on the received signal information, the covariance matrix is ​​calculated. ; S2: For the covariance matrix Vectorization is performed to obtain the virtual array received signal. Calculate the sparse spatial spectrum of the received signal. ; S3: Based on the sparse spatial spectrum of the received signal Create a dataset and corresponding labels; the dataset is a collection of sparse spatial spectra of the signal after traversing a certain range, and the corresponding labels are set to 1 for the position of the corresponding DOA and 0 for the rest, and are divided into training set and validation set. S4: Construct an improved spiking neural convolutional network and set up the SNC network; S5: Import the training data into the network, perform forward propagation, minimize the loss function, and then perform back propagation to calculate the weights. and deviation Update; S6: Based on the trained network, input the spatial sparse spectrum of the test signal. Estimate the direction of arrival of the target signal source; Step S4 specifically includes: The SNC network uses convolutional layers and spiking neural networks to learn spectral features and reconstructs them in the output layer. Five hidden layers are selected to realize the non-linear expression of the network. The SNC network contains five overall modules, each consisting of a one-dimensional convolution, an activation function, and a LIFNode layer. The kernel size and convolution dimension of each convolution layer are different, with kernel sizes of 24, 12, 6, 3, and 1, and convolution dimension lengths of 35, 25, 15, 5, and 3, respectively. After convolution, each module passes through a ReLU activation function, then through spiking neurons, and then to the next module. In this way, the SNC network is constructed.

2. The method as described in claim 1, characterized in that: Step S5 specifically includes: The training data is imported into the network to perform forward propagation. For a given input... , No. The output of the layer SNC is represented as when hour, when hour, The initial value is The output value is , Meaning and index and Related, indicating the input values ​​for each layer. and The first The weights and biases of the convolutional layers. This represents the convolution operation. Represents the activation function and the fill operator. Will The output obtains the original input size through zero padding. This indicates the process of entering the spiking neural network after the convolution operation.

3. The method as described in claim 2, characterized in that: The working principle of LIF neurons is as follows: Assuming there is a voltage inside each spiking neuron When a neuron does not receive any pulse signal input, the voltage... It will exponentially stabilize to the equilibrium voltage over time. This process is represented by the LIF model as follows: The LIF model is modeled as a loop circuit formed by a capacitor C and a resistor R connected in parallel. Using the law of conservation of current, the driving current is divided into two parts. Assume the initial voltage of the neuron is When the driving current is stopped being injected into the neuron, the voltage of the capacitor changes from... It indicates that, in time Internally, the drive current is rewritten as Further simplification Introducing the time parameter of the Leaky Integrator To control the rate of exponential decline, the above equation becomes the standard passive membrane equation: Assuming time At this time, the membrane voltage is ; If the incident current is applied for a sufficiently long time, the membrane voltage will inevitably return to its resting state. As a continuous incident current flows, the membrane voltage will gradually increase to the voltage of the capacitor, reaching... The solution to the passive membrane equation is in When the input current causes the membrane voltage to reach the voltage required for activation at a certain moment, the activation potential will immediately release a pulse voltage. ,Right now At this point, for the first For each neuron, this pulse sequence is represented as in For pulse tags, It is a Dirac function; the LIF model consists of two parts, namely the leakage formula and the adjustment formula; the first The voltage of a neuron at any given time is expressed as: At this point, the forward propagation is complete.

4. The method as described in claim 2, characterized in that: The goal of network training is to minimize the reconstructed spectrum on the training dataset. and the original spectrum The mean square error (MSE) between the training dataset and the mean square error between the training dataset is denoted as . ,in Indicates the batch number; MSE (Minimum Score) is a suitable criterion for minimizing the error between the learning objective and the true objective. To continuously reduce the loss function, backpropagation of variables is needed to update the weight matrix and weights. The update process is as follows: Wherein, the loss function is , and For parameters on the first The partial derivatives of layer neurons, using This indicates that the final loss reflects the impact of the first... The sensitivity of layer neurons, The learning rate is used to train the network parameters. Once training is complete, the network is used to predict the corresponding output spatial spectrum in near real-time. .

5. The method as described in claim 4, characterized in that: An adaptive moment estimation Adam update algorithm is used to optimize the parameters of the neural network; a dynamically changing learning rate is selected to adaptively adjust the convergence of the loss function. Assumption The first moment, representing the partial derivative, The second moment of the partial derivative is represented by the RMSprop algorithm and momentum-based algorithms. To ensure that each update is related to historical values, a sliding operation is first performed on the gradient and the square of the gradient, respectively. in and These are the decay rates of two moving averages; then, the initial glide value is corrected, i.e. Finally, update the parameters. in, This is the adjusted dynamic learning rate.

6. The method as described in claim 5, characterized in that: ， ， 。

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