Radar working mode recognition system based on Bayesian theory and training method thereof

Abstract

The invention belongs to the technical field of electronic reconnaissance, and relates to a radar working mode recognition system based on the Bayesian theory and a training method thereof. The radar working mode recognition system comprises a data preprocessing module and a deep neural network module based on Bayesian reasoning. A deep neural network module based on Bayesian reasoning performs Bayesian reasoning on the prediction subset based on the prior subset to obtain a high-dimensional reasoning matrix of the prediction subset; according to the Bayesian theory, real posterior prediction distribution of the prediction subset is obtained based on the priori subset; probabilistically converting the high-dimensional reasoning matrix into posterior prediction distribution approximate to a neural network; and training the neural network to obtain an optimal parameter, so that the approximate posterior prediction distribution of the neural network is approximate to the real posterior prediction distribution, and carrying out radar working mode recognition by using the deep neural network with the optimal parameter. According to the method, the problems of pulse random deletion and prior deletion can be effectively solved, and the working mode recognition capability of pulse random deletion and prior unknown pulse sequences is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electronic reconnaissance, and in particular, to a radar working mode recognition system based on Bayesian theory and its training method. Background Art

[0002] As the core equipment of modern electronic warfare, the Multi-Function Radar (MFR) can perform multiple working modes such as search, tracking, and imaging all day and all weather. As the core equipment for environmental situation awareness, the recognition of its working mode can provide intelligence support for subsequent threat assessment and countermeasure decision-making. The recognition of the MFR working mode is a major challenge in the field of electronic reconnaissance. The beam direction of the MFR is flexible, making it difficult for reconnaissance equipment to align with the airspace of the main beam of the antenna; it can randomly hop over a large frequency range, resulting in difficulty in frequency domain alignment and random pulse loss. The waveform parameters and pulse arrangement methods of the MFR are diverse, and the transfer law between pulse groups is complex, resulting in an incomplete prior waveform sample library of the MFR accumulated by the reconnaissance side and pulse prior loss. These factors significantly increase the difficulty of recognizing the working mode of MFR signals.

[0003] The Transformer network uses the attention mechanism to capture the long-term dependencies in the MFR pulse sequence and distinguish the differences between pulse sequences in different working modes. The Convolutional Neural Network (CNN) slides a convolutional kernel over the MFR pulse sequence and calculates with the local area to effectively capture the local changes of the pulse sequence. The Depthwise Separable Convolution decomposes the standard convolution into two steps: Depthwise Convolution and Pointwise Convolution, significantly reducing the amount of calculation and the number of parameters. Bayesian inference takes known events as priors and continuously corrects the posterior probability in the inference. It uses the statistical information of the MFR prior pulse data to provide membership inference based on conditional probability for unknown pulse data.

[0004] In recent years, temporal neural networks such as Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), and Gate Recurrent Unit (GRU) have been used to capture the temporal patterns of MFR pulse sequences, and certain progress has been made. Some literature has proposed a Balanced-NAS based on RNN to identify radar modulation types under dynamically changing signal-to-noise ratios, but the problem of random pulse missing has not been solved. There is also literature using the RNN to distinguish and roughly cluster different pulse groups, achieving non-cooperative MFR working mode recognition, but the recognition effect is not good when the prior pulse missing rate is high. In addition, there is literature combining CNN and bidirectional LSTM to extract time-frequency domain features, effectively identifying the intra-pulse modulation types of MFR signals in a low signal-to-noise ratio environment, but the problems of random pulse missing and prior missing have not been solved. Summary of the Invention

[0005] The purpose of the present invention is to address the problems of weak inference ability for prior missing pulse sequences, poor feature extraction ability for randomly missing pulse sequences, and poor generalization ability for high-complexity, high-randomness, and high-noise pulse data in existing working mode recognition algorithms. A radar working mode recognition system and its training method based on Bayesian theory are proposed. A radar working mode probability model based on Bayesian theory is established, and the working mode recognition is transformed into the solution of the posterior predictive distribution. The attention mechanism and depthwise separable convolution are used to extract the global and local features of the MFR pulse sequence respectively. The Bayesian backpropagation method is introduced to sample and optimize the Gaussian model parameter distribution, and finally the working mode information of the MFR pulse signal is output.

[0006] To achieve the above objective, the present invention adopts the following technical solutions:

[0007] In the first aspect, the present invention provides a radar working mode recognition system based on Bayesian theory, including:

[0008] A data preprocessing module, which is used to divide the MFR pulse data set into a training set and an application set, and preprocess the training set and the application set respectively; sample the preprocessed training set to obtain a prior subset, and use the remaining part as a prediction subset, and input the prior subset and the prediction subset into the deep neural network module based on Bayesian inference;

[0009] A deep neural network module based on Bayesian inference uses a deep neural network to perform Bayesian inference on a prediction subset based on a prior subset to obtain a high-dimensional inference matrix of the prediction subset; according to Bayes' theorem, a true posterior prediction distribution of the prediction subset is obtained based on the prior subset; the high-dimensional inference matrix is probabilistically transformed into an approximate posterior prediction distribution of the deep neural network; the deep neural network is trained to obtain optimal parameters so that the approximate posterior prediction distribution of the deep neural network approaches the true posterior prediction distribution.

[0010] The preprocessed application set is input into a deep neural network with optimal parameters for radar working mode recognition.

[0011] As a possible implementation, preprocessing the training set includes random missing processing and prior missing processing; random missing processing: modeling the random missing of the training set using Bernoulli missing, that is, the probability of each MFR pulse signal being missing is fixed, and the missing events occur independently.

[0012] Prior missing processing: hierarchically modeling the MFR pulse signal as a pulse level, a working state level, and a working mode level, assuming that the total number of working modes in the training set is known, and some working states are unknown under each working mode.

[0013] As a possible implementation, training the deep neural network to obtain optimal parameters includes: probabilistically transforming the starting parameters of the deep neural network into a Gaussian distribution, sampling the Gaussian distribution to select parameters, and performing multi-round backpropagation optimization on the selected parameters to obtain optimal parameters.

[0014] In a second aspect, the present invention provides a training method for a radar working mode recognition system based on Bayesian theory, which is used to train the radar working mode recognition system provided in the first aspect, and includes the following steps:

[0015] S1. Configure an MFR pulse training data set, preprocess the MFR pulse training data set, sample the preprocessed MFR pulse training data set to obtain a prior subset, and the remaining part as a prediction subset;

[0016] S2. Use a deep neural network to perform Bayesian inference on the prediction subset based on the prior subset to obtain a high-dimensional inference matrix of the prediction subset; according to Bayes' theorem, obtain the true posterior prediction distribution of the prediction subset based on the prior subset;

[0017] S3. Probabilistically transform the high-dimensional inference matrix into an approximate posterior prediction distribution of the deep neural network;

[0018] S4. Train the deep neural network based on the Bayesian backpropagation method to obtain optimal parameters so that the approximate posterior prediction distribution of the deep neural network approaches the true posterior prediction distribution.

[0019] As a possible implementation, preprocessing the MFR pulse training dataset includes random missing processing and prior missing processing. The random missing processing is as follows: Bernoulli missing is used to model the random missing of the MFR pulse training dataset, that is, the probability of each MFR pulse signal being missing is fixed, and the missing events occur independently.

[0020] The prior missing processing is as follows: The MFR pulse signals are hierarchically modeled as the pulse level, the working state level, and the working mode level. It is assumed that the total number of working modes in the training set is known, while some of the working states are unknown under each working mode.

[0021] As a possible implementation, a deep neural network is used to perform Bayesian inference on the prediction subset based on the prior subset to obtain the high-dimensional inference matrix of the prediction subset, including:

[0022] S20. Respectively extract the temporal features of the MFR pulse data in the prior subset and the prediction subset to obtain the MFR pulse high-dimensional feature matrix;

[0023] S21. Linearly map the working mode information in the prior subset to a high dimension to obtain the high-dimensional prior information matrix, and input the high-dimensional prior information matrix into the MFR pulse high-dimensional feature matrix;

[0024] S22. Perform inference on the MFR pulse high-dimensional feature matrix to obtain the high-dimensional inference matrix of the prediction subset.

[0025] As a possible implementation, the following method is used to obtain the true posterior predictive distribution of the prediction subset based on the prior subset. Assume that the hidden states and transition laws contained in the prior subset and the prediction subset are hidden variables z, and its prior distribution is p(z). According to Bayes' theorem, the posterior distribution of the hidden variable z is p(z|D prior ), then:

[0026] P(y j │x j ,D prior )=∫p(y j │x j ,z)p(z│D prior )dz,(x j ,y j )∈D pre

[0027] where D prior represents the prior subset, D pre represents the prediction subset, P(y j │x j ,D prior ) represents the true posterior predictive distribution of the prediction subset, x j ,yj represents the j-th value in the prediction subset, and dz represents the differential of the hidden variable z.

[0028] As a possible implementation, S3 includes:

[0029] S30. Perform a linear mapping on the high-dimensional inference matrix to reduce the dimension of the high-dimensional inference matrix;

[0030] S31. Use the normalized exponential function Softmax to probabilize the high-dimensional inference matrix with reduced dimension into the posterior predictive distribution approximated by the deep neural network.

[0031] As a possible implementation, train the deep neural network based on the Bayesian backpropagation method to obtain the optimal parameters, including:

[0032] S40. Probabilize the parameters of the deep neural network into a Gaussian distribution;

[0033] S41. Sample and select parameters from the Gaussian distribution, and perform multi-round backpropagation optimization on the selected parameters to obtain the optimal parameters.

[0034] As a possible implementation, the posterior predictive distribution approximated by the deep neural network approximates the true posterior predictive distribution. Specifically, the expected value of the KL divergence between the posterior predictive distribution approximated by the deep neural network and the true posterior predictive distribution is minimized.

[0035] Compared with the prior art, the beneficial effects produced by the present invention are as follows:

[0036] 1. The radar working mode recognition system and its training method based on the Bayesian theory proposed by the present invention transform the MFR working mode recognition problem into a problem of solving the posterior predictive distribution, utilize prior knowledge to improve the inference ability of the system for unknown waveforms, and through the Bayesian inference method, can effectively handle the problem of prior absence and improve the inference ability for unknown waveforms.

[0037] 2. The radar working mode recognition system and its training method based on the Bayesian theory proposed by the present invention combine the self-attention mechanism with depthwise separable convolution, extract the global and local timing features of the MFR pulse train through the self-attention mechanism and depthwise separable convolution, and improve the ability to distinguish pulses of different working modes.

[0038] 3. The radar working mode recognition system and its training method based on the Bayesian theory proposed by the present invention avoid the deep neural network falling into "local optimum" through the Bayesian backpropagation method. This method combines the advantages of the Bayesian method and deep learning, and improves the fitting ability of the present invention for MFR pulse signals with high complexity, high missingness, and high noise. Description of the Drawings

[0039] The accompanying drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0040] Figure 1 It is a schematic structural diagram of a radar operating mode recognition system based on Bayesian theory proposed in an embodiment of the present invention;

[0041] Figure 2 It is a schematic diagram of pulse random missing modeling in an embodiment of the present invention;

[0042] Figure 3 It is a schematic diagram of pulse prior missing modeling in an embodiment of the present invention;

[0043] Figure 4 It is a schematic diagram of co - existing modeling of pulse random missing and prior missing in an embodiment of the present invention;

[0044] Figure 5 It is a schematic structural diagram of a masked attention mechanism in an embodiment of the present invention;

[0045] Figure 6 It is a flowchart of a training method for a radar operating mode recognition system based on Bayesian theory in an embodiment of the present invention;

[0046] Figure 7 It is a schematic diagram of a Bayesian inference process based on a Transformer network and combined with depth - separable convolution in an embodiment of the present invention;

[0047] Figure 8 It is a confusion matrix diagram of the recognition results of a working mode recognition system in a pulse dataset with 9 working modes of 30% random missing and 60% prior missing in an embodiment of the present invention.

[0048] Reference numerals

[0049] 1 - Data pre - processing module, 2 - Deep neural network module based on Bayesian inference. Detailed implementation manners

[0050] In order to clearly describe the technical solutions of the embodiments of the present invention, in the embodiments of the present invention, terms such as "first" and "second" are used to distinguish the same items or similar items with basically the same functions and effects. For example, the first threshold and the second threshold are only used to distinguish different thresholds and do not limit their order. Those skilled in the art can understand that the terms "first" and "second" do not limit the quantity and execution order, and the terms "first" and "second" do not necessarily mean different.

[0051] It should be noted that in the present invention, words such as "exemplary" or "for example" are used to give examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0052] In the present invention, "at least one" means one or more, and "a plurality" means two or more. "And / or" describes the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone, where A and B can be singular or plural. The character " / " generally represents an "or" relationship between the associated objects before and after. The following at least one (item) or its similar expression refers to any combination of these items, including any combination of single item (item) or plural items (items). For example, at least one (item) of a, b or c can represent: a, b, c, the combination of a and b, the combination of a and c, the combination of b and c, or the combination of a, b and c, where a, b and c can be single or multiple.

[0053] The embodiments of the present invention aim to provide a radar working mode recognition system based on the Bayesian theory and its training method, which can solve the problems of weak inference ability of existing working mode recognition algorithms for prior missing pulse sequences, poor feature extraction ability for randomly missing pulse sequences, and poor generalization ability for high-complexity, high-randomness, and high-noise pulse data. The present invention establishes a radar working mode probability model based on the Bayesian theory, transforms the working mode recognition into the solution of the posterior predictive distribution; uses the attention mechanism (transformer) and depthwise separable convolution (RNN, LSTM) to extract the global and local features of the MFR pulse sequence respectively; introduces the Bayesian backpropagation method to sample and optimize the Gaussian model parameter distribution, and finally outputs the working mode information of the unknown pulse signal.

[0054] In a first aspect, the embodiments of the present invention provide a radar working mode recognition system based on the Bayesian theory, see Figure 1 , including: a data preprocessing module 1 and a deep neural network module 2 based on Bayesian inference;

[0055] The data preprocessing module 1 is used to divide the MFR pulse data set into a training set and an application set, and preprocess the training set and the application set respectively; sample the preprocessed training set to obtain a prior subset, and use the remaining part as a prediction subset, and input the prior subset and the prediction subset into the deep neural network module 2 based on Bayesian inference;

[0056] As an example, the MFR pulse data set is a pulse sequence of the same length obtained by performing min-max normalization on the acquired original MFR pulse data. In specific implementation, the pulse signal parameters intercepted by the reconnaissance system include multiple dimensions such as pulse width (PW), carrier frequency (RF), pulse repetition interval (PRI), etc. Pulse signals are characterized by pulse description words, and pulse signal data is generated according to the characteristic parameters of different working modes of the same type of MFR. Data processing is performed using the min-max normalization principle, and the MFR pulse data set is divided into multiple segments of sequences according to a fixed length, that is, the MFR pulse data set used in this embodiment is obtained.

[0057] As an example, the MFR pulse data set is divided into a training set and an application set in a ratio of 8:2 or 7:3; alternatively, it is ensured that each working mode in the divided training set includes at least one hundred pieces of data, and each piece of data contains at least one hundred pulses, and the rest is used as the application set.

[0058] As a possible implementation manner, preprocessing the training set includes random missing processing and prior missing processing.

[0059] See Figure 2 , due to the ability of the MFR to quickly switch the beam direction, it is difficult to effectively capture its signal. The use of low-intercept technology increases the difficulty of capturing MFR pulse signals, and other MFR signal interferences cause the reconnaissance equipment to be unable to correctly decode and capture all pulses. This leads to the problem of random pulse loss.

[0060] The specific implementation of the random missing processing in this embodiment is as follows: Bernoulli missing is used to model the random missing, that is, the probability of each MFR pulse signal being missing is fixed, and the missing events occur independently;

[0061] As an example, assume that W i represents whether the i-th pulse signal is missing, then:

[0062] W i ~Bernoulli(p) (1)

[0063] The probability mass function of Bernoulli missing is:

[0064]

[0065] where p represents the probability of loss, 1 - p represents the probability of non-loss, and w is a random variable of Bernoulli distribution, representing whether the pulse signal is missing.

[0066] The mathematical expectation of Bernoulli missing is expressed as:

[0067] E(W) = 1×P(W = 1) + 0×P(W = 0) = P (3)

[0068] Assume that the total number of pulses is N, then the mathematical expectation of the total number of lost pulses is expressed as:

[0069] E(NW) = N × P (4)

[0070] Therefore, the random missing rate Random_miss is defined as:

[0071]

[0072] See Figure 3 , when the MFR executes complex tasks, the waveform parameters and arrangement methods are diverse, and the transition law between each group of pulses is complex, making it difficult for the reconnaissance party to obtain a large number of high-quality labeled samples. In addition, many working modes of the MFR are hidden usually, and the "hidden" working modes may be activated during confrontation, resulting in the reconnaissance party not knowing all the working modes and working state information to which the MFR belongs, that is, the problem of prior pulse missing.

[0073] In this embodiment, the prior missing processing is specifically as follows: hierarchically model the MFR pulse signal into a pulse level, a working state level, and a working mode level. Assume that the total number of working modes in the training set is known, while some working states under each working mode are unknown.

[0074] As an example, for the problem of prior pulse missing, this embodiment models the MFR pulse signal into a pulse level, a working state level, and a working mode level. Assume that the total number of working modes in the MFR pulse training data set is known, while some working states under each working mode are unknown. Let the total number of working states be M, and the number of missing working states in the sample space be M D , after some working states are missing, the total number of working states in the training set becomes M - M D , then the prior missing rate Prior_miss is defined as:

[0075]

[0076] In the real electromagnetic environment, both random missing and prior missing may exist in the MFR pulse sequence intercepted by the reconnaissance party, as Figure 4 shown.

[0077] This embodiment uses Bayesian inference to solve the problem of working mode recognition under random missing and prior missing of the MFR.

[0078] See Figure 1 , the deep neural network module 2 based on Bayesian inference uses a deep neural network to perform Bayesian inference on the prediction subset based on the prior subset to obtain a high-dimensional inference matrix of the prediction subset;

[0079] As an example, first extract the temporal features of the MFR pulse data in the prior subset and the prediction subset respectively to obtain the high-dimensional feature matrix of the MFR pulse. Since the MFR pulse sequence has the Markov causal state transition characteristic, random sampling cannot be performed on the MFR pulse training set, and the segmentation points should be set according to the temporal features of the MFR pulse sequence. Given the working mode information of the pulses before the segmentation point and the lack of the working mode information of the pulses after the segmentation point, the MFR prior knowledge in the prior subset is incomplete.

[0080] Next, linearly map the working mode information in the prior subset to high dimensions to obtain the high-dimensional prior information matrix, and input the high-dimensional prior information matrix into the high-dimensional feature matrix of the MFR pulse; perform inference on the high-dimensional feature matrix of the MFR pulse to obtain the high-dimensional inference matrix of the prediction subset.

[0081] See Figure 1 , as an example, the deep neural network includes depthwise separable convolution, masked attention mechanism, and two fully connected layers, and maps the three-dimensional pulse sequence and the working mode information D in the prior subset yprior to high dimensions respectively through depthwise separable convolution and the first fully connected layer to make full use of the prior information:

[0082] x′ prior = DW(x prior ), x′ pre = DW(x pre ) (7)

[0083] y′ prior = W y_prior y prior + b y_prior (8)

[0084] where W y_prior and b y_prior are the weight and bias of the first fully connected layer respectively.

[0085] X = [x′ prior |x′ pre + y′ prior (9)

[0086] In the self-attention mechanism, Q, K, and V can be expressed as:

[0087] Q = XW Q , K = XW K , V = XW V (10)

[0088] where W Q , W K and W V are weight matrices.

[0089] Since the MFR pulse sequence has the Markov causal state transition law, it is necessary to avoid future information leakage during inference. Therefore, a masked attention mechanism is introduced, and QK is adjusted through the masking matrix U (with dimensions seq_num×seq_num). T . See the structure diagram of the masked attention mechanism in Figure 5 . The masking method is as follows: for QK at irrelevant positions T → -∞, then the masked attention formula adopted in this embodiment is:

[0090]

[0091] Then the high-dimensional inference matrix Z of the prediction subset is expressed as:

[0092] Z = ReLU(Mask Attention ·W1 + b1)W2 + b2 (12)

[0093] Among them, W1, W2, b1, and b2 are the weight and bias parameters of the two fully connected layers of the feedforward neural network adopted in the masked attention mechanism, and ReLU is the activation function.

[0094] According to Bayes' theorem, the true posterior prediction distribution of the prediction subset is obtained based on the prior subset; the high-dimensional inference matrix is probabilistically transformed into the posterior prediction distribution approximated by the deep neural network;

[0095] As an example, given the MFR pulse dataset x i is the PDW of the radar pulse signal, y i is the working mode information corresponding to the pulse signal, and n is the total number of pulses. Assume that the hidden states and transition laws contained in the prior subset and the prediction subset are the hidden variable z, and its prior distribution is p(z). According to Bayes' theorem, the posterior distribution of the hidden variable z is p(z|D prior ), then the true posterior prediction distribution is expressed as:

[0096] P(y│x,D prior ) = ∫p(y│x,z)p(z│D prior )dz (13)

[0097] Among them, x and y represent the unknown pulse signal and the corresponding working mode information respectively.

[0098] Exemplarily, in the deep neural network module based on Bayesian inference, there is a deep neural network q θ , then the posterior prediction distribution approximated by the deep neural network is expressed as q θ (y|x,D prior) To make the posterior predictive distribution approximated by the deep neural network approach the true posterior predictive distribution, the Kullback-Leibler (KL) divergence is used to evaluate the similarity between the above two probability distributions, and the expectation of the KL divergence between the posterior predictive distribution approximated by the deep neural network and the true posterior predictive distribution is calculated:

[0099]

[0100] where C is a constant.

[0101] As an example, the high-dimensional inference matrix Z is input into the second fully-connected layer included in the deep neural network, and the output is converted into the posterior predictive distribution approximated by the deep neural network through the Softmax function:

[0102] q θ (y│x,D prior )=softmax(W out Z+b out ) (15)

[0103] where W out and b out are the weight and bias of the second fully-connected layer respectively.

[0104] Train the deep neural network to obtain the optimal parameters so that the posterior predictive distribution approximated by the deep neural network approaches the true posterior predictive distribution; assign the optimal parameters to the deep neural network;

[0105] As a possible implementation, training the deep neural network to obtain the optimal parameters includes: probabilizing the initial parameters of the deep neural network into a Gaussian distribution, sampling parameters from the Gaussian distribution, and performing multi-round backpropagation optimization on the selected parameters to obtain the optimal parameters.

[0106] See Figure 1 , as an example, the Bayesian backpropagation method is used to train the deep neural network. The Bayesian backpropagation method assigns a probability distribution to each weight and bias in the deep neural network q θ instead of a fixed value. First, the prior distribution of the deep neural network parameters θ is modeled as a Gaussian distribution where μ0, σ0 are the mean and standard deviation of the prior distribution of the parameters. The posterior distribution is updated using the Bayesian method μ θ , σ θ are the mean and standard deviation of the posterior distribution of the parameters.

[0107] Use the standard Gaussian distribution z~Gaussian(0,1) and the mean μ θ and variance σθ Reparameterize θ:

[0108] θ = μ θ + z·σ θ (16)

[0109] The analytical solution of the KL divergence between the prior distribution P(θ) and the posterior distribution q(θ) of the parameter θ is:

[0110]

[0111] Therefore, define the loss function L(θ) of the deep neural network q θ as:

[0112] L(θ) = E x,y,D [-logq θ (y│x,D)] + β × KL[q(θ)||p(θ)] (18)

[0113] where β is a balancing term, representing the weight of the fitting loss of the posterior predictive distribution approximated by the deep neural network and the fitting loss of the posterior distribution of the model parameters. As the number of training rounds increases, the weight of the fitting loss of the posterior distribution of the model parameters is gradually reduced. Therefore, set the dynamic exponential decay factor β:

[0114]

[0115] where N epoch represents the number of training rounds.

[0116] Input the preprocessed application set into the deep neural network with optimal parameters for radar operating mode recognition. The preprocessing of the application set is random missing processing, and the processing method is the same as that of the training set's random missing processing, which will not be elaborated here.

[0117] In a second aspect, an embodiment of the present invention provides a training method for a radar operating mode recognition system based on Bayesian theory, which is used to train the radar operating mode recognition system provided in the first aspect. Refer to Figure 6 and includes the following steps:

[0118] S1. Configure the MFR pulse training data set, preprocess the MFR pulse training data set, sample the preprocessed MFR pulse training data set to obtain a prior subset, and use the remaining part as a prediction subset;

[0119] As a possible implementation, preprocessing the MFR pulse training data set includes random missing processing and prior missing processing. The random missing processing is specifically: model the random missing of the MFR pulse training data set using Bernoulli missing, that is, the probability of each MFR pulse signal missing is fixed, and the missing events occur independently;

[0120] The prior missing processing is specifically as follows: hierarchically model the MFR pulse signal into a pulse level, a working state level, and a working mode level. Assume that the total number of working modes in the MFR pulse training data set is known, while some working states are unknown under each working mode.

[0121] S2. Configure a deep neural network, and use the deep neural network to perform Bayesian inference on the prior subset to obtain a high-dimensional inference matrix of the prediction subset; according to Bayes' theorem, obtain the true posterior prediction distribution of the prediction subset based on the prior subset.

[0122] As a possible implementation method, configuring a deep neural network and using the deep neural network to perform Bayesian inference on the prediction subset based on the prior subset to obtain a high-dimensional inference matrix of the prediction subset includes:

[0123] S20. Respectively extract the time series features of the MFR pulse data in the prior subset and the prediction subset to obtain an MFR pulse high-dimensional feature matrix.

[0124] S21. Linearly map the working mode information in the prior subset to a high dimension to obtain a high-dimensional prior information matrix, and input the high-dimensional prior information matrix into the MFR pulse high-dimensional feature matrix.

[0125] S22. Perform inference on the MFR pulse high-dimensional feature matrix to obtain a high-dimensional inference matrix of the prediction subset.

[0126] As an example, configure the MFR pulse data set D MFR , sample the prior subset D MFR from the MFR pulse data set D prior , and the remaining part is used as the prediction subset D pre . See Figure 7 , next, implement Bayesian inference based on the Transformer network combined with depthwise separable convolution, and continuously train the inference ability of the model during the inference process. The formula of the Transformer attention mechanism is as follows:

[0127]

[0128] Among them, Q is the query, with a dimension of seq_num × d k , K is the key, with a dimension of seq_num × d k , V is the value, with a dimension of seq_num × d v , is the scaling factor, and seq_num is the length of each sequence segment.

[0129] For the specific implementation of steps S20 to S22, please refer to Equations (7) to (12), which will not be elaborated here.

[0130] Based on the prior subset D prior , infer the true posterior predictive distribution of the prediction subset D pre . Assume that the hidden states and transition laws contained in the prior subset and the prediction subset are hidden variables z, and its prior distribution is p(z). According to Bayes' theorem, the posterior distribution of the hidden variable z is p(z|D prior ). The following method is used to obtain the true posterior predictive distribution of the prediction subset based on the prior subset:

[0131] P(y j │x j ,D prior ) = ∫p(y j │x j ,z)p(z│D prior )dz, (x j ,y j ) ∈ D pre (21)

[0132] where D prior represents the prior subset, D pre represents the prediction subset, P(y j │x j ,D prior ) represents the true posterior predictive distribution of the prediction subset, x j ,y j represents the j-th value in the prediction subset, and dz represents the differential of the hidden variable z.

[0133] S3. Probabilize the high-dimensional inference matrix into an approximate posterior predictive distribution of a deep neural network;

[0134] As a possible implementation, S3 includes:

[0135] S30. Perform a linear mapping on the high-dimensional inference matrix to reduce the dimension of the high-dimensional inference matrix;

[0136] S31. Use the normalized exponential function Softmax to probabilize the high-dimensional inference matrix with reduced dimension into an approximate posterior predictive distribution of a deep neural network.

[0137] S4. Train the deep neural network based on the Bayesian backpropagation method to obtain the optimal parameters, so that the approximate posterior predictive distribution of the deep neural network approaches the true posterior predictive distribution, that is, the expected value of the KL divergence between the approximate posterior predictive distribution of the deep neural network and the true posterior predictive distribution is minimized.

[0138] Combined with Equation (14), the training objective is to find the parameter θ such that Minimum:

[0139]

[0140] As a possible implementation, a deep neural network is trained based on the Bayesian backpropagation method to obtain optimal parameters, including:

[0141] S40. Probabilize the parameters of the deep neural network into a Gaussian distribution;

[0142] S41. Sample parameters from the Gaussian distribution, perform multi-round backpropagation optimization on the selected parameters to obtain optimal parameters, and assign the optimal parameters to the deep neural network.

[0143] In this embodiment, when training the deep neural network, the prior distribution of the model parameter θ is set as the standard Gaussian distribution Gaussian(0,1), and the parameter θ is updated in a Bayesian manner to increase the uncertainty of the parameter and avoid the deep neural network falling into "local optimum". This method combines the advantages of the Bayesian method and deep learning, and improves the fitting ability of this solution for MFR pulse signals with high complexity, high missingness, and high noise.

[0144] The outstanding effects of this application are described below in combination with specific experimental data.

[0145] A simulated MFR pulse data set is constructed, and the pulses are saved in PDW format. The data set covers nine working modes of a certain radar, and each mode contains five working states, generating a total of 192,000 pulses. The specific parameters of the nine working modes are shown in Table 1.

[0146] Table 1 Simulation parameters of the MFR pulse data set

[0147]

[0148] Given the large number of working states, only the parameters of each working state in working mode 1 are shown here, as shown in Table 2:

[0149] Table 2: Parameters of each working state in working mode 1 of this type of MFR

[0150]

[0151] Known radar pulse data set The PDW of the i-th pulse signal consists of three-dimensional feature parameters of RF, PRI, and PW. Since these parameters have different units and orders of magnitude, the feature parameters need to be normalized to unify the scale. The maximum-minimum normalization principle is used for data preprocessing as follows:

[0152]

[0153] The MFR pulse dataset D is divided into m1 segments of sequences according to the fixed length Seq_num = 100 as follows:

[0154]

[0155] Symbol represents rounding down x. Thus, the MFR pulse dataset D is transformed into a three-dimensional array of [m1, Seq, n_feature].

[0156] Then, the normalized dataset is divided into a training set and an application set in a ratio of 8:2. After that, random missing and prior missing scenario modeling are carried out. The random missing rate is set to 0.3, and the prior missing is 0.6. The training set is used to train the working mode recognition system proposed in this application, and the iteration ends after 100 rounds or the loss is reduced to less than 0.2. Then, the application set is used to test the working mode recognition accuracy of this application. The accuracy calculation formula is as follows:

[0157]

[0158] Among them, N represents the number of pulse signal samples, represents the predicted label of the i-th sample algorithm, Y i represents the true label of the i-th sample.

[0159] Next, the accuracy of this application is compared with the currently commonly used advanced MFR working mode recognition algorithms, including: Transformer, GRU-attention, CNN-attention, LSTM-FCN, and Bayesian Variational Inference (BVI). Under the condition that the random missing rate is 30%, the comparison results of the MFR working mode recognition accuracy in datasets with different prior missing rates (20%, 40%, 60%) are shown in Table 3.

[0160] Table 3 Comparison of algorithm recognition accuracies under different prior missing rates when the random missing rate is 30%

[0161]

[0162] Figure 8Confusion matrix diagram of the recognition results of the system proposed in the invention in the pulse data set with 9 working modes of 30% random missing and 60% prior missing. The experimental results show that as the random missing rate and the prior missing rate increase, the performance of all algorithms decreases, but the performance of this application decreases less, showing strong robustness. And under the conditions of 30% random missing rate and 60% prior missing rate, the recognition accuracy of this application is 70.6%, while the recognition accuracies of the four deep learning algorithms are all around 50%, and the classic inference algorithm BVI drops to 0.271%, all far lower than this application. This shows that compared with other comparison algorithms, this application not only maintains a high accuracy rate when processing MFR pulse signals in a real electromagnetic environment, but also has good robustness and adaptability. It demonstrates the application potential of the method proposed in the present invention in the field of MFR working mode recognition.

[0163] Although the present invention has been described in connection with various embodiments, however, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings, the disclosure, and the accompanying drawings. In the specification, the term "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality. A single processor or other unit can implement several functions listed in the specification. Certain measures are described in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0164] Although the present invention has been described in connection with specific features and their embodiments, it is obvious that various modifications and combinations can be made without departing from the spirit and scope of the present invention. Accordingly, the present specification and the drawings are merely exemplary descriptions of the present invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalent technologies, the present invention is also intended to include these changes and modifications.

Claims

1. A radar working mode recognition system based on Bayesian theory, characterized in that: include: A data preprocessing module, used for dividing the MFR pulse data set into a training set and an application set, and preprocessing the training set and the application set respectively; Sampling the preprocessed training set to obtain a priori subset, and using the rest as a prediction subset, and inputting the priori subset and the prediction subset into a deep neural network module based on Bayesian reasoning; A deep neural network module based on Bayesian reasoning, using the deep neural network to perform Bayesian reasoning on the prediction subset based on the prior subset to obtain a high-dimensional reasoning matrix of the prediction subset; according to the Bayesian theorem, the true posterior prediction distribution of the prediction subset is obtained based on the prior subset; the high-dimensional reasoning matrix is ​​probabilized into the posterior prediction distribution approximated by the deep neural network; the deep neural network is trained to obtain optimal parameters so that the posterior prediction distribution approximated by the deep neural network approaches the true posterior prediction distribution; The preprocessed application set is input into a deep neural network with optimal parameters for radar working mode recognition.

2. The radar working mode recognition system based on Bayesian theory according to claim 1 is characterized in that: The preprocessing of the training set includes random missing processing and a priori missing processing; the random missing processing is: using Bernoulli missing to model the random missing of the training set, that is, the probability of missing each MFR pulse signal is fixed, and the missing events occur independently; The a priori missing processing is: hierarchically modeling the MFR pulse signal into pulse level, working state level and working mode level, assuming that the total number of working modes in the training set is known, while some working states in each working mode are unknown.

3. The radar working mode recognition system based on Bayesian theory according to claim 1 is characterized in that: Training the deep neural network to obtain optimal parameters includes: probabilizing the initial parameters of the deep neural network into a Gaussian distribution, sampling the Gaussian distribution to select parameters, and performing multiple rounds of back propagation optimization on the selected parameters to obtain the optimal parameters.

4. A training method for a radar working mode recognition system based on Bayesian theory, characterized in that: Used to train the radar working mode recognition system according to any one of claims 1 to 3, comprising the following steps: S1. Configure an MFR pulse training data set, preprocess the MFR pulse training data set, sample the preprocessed MFR pulse training data set to obtain a priori subset, and use the rest as a prediction subset; S2. Use a deep neural network to perform Bayesian inference on the prediction subset based on the prior subset to obtain a high-dimensional inference matrix of the prediction subset; according to the Bayesian theorem, obtain the true posterior prediction distribution of the prediction subset based on the prior subset; S3. probabilizing the high-dimensional inference matrix into a posterior predictive distribution approximated by a deep neural network; S4. Train the deep neural network based on the Bayesian back-propagation method to obtain optimal parameters so that the approximate posterior predictive distribution of the deep neural network approaches the true posterior predictive distribution.

5. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4 is characterized in that: Preprocessing the MFR pulse training data set includes random missing processing and a priori missing processing, wherein the random missing processing is: using Bernoulli missing to model the random missing of the MFR pulse training data set, that is, the probability of missing each MFR pulse signal is fixed, and the missing events occur independently; The a priori missing processing is: hierarchically modeling the MFR pulse signal into pulse level, working state level and working mode level, assuming that the total number of working modes in the training set is known, while some working states in each working mode are unknown.

6. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4 is characterized in that: A deep neural network is used to perform Bayesian inference on the prediction subset based on the prior subset to obtain a high-dimensional inference matrix of the prediction subset, including: S20. extracting the time series features of the MFR pulse data in the prior subset and the predicted subset respectively, and obtaining a high-dimensional feature matrix of the MFR pulse; S21. Linearly mapping the working mode information in the prior subset to a high dimension to obtain a high-dimensional prior information matrix, and inputting the high-dimensional prior information matrix into the MFR pulse high-dimensional feature matrix; S22. Inferring the MFR pulse high-dimensional feature matrix to obtain a high-dimensional inference matrix of the prediction subset.

7. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4 is characterized in that: The following method is used to obtain the true posterior prediction distribution of the prediction subset based on the prior subset. Assume that the implicit state and transition law contained in the prior subset and the prediction subset are hidden variables z, and its prior distribution is p(z). According to Bayes' theorem, the posterior distribution of the hidden variable z is p(z|D prior ),but: P(y j │x j ,D prior )=∫p(y j │x j ,z)p(z│D prior )dz,(x j ,y j )∈D pre Among them, D prior represents the prior subset, D pre represents the prediction subset, P(y j │x j ,D prior ) represents the true posterior predictive distribution of the prediction subset, x j ,y j represents the jth value in the prediction subset, and dz represents the differential of the latent variable z.

8. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4 is characterized in that: The S3 includes: S30. Performing linear mapping on the high-dimensional reasoning matrix to reduce the dimension of the high-dimensional reasoning matrix; S31. Use a normalized exponential function to probabilize the high-dimensional inference matrix after dimensionality reduction into the posterior predictive distribution approximated by the deep neural network.

9. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4 is characterized in that: The deep neural network is trained based on the Bayesian back propagation method to obtain optimal parameters, including: S40. Probabilizing the parameters of the deep neural network into a Gaussian distribution; S41. Sampling the Gaussian distribution to select parameters, performing multiple rounds of back propagation optimization on the selected parameters to obtain the optimal parameters.

10. The training method of the radar working mode recognition system based on Bayesian theory according to claim 4, characterized in that: The posterior predictive distribution approximated by the deep neural network approaches the true posterior predictive distribution. Specifically, the expected value of the KL divergence between the posterior predictive distribution approximated by the deep neural network and the true posterior predictive distribution is minimized.

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