A dynamic modeling method for reducing parameter uncertainty of electronic reconnaissance system

Abstract

In modern information battlefield, radar and radio frequency communication system are very dense, and the signal environment is very complex. It is a very difficult problem to identify friend or foe, to know whether oneself is monitored and to take what kind of countermeasures. In order to solve this problem, a dynamic modeling method for reducing the uncertainty of the measurement parameters of electronic reconnaissance system is proposed: intercepted radar pulse is used to extract radar state parameters and construct state feature matrix, the feature matrix is analyzed by piecewise similarity, the working state of the radar is judged according to the value range distribution of the similarity and is classified, the slice sampling algorithm is used to generate the prior probability distribution of the radar state according to different radar working states, and the influence of uncertainty on the detection result is reduced by using Bayesian estimation.

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 modeling method for Bayesian dynamic models based on Markov chains and Monte Carlo algorithms. Background Technology

[0002] Electronic reconnaissance systems are one of the core systems in cognitive warfare, a new concept of information warfare that emerged with electromagnetic spectrum warfare. Cognitive warfare involves using electronic reconnaissance systems to perceive the opponent's state in real time and adjust one's own countermeasures to maximize jamming / anti-jamming effectiveness. Existing cognitive warfare approaches all assume complete perception of the opponent's state information, formulating corresponding countermeasures in terms of power allocation, operating frequency bands, confrontation time, and airspace, and establishing effectiveness evaluation models. However, actual confrontation is an "open-loop" environment; neither side can completely grasp the other's state. Under conditions of incomplete perception information, how to appropriately assess the uncertainties brought about by incomplete information and, consequently, establish an evaluation model for the measurement parameters of electronic reconnaissance systems remains an unsolved scientific problem.

[0003] Cognitive countermeasures originated from cognitive radio technology. "Cognition" refers to a conscious intellectual activity involving thinking, reasoning, memory, imagination, learning, information processing, knowledge application, and prioritization. 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 these goals, 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 the probability of identifying multiple false targets. Identifying false targets requires a large number of manually labeled jamming signal samples covering all jamming patterns and strategies, which is practically impossible. Similarly, for the jamming side, it is impossible to fully grasp all the radar's anti-jamming measures and signal processing methods, especially its ability to identify false targets. In actual combat, 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 at the radar antenna aperture. Under incomplete information conditions, existing AI-based adversarial models and effectiveness evaluation methods do not conform to the actual combat environment and cannot achieve true cognitive warfare. Therefore, establishing an uncertainty model for the measurement parameters of electronic reconnaissance systems is one of the key issues that urgently needs to be addressed in cognitive electromagnetic spectrum warfare. Summary of the Invention

[0004] To achieve the above objectives, this invention provides a dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems. The technical solution adopted is as follows:

[0005] A dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems includes the following steps:

[0006] Step 1: Based on the characteristic parameters x of the N radar pulses intercepted by the detection receiver, and using the mean μ and variance σ of their measured values, evaluate the radar operating status type, including:

[0007] Type 1: (μ, σ) is a fixed statistic [μ * ,σ * ];

[0008] Type 2: (μ,σ) within a fixed interval fluctuation;

[0009] Type 3: μ varies randomly, variance σ remains constant;

[0010] Type 4: (μ,σ) within the range of variation fluctuation;

[0011] Type 1 corresponds to the case where the radar is not jammed, i.e., the characteristic parameter x of the radar pulse remains unchanged; Type 2 corresponds to the case where the radar is subjected to suppressive jamming, and one or more parameters in x change randomly within a fixed range; Type 3 corresponds to radars where one or more parameters in x are agile, and the agility follows a specific probability distribution function; Type 4 corresponds to radars where one or more parameters in x are agile, and the agility cannot be described by a probability distribution function; where μ * For a fixed mean, σ * To keep the variance constant, μ To fix the lower limit of the mean, To fix the upper limit of the mean, σ To fix the lower limit of variance, To fix the upper limit of variance, μ c The lower limit of the mean is not fixed. The upper limit of the mean is not fixed. σ c This is the lower bound for non-fixed variance. The upper limit of the variable variance;

[0012] Step 2: Select the corresponding random distribution function according to the radar operating state type, and generate the prior probability distribution function P(x) of the radar operating mode. i Construct a prior probability distribution dataset X from the corresponding random sequence.

[0013] Step 3: Generate the prior probability distribution function and calculate the Bayesian posterior probability of the radar state feature matrix Y to reduce the uncertainty of intercepted radar pulse measurement parameters.

[0014] Compared with the prior art, the beneficial effects of the present invention are:

[0015] 1. Based on the various uncertainties faced by electronic reconnaissance systems in cognitive electromagnetic spectrum warfare, this invention classifies radar transmitter state characteristics into four types, providing theoretical support for identifying radar operating modes.

[0016] 2. This invention extracts intercepted pulse features and constructs a radar state feature matrix based on the signal processing methods of electronic reconnaissance systems. It uses a segmented similarity index to identify the radar's operating state, providing a basis for the rational design of the prior probability distribution in Bayesian posterior probability calculation. This can effectively reduce the impact of uncertainties on the Bayesian posterior probability calculation results.

[0017] 3. Use slice sampling to generate the prior probability distribution function P(x) i The corresponding random sequence can reduce the impact of uncertainty on the Bayesian posterior probability calculation results. Slice sampling is an algorithm used to sample from a distribution with arbitrary density functions, where at most one scaling constant is known, which is exactly what is needed when sampling from a complex posterior distribution with an unknown normalization constant. This algorithm does not generate independent samples, but rather generates Markov sequences whose stationary distribution is the target distribution. Therefore, slice sampling is a Markov Chain Monte Carlo (MCMC) algorithm. However, it differs from other well-known MCMC algorithms because it only requires specifying the scaled posterior probability and does not require the proposal distribution or marginal distribution probability. Attached Figure Description

[0018] Figure 1 A diagram illustrating cognitive electronic warfare operations.

[0019] Figure 2 This is a flowchart of the modeling and simulation process for this invention.

[0020] Figure 3 This is the time-frequency diagram of the transmitted pulse train.

[0021] Figure 4 To capture a binarized image of the time-frequency map of the radar signal.

[0022] Figure 5 This represents the peak distribution of the binarized image after Hough transform.

[0023] Figure 6 S is the similarity index between adjacent submatrices. idx .

[0024] Figure 7 Let Y be the Bayesian posterior probability of the radar state feature matrix Y. Detailed Implementation

[0025] 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.

[0026] 1. Uncertainty model of measurement parameters of electronic reconnaissance system.

[0027] From a system-on-systems confrontation perspective, 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 diagram. 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.

[0028] Taking cognitive radar countermeasures as an example, the envisioned countermeasure simulation model is as follows:

[0029]

[0030]

[0031]

[0032]

[0033] Equation (1) is the radar state equation, x = [A m ,f c B w M d [,prf] represents the 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 aThis represents radar anti-jamming measures. Here, x represents the radar state measurable by the jamming party through its sensing system, and μ... a These are unmeasurable system variables.

[0034] 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, and z includes the estimation error of the radar's operating state. 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 radar operating status; h() represents the signal processing method of the detection receiver.

[0035] Equation (3) is the estimation of the radar's current operating state by the jammer's cognitive system, which has a large degree of uncertainty. Here, E() represents the estimation method for the radar's operating state.

[0036] Equation (4) is the interference pattern derived from the estimation result of equation (3), P j () represents the functional relationship between the interference pattern and the radar operating state. 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) and then correct the μ. a Based on the estimation, the entire adversarial process can be implemented using a "Bayesian updating model with Markov chain Monte Carlo algorithm".

[0037] A brief description of the operation of the detection receiver in 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 their characteristic parameters x, i.e., the aforementioned radar state variables [A]. m ,f c B w M d [prf]. Due to factors such as signal sorting errors and random fading in the channel, these measurements appear as random sequences of length N that follow 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. A common practice is to determine a threshold based on σ. When the measurement value is below the threshold, the change is considered insignificant; when it exceeds the threshold, the change is considered significant. Therefore, different threshold selection principles will lead to different cognitive results. To measure this phenomenon, the above measurement parameters can be divided into several random types.

[0038] Therefore, refer to Figure 2 As shown, the dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to the present invention includes the following steps:

[0039] Step 1: Based on the characteristic parameters x of the N radar pulses intercepted by the detection receiver, and using the mean μ and variance σ of their measured values, evaluate the radar operating status type, including:

[0040] Type 1: (μ, σ) is a fixed statistic [μ * ,σ * ].

[0041] Type 2: (μ,σ) within a fixed interval fluctuation.

[0042] Type 3: μ varies randomly, while variance σ remains constant.

[0043] Type 4: (μ,σ) within the range of variation fluctuation.

[0044] Type 1 corresponds to the case where the radar is not interfered with, i.e., the characteristic parameter x of the radar pulse = [A m ,f c B w M d [prf] remains unchanged; Type 2 corresponds to the case where the radar randomly changes one or more parameters in x under suppression interference, and the range of change is fixed; Type 3 corresponds to radars where one or more parameters in x change rapidly and the rapid change follows a specific probability distribution function; Type 4 corresponds to radars where one or more parameters in x change rapidly and the rapid change cannot be described by a probability distribution function. Where μ * For a fixed mean, σ * To maintain a constant variance, μ is a fixed lower limit of the mean. σ is a fixed upper bound for the mean and a fixed lower bound for the variance. To fix the upper limit of variance, μ c The lower limit of the mean is not fixed. For a variable upper limit of the mean, σ c This is the lower bound for non-fixed variance. This represents the upper limit of the variable variance.

[0045] Step 2: Select the corresponding random distribution function according to the radar operating state type, and generate the prior probability distribution function P(x) of the radar operating mode. i Given the random sequence corresponding to ), construct the prior probability distribution dataset X.

[0046] Step 3: Generate the prior probability distribution function and calculate the Bayesian posterior probability of the radar state feature matrix Y to reduce the uncertainty of intercepted radar pulse measurement parameters. For example, this invention can use the Matlab function gm=fitgmdist(X,5) to generate the prior probability distribution function and the Matlab function P=posterior(gm,Y) to calculate the Bayesian posterior probability of the radar state feature matrix Y.

[0047] In an embodiment of the present invention, the observation time period (0~t) will be... d The radar pulses received by the internal detection receiver are represented as Y = [y1, y2, ..., y]. N ]∈R N×M M is the radar pulse quantization length, and N is the number of radar pulses intercepted.

[0048] The radar transmitter state, i.e., the characteristic parameter x, is estimated using Bayesian posterior probability:

[0049]

[0050] In the formula, P L (Y|x) is the likelihood function, P(x) is the prior probability distribution function of the radar transmitter state, and P(Y) is the probability distribution function of the intercepted pulse.

[0051] The main technical parameters of a radar include time-domain parameters and frequency-domain parameters, among which the time-domain parameters include the radar pulse amplitude A. m , pulse repetition frequency pref; frequency domain parameters include pulse carrier frequency f c Pulse bandwidth B w Intrapulse modulation mode M d Because 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 amplitude of each intercepted pulse is taken, and the N pulse maxima form a random sequence with a relatively fixed mean and variance (Type 1); for the pulse carrier frequency f c Pulse 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 3 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:

[0052] Pulse power P t =100W;

[0053] The emission pulse width T = 3 μs;

[0054] Intra-pulse modulation method: LFM, frequency modulation bandwidth B = 30MHz;

[0055] Pulse carrier frequency f c =1.8GHz;

[0056] The pulse repetition period PRI = 15 μs.

[0057] As attached Figure 4 The image shown is a binarized time-frequency plot of the intercepted radar signal. The pulse 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 4 Transforming the oblique lines in the image into points on the time-frequency plane, as shown in the attached figure. Figure 5 The position of the peak point is used to obtain the pulse carrier frequency f. c The estimated value.

[0058] The above parameter measurements impose certain requirements on the quality of the intercepted signal. Under the condition of meeting a certain signal-to-noise ratio (SNR), for non-agile radar, the measured values ​​of these three parameters should belong to a type 1 random sequence; for waveform agile radar, its pulse bandwidth B... w The measured value should belong to type 2 random sequence, as it will change with the waveform; for frequency-agile radar, because its pulse carrier frequency f c Randomly jumps within a defined frequency band, pulse carrier frequency f c The measured values ​​should belong to type 3 random sequence; if the radar adopts frequency, waveform and intra-pulse modulation agile mode, the measured values ​​of the above three parameters belong to type 4 random sequence.

[0059] Intrapulse modulation mode M d The measurement of radar pulses is relatively complex, and machine learning methods are typically used to identify the intra-pulse modulation scheme of the intercepted pulse. According to radar field knowledge and published literature, radar intra-pulse modulation schemes include linear frequency modulation (LFM), nonlinear frequency modulation (NLFM), and sub-pulse coded phase modulation (P2, P4, M-sequences, etc.). Deep learning-based intra-pulse modulation identification methods are effective, but they require a large number of typical radar intra-pulse modulation signals as a training set. When identifying the modulation scheme of the intercepted pulse, different modulation schemes are usually represented in coded form. Due to the influence of noise and random fading in the channel, and the difficulty of the training set covering unknown radar intra-pulse modulation schemes, the identification of the intra-pulse modulation scheme M...d The measured value has a high degree of uncertainty and belongs to type 4 random sequence.

[0060] Given the above factors, the radar transmitter state x = [A m ,f c B w M d The Bayesian posterior probabilities shown in equation (5) should be used to estimate A respectively. m ,f c B w M d Since the values ​​of x and pf belong to different types of random sequences, their prior probability distribution functions P(x) and pf should be set separately. i ) and likelihood function P L (Y i |x i (i = 1, 2, ... 5).

[0061] Because the denominator P(Y) of equation (5) i )=∫P L (Y i |x i )P(x i )dx i To ensure that the normalization coefficient is not greater than 1, which is not readily available in practice, equation (6) is often used to calculate the Bayesian posterior probability:

[0062]

[0063] In the formula, P j (x i |Y i Let x represent the Bayesian posterior probability obtained in the j-th iteration. i Let β represent the i-th element in the feature parameter x. j Let represent the iteration exponent, and M0 be the maximum number of iterations. From equation (6), it can be seen that when β1 = 0, P... 1 (x i |Y i )=P(x i ), when β M0 When P = 1, M0 (x i |Y i The likelihood function P approaches the true value of the Bayesian posterior probability. L (Y i |x i Implemented using the Matlab function (7):

[0064]

[0065] In the formula, σi For x i The standard deviation.

[0066] To reduce the impact of uncertainty on the measured values, it is necessary to select the appropriate prior probability distribution function P(x) for different radar operating modes. i Since the prior probability distribution of the radar cannot be accurately obtained solely from intercepted radar pulses, different probability distribution functions are preset for the aforementioned four random types. Slice sampling is then used to generate the prior probability distribution function P(x). i The corresponding random sequence is then used to calculate the posterior probability of each measurement sequence. Specifically:

[0067] For type 1: Choose a multivariate probability normal distribution function with fixed mean μ and variance σ;

[0068] For type 2: Choose the mean μ and variance σ within a fixed interval. The multivariate probability normal distribution function;

[0069] For type 3: Choose a gamma distribution function where alpha follows the average probability distribution and beta is a fixed value;

[0070] For type 4: Select the mean μ and variance σ within the range of variation. The multivariate probability normal distribution function, where the upper and lower bounds are... μ c , σ c , They follow an independent uniform probability distribution.

[0071] Slice sampling is an algorithm for sampling from a distribution with arbitrary density functions, where at most one scaling constant is known—precisely necessary for sampling from complex posterior distributions with unknown normalization constants. Instead of generating independent samples, this algorithm generates Markov sequences whose stationary distribution is the target distribution. Therefore, slice sampling is a Markov Chain Monte Carlo (MCMC) algorithm. However, it differs from other well-known MCMC algorithms because it only requires specifying the scaled posterior probabilities, without needing to suggest or marginal distribution probabilities.

[0072] In one embodiment, P(x) is generated using slice sampling. i The steps for the corresponding random sequence can be described as follows:

[0073] S1: Set the number of radar pulses intercepted, N; for example, N = 1000.

[0074] S2: Set the pulse amplitude mean mu1, pulse amplitude variance sigma1, and prior probability distribution function pdf1, and generate a pulse amplitude sampling sequence using slice sampling. For example, mu1 = 2; sigma1 = 3; pdf1 = @(x)mvnpdf(x,mu1,sigma1), where mvnpdf represents the multivariate probability normal distribution function; @ represents the prefix of the independent variable of the Matlab function, and the generated pulse amplitude sampling sequence is represented as slicesample(1,N,'pdf1',pdf1); 'pdf1' indicates that pdf1 is the target probability distribution function.

[0075] S3: Set the pulse carrier frequency to follow a gamma distribution, and set the values ​​of α and β, as well as the prior probability distribution function pdf2. Generate a pulse carrier frequency sampling sequence using slice sampling. For example, α = 2.43; β = 1; pdf2 = @(x)gampdf(x,alpha,beta), where gampdf represents the gamma probability distribution function, and the generated pulse carrier frequency sampling sequence is represented as slicesample(1,N,'pdf2',pdf2); 'pdf2' indicates that pdf2 is the target probability distribution function.

[0076] S4: Set the pulse bandwidth mean mu3, pulse bandwidth variance sigma3, and prior probability distribution function pdf3, and generate a pulse bandwidth sampling sequence using slice sampling. For example, mu3 = 4; sigma3 = 1; pdf3 = @(x)mvnpdf(x,mu3,sigma3), and the generated pulse bandwidth sampling sequence is represented as slicesample(1,N,'pdf3',pdf3); 'pdf3' indicates that pdf3 is the target probability distribution function.

[0077] S5: Set the slice thickness 'thin', the number of data to discard 'burnin', and the prior probability distribution function pdf4 to generate an intra-pulse modulation sampling sequence using slice sampling. For example, 'thin' = 5; 'burnin' = 500; pdf4 = @(x)exp(-x 2 / 2)·(1+(sin3x) 2 )·(1+(cos5x) 2 The generated intra-pulse modulation sampling sequence is represented as: slicesample(1,N,'pdf4',pdf4,'thin','burnin'); 'pdf4' indicates that pdf4 is the target probability distribution function.

[0078] S6: Set the pulse repetition frequency mean mu5, pulse repetition frequency variance sigma5, and prior probability distribution function pdf5, and generate a pulse repetition frequency sampling sequence using slice sampling. For example, mu5 = 1; sigma5 = 3, pdf5 = @(x)mvnpdf(x,mu5,sigma5), and the generated pulse repetition frequency sampling sequence is represented as slicesample(1,N,'pdf5',pdf5), where 'pdf5' indicates that pdf5 is the target probability distribution function.

[0079] S7: Use the sampling sequences obtained from S2 to S6 to form a prior probability distribution dataset.

[0080] To accurately construct the radar operating mode, select the appropriate prior probability distribution function P(x) i To estimate the radar operating state type, the present invention provides a method for evaluating the radar operating state type as follows:

[0081] Step 11: After extracting the measurement parameters of the intercepted pulses, extract the characteristic parameters x = [A] of N radar pulses. m ,f c B w M d Construct a feature matrix with x as the descriptor, i.e., the radar state feature matrix Y∈R. N×5 .

[0082] Step 12, set the submodule length L, and divide Y into M = N / L submatrices {y i}, i = 1, 2, ..., M, 2 ≤ L ≤ N / 2, calculate the Bhattacharyya distance between adjacent submatrices:

[0083]

[0084] In the formula, d B (y i ,y i+1 ) represents the i-th submatrix y i With the (i+1)th submatrix y i+1 The distance between Bhattacharyya, P(y) i ) represents the i-th submatrix y i The probability distribution function, P(y) i+1 ) represents the (i+1)th submatrix y i+1 The probability distribution function. In this step, the submodule represents a segment of Y, corresponding to the radar state parameters extracted from L pulses. The modeling of this invention is based on the state analysis results of the segmented submodules.

[0085] Step 13: Calculate the similarity index S between adjacent submatrices based on the Bhattacharyya distance. idx :

[0086]

[0087] In the formula, σ d For Bhattacharyya distance d B The standard deviation.

[0088] Since the radar state characteristic matrix Y is equally divided into M sub-matrices, that is, there are M / 2 sub-matrix pairs, therefore S idx It is a sequence of length M / 2, and the range of its values ​​corresponds to different radar operating modes.

[0089] As can be seen from equation (9), if d B (y i ,y i+1 When ) = 0, S idx =1 indicates that adjacent submatrices are indistinguishable, corresponding to the radar operating in a non-agile state; otherwise, the radar is in an agile state, and S idx The lower the value, the more agility parameters the radar has.

[0090] Step 14: Divide the [0,1] interval into 4 equal sub-intervals, and apply the similarity index S. idx The sub-interval determines the radar's operating status type. Specifically, interval 1 is (0.75, 1], corresponding to type 1; interval 2 is (0.50, 0.75], corresponding to type 2; interval 3 is (0.25, 0.5], corresponding to type 3; and interval 4 is [0, 0.25], corresponding to type 4.

[0091] 2. Simulation Experiment

[0092] To verify the effectiveness of the proposed method, the radar operating states selected in this invention are shown in Table 1:

[0093] Table 1. Simulation Parameter Settings

[0094] <![CDATA[A m ]]> 2 3 <![CDATA[Multivariate normal distribution pdf 1]]> <![CDATA[f c ]]> α＝2.43 β＝1 <![CDATA[Gamma distribution pdf2]]> <![CDATA[B w ]]> 4 1 <![CDATA[Multivariate normal distribution pdf3]]> <![CDATA[M d ]]> 1 [1,4] <![CDATA[pdf4]]> prf 1 3 <![CDATA[Multivariate normal distribution pdf 5]]>

[0095] Assume the number of intercepted radar pulses N = 1000; generate the radar state feature matrix Y using the random function generator in Matlab according to the parameter settings in Table 1, select the submodule length L = 5, and obtain the similarity index S between adjacent submatrices through Step 2 to Step 3. idx The curve is attached. Figure 6 As shown.

[0096] From the appendix Figure 6 It can be seen that the similarity index S between adjacent submatricesidx Fluctuations between 0 and 0.45 indicate that the radar is operating in a multi-parameter agile state.

[0097] Select the appropriate random distribution function according to the radar state type, and generate the prior probability distribution function P(x) using slice sampling. i For the corresponding random sequence, construct the prior probability distribution dataset X; use the Matlab function gm=fitgmdist(X,5) to generate the prior probability distribution function, and use the Matlab function P=posterior(gm,Y) to calculate the Bayesian posterior probability of the radar state feature matrix Y, as shown in the appendix. Figure 7 As shown.

[0098] Appendix Figure 7 The histogram shown on the diagonal represents the Bayesian posterior probabilities of the eigenvalue matrix Y, and their marginal distribution reflects the statistical regularity of the radar state.

[0099] In summary, this invention extracts radar state parameters from intercepted radar pulses and constructs a state feature matrix. It then performs segmented similarity analysis on the feature matrix, determines the radar's operating state based on the similarity value range distribution, and classifies it accordingly. For different radar operating states, a slice sampling algorithm is used to generate the radar state prior probability distribution, and Bayesian estimation is employed to reduce the impact of uncertainty on the detection results.

Claims

1. A dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems, characterized in that, Includes the following steps: Step 1, based on the intercepted data from the detection receiver N Characteristic parameters of a radar pulse x Using the mean of its measured values μ and variance σ Assess the radar's operational status, including: Type 1: ( μ , σ () is a fixed statistic ; Type 2: ( μ , σ Within a fixed interval fluctuation; Type 3: μ Random variation, variance σ constant; Type 4: ( μ , σ Within the range of change fluctuation; Type 1 corresponds to the case where the radar is not interfered with, i.e., the characteristic parameters of the radar pulse. x The type 2 radar remains unchanged when subjected to suppressive jamming; however, the type 2 radar changes randomly when subjected to suppressive jamming. x The case where one or more parameters are involved and their range of variation is fixed; Type 3 corresponds to... x A radar with one or more parameters that are agile and whose agility follows a specific probability distribution function; Type 4 corresponds to x A radar with one or more parameters that are agile, and whose agility cannot be described by a probability distribution function; where, For a fixed mean, To keep the variance constant, To fix the lower limit of the mean, To fix the upper limit of the mean, To fix the lower limit of variance, To fix the upper limit of variance, The lower limit of the mean is not fixed. The upper limit of the mean is not fixed. This is the lower bound for non-fixed variance. The upper limit of the variable variance; Step 2: Select the corresponding random distribution function according to the radar operating state type, and generate the prior probability distribution function of the radar operating mode. P ( x i Construct a prior probability distribution dataset based on the corresponding random sequence. X ; Step 3: Generate the prior probability distribution function and calculate the radar state feature matrix. Y The Bayesian posterior probability reduces the uncertainty of intercepted radar pulse measurement parameters.

2. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 1, characterized in that, The method for evaluating the radar operating status type in step 1 is as follows: Step 11, extract the N Characteristic parameters of a radar pulse x = [ A m , f c , B w , M d , prf Construct the radar state feature matrix. ; 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, Set the submodule length L ,Will Y Divided into equal parts M = N / L Submatrices { y i }, i =1,2,… M ,2 Calculate the Bhattacharyya distance between adjacent submatrices; where the submodule represents Y The segment, corresponding to from L Radar state parameters extracted from each pulse; Step 13: Calculate the similarity index between adjacent submatrices based on the Bhattacharyya distance. S idx ; Step 14: Divide the [0,1] interval into 4 equal sub-intervals, and apply the similarity index... S idx The type of radar operation is determined by the sub-interval it is in.

3. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 2, characterized in that, In step 12, the Bhattacharyya distance between adjacent submatrices is calculated as follows: In the formula, Indicates the first i Submatrix With the i +1 submatrix The distance between Bhattacharyya, For the first i Submatrix The probability distribution function, For the first i +1 submatrix The probability distribution function; In step 13, the similarity index between adjacent submatrices is calculated. S idx as follows: In the formula, σ d Distance to Bhattacharyya d B Standard deviation; like When =0, S idx =1 indicates that adjacent submatrices are indistinguishable, corresponding to the radar operating in a non-agile state; otherwise, the radar is in an agile state, and S idx The lower the value, the more agility parameters the radar has.

4. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 2 or 3, characterized in that, In step 14, interval 1 is (0.75, 1], corresponding to type 1; interval 2 is (0.50, 0.75], corresponding to type 2; interval 3 is (0.25, 0.5], corresponding to type 3; and interval 4 is [0, 0.25], corresponding to type 4.

5. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 2 or 3, characterized in that, To counter cognitive radar, the following simulation model is constructed: （1） （2） （3） （4） Equation (1) is the radar state equation, and radar anti-jamming measures. μ a It is an unmeasurable system variable; Equation (2) represents the perception result of the jamming party's cognitive system on the radar's operating status, which includes measures to counter radar jamming. μ a The estimate is based on incomplete information. z This includes estimation errors of the radar's operating status. Once the adversarial scenario is determined, signal detection and estimation methods are used to obtain the... x The estimated value, It is an estimated value obtained through prior knowledge and the radar's operating status; This indicates the signal processing method of the detection receiver; Equation (3) is the jammer's cognitive system's estimate of the radar's current operating state; This describes a method for estimating the radar's operational status. Equation (4) is the interference pattern derived from the estimation results of equation (3). y After being applied to the radar, the radar state is observed to see if it changes through equation (2), and then the adjustment is made accordingly. μ a The estimate, This represents the functional relationship between the jamming pattern and the radar's operating state. Radar transmitter state, i.e., characteristic parameters, are estimated using Bayesian posterior probability. x : (5) In the formula, Let be the likelihood function. Let be the prior probability distribution function of the radar transmitter state. This is the probability distribution function for intercepting pulses.

6. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 1, characterized in that, Step 2 involves generating [the product] using slice sampling. P ( x i The corresponding random sequence; in step 3, the Matlab function gm= fitgmdist( X 5) Generate the prior probability distribution function using the Matlab function P = posterior(gm, Y Calculate the radar state feature matrix Y The Bayesian posterior probability.

7. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 6, characterized in that, The method of generating by slice sampling P ( x i The corresponding random sequence is obtained through the following steps: S1: Set the number of radar pulses to be intercepted N ; S2: Set the average pulse amplitude mu 1. Pulse amplitude variance sigma 1 and prior probability distribution function pdf 1. Generate pulse amplitude sampling sequence using slice sampling; S3: Set the pulse carrier frequency to follow a gamma distribution, and set... α and β Values ​​and setting the prior probability distribution function pdf 2. Generate a pulse carrier frequency sampling sequence using slice sampling; S4: Set the average pulse bandwidth mu 3. Pulse bandwidth variance sigma 3 and prior probability distribution function pdf 3. Generate a pulse bandwidth sampling sequence using slice sampling; S5: Set slice thickness thin' Discarding data quantity burnin 'and prior probability distribution function pdf 4. Generate intrapulse modulation sampling sequences using slice sampling; S6: Set the average pulse repetition frequency mu 5. Variance of pulse repetition frequency sigma 5 and prior probability distribution function pdf 5. Generate a pulse repetition frequency sampling sequence using slice sampling; S7: Use the sampling sequences obtained from S2 to S6 to form a prior probability distribution dataset.

8. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 7, characterized in that, S2, the prior probability distribution function pdf 1 = @( x mvnpdf( x , mu 1, sigma 1), mvnpdf represents the multivariate probability normal distribution function; @ represents the Matlab function's independent variable prefix, and the generated pulse amplitude sampling sequence is represented as slicesample(1, N , ' pdf 1', pdf 1);' pdf 1' indicates that with pdf 1 represents the target probability distribution function; S3, the prior probability distribution function pdf 2 = @( x gampdf ( x , alpha , beta ), gampdf represents the gamma probability distribution function, and the generated pulse carrier frequency sampling sequence is represented as slicesample(1, N , ' pdf 2', pdf 2);' pdf 2' indicates that pdf 2 represents the target probability distribution function; S4, the prior probability distribution function pdf 3 = @( x mvnpdf( x , mu 3, sigma 3) The generated pulse bandwidth sampling sequence is represented as slicesample(1, N , ' pdf 3', pdf 3);' pdf 3' indicates that pdf 3 represents the target probability distribution function; S5, the prior probability distribution function The generated intra-pulse modulation sampling sequence is represented as: slicesample(1, N, ' pdf 4', pdf 4, ' thin' , ' burnin '); S6, the prior probability distribution function pdf 5 = @( x mvnpdf( x , mu 5, sigma 5) The generated pulse repetition frequency sampling sequence is represented as slicesample(1, N , ' pdf 5', pdf 5),' pdf 5' indicates that pdf 5 represents the target probability distribution function.

9. The dynamic modeling method for reducing the uncertainty of measurement parameters in electronic reconnaissance systems according to claim 1, 7, or 8, characterized in that, The selection of the appropriate random distribution function according to the radar operating status type follows the following rules: Type 1: Select Mean μ and variance σ The distribution function of a multivariate probability normal distribution with fixed values; Type 2: Select Mean μ and variance σ In a fixed range The multivariate probability normal distribution function; Type 3: Choose a gamma distribution function where alpha follows the average probability distribution and beta is a fixed value; Type 4: Select the mean μ and variance σ Within the range of change ([ , ][ , The multivariate probability normal distribution function is given by [ ], where the upper and lower bounds are [ ]. , , , They follow an independent uniform probability distribution.

10. The dynamic modeling method for reducing the uncertainty of measurement parameters in an electronic reconnaissance system according to claim 1, 6, or 7, characterized in that, In step 3, the Bayesian posterior probability is calculated using the following formula: Indicates the first j The Bayesian posterior probability obtained in the next iteration. Representing characteristic parameters x The first in i One yuan, Indicates the iteration index, M 0 represents the maximum number of iterations. The likelihood function is represented using a Matlab function, as follows: In the formula, σ i for x i The standard deviation.

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