A method for sorting multifunctional radar pulse sequences based on probabilistic graphical model

Abstract

The present invention discloses a method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model, belonging to the field of radar electronic reconnaissance technology. The method mainly comprises two steps: constructing a radar pulse sequence interleaving model and sorting the radar pulse sequence. First, a hidden Markov model is used to model each radiation source to adapt to the type of interpulse modulation of the multifunctional radar. Second, a Markov chain is used to control the interleaving process. The present invention simultaneously infers the component Markov chain and the interleaving Markov chain, and has the characteristics of fast convergence speed and the ability to adapt to pulse missing. The present invention can sort radars with agile parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of radar electronic reconnaissance, and in particular relates to a method for sorting multifunctional radar pulse sequences based on a probability graph model. Background Art

[0002] The primary task of an electronic warfare system is to detect the presence of emitters and quickly generate countermeasure strategies. A key component of this system is the sorting of input pulse sequences from multiple emitters, laying the foundation for the selection of subsequent jamming measures. Traditional emitter sorting algorithms rely on matching existing feature templates or performing histogram analysis based on the time-of-arrival (TOA) parameters of the pulse descriptor word (PDW). Two popular early approaches were the cumulative difference histogram (CDIF) and the sequence difference histogram (SDIF) methods. However, existing unsupervised sorting methods struggle with two major issues. First, in real-world electronic warfare scenarios, TOA estimation can exhibit significant deviations due to low signal-to-noise ratios, leading to incorrect sorting. Second, existing unsupervised methods are primarily based on clustering, but struggle to adapt to the dynamic and agile nature of multifunction radar parameter values. With the development of deep learning, deep networks have gained widespread use. However, these methods require a large amount of data to train a neural network classification model. While effective, obtaining sufficient amounts of valid data is difficult in real-world environments. Furthermore, these methods are unable to sort unknown emitters for which no samples are available. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method for sorting multi-function radar pulse sequences based on a probabilistic graphical model. The method integrates radar inter-pulse modulation information and pulse arrival order information for sorting, which can solve the problem of sorting multi-function radar pulse sequences.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] The present invention provides a method for sorting multifunctional radar pulse sequences based on a probability graph model, comprising the following steps:

[0006] S1: For each received PDW sample p containing F characteristic parameters t ={p 1 ,p 2 ,…,p F} are accumulated; when the amount of data reaches T samples, T samples are taken as a data segment p={p1,p2,…,p T};

[0007] S2: Establish a generative model for characterizing pulse sequences. Generate interleaved observation sequences of multiple radar pulse sequences by interleaving data. The generation process is expressed as:

[0008]

[0009]

[0010] Where Z = Z1…Z T represents the hidden state sequence corresponding to the interleaving process generated by the interleaving chain, represents the hidden state sequence corresponding to the component process generated by the component chain. The component process represents the observation sequence generated by each radar. P(·) represents the probability distribution function. π, A are the initial state distribution and state transfer matrix of the component chain. π z , A z is the initial state distribution and state transition matrix of the interwoven chain;

[0011] In the interwoven chain, P(Z1|π z ) represents the probability of the initial state of the interleaving process, P(Z t |Z t-1 , A z ) is expressed as the state transition probability of the interleaving process, is the initial state distribution of the interleaving process, is the probability that the initial state of the interleaving process is in state i, M is the number of component processes, in, represents the probability of the hidden Markov model transitioning from state j to state i;

[0012] In the component chain, represents the probability of the initial state of the mth component process, is the initial state distribution of the component process, is the probability that the initial state of the component process is in state i, K m is the number of hidden states that the mth component chain has, is represented as the set of alphabets emitted by each component process, where

[0013]

[0014] Where, Represents the sub-alphabet emitted by the mth component process. Each component process emits multiple letters. The observation of the letter is given by To parameterize, its probability density function is expressed as Cm is the normalization term, p t is the t-th element of the observation sequence, i.e. the PDW parameter of the t-th pulse, are the mean and covariance of the Gaussian random variable corresponding to the i-th hidden state of the m-th component chain;

[0015]

[0016] Where, E m represents a diagonal matrix of size Km, represents the probability that the mth component chain transitions from state j to state i;

[0017] S3: Use structured variational inference to reason about the generative model and calculate the emission variables g of the interleaving process respectively. t，m and emission variables of component processes Use the forward-backward algorithm to calculate the hidden state variables of the interwoven chain and the component chain, and determine whether the model likelihood has converged. If not, continue to update the hidden state variables. If converged, update the model mean according to the preset algorithm;

[0018] S4: Determine whether the likelihood value converges. If it converges, φ is used to represent the probability that the observation value comes from each radiation source. If it does not converge, continue to use the preset algorithm to update the model mean.

[0019] Furthermore, in step S3, the transmission variable g of the interleaving process t，m Calculated by the following formula:

[0020]

[0021] Where exp{·} represents the logarithm of each element in the matrix, ∑ m-1 Represents the covariance matrix of the mth component chain, μ m represents the mean of the mth component chain, (·)T represents the transpose of the matrix, tr{·} represents the trace of the matrix, diag{·} represents the generated diagonal matrix.

[0022] Further, in step S3, the emission variable of the component process Calculated by the following formula:

[0023]

[0024] Where idiag(·) represents taking the diagonal elements of the matrix and generating a vector.

[0025] Furthermore, in step S3, the step of calculating the expectation of the interwoven chain and the component chain includes:

[0026] A1: Establish the variational distribution expression:

[0027]

[0028] Where, Q(·) represents the variational distribution, Z=Z1…Z TRepresents the interweaving process of interweaving chain generation

[0029] The corresponding hidden state sequence is, Represents the hidden state sequence corresponding to the component process generated by the component chain;

[0030] A2: Let Q(Γ) = 1. The initial state can be expressed as:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] E(Z t，m )=φ t，m

[0037] Where, For the component chain expectation, use Indicates that E(Z t，m ) is the expectation of the interwoven chain, and φ t，m express;

[0038] A3: Calculate the variational lower bound using the following formula:

[0039]

[0040] Where, represents the variational lower bound, diag means taking the elements on the diagonal of the matrix, and tr means finding the trace of the matrix.

[0041] Furthermore, in step S4, the mean value μ of the probability distribution m Calculated by the following formula:

[0042]

[0043] Where, Represents the inverse operation.

[0044] Furthermore, the F characteristic parameters include six pulse characteristic parameters: arrival angle, pulse repetition interval, frequency lower limit, pulse width, intra-pulse modulation mode and bandwidth.

[0045] The beneficial effects of the present invention are:

[0046] The present invention addresses the problem of sorting multi-function radars in complex electromagnetic environments and proposes an unsupervised sorting method that can adapt to scenarios with agile parameter changes. The method can simultaneously label the pulses of the multi-function radar without using artificial labeling information. The present application introduces the time relationship of a single radiation source, the time relationship of multiple radiation sources, and the distance information of the parameters. By fusing multiple types of information, radars with agile PDW parameters can be sorted. Secondly, the present application completes the sorting based on the variational inference method, which has low time complexity. The present application can adapt to situations where a single radar adopts multiple parameter values ​​(such as frequency agile radar).

[0047] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0049] Figure 1 Schematic diagram of the probability graph model of the present invention;

[0050] Figure 2 Schematic diagram of the structured variational approximation in the present invention;

[0051] Figure 3 It is the algorithm flow chart of the present invention;

[0052] Figure 4 This is an example of parameter estimation according to an embodiment of the present invention;

[0053] Figure 5 Detailed diagram of parameter estimation for non-ideal situations according to the present invention. DETAILED DESCRIPTION

[0054] like Figures 1 to 5 As shown, the present invention provides a method for sorting multi-function radar pulse sequences based on a probabilistic graphical model. The method mainly includes two steps: radar pulse sequence interleaving model construction and model hidden state inference. First, a hidden Markov model is used to model each radiation source to adapt to the type of inter-pulse modulation of the multi-function radar. Second, a hidden Markov model is used to control the interleaving process. The present invention simultaneously infers the component Markov chain and the interleaved Markov chain, which has a fast convergence speed and can adapt to the situation of missing pulses. In addition, structured variational inference can share data between data batches, thereby improving the accuracy of parameter estimation and the convergence speed of the algorithm.

[0055] The following is an embodiment of the present invention:

[0056] (1) Experimental scene setting

[0057] This method is evaluated using a simulated multi-function radar scenario. To simplify the simulation experiment without loss of generality, three radars are set up in the scenario, and each radar is sorted using information about its center frequency (RF) and pulse arrival order. This is shown in Table 1. This experiment randomly samples 100 data points for each operating state according to the parameters shown in Table 1 and conducts a parameter estimation experiment.

[0058] Table 1 Radiation source parameters of simulation scenarios

[0059]

[0060] (2) Evaluation index setting: The experiment evaluated the sorting results of three radars using various parameters. This experiment used sorting accuracy to evaluate the sorting results. During the experiment, the sorting accuracy was calculated using the Munkres algorithm to map the randomly assigned hidden state labels to the real label sequence. The sorting accuracy can be expressed as:

[0061]

[0062] here, Represents the estimated radiation source label of the t-th arriving pulse, D t represents the true source label of the t-th arriving pulse. I(·) is an indicator function that returns 1 when the equation in the brackets holds, and 0 otherwise.

[0063] (3) Experimental process

[0064] The algorithm flow chart of the present invention is as follows Figure 3 As shown, for each pulse sample, the corresponding PRI value is recorded.

[0065] Step 1: Data accumulation: For each received PDW sample p containing F feature parameters t ={p 1 , p 2 ,…,p F} are accumulated; when the amount of data reaches T samples, T samples are taken as a data segment p = {p1, p2, ..., p T In this experiment, when T=1000 pulses are accumulated, the data sample segment P=[p1, p2, ..., p T ] Input parameter estimation module;

[0066] Step 2: Establish a generative model for characterizing pulse sequences. The probability graph model is as follows: Figure 1 As shown, where Z = Z1…Z T represents the hidden state sequence corresponding to the switching process generated by the switching chain, represents the hidden state sequence corresponding to the component process generated by the component chain. The component process represents the observation sequence generated by each radar. The interleaved observation sequence of multiple radar pulse sequences is expressed through the interleaved data generation process as:

[0067]

[0068] Where P(·) represents the probability distribution function, is the initial state distribution of the interleaving process, where is the probability that the initial state of the interleaving process is in state i, M is the number of component processes, is the initial state distribution of the component process, is the probability that the initial state of the component process is in state i, K m is the number of hidden states of the mth component chain. P(Z1|π z ) represents the probability of the initial state of the interleaving process, represents the probability of the initial state of the mth component process; is represented as the set of alphabets emitted by each component process;

[0069] The transition process of the hidden state of each Markov process is controlled by the state transition matrix.

[0070] For interwoven Markov chains, in, represents the probability of the hidden Markov model transitioning from state j to state i, P(Z t |Z t-1 , A z ) is expressed as the state transition probability of the interleaving process.

[0071] For component Markov chains, represents the probability that the mth component chain transitions from state j to state i. The interleaving process determines which component process is activated in each time slot and the other component processes are frozen, as shown in the following formula:

[0072]

[0073] Where, E m Represents size K m A diagonal matrix of . Represents the sub-alphabet emitted by the mth component process. Each component process emits multiple letters, and the observation of the letter is given by To parameterize, its probability density function is expressed as

[0074]

[0075] Where C m is the normalization term.

[0076] Step 3: Model reasoning. Radar pulse sequence sorting is equivalent to reasoning about the proposed model. The present invention uses structured variational inference to reason about the proposed model. Structured variational inference retains the time dependency of each component process and discards other dependencies. The schematic diagram of structured variational inference is as follows: Figure 2 As shown. Then the variational distribution can be expressed as:

[0077]

[0078] Here, let Q(Γ) = 1, and the initial state can be expressed as:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] E(Z t,m )=φ t,m

[0085] Here E(·) represents the expectation operation, and the variational lower bound can be expressed as:

[0086]

[0087]

[0088] here diag represents the elements on the diagonal of the matrix, and tr represents the trace of the matrix. Then the emission variable g of the interleaving process is t,m and emission variables of component processes The update formula can be written as:

[0089]

[0090]

[0091] The likelihood of the interleaving chain and the component chain is calculated using a forward-backward algorithm, iterating the expectation of the interleaving chain and the component chain until convergence. The above process is the variational expectation step. The update formula for the average value of the letter is:

[0092]

[0093] here Represents the inverse operation.

[0094] Step 4: Determine whether the likelihood value converges. If it converges, φ represents the probability that the observation value comes from each radiation source; if it does not converge, continue to use the update formula of the average value of the letter to update the model mean. The iterative operation is run 200 times in total. Assume that the variance of each letter remains unchanged and only the mean μ is updated. m Update. Iterate the variation expectation step and variation maximization step until convergence, at which time φ t Represents the radiation source label of the pulse at the current moment. If the difference in likelihood between two model iterations is less than 0.01, it is considered converged.

[0095] Step 5: Result Analysis

[0096] Figure 4 The figure shows the sorting results of this algorithm. Different symbols represent the radiation source labels of each pulse. It can be seen that the sorting can be completed accurately under the condition that the radiation source variance is 0.2MHz2.

[0097] Figure 5 The figure shows the sorting accuracy of the proposed algorithm under different random missing pulse ratios (0% to 56%) with an observation variance of 0.2. As can be seen from the figure, the proposed structured variational inference algorithm can complete sorting relatively accurately when the missing ratio is 20%, achieving a sorting accuracy of 99%. As the missing pulse ratio increases, its sorting accuracy decreases. When the missing pulse ratio reaches 56%, the sorting accuracy can reach 94%. This proves the robustness of the proposed algorithm in the pulse missing scenario.

[0098] This algorithm aims at the problem of sorting multi-function radars in complex electromagnetic environments, and proposes an unsupervised sorting method that can adapt to scenarios with agile parameter changes. It can simultaneously label the pulses of multi-function radars without using artificial labeling information. This application introduces the time relationship of a single radiation source, the time relationship of multiple radiation sources, and the distance information of parameters. By fusing multiple types of information, radars with agile PDW parameters can be sorted. Secondly, this application completes the sorting based on the variational inference method, which has low time complexity. This application can adapt to situations where a single radar adopts multiple parameter values ​​(such as frequency agile radar).

[0099] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model, characterized in that: The following steps are involved: S1: For each received PDW samples of characteristic parameters Accumulate; when the amount of data reaches When a sample is A sample as a data segment ; S2: Establish a generative model for characterizing pulse sequences. Generate interleaved observation sequences of multiple radar pulse sequences by interleaving data. The generation process is expressed as: Where, represents the hidden state sequence corresponding to the interleaving process generated by the interleaving chain, represents the hidden state sequence corresponding to the component process generated by the component chain, and the component process represents the observation sequence generated by each radar. represents the probability distribution function; is the initial state distribution and state transfer matrix of the component chain, is the initial state distribution and state transition matrix of the interwoven chain; In the interwoven chain, represents the probability of the initial state of the interleaving process, Expressed as the state transition probability of the interleaving process, is the initial state distribution of the interleaving process, The initial state of the interleaving process is in state The probability of is the number of component processes, ,in, Represents the hidden Markov model from the state Transfer to state probability; In the component chain, Representative The probability of the initial state of each component process, is the initial state distribution of the component process, The initial state of the component process is in state The probability of For the The number of hidden states a component chain has, is represented as the set of alphabets emitted by each component process, where Where, Representative The sub-alphabet emitted by the component processes, each component process emits multiple letters, and the observation of the letter is given by To parameterize, its probability density function is expressed as , is the normalization term, The observation sequence element, that is, the PDW parameters of each pulse, 、 Respectively The first component chain The mean and covariance of the Gaussian random variable corresponding to each hidden state; Where, The matrix size is The diagonal matrix of , Indicates the Component chain from state Transfer to state probability; S3: Use structured variational inference to reason about the generative model and calculate the emission variables of the interleaving process respectively. and emission variables of component processes , use the forward-backward algorithm to calculate the hidden state variables of the interweaving chain and the component chain, and judge whether the model likelihood converges. If not, continue to update the hidden state variables. If converged, update the model mean according to the preset algorithm; S4: Determine whether the likelihood value converges. If so, pass Represents the probability that the observation value comes from each radiation source. If it does not converge, continue to use the preset algorithm to update the model mean.

2. The method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model according to claim 1, characterized in that: In step S3, the transmission variables of the interleaving process Calculated by the following formula: Where, It means taking the logarithm of each element in the matrix. Representative The covariance matrix of the component chain, Representative The mean of the component chains, represents the transpose of the matrix, represents the trace of the matrix, , Represents a generated diagonal matrix.

3. The method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model according to claim 2, characterized in that: In step S3, the emission variable of the component process Calculated by the following formula: Where, It means taking the diagonal elements of the matrix and generating a vector.

4. The method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model according to claim 3, characterized in that: In step S3, the steps of calculating the expectation of the interweaving chain and the component chain include: A1: Establish the variational distribution expression: Where, , represents the variational distribution, represents the hidden state sequence corresponding to the interleaving process generated by the interleaving chain, Represents the hidden state sequence corresponding to the component process generated by the component chain; A2: Order ， The initial state is expressed as: Where, For the component chain expectation, use express, For the expectation of interweaving chains, use express; A3: Calculate the variational lower bound using the following formula: Where, represents the variational lower bound, , Represents taking the elements on the diagonal of the matrix, Represents finding the trace of a matrix.

5. The method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model according to claim 4, characterized in that: In step S4, the average value of the probability distribution Calculated by the following formula: Where, Represents the inverse operation.

6. The method for sorting multifunctional radar pulse sequences based on a probabilistic graphical model according to claim 5, characterized in that: The The six characteristic parameters of the pulse include arrival angle, pulse repetition interval, frequency lower limit, pulse width, intra-pulse modulation mode and bandwidth.

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