Performance forecasting method of passive true and false target identification model based on Bayesian network

Abstract

The invention discloses a performance forecasting method of a passive true and false target identification model based on a Bayesian network. The method comprises the following steps: step 1, mathematical modeling of a sonar equation; 2, modeling a Bayesian network identification model structure; 3, Bayesian network identification model parameter modeling is carried out; and 4, identifying and forecasting true and false targets. In order to solve the problem of passive sonar true and false target identification under false target interference, a sonar equation model for true and false target identification under false target interference is constructed, and an environmental condition-target-difference feature joint probability density estimation method based on a Bayesian network is provided. Under different conditions, the true and false target identification accuracy can be predicted according to the sonar equation model, a necessary basis is provided for true and false target identification capability evaluation and decision support in an actual false target interference environment, and the method has good application value.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustics and underwater acoustic signal processing, specifically relating to passive real and false target identification under false target interference environment, and in particular a performance prediction method for a passive real and false target identification model based on Bayesian network. Background Technology

[0002] With the rapid development of technology and the increasing complexity of underwater exploration environments, passive false target interference has become one of the important factors restricting the improvement of passive sonar performance. Passive false targets refer to signals that are similar to the acoustic characteristics of real targets, whether caused by humans or nature, making it difficult for passive sonar systems to accurately distinguish between real and false targets.

[0003] Target identification refers to the process of distinguishing real targets from false targets in an environment with interference from false targets by analyzing their multidimensional differences. Real and false targets differ in characteristics such as the proportion of high and low frequency energy, spectral fluctuations, and large-cycle patterns. By extracting these differences and making classification decisions, target identification can be achieved. However, the dynamic evolution of the complex marine environment increases the difficulty of identification and weakens the differences in target characteristics. Under actual underwater acoustic target identification conditions, a performance prediction model for target identification is needed to provide a scientific basis for decision optimization, resource allocation, and risk control. Therefore, establishing an identification prediction model is of great significance for improving underwater detection and identification capabilities.

[0004] The function of the sonar equation for distinguishing between real and false targets under false interference can be defined as follows: given conditions such as target source level, distance, marine environmental noise, receiving platform parameters, and the set of differences between real and false targets, it provides a prediction of the accuracy of real and false target identification. In actual marine environments, the distinguishability of real and false targets under passive false target interference is mainly affected by factors such as underwater acoustic multi-target interference, environment, channel transmission, target operating conditions and motion status, receiving characteristics of the receiving array, and real and false target decision criteria. Different influencing factors cause a certain degree of distortion in the differences between false target interference and real targets, resulting in changes in the separability of real and false target features at the receiving end, which affects the target identification performance based on multi-dimensional features. These influencing factors can be summarized as target source characteristics, environmental characteristics, platform characteristics, etc.

[0005] Therefore, to effectively predict whether true and false targets can be identified under different false target interference environments or parameter state changes, it is necessary to establish a model for true and false target identification and prediction. This requires analyzing the mapping relationship between conditions such as target-environment-platform and the characteristics for true and false target identification. In the absence of formalized modeling, a joint probability distribution of conditions and features can be constructed. However, various features contain numerous parameters, forming a high-dimensional parameter domain distribution. Furthermore, the combinations of parameters from different dimensions cause the order of magnitude of parameter combinations to grow exponentially, posing a challenge to the estimation of the joint probability distribution. Therefore, it is necessary to construct a corresponding sparse feature model based on appropriate physical modeling and statistical data analysis. Here, Bayesian networks are used to estimate the joint probability distribution of conditions and features. As a probabilistic graphical model, Bayesian networks have a solid theoretical foundation and are a powerful tool for representing and reasoning about uncertain knowledge. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a performance prediction method for a passive real / false target identification model based on Bayesian networks. Under different conditions, the accuracy of real / false target identification can be predicted according to the sonar equation model. It has the advantages of good robustness and accuracy, and is suitable for evaluating the performance of passive real / false target identification in environments with false target interference.

[0007] The technical solution of this invention is as follows:

[0008] A performance prediction method for a passive real / fake target identification model based on Bayesian networks includes the following steps:

[0009] Step 1: Mathematical Modeling of Sonar Equations: Establish sonar equations for identifying true and false targets under passive false target interference, and map these equations to the probability distribution function. Correlation, and the probability distribution mapping function Characterized by the Bayesian joint probability distribution network B;

[0010] Step 2: Bayesian network identification model structure modeling: Construct a Bayesian network structure for target type, target received signal-to-noise ratio, and target differential feature set, and obtain a set of random variables as network nodes, where the target differential feature set includes high and low frequency energy ratio, line spectrum fluctuations, and large periodic cycles;

[0011] Step 3: Bayesian network identification model parameter modeling: Analyze the multidimensional differential features under different signal-to-noise ratios to obtain the conditional probability density θ1 of high and low frequency energy ratio features, the conditional probability density θ2 of line spectrum fluctuation features, and the conditional probability density θ3 of large periodic cycle features. Form a set of conditional probability density parameters, and then obtain the Bayesian joint probability distribution network B.

[0012] Step 4: Real / False Target Identification and Prediction: Given a real / false target identification model Based on the Bayesian joint probability distribution network B, a large number of real and fake target samples are generated using the Monte Carlo method to evaluate the real and fake target identification model. The accuracy and false alarm rate of target recognition.

[0013] In step one, the sonar equation for distinguishing real and false targets under passive false target interference is expressed as follows:

[0014] ,

[0015] In the formula, P correct Model for distinguishing between real and fake targets The recognition accuracy To identify the forecast function, This represents a model for distinguishing between real and fake targets. Let SL-TL-NL+DI be the probability distribution mapping function, which equals the target received signal-to-noise ratio Snr. The interference radiated noise level for real or decoy targets. To spread the loss, Background ambient noise level, As a directional index, For the target set of differential features, Indicates the target type.

[0016] In step two, the Bayesian joint probability distribution network ,in, Node V represents a set of random variables, and edge E represents the dependencies between variables. It is a set of conditional probability density parameters that quantifies the strength of the dependencies between variables.

[0017] In step two, the set of random variables for constructing the Bayesian network is expressed as follows:

[0018] ;

[0019] In the formula, This refers to the target type. Target signal-to-noise ratio, ERL is the high-frequency and low-frequency energy ratio, VarFrep is the line spectrum fluctuation, and Floop is the large-cycle loop.

[0020] In step four, after the false target interference real / false target identifier and the target observable feature parameters are determined, the target difference feature set is obtained. Model the underwater acoustic environment based on hydrological information and calculate the target output signal-to-noise ratio. The range, then based on the target difference feature set. Signal-to-noise ratio A Bayesian joint probability distribution network B is used to randomly generate a large number of samples using the Monte Carlo method. Based on these samples, a model for identifying real and fake targets is developed. Conduct performance analysis and statistical analysis of the real / false target identification model. The accuracy and false alarm rate are used to complete the prediction process of identification performance.

[0021] In step four, based on the real and fake target samples generated by the Bayesian network, a real and fake target identification model is given. , feature set Input into the real / fake target identification model The results of identifying true targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. One; feature set Input into the real / fake target identification model The results of identifying false targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. The true / false target identification model is calculated using the following formula. accuracy With false alarm rate :

[0022] ,

[0023] .

[0024] This invention first analyzes the factors affecting the performance of passive real / false target identification and establishes a mathematical model for the identification sonar equation. The key to determining this model lies in estimating the joint probability density of target type, distinctive features, and signal-to-noise ratio. Using Bayesian networks, this invention fits this joint probability distribution through structural modeling, analysis of the influence of identification features, and parameter learning. Finally, based on the probability distribution, a method for predicting the identification accuracy is provided, realizing a complete prediction process.

[0025] This invention can bring the following beneficial effects:

[0026] (1) This invention provides a method for predicting the performance of true and false target identification. It constructs a sonar equation prediction framework and model for true and false target identification. The key joint probability density distribution model is constructed based on a Bayesian network. The Bayesian network sparsifies the joint probability density distribution and allows for the input of the default part, which makes the prediction model more robust in actual use.

[0027] (2) Actual sea trial data verification results show the accuracy and effectiveness of the method of the present invention. Under given detection conditions, it can predict the accuracy of the identification of true and false targets under different false target interference conditions, providing a necessary basis for the evaluation of the ability to identify true and false targets and tactical decision support under false target interference environment. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the performance prediction method of a passive real / false target identification model based on Bayesian networks according to the present invention.

[0029] Figure 2a This is a schematic diagram of the Bayesian network structure one. Figure 2b For and Figure 2a A schematic diagram of the equivalent Bayesian network structure 2;

[0030] Figure 3 A Bayesian network structure for the joint probability distribution of target type, received signal-to-noise ratio, and differential features;

[0031] Figure 4a This comparison illustrates the distribution characteristics of high and low frequency energy proportions for typical real and false targets under a signal-to-noise ratio (SNR) of 5 dB. Figure 4b A comparison of the high and low frequency energy distribution characteristics of typical real and fake targets under a signal-to-noise ratio of SNR=-10dB;

[0032] Figure 5a-1 A comparison of the fluctuation characteristics of line spectrum 1 under a typical real and false target signal-to-noise ratio condition of SNR=10dB is presented. Figure 5a-2 A comparison of the fluctuation characteristics of line spectrum 2 under a typical real and false target signal-to-noise ratio condition of SNR=10dB is presented. Figure 5a-3 A comparison of the fluctuation characteristics of line spectrum 3 under a typical real and false target signal-to-noise ratio condition of SNR=10dB;

[0033] Figure 5b-1 A comparison of the distribution characteristics of line spectrum fluctuations for typical real and false targets under a signal-to-noise ratio (SNR) of -10 dB is presented. Figure 5b-2 A comparison of the fluctuation characteristics of line spectrum 2 under a typical signal-to-noise ratio (SNR) of -10 dB between real and false targets. Figure 5b-3 A comparison of the fluctuation characteristics of line spectrum 3 under a typical signal-to-noise ratio of SNR=-10dB for real and false targets;

[0034] Figure 6a This section compares the distribution of long-period cyclic features of typical real and false targets under a signal-to-noise ratio (SNR) of 10 dB. Figure 6b A comparison of the distribution characteristics of large-cycle cyclic features of typical real and false targets under a signal-to-noise ratio of SNR=-7dB;

[0035] Figure 7a The curves show the typical performance of distinguishing between real and false targets under different signal-to-noise ratio conditions (the change in target detection rate under a constant false positive rate). Figure 7b The curves show the accuracy of identifying real and fake targets under different signal-to-noise ratio conditions.

[0036] Figure 8a A comparison of frequency band energy ratio features in the extraction of differential features between real and false targets during actual sea trials. Figure 8b For comparison of spectral undulation characteristics, Figure 8c This represents the characteristics of a true target's large-cycle cycle. Figure 8d It is a false target with large-cycle cyclical characteristics. Detailed Implementation

[0037] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0038] (I) Implementation process:

[0039] This invention provides a performance prediction method for a passive real / fake target identification model based on Bayesian networks, such as... Figure 1 As shown, the process includes: Step 1: Mathematical modeling of sonar equations; Step 2: Structural modeling of Bayesian network identification model; Step 3: Parameter modeling of Bayesian network identification model; Step 4: Identification and prediction of real and false targets.

[0040] The specific implementation process is as follows:

[0041] Step 1: Mathematical Modeling of Sonar Equations

[0042] Whether real and false targets can be distinguished in a passive false target interference environment is reflected in the degree of similarity between them. Given a fixed classifier design, this primarily depends on the similarity between the two targets; the higher the similarity, the greater the difficulty of identification. The degree of similarity can be characterized by the inter-class distance.

[0043] The class spacing of true and false target features under different conditions in the marine environment can be represented as follows:

[0044] ,

[0045] In the formula, Represented as a functional relationship; The real target signal can be represented by the real target's multidimensional feature vector; The signal is a false target and can be characterized by the multidimensional feature vector of the false target; The ocean propagation channel and environment from the real target signal to the sonar receiver; The ocean propagation channel and environment for false target signals to sonar receivers; This indicates platform information.

[0046] Therefore, the distance between true and false target classes can be represented as follows:

[0047] In real-world environments, different target source levels, propagation distances, marine environmental noise, and different receiver array parameters directly affect the receiver signal-to-noise ratio (SNR) for distinguishing between real and false targets. In other words, the main factors influencing the receiver's ability to correctly identify real and false targets are the changes in the SNR caused by channel transmission and variations in marine environmental noise. Furthermore, characteristic distortions caused by channel transmission also affect the distinguishability of real and false targets to some extent. For engineering and practical considerations, this invention simplifies the inter-class distance model to a function of the signal and the output SNR, i.e.:

[0048] ,

[0049] and These represent the output signal-to-noise ratios of the real signal and the fake target signal at the receiving end, respectively, and are closely related to the ocean propagation channel and propagation distance.

[0050] Given target parameters and hydrological information, a channel transfer function is generated through acoustic field modeling. Based on the source-end underwater acoustic interference and target signal parameters, the signal-to-noise ratio (SNR) of the receiver signal under specific conditions can be obtained. Generally, the source level of the specified target... and receiver background noise Given the target sea depth, target depth, receiver array depth, sound velocity profile, and seabed medium, the propagation loss curve is obtained based on the normal mode sound field model. The target strength at the receiving end is obtained. According to the array processing gain The final signal-to-noise ratio of the target receiver output can be obtained. .

[0051] Based on the passive detection sonar equations and considering the factors affecting the distinguishability of real and false targets under passive decoy interference, the following sonar equations for distinguishing real and false targets under passive decoy interference are established:

[0052] ,

[0053] In the formula, P correct Model for distinguishing between real and fake targets The recognition accuracy To identify the forecast function, based on The established distribution and detection theory determine the forecast results. This represents the model for identifying true and false targets, which is the object of evaluation. Let be the probability distribution mapping function, representing the probability distribution of target features under different received signal-to-noise ratios (SNRs). SL - TL - NL + DI equals the target received SNR, Snr. The interference radiated noise level for real or decoy targets. To spread the loss, Background ambient noise level, As a directional index, For the target set of differential features, This indicates the target type. Among them, the probability distribution model... It is crucial in the forecasting process; solving this model is essentially a problem of estimating the joint probability distribution parameters.

[0054] This invention uses Bayesian networks as a tool to analyze the joint probability distribution. Make an estimate.

[0055] Step 2: Bayesian network identification model structure modeling:

[0056] As can be seen from step one, the determination of the identification index and identification domain for true and false target identification depends on the joint probability distribution of all differential features at different distances. Based on Bayesian network related theories, this invention simplifies the joint probability distribution problem and obtains the fitting result of the joint distribution by combining expert priors with data training.

[0057] Bayesian networks are probabilistic graphical models used to represent and reason about uncertain knowledge. They consist of a directed acyclic graph and a set of conditional probability parameters, i.e. A directed acyclic graph consists of nodes and edges, i.e. In the graph, the nodes represent sets of random variables, and the edges E represent dependencies between variables. This quantifies the strength of this dependency. In this invention, the identification of true and false targets employs several robust and separable differential features, including high- and low-frequency energy ratio features, spectral fluctuation features, and large-cycle cyclic features.

[0058] Therefore, the set of random variables for constructing the Bayesian network is as follows:

[0059] ,

[0060] In the formula, The identification results are output for the target type. The set of differential features to be detected;

[0061] Using the above variables as network nodes, construct a Naive Bayes network structure. With the central node, The variables in the diagram are the outer nodes, and a star-shaped causal network is constructed.

[0062] To facilitate the visualization of the network structure, this invention simplifies the Bayesian network structure, defining the equivalent transformation method of the network structure as follows: Figure 2a , Figure 2b As shown, Figure 2a Bayesian network structure and Figure 2b The Bayesian network structure is biequivalent.

[0063] Based on this transformation, a Bayesian network is constructed that incorporates target type, target received signal-to-noise ratio, and target differential characteristics, such as... Figure 3 As shown, Figure 3 The arrows in the diagram represent causal relationships between random variables.

[0064] This invention employs a discrete Bayesian network model, with the discretized representation of each variable as follows:

[0065] 1) Target type: ;

[0066] 2) Target received signal-to-noise ratio: ;

[0067] 3) Ratio of high-frequency and low-frequency energy: ;

[0068] 4) Spectral variations: ;

[0069] 5) Large-cycle cyclical characteristics: .

[0070] Step 3: Modeling the parameters of the Bayesian network identification model:

[0071] This invention constructs parameters using a combination of theoretical and simulation analysis. First, it analyzes the multidimensional differential features under different signal-to-noise ratios, estimating the distribution patterns of these features under different SNR conditions. Then, it further solves for the probability distribution of individual differential features. This forms the parameter set. .

[0072] (1) Performance analysis of differential feature recognition:

[0073] 1) Analysis of the proportion of high and low frequency energy:

[0074] The high-low frequency energy ratio is a characteristic information that characterizes the energy distribution of a signal in the high and low frequency bands. Real targets have a wide energy coverage and often exhibit strong low-frequency energy, while false targets have poor low-frequency transmission response due to the influence of the transmitting transducer, resulting in weak low-frequency energy. Therefore, this characteristic can be used to effectively identify real and false targets.

[0075] A set of typical real signals and recorded fake target signals is designed. Based on real target signals and recorded fake target signals collected from multiple experiments, sets of real and fake target signals under different signal-to-noise ratio (SNR) conditions are constructed by superimposing noise of different intensities. For the target signal under each specific SNR condition, a piecewise sliding window analysis method is used to collect the characteristic values ​​of the high- and low-frequency energy ratios, which can form a set of characteristic values ​​of real and fake targets under multiple SNR conditions. Based on this set, the distribution characteristics and probability density function estimation of the high- and low-frequency energy ratio characteristic values ​​can be realized.

[0076] The following figures show the characteristic distribution of the high- and low-frequency energy ratios of the real and false targets under two different signal-to-noise ratios (SNR=5dB and SNR=-10dB). Figure 4a , Figure 4b As shown, the higher the signal-to-noise ratio, the better the separability of the high- and low-frequency energy ratio characteristics.

[0077] The conditional probability density of the high-frequency and low-frequency energy ratio can be obtained: ,

[0078] In the formula, For the target received signal-to-noise ratio, This refers to the identification result output by the target type.

[0079] 2) Characteristics of line spectrum fluctuations:

[0080] Because simulated false target signals have relatively stable continuous and line spectra, the line spectrum positions and signal-to-noise ratios of the false target signals are relatively fixed and fluctuate little over time, while real target signals generally fluctuate more significantly. Generally, as the received signal-to-noise ratio decreases, the detected line spectra of both real and simulated false targets tend to become unstable, with increased fluctuations.

[0081] A set of typical real signals and recorded fake target signals is designed, each containing three spectral lines with approximately the same frequency. Based on real and fake target signals collected from multiple experiments, sets of real and fake target signals under different signal-to-noise ratio (SNR) conditions are constructed by superimposing noise of varying intensities. For the target signal under each specific SNR condition, a piecewise sliding window analysis method is used to collect spectral fluctuation feature values, forming a set of spectral fluctuation feature values ​​for real and fake targets under multiple SNR conditions. Based on this set, the distribution characteristics and probability density function of the spectral fluctuation feature values ​​can be estimated.

[0082] Figure 5a-1 , Figure 5a-2 , Figure 5a-3 The frequency fluctuation distributions of line spectra 1, 2, and 3 extracted from the real target and the simulated false target are given respectively under a signal-to-noise ratio of SNR=10dB. Figure 5b-1 , Figure 5b-2 , Figure 5b-3The frequency fluctuation distributions of line spectra 1, line spectra 2, and line spectra 3 extracted from the real target and the simulated false target are given respectively under the signal-to-noise ratio of SNR=-10dB.

[0083] The conditional probability density of the spectral fluctuations can be obtained as follows: ,

[0084] In the formula, For the target received signal-to-noise ratio, This refers to the identification result output by the target type.

[0085] 3) Large-cycle cyclical characteristics:

[0086] In practice, due to the limited storage capacity of artificial decoys, the length of the interference signal played is generally on the order of minutes. It is played repeatedly during interference, exhibiting a large periodicity. However, during the actual movement of a target, it often needs to constantly adjust its attitude, and the target signal generally does not have a large periodicity.

[0087] The maximum value of the mean similarity of the process under different window lengths is used as the long-cycle loop detection metric. Spectrum history over a period of time Its cyclic eigenvalues ​​are represented as follows:

[0088] ,

[0089] In the formula, express Time spectrum and Cosine similarity of the spectra.

[0090] A set of typical real signals and recorded fake target signals is designed. Based on real target signals and recorded fake target signals collected from multiple experiments, sets of real and fake target signals under different signal-to-noise ratio (SNR) conditions are constructed by superimposing noise of different intensities. For the target signal under each specific SNR condition, a piecewise sliding window analysis method is used to collect long-cycle cyclic feature values, forming a set of real and fake target feature values ​​under multiple SNR conditions. Based on this set, the distribution characteristics and probability density function estimation of long-cycle cyclic feature values ​​can be realized. Two different SNRs (SNR=10dB, SNR=-7dB) are selected, and the results of the long-cycle cyclic detection quantity changes are as follows. Figure 6a , Figure 6b As shown.

[0091] Depend on Figure 6a , Figure 6b It can be seen that when the received signal-to-noise ratio is high (10dB), the large-cycle cyclicity of the false target is much higher than that of the real target, and the difference in distribution is obvious. As the signal-to-noise ratio decreases, the distribution becomes closer.

[0092] The conditional probability density of the large-cycle cyclic feature can be obtained: ,

[0093] In the formula, For the target received signal-to-noise ratio, This refers to the identification result output by the target type;

[0094] Based on the probability distribution under the single differential feature obtained This forms a complete set of conditional probability density parameters. .

[0095] Step 4: Identification and Forecasting of Real and False Targets:

[0096] Given a real / fake target identification model This invention can evaluate the probability of correct target identification under this model. Based on the Bayesian joint probability distribution network obtained in steps two and three... Based on this distribution, a large number of samples are randomly generated using the Monte Carlo method. These randomly generated samples are then input into the identification model. In the process, the identification results are obtained, the accuracy rate and false alarm rate are calculated, and the performance forecast is completed.

[0097] Specifically, based on the proposed sonar equation for distinguishing between true and false targets, the accuracy prediction process in practice is as follows: After the false target interference with the true / false target identifier and the observable characteristic parameters of the target are determined, the set of target difference features is obtained. Modeling the underwater acoustic environment based on hydrological information and calculating propagation loss using target location information. Then obtain the background ambient noise level. And calculate the directivity index based on the receiving platform parameters. Estimate the target output signal-to-noise ratio The range.

[0098] Steps two and three yield a Bayesian joint probability distribution network for target type, differential features, and signal-to-noise ratio. At this point, based on the target difference feature set Target signal-to-noise ratio Scope, Bayesian joint probability distribution network A large number of samples are randomly generated using the Monte Carlo method. The specific steps are as follows:

[0099] 1) Network state initialization: Randomly initialize and assign values ​​to all discrete variables in the network;

[0100] 2) Random sampling: Sequential Gibbs sampling is used. The state of each node is updated in a fixed order from the parent node to the child node. The probability of all possible values ​​of each node is calculated. Finally, the latest state is determined by roulette wheel sampling.

[0101] 3) Convergence judgment and sample selection: Observe whether the fluctuation amplitude of the sample generation is less than the preset amplitude and thus tends to be stable. If it is stable, it means that convergence has been achieved, and sampling can be repeated N times (N>1000). Finally, discard the first 10% of the samples at the beginning of each sampling to avoid interference from the initial value.

[0102] 4) Generate true target samples Let there be , and denote its feature set as . False targets have Let there be , and denote its feature set as . .

[0103] Furthermore, based on the real and fake target samples generated by Bayesian networks, a real and fake target identification model is given. This allows us to assess the probability of correctly identifying the target under this model. The feature set... Input into the real / fake target identification model The results of identifying true targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. One; feature set Input into the real / fake target identification model The results of identifying false targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. The true / false target identification model is calculated using the following formula. accuracy With false alarm rate (Here, a false alarm is defined as an incorrect identification):

[0104] ,

[0105] ,

[0106] At this point, the performance forecast is completed.

[0107] Based on the above method, the recognition performance curves under different signal-to-noise ratio conditions can be calculated as follows: Figure 7a , Figure 7b As shown, where Figure 7a The change in target detection rate under a constant false positive rate. Figure 7b The curves show the accuracy of identifying real and fake targets under different signal-to-noise ratio conditions.

[0108] It can be seen that the recognition performance weakens as the signal-to-noise ratio decreases.

[0109] (II) Sea Trial Data Test Results:

[0110] Based on “(I) Implementation Process”, the processing results of this invention are presented through analysis and processing of sea trial data.

[0111] Sea trial data processing results: Data from a certain marine scientific research experiment was selected, in which a pair of real and false targets existed. Data from a specific voyage segment was selected, and the real and false targets were tracked separately. Based on the experimental conditions, the performance of real and false target identification for this voyage segment was predicted, and the average accuracy rate of the prediction was 85.51%.

[0112] Analyze the differences between real and fake targets, such as Figure 8a , Figure 8b , Figure 8c , Figure 8d As shown, where Figure 8a For comparison of energy ratio characteristics in different frequency bands, Figure 8b For comparison of spectral undulation characteristics, Figure 8c This represents the characteristics of a true target's large-cycle cycle. Figure 8d The false target has a large-cycle cyclical characteristic. Figure 8c This represents the characteristics of a true target's large-cycle cycle. Figure 8d The large-cycle cyclical characteristics of the false target are shown. Since a section of data is invalid due to the presence of strong interfering targets nearby, which suppress the signals of both the real and false targets, there are invalid data periods in the above figure, which are not included in the statistics.

[0113] Statistical analysis of the automatic identification results shows that the average identification accuracy rate is 91%, while the average forecast accuracy rate is 93.58%.

[0114] Therefore, the results of sea trial data processing show that the method proposed in this invention can predict the accuracy of identifying true and false targets based on actual false target interference conditions, with high accuracy and strong practicality.

[0115] In summary, this invention addresses the problem of identifying true and false targets using passive sonar under false target interference. It constructs a sonar equation model for this purpose and proposes a joint probability density estimation method based on Bayesian networks, encompassing environmental conditions, target characteristics, and differences. Under different conditions, the sonar equation model can predict the accuracy of true and false target identification, providing a necessary foundation for evaluating the ability to identify true and false targets and supporting decision-making in real-world false target interference environments. This invention has significant application value.

[0116] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

Claims

1. A performance prediction method for a passive real / fake target identification model based on Bayesian networks, characterized in that, Includes the following steps: Step 1: Establish the sonar equation for distinguishing between real and false targets under passive false target interference, and map this sonar equation to the probability distribution function. Correlation, and the probability distribution mapping function Characterized by the Bayesian joint probability distribution network B; Step 2: Construct a Bayesian network structure for target type, target received signal-to-noise ratio, and target differential feature set, and obtain a random variable set V as network nodes, where the target differential feature set includes high and low frequency energy ratio, line spectrum fluctuations, and large periodic cycles; Step 3: Analyze the multidimensional differences under different signal-to-noise ratios to obtain the conditional probability density θ1 of the high and low frequency energy ratio characteristics, the conditional probability density θ2 of the line spectrum fluctuation characteristics, and the conditional probability density θ3 of the large periodic cycle characteristics. Form a set of conditional probability density parameters, and then obtain the Bayesian joint probability distribution network B. Step 4: Given a model for identifying real and fake targets Based on the Bayesian joint probability distribution network B, a large number of real and fake target samples are generated using the Monte Carlo method to evaluate the real and fake target identification model. The accuracy and false alarm rate of target recognition.

2. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step one, the sonar equation for distinguishing real and false targets under passive false target interference is expressed as follows: ， In the formula, P correct Model for distinguishing between real and fake targets The recognition accuracy To identify the forecast function, This represents a model for distinguishing between real and fake targets. Let SL-TL-NL+DI be the probability distribution mapping function, which equals the target received signal-to-noise ratio Snr. The interference radiated noise level for real or decoy targets. To spread the loss, Background ambient noise level, As a directional index, For the target set of differential features, Indicates the target type.

3. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that, In step two, the Bayesian joint probability distribution network ,in, Node V represents a set of random variables, and edge E represents the dependencies between variables. It is a set of conditional probability density parameters that quantifies the strength of the dependencies between variables.

4. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step two, the set of random variables for constructing the Bayesian network is expressed as follows: ； In the formula, This refers to the target type. Target signal-to-noise ratio, ERL is the high-frequency and low-frequency energy ratio, VarFrep is the line spectrum fluctuation, and Floop is the large-cycle loop.

5. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step three, the actual collected real signal and false target signal are analyzed to give the characteristic distribution of the high and low frequency energy ratio of the real target and the false target under different signal-to-noise ratio conditions, and the conditional probability density θ1 of the high and low frequency energy ratio is obtained: ， In the formula, For the target received signal-to-noise ratio, This refers to the target type.

6. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step three, the actual collected real signal and false target signal are analyzed, and the characteristic distribution of the high and low frequency energy ratios of the real and false targets under different signal-to-noise ratio conditions is given, thus obtaining the conditional probability density θ2 of the line spectrum fluctuations: ， In the formula, For the target received signal-to-noise ratio, This refers to the target type.

7. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step three, the maximum value of the mean similarity of the process under different window lengths is calculated as the large-cycle loop detection quantity. Spectral history of time Its cyclic eigenvalues ​​are represented as follows: ， In the formula, express Time spectrum and Cosine similarity of spectra; By analyzing the actual acquired real and false target signals, and analyzing the changes in the detection quantity of large-cycle cycles under different signal-to-noise ratios, the conditional probability density θ3 of the large-cycle cycle features is obtained. ， In the formula, For the target received signal-to-noise ratio, This refers to the target type.

8. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 1, characterized in that: In step four, after the false target interference real / false target identifier and the target observable feature parameters are determined, the target difference feature set is obtained. Model the underwater acoustic environment based on hydrological information and calculate the target output signal-to-noise ratio. The range, then based on the target difference feature set. Signal-to-noise ratio A Bayesian joint probability distribution network B is used to randomly generate a large number of samples using the Monte Carlo method. Based on these samples, a model for identifying real and fake targets is developed. Conduct performance analysis and statistical analysis of the real / false target identification model. The accuracy and false alarm rate are used to complete the prediction process of identification performance.

9. The performance prediction method for a passive real / fake target identification model based on Bayesian networks according to claim 8, characterized in that: In step four, a real / fake target identification model is given. The method for calculating its accuracy and false alarm rate is as follows: feature set Input into the real / fake target identification model The results of identifying true targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. One; feature set Input into the real / fake target identification model The results of identifying false targets are obtained, and the number of targets identified as true targets is denoted as . The number of targets identified as false targets is [number]. The true / false target identification model is calculated using the following formula. accuracy With false alarm rate : ， 。

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