A cognitive radar countermeasure dynamic modeling method based on HMM

Abstract

The application discloses a dynamic modeling method of a hidden Markov model, defines radar-jammer as a master-slave confrontation mode, namely, when the radar is not interfered, sets an information scheduling strategy matrix A and a transmission pulse time-frequency parameter control strategy matrix B in a coherent processing time according to a target detection task of the radar, and generates a transmission pulse sequence. An interference party extracts radar state parameters and estimates the information scheduling strategy matrix A and the transmission pulse time-frequency parameter control strategy matrix B of the radar by using intercepted radar pulses, formulates an interference strategy matrix A j and a jamming signal time-frequency parameter control strategy matrix B j , and sends a jamming signal to the radar, wherein the radar estimates the A j and B j of the interference party after receiving the jamming signal. Whether the interference is effective is judged, and the matrixes A and B are adjusted accordingly, and the process is repeated, so that dynamic modeling of cognitive radar confrontation can be realized.

Description

Technical Field

[0001] This invention belongs to the field of electronic reconnaissance system modeling technology under the background of cognitive electronic warfare, and specifically relates to a cognitive radar countermeasure dynamic modeling method based on Hidden Markov Models (HMM). Background Technology

[0002] Implicit Markov models have broad application value in cognitive electronic warfare, with their core capability lying in modeling and reasoning about dynamic and uncertain environments. Existing cognitive radar countermeasures all assume complete perception of the opponent's state information, establishing cognitive countermeasure models by formulating corresponding information scheduling methods and countermeasures in waveform design and optimization, power allocation, operating frequency bands, countermeasure time, and airspace. However, actual countermeasures are an "open-loop" environment, where neither side can fully grasp the other's state. For example, the jamming side can only observe the radar transmitter state through its electronic support system, but cannot directly perceive the radar's information scheduling and signal processing methods. Similarly, the radar cannot fully understand the jamming strategy adopted by the jamming side. Therefore, under conditions of incomplete perception information, how to properly assess the uncertainty brought about by incomplete information and thus establish a dynamic model of cognitive radar countermeasures is one of the scientific problems yet to be solved in the field of cognitive electronic warfare.

[0003] Cognitive electronic warfare originated from cognitive radio technology. "Cognition" refers to a conscious intellectual activity involving thinking, reasoning, memorizing, imagining, learning, processing information, applying knowledge, and changing priorities. In the field of radar countermeasures, "cognitive radar" endows radar systems with the ability to perceive their environment and continuously learn and reason about changes in the external environment using artificial intelligence. It adaptively adjusts its operating methods, such as adjusting transmission power, operating frequency, modulation method, transmission waveform, and employing beam sidelobe blanking, thereby reducing the likelihood of interference and damage in complex adversarial environments. To achieve this, the radar must possess information on the jammer's jamming power, jamming patterns, network configuration, and location, and also assess the jammer's electronic reconnaissance capabilities. The core anti-jamming capability of radar lies primarily in its ability to identify the jamming signals and strategies of the jammer. Achieving this requires a large number of manually labeled jamming signal samples covering all jamming patterns and strategies, which is practically impossible. Similarly, for the jamming party, it is impossible to fully grasp all the radar's anti-jamming measures and signal processing methods, especially to identify the radar's information scheduling strategies. In actual confrontation, only partial operational status of the radar transmitter can be obtained through electronic support systems. The effectiveness of its jamming does not entirely depend on the radar's changing information. For example, traditional suppression coefficients do not consider the radar's anti-jamming improvement factor, and therefore can only represent the signal-to-interference ratio (SJR) at the radar antenna aperture. Under incomplete information conditions, existing AI-based adversarial models and effectiveness evaluation methods do not conform to the actual adversarial environment and cannot achieve true cognitive adversarial capabilities. Therefore, dynamic modeling of cognitive radar adversarial capabilities is a key issue that urgently needs to be addressed in cognitive electromagnetic spectrum warfare. Summary of the Invention

[0004] In order to overcome the shortcomings of the prior art, the present invention aims to provide a cognitive radar countermeasure dynamic modeling method based on HMM, which solves the problems in cognitive radar countermeasure modeling, such as the difficulty in describing the radar information scheduling strategy after the jammer intercepts the radar transmission pulse sequence and the countermeasures taken by the radar after receiving the jamming signal, and realizes cognitive electronic countermeasures under incomplete information conditions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A cognitive radar countermeasure dynamic modeling method based on Hidden Markov Models (HMM) includes the following steps:

[0007] Step 1: Construct the master-slave confrontation scenario between the radar and the jammer, set the confrontation round iter, formulate the information scheduling strategy matrix A based on the hidden Markov model and the time-frequency parameter control strategy matrix B of the transmitted pulse during the coherent processing time according to the target detection task under the condition that the radar is not jammed, and generate the transmitted pulse sequence S r =[s1, s2,..., s N , where s N represents the Nth radar pulse, and N represents the number of transmitted radar pulses;

[0008] Step 2: The jammer estimates the matrices A and B based on the intercepted radar transmitted pulse sequence S r ′ = [s1, s2,..., s M , formulates the jamming strategy matrix A j and the time-frequency parameter control strategy matrix B j of the jamming signal according to the jamming strategy, and jams the radar with the jamming signal S j = [s 1j , s 2j ,... s Nj , where M represents the number of intercepted pulses, M ≤ N, and s Nj represents the Nth jamming signal;

[0009] Step 3: The radar receives the jamming signal S j , estimates the matrices A j and B j , calculates the adjusted Rand index (ARI) of {S j , S r}, and judges the jamming effect of S j : If the adjusted Rand index is greater than 0, the jamming is effective, and the radar adjusts the matrices A and B to generate a new transmitted pulse sequence;

[0010] Step 4: If the confrontation round < iter, return to Step 2, otherwise, output the confrontation result.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0012] 1. According to various uncertain factors faced by the cognitive radar confrontation dynamic modeling, the present invention regards the state characteristic quantity of the radar transmitter as a Markov process hidden in the transmitted pulse sequence, establishes a cognitive radar confrontation dynamic model based on HMM, that is, according to the signal processing and information scheduling methods possessed by the radar, constructs the information scheduling strategy matrix A of the radar and the time-frequency parameter control strategy matrix B of the transmitted pulse during the coherent processing time, and thus generates the radar transmitted pulse sequence S r , providing a theoretical support for identifying the radar working mode.

[0013] 2. This invention, based on the signal processing methods of the jamming party's electronic support system, uses intercepted radar pulses as training samples for an unsupervised learning algorithm, employs the Baum-Welch algorithm to identify the radar's operational status, and formulates an jamming strategy matrix A based on this. j Interference signal time-frequency parameter control strategy matrix B j Emitting interference signal S to the radar j It can effectively simulate the process of interfering with radar.

[0014] 3. This invention, based on the anti-jamming strategy after radar is jammed, uses Hidden Markov Model (HMM) to estimate the jamming strategy matrix A of the jamming signal. j Interference signal time-frequency parameter control strategy matrix B j Calculate {S j ,S r The Adjusted Rand Index (ARI) is used to determine whether the jamming is effective, based on whether the ARI is greater than 0, thereby realistically simulating the radar's anti-jamming process. Attached Figure Description

[0015] Figure 1 A diagram illustrating cognitive electronic warfare operations.

[0016] Figure 2 This is the time-frequency diagram of the transmitted pulse train.

[0017] Figure 3 To capture a binarized image of the time-frequency map of the radar signal.

[0018] Figure 4 This represents the peak distribution of the binarized image after Hough transform.

[0019] Figure 5 This is a flowchart of the modeling and simulation process for this invention.

[0020] Figure 6 A graph showing the changes in the RAND index ARI (Rand Index RI) during cognitive radar countermeasures.

[0021] Figure 7 This is a graph showing the change in radar's state estimation error for the jammer during radar countermeasures. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0023] From the perspective of system-on-system confrontation, cognitive electronic warfare operations mainly consist of processes such as "cognitive interception—cognitive processing—cognitive decision-making—cognitive jamming," forming a closed loop from reconnaissance to jamming to assessment, as shown in the attached figure. Figure 1 As shown, incomplete information exists in the cognitive interception stage, resulting in significant cognitive biases and uncertainties in the cognitive processing stage, which in turn leads to cognitive decision-making errors and prevents the implementation of effective cognitive interference.

[0024] Taking cognitive radar countermeasures as an example, the envisioned countermeasure simulation model is as follows:

[0025]

[0026] Equation (1) is the radar state equation, x = [A m ,f c B w M d [,prf] represents radar characteristic parameters, also known as radar state variables, where A m f represents the pulse amplitude. c Indicates the pulse carrier frequency, B w M represents the pulse bandwidth. d Indicates the intrapulse modulation method; pref represents the pulse repetition frequency; μ a This represents radar anti-jamming measures. Specifically, the jamming party can measure the radar state x through a sensing system, while μ... a These are unmeasurable system variables and can be considered as "hidden variables" of radar.

[0027] Equation (2) represents the perception result of the jamming party's cognitive system on the radar's operating status, which includes the radar anti-jamming measures μ. a The estimate is incomplete information; z includes the estimation error of the radar state x. Once the adversarial scenario is determined, signal detection and estimation methods can be used to obtain an estimate of x. It is an estimate obtained through prior knowledge and the radar's operating status.

[0028] Equation (3) is the jammer's cognitive system's estimate of the radar's current operating state, which has significant uncertainty. Equation (4) is the jamming pattern based on the estimation result of Equation (3). Due to the incompleteness of the estimation of radar anti-jamming measures, after y is applied to the radar, it is necessary to observe whether the radar state changes through Equation (2) to correct the estimation of μ. a Based on the estimation, the entire adversarial process can be implemented using the "dynamic modeling method based on hidden Markov models":

[0029] First, a brief description of the working process of the detection receiver of the electronic reconnaissance system is given, during the observation period (0~t). d Within its monitoring frequency band, the receiver receives a mixed signal including the target radar signal and other interference signals. After signal sorting, it obtains N target radar transmitted pulses. The receiver will then measure the pulse amplitude A of each pulse. m Center frequency f c Instantaneous bandwidth B w Intrapulse modulation mode M d The pulse repetition frequency (PRF), due to signal sorting errors and random fading in the channel, causes these measurements to appear as a random sequence of length N that follows a certain probability distribution. The mean and variance (μ, σ) of the measurement sequence are the basis for judging its true value and random error. The usual practice is to determine a threshold based on σ. When the measurement value is below the threshold, the change in the measurement value is considered to be insignificant, and when it exceeds the threshold, the measurement value is considered to have changed significantly.

[0030] When the radar is not interfered with, it will set the transmit pulse state x = [A] according to its mission plan. m ,f c B w M d [prf] remains unchanged during its coherent processing time; when the radar is subjected to suppressive interference, one or more parameters in x are randomly changed according to its anti-jamming strategy, such as changing the center frequency f according to a certain rule. c When the radar is subjected to deception interference, based on the identification of the type of deception interference, the amplitude A of the transmitted pulse is changed according to the information scheduling rules. m Center frequency f c Instantaneous bandwidth B w Intrapulse modulation mode M d And the pulse repetition frequency prrf, generate a new transmit pulse sequence S r =[s1,s2,…,s N To avoid interference from the jammer, the jammer must re-intercept the radar's transmitted pulses, analyze their status, adjust its jamming strategy, and continue the game with the radar.

[0031] During the observation period (0~t) dThe radar pulse received by the detection receiver of the interfering party is represented as follows: For radar pulse quantization length, To capture the number of radar pulses. Since the receiver is measuring the radar transmitter state x = [A] m ,f c B w M d When [prf], a relatively independent measurement method is used for each measurand, for example, pulse amplitude A m Typically, the maximum value of the amplitude of each intercepted pulse is taken. The pulse maxima form a random sequence with a relatively fixed mean and variance; for the center frequency f c Instantaneous bandwidth B w The measurement of the pulse repetition frequency (PRF) is usually obtained by performing time-frequency joint analysis on each intercepted pulse, as shown in the attached figure. Figure 2 The image shows the pseudo Wigner-Ville transform time-frequency diagrams of the four captured radar pulses. The main parameters of the radar transmitter are as follows:

[0032] Pulse power P t =100W; transmit pulse width T = 3μs; intra-pulse modulation method: LFM, frequency modulation bandwidth B = 30MHz; center frequency f c =1.8GHz; Pulse repetition period PRI=15μs.

[0033] As attached Figure 3 The image shown is a binarized time-frequency plot of the intercepted radar signal. The bandwidth B of the radar signal can be estimated by detecting the lengths of the three diagonal lines along the frequency axis. w Measuring the interval of the diagonal lines along the time axis can estimate the repetition period PRI of the radar pulse (prf = 1 / PRI), and the slope of the measured diagonal lines can estimate the frequency modulation slope k of the LFM signal. The time difference between the start and end points of the diagonal lines is the pulse width T, etc. This is used to estimate the carrier frequency f of the radar pulse. c The Hough transform is used to... Figure 3 Transforming the oblique lines in the image into points on the time-frequency plane, as shown in the attached figure. Figure 4 The carrier frequency f is obtained by detecting the position of the peak point. c The estimated value.

[0034] Once the jamming party obtains the radar transmitted pulse state parameters, it will use its jamming strategy S. j ={′WBJ’,′NBJ’,′C&I’,′DenseTargets’,′R&VDecept’}, where the five terms represent broadband noise suppression, narrowband agile noise suppression, slice jamming, dense false target jamming, and range-velocity deception jamming, respectively, to formulate the jamming strategy matrix A. j Interference signal time-frequency parameter control strategy matrix Bj Emitting interference signal S to the radar j =[s 1j ,s 2j ,...s Nj ].

[0035] When the radar receives the changed interference signal S released by the interfering party... j Next, its interference strategy matrix A will be analyzed. j Interference signal time-frequency parameter control strategy matrix B j Compare the new transmitted pulse sequence S r With interference signal S j To address the differences, when the interference is deemed valid, the state characteristic transition matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time are adjusted to generate a new transmit pulse sequence S. r .

[0036] In summary, for reference Figure 5 As shown, the method proposed in this invention consists of the following steps:

[0037] Step 1: Construct a radar-jamming master-slave adversarial scenario, set the adversarial rounds (iter), and formulate an information scheduling strategy matrix A based on a Hidden Markov Model (HMM) and a transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time, based on the target detection task under unjammed radar conditions, to generate the transmit pulse sequence S. r =[s1,s2,…,s N ], where s N This represents the Nth radar pulse, where N represents the number of radar pulses transmitted.

[0038] Step 2: The jamming party uses the intercepted radar transmitted pulse sequence S′ r =[s1,s2,…,s M For cases M≤N, the radar's information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time are estimated using methods such as the Baum-Welch algorithm. Based on the jamming strategy S... j ={′WBJ′,′NBJ′,′C&I′,′DenseTargets′,′R&VDecept′}, where the five terms represent broadband noise suppression, narrowband agile noise suppression, slice jamming, dense false target jamming, and range-velocity deception jamming, respectively, to formulate the jamming strategy matrix A. j Interference signal time-frequency parameter control strategy matrix B j Emitting interference signal S to the radar j =[s 1j ,s 2j ,…sNj . Where M represents the number of intercepted pulses, s Nj represents the Nth interference signal.

[0039] Step 3: The radar receives the interference signal S j , estimates the interference strategy matrix A of the interference signal j and the time-frequency parameter control strategy matrix B of the interference signal j , calculates the adjusted Rand index (ARI) of {S j , S r}, and judges the interference effect of S j : If ARI > 0, the interference is effective, and the radar adjusts the information scheduling strategy matrix A and the time-frequency parameter control strategy matrix B of the transmitted pulses within the coherent processing time to generate a new transmitted pulse sequence.

[0040] Step 4: If the number of confrontation rounds < iter, return to Step 2; otherwise, output the confrontation result.

[0041] In Step 1, the method for formulating the information scheduling strategy matrix A based on the Hidden Markov Model (HMM) and the time-frequency parameter control strategy matrix B of the transmitted pulses within the coherent processing time is as follows:

[0042] Step 11, let the characteristic parameters x of N radar pulses S r be x = [A m , f c , B w , M d , prf], where A m represents the pulse amplitude, f c represents the pulse carrier frequency, B w represents the pulse bandwidth, M d represents the intra-pulse modulation mode, and prf represents the pulse repetition frequency. The radar changes these characteristic parameters according to its information scheduling strategy.

[0043] Step 12, define the Hidden Markov Model (HMM) of the radar to be composed of the following five-tuple:

[0044] λ = (S r , O, A, B, π)

[0045] Where: The state set is the transmitted pulse sequence S r , the observation set is represented as O = {o1, o2,..., o M}, o M is the Mth observation value, M is the number of possible observation values, and the information scheduling strategy matrix A is used as the state transition matrix, represented as A = [aij ] N×N a ij Indicates from state s i Transfer to s j The probability, The transmit pulse time-frequency parameter control strategy matrix B during the coherent processing time is used as the observation probability matrix, expressed as B = [b j (k)] N×M b j (k) represents the state s j Next, generate observations o k The probability (e.g., the probability of emission), The initial state distribution π is represented as π = [π i ],π i This indicates that the initial state is s. i probability

[0046] Step 13: Based on the radar pulse characteristic parameter x from Step 11, and combined with the target detection task under the condition that the radar is not interfered with, construct the information scheduling strategy matrix A and the time-frequency parameter control strategy matrix B for the transmitted pulse within the coherent processing time.

[0047] Step 14, generate the emission pulse sequence S r =[s1,s2,...,s N ].

[0048] In Step 2, the Baum-Welch algorithm is used to estimate the radar's information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time, as follows:

[0049] Step 21, construct the objective function.

[0050] The jammer obtains the intercepted radar transmitted pulse sequence S r Extract the observation sequence O = {o1, o2, ..., o M The goal of the Baum-Welch algorithm is to maximize the likelihood function of the observed sequence O:

[0051]

[0052] In the formula, Q = (q1, q2, ..., q M ) is the hidden state sequence, q M It is the Mth hidden state in Q, and P(O,Q|λ) is the joint probability of (O,Q) of the known radar countermeasure model λ.

[0053] Step 22, Step E: Calculate the expectation.

[0054] The following key probabilities were calculated using the forward-backward algorithm:

[0055] (1) Forward probability a t (i), i = 1, 2, ..., N

[0056] a t (i) = P(o1,o2,…,o M ,q t =s i |λ),t=1,2,…M recurrence formula:

[0057]

[0058] (2) Backward probability β t (i), i = 1, 2, ..., N

[0059] β t (i)=P(o t+1 ,o t+2 ,…,o M |q t =s i Recurrence formula for t=1,2,…M:

[0060]

[0061] (3) State transition probability ξ t (i,j),i=1,2,…N,j=1,2,…N

[0062] ξ t (i,j)=P(q t =s i ,q t+1 =s j |O,λ),t=1,2,…M

[0063] Calculation formula:

[0064]

[0065] Where the denominator

[0066] (4) State dwell probability γ t (i)

[0067]

[0068] Step 23, M step: Parameter update.

[0069] Using the expected value calculated in the E-step, update the model parameters, including:

[0070] (1) Update the initial state distribution π

[0071] π i =γ1(i), i = 1, 2, ... N

[0072] (2) Update the information scheduling strategy matrix A

[0073]

[0074] (3) Update the transmit pulse time-frequency parameter control strategy matrix B

[0075]

[0076] Among them, v k It is the observed value o t The corresponding index, γ1(i), is the initial value of the state dwell probability.

[0077] Step 24, convergence judgment.

[0078] Calculate the log-likelihood logP(O|λ). If the change is less than the set value ∈, stop the iteration, where 0 < ∈ < 1.

[0079] In Step 3, the radar receives the interference signal S. j Estimate the interference strategy matrix A of the interference signal. j Interference signal time-frequency parameter control strategy matrix B j Calculate {S j ,S r The steps to adjust the Rand Index (ARI) are as follows:

[0080] Step 31: Set and It is for {S j ,S r The two clustering results are as follows, where n is the total number of samples. Indicates in S j and S r All samples were grouped into the same class. Indicates in S j and S r The samples were all divided into different classes. It represents the total number of all sample pairs.

[0081] Step 32: Calculate the Rand Index (RI):

[0082]

[0083] Step 33: Calculate the expected value of the RAND index RI:

[0084]

[0085] Where r and s are the number of clusters in the two clustering results, respectively, and n ij It belongs to both clustering and clustering The number of samples, n i It belongs to clustering The number of samples in n j It belongs to clustering The number of samples in the sample.

[0086] Step 34: Calculate the Adjusted Rand Index (ARI)

[0087]

[0088] The ARI value ranges from [-1, 1], where 1 indicates that the two clustering results are completely identical, 0 indicates that the two clustering results are equivalent to random partitioning, and -1 indicates that the two clustering results are completely opposite.

[0089] Step 35: If ARI > 0, the jamming is effective. The radar adjusts the information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time to generate a new transmit pulse sequence S. r =[s1,s2,...,s N Otherwise, keep matrices A and B unchanged. The adjustment method could be, for example, changing the probability values ​​or probability distribution functions of each row in matrices A and B.

[0090] To verify the effectiveness of the proposed method, this invention selects the radar operating state characteristic parameter x = [A m ,f c B w M d The center frequency f in prf] c Using {f1,f2,f3,f4,f5} as the object, implement the frequency hopping anti-jamming strategy for the radar.

[0091] Let the radar information scheduling strategy matrix A be:

[0092] A=[0.5 0.3 0.1 0.05 0.05; 0.2 0.5 0.1 0.1 0.1; 0.1 0.1 0.5 0.2 0.1; 0.10.1 0.2 0.5 0.1; 0.1 0.1 0.1 0.2 0.5]

[0093] Each row of A corresponds to a frequency hopping strategy, namely the center frequency f. cIt jumps in {f1,f2,f3,f4,f5} with the corresponding probability.

[0094] The transmit pulse time-frequency parameter control strategy matrix B is:

[0095] B=[1 / 6 1 / 6 1 / 6 1 / 6 1 / 6 1 / 6; 1 / 5 1 / 5 1 / 5 1 / 5 1 / 10 1 / 10; 0 1 / 2 0 1 / 4 1 / 40; 1 / 2 1 / 5 1 / 5 0 1 / 10 0; 1 / 10 1 / 10 1 / 10 1 / 10 1 / 10 1 / 2]

[0096] The column number of B corresponds to the frequency hopping strategy of the transmitted pulse during the radar coherent processing time, and each row number of B represents a different frequency hopping transition probability.

[0097] The radar generates a transmit pulse sequence S by using matrices A and B to generate frequency-hopping transmit pulses. r =[s1,s2,…,s N ], where N = 1000.

[0098] Suppose the jammer intercepts radar pulse S r = [s1,s2,…s] M With M=100, through Steps 21 to 24, the estimated values ​​of the radar information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time are obtained:

[0099]

[0100] The interfering party follows the matrix and According to interference strategy S j ={'WBJ','NBJ','C&I','DenseTargets','R&VDecept'}, where WBJ represents broadband noise suppression, narrowband agile noise suppression, slice jamming, dense false target jamming, and range-velocity deception jamming, respectively. The jamming strategy matrix A is then defined. j Interference signal time-frequency parameter control strategy matrix B j Emitting interference signal S to the radar j =[s 1j ,s 2j ,…s Nj ].

[0101] The radar received an interference signal S j Then, calculate {S} j ,S rThe radar adjusts the Rand Index (ARI). If ARI > 0, the jamming is effective. The radar then adjusts the information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time to generate a new transmit pulse sequence S. r =[s1,s2,...,s N Otherwise, keep matrices A and B unchanged.

[0102] As attached Figure 6 The figure shows the simulation results for adversarial rounds with iter=30, and the curves showing the changes in RI and ARI are presented. As can be seen from the figure, whenever the radar changes its information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time, the jammer will fail in multiple adversarial rounds. The main reason is that the jammer uses a much smaller number of intercepted pulses than the radar transmits when estimating the radar's information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B within the coherent processing time. Meanwhile, the radar, in analyzing the jammer's jamming strategy matrix A… j Interference signal time-frequency parameter control strategy matrix B j The entire interference pulse sequence was used, with... Figure 7 The graph shows the change curve of the radar's estimation error of the jammer's state during radar countermeasures. As can be seen from the graph, the radar accurately estimated the jammer's jamming strategy.

[0103] In summary, dynamic modeling in cognitive radar countermeasures faces numerous challenges. Radar countermeasures are a dynamic game between opposing sides, with both sides constantly adjusting their strategies based on the other's actions. Dynamic modeling must simultaneously consider the strategic changes of both sides and their mutual influences, making the creation of a model that accurately describes this dynamic game process extremely complex. To address this challenge, this invention proposes a cognitive radar countermeasures dynamic modeling method based on Hidden Markov Models (HMMs): A master-slave countermeasure mode is defined for the radar-jammer. When the radar is not jammed, it sets an HMM-based information scheduling strategy matrix A and a transmit pulse time-frequency parameter control strategy matrix B based on its target detection task, generating a transmit pulse sequence. The jammer uses the intercepted radar pulses to extract radar state parameters and estimate the radar information scheduling strategy matrix A and the transmit pulse time-frequency parameter control strategy matrix B, thus formulating a jamming strategy matrix A. j Interference signal time-frequency parameter control strategy matrix B j The system sends an interference signal to the radar. After receiving the interference signal, the radar estimates the A of the interfering party. j and B j By determining whether the jamming is effective and adjusting matrices A and B accordingly, and repeating this process, dynamic modeling of cognitive radar countermeasures can be achieved.

Claims

1. A cognitive radar countermeasure dynamic modeling method based on Hidden Markov Models (HMM), characterized in that, It includes the following steps: Step 1: Construct a radar-jamming machine master-slave adversarial scenario, set the adversarial rounds (iter), and formulate an information scheduling strategy matrix based on a hidden Markov model according to the target detection task under the condition that the radar is not jammed. A and the time-frequency parameter control strategy matrix for transmitted pulses within the coherent processing time B Generate a sequence of emitted pulses The method is as follows: Step 11, set N Characteristic parameters of a transmitted radar pulse x = [ A m , f c , B w , M d , prf The radar changes the characteristic parameters according to its information scheduling strategy, wherein... A m Indicates pulse amplitude. f c Indicates the pulse carrier frequency. B w Indicates pulse bandwidth. M d Indicates the intrapulse modulation mode. prf Indicates the pulse repetition frequency; Step 12, defining that the hidden Markov model of the radar consists of the following five-tuple: Among them: the emission pulse sequence As a set of states, the set of observations is represented as , For the first M 1 observation, initial state distribution π Represented as , Indicates the initial state. s i The probability of; Step 13, based on the feature parameters x Based on the target detection mission under conditions where radar is not interfered with, an information scheduling strategy matrix is ​​constructed. A and the time-frequency parameter control strategy matrix for transmitted pulses within the coherent processing time B ; Step 14: Generate the transmit pulse sequence ,in Indicates the first N One radar pulse, N Indicates the number of radar pulses transmitted; Step 2: The jamming party uses the intercepted radar transmission pulse sequence... Estimated matrix A and B Based on the interference strategy, formulate an interference strategy matrix. A j Interference signal time-frequency parameter control strategy matrix B j Emitting interference signals to radar ,in, M This indicates the number of pulses intercepted. , Indicates the first N One interference signal; Step 3, the radar receives the interference signal. Estimating the matrix A j and B j ,calculate The Adjusted Rand Index (ARI) is used to determine... Interference effect: If the RAND index is adjusted to be greater than 0, the interference is effective, and the radar adjusts the matrix. A and B This generates a new sequence of emission pulses; Step 4, if the adversarial round < iter, return to Step 2, otherwise, output the adversarial result.

2. The cognitive radar countermeasure dynamic modeling method based on HMM according to claim 1, characterized in that, In the quintuple, the information scheduling strategy matrix A As a state transition matrix, it is expressed as , Indicates from state s i Transferred to s j The probability, ; Transmit pulse time-frequency parameter control strategy matrix within coherent processing time B As the observation probability matrix, it is represented as , Indicates the state s j Lower generation observation o k The probability, Initially in state s i probability , .

3. The cognitive radar countermeasure dynamic modeling method based on HMM according to claim 1, characterized in that, In step 2, the Baum-Welch algorithm is used to estimate the matrix. A and B ,as follows: Step 21, the jamming party obtains the intercepted radar transmitted pulse sequence Extract observation sequence The goal of the Baum-Welch algorithm is to maximize the observed sequence. O Likelihood function: In the formula, It is a hidden state sequence. It is an observation sequence O The Mth hidden state in the data. It is a known radar countermeasure model of Joint probability; Step 22: Calculate the forward probability using the forward-backward algorithm. Backward probability State transition probability and state dwell probability ; Step 23, updating the model parameters using the calculation result of Step 22, including: (1) Update the initial state distribution π , ; (2) Update the state feature transition matrix, i.e., the matrix A , ; (3) Update the observation probability matrix, i.e., the matrix B , in, v k Observed values o t The corresponding index, , , , , It is the initial value of the state dwell probability; Step 24, calculate the log-likelihood. If the change is less than Stop iteration, where 0 < <1.

4. The cognitive radar countermeasure dynamic modeling method based on HMM according to claim 3, characterized in that, In step 22, the forward probability The recursive formula is as follows: Backward probability The recursive formula is as follows: State transition probability The calculation formula is as follows: in, , .

5. A cognitive radar adversarial dynamic modeling method based on HMM according to claim 1, 3, or 4, characterized in that, The interference strategies include broadband noise suppression, narrowband smart noise suppression, slice interference, dense false target interference, and range-velocity deception interference.

6. The cognitive radar countermeasure dynamic modeling method based on HMM according to claim 1, characterized in that, In step 3, the radar receives an interference signal. Estimating the matrix A j and B j ,calculate The steps for adjusting the RAND Corporation index are as follows: Step 31, set and Yes The two clustering results, n It is the total number of samples. Indicates in and All samples were grouped into the same class. Indicates in and The samples were all divided into different classes. It is the number of all sample pairs; Step 32, calculating the Rand index: Step 33, calculating the expected value of the Rand index: in, r and s These are the number of categories in the two clustering results, respectively. n ij It belongs to both clustering and clustering The number of samples, n i It belongs to clustering The number of samples, n j It belongs to clustering The number of samples; Step 34, calculating the adjusted Rand index: ARI The value ranges from [-1, 1], where 1 indicates that the two clustering results are completely identical, 0 indicates that the two clustering results are equivalent to random partitioning, and -1 indicates that the two clustering results are completely opposite. Step 35, if ARI >0, jamming effective, radar adjustment. A and B Generate a new sequence of transmitted pulses. Otherwise, preserve the matrix. A , B constant.

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