Networked radar target detection method based on non-uniform signal-to-noise ratio fusion criteria

Abstract

The present invention discloses a networked radar target detection method based on a non-identical signal-to-noise ratio fusion criterion. It mainly solves the problem of poor fusion detection performance of the existing technology in different scenarios of networked radar signal-to-noise ratio distribution. The scheme is: select the probability density function of the expected observed target signal-to-noise ratio distribution and the number of signal-to-noise ratio sampling points; initialize the support signal-to-noise ratio weight vector and the support signal-to-noise ratio matrix; construct a non-identical signal-to-noise ratio fusion criterion; sample the signal-to-noise ratio probability density function to calculate the target detection probability to obtain the objective function for training; maximize the objective function and iteratively update the weight vector and the support signal-to-noise ratio matrix, substitute it into the non-identical signal-to-noise ratio test statistic function to calculate the actual value of the non-identical signal-to-noise ratio test statistic, and use the non-identical signal-to-noise ratio fusion criterion to judge the target based on the actual value. The present invention can achieve a trade-off between the optimal detection performance of each local radar under a variety of signal-to-noise ratio distributions, improve the fusion detection performance of the radar network in different signal-to-noise ratio distribution scenarios, and can be used for radar target detection.

Description

Technical Field

[0001] The present invention relates to the field of radar technology, in particular to a radar fusion detector design method, which can be used for target fusion detection in a networked radar system. Technical Background

[0002] As modern battlefield environments become increasingly complex and volatile, single-station radars, with limited available resources such as structural space and power, are susceptible to environmental influences such as electromagnetic interference and are no longer adaptable to complex modern battlefield environments. However, collaborative detection using multi-station radars offers advantages such as spatial diversity, frequency domain diversity, and damage resistance, and has become an important research direction in the current field of target detection. Currently, common networked radar detection systems are divided into two types: distributed radar detection systems and centralized radar detection systems. Because the communication capacity between radars is limited, and distributed radar detection systems offer advantages such as large coverage, fast response, and high reliability, distributed radar detection systems have a wider range of applications and advantages over centralized radar detection systems in radar, sonar, and other fields.

[0003] A distributed radar detection system first preprocesses the raw observation data and then sends the preprocessing results from each local radar to a fusion center for target detection. Assuming the processors for each local radar have already been designed, the goal of the distributed radar detection system is to design a detector at the fusion center that determines the presence of a target by evaluating the signals from multiple radar stations and background clutter estimates. It is well known that the design of an optimal fusion detector involves performing a likelihood ratio test on the data received from each local radar at the fusion center based on the Neyman-Pearson criterion. Existing research on fusion detector design often assumes that the signal-to-noise ratio (SNR) of the target observations from each local radar is known. However, in real-world applications, targets to be detected often exhibit complex scattering characteristics, making it costly for each radar to acquire the target's backscatter intensity from different angles and frequencies. This is particularly true for non-cooperative targets, whose scattering characteristics are difficult to obtain in advance. In this case, weighting target echoes according to a predetermined set of SNRs often results in degraded detection performance due to model mismatch. Therefore, designing an optimal networked radar fusion detector that better suits real-world application scenarios and improves target detection performance has been a research hotspot in recent years.

[0004] In the journal IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 1, pp. 13–22, 1998, A. Mathur et al. proposed a decentralized detection algorithm that considers local signal-to-noise ratios. They designed an optimal detector and two suboptimal detectors that directly sum the estimated signal-to-noise ratios of each local radar. This detector achieves optimal or near-optimal detection performance only when the target observation signal-to-noise ratios of each local radar are the same or very large. However, in practical applications, the signal-to-noise ratio distributions of different radars often vary significantly. Therefore, in such cases, the detection performance of this detector may even be worse than that of a single sensor.

[0005] Purpose of the Invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned existing networked radar fusion detection technology and to improve the detection performance in scenarios with different signal-to-noise ratio distributions.

[0007] The technical solution of the present invention is to achieve a trade-off in fusion detection performance under various SNR distributions by designing a non-uniform SNR fusion criterion (NDFR) based on multi-objective optimization. Furthermore, the covariance matrix adaptive evolution strategy (CMA-ES) is used to learn the support SNR matrix and the support SNR weight vector, thereby obtaining the form of the non-uniform SNR fusion criterion. The implementation steps include the following:

[0008] (1) Select the probability density function p(S) of the expected observation target signal-to-noise ratio distribution and randomly set the number of signal-to-noise ratio sampling points to N S ;

[0009] (2) Initialize unknown parameters: support signal-to-noise ratio weight vector and M groups of signal-to-noise ratios ζ corresponding to N radar stations m Support signal-to-noise ratio matrix composed of

[0010] (3) Constructing the fusion criteria of different signal-to-noise ratios:

[0011] (3a) Using the Lagrange multiplier method to construct the optimization objective function of distributed fusion detection

[0012]

[0013] Among them, η represents the Lagrange coefficient, α is the maximum allowed false alarm probability, and x n is the observation value of the nth radar, represents the decision region, ζ m represents the mth signal-to-noise ratio distribution, Denotes a given signal-to-noise ratio distribution ζm The detection probability of the target, m=1,...,M,P FA represents the false alarm probability, λ m Denotes a given signal-to-noise ratio distribution ζ m The supported signal-to-noise ratio weight of each radar, ζ m,n Indicates ζ m The nth element in p(x n |ζ m,n ,H1) represents the given signal-to-noise ratio distribution ζ m,n When the target exists, x n The probability density function, p(x n |H0) indicates that the target does not exist when x n The probability density function of , H1 means the target exists, H0 means the target does not exist;

[0014] (3b) Based on the result of step (3a), construct the non-identical signal-to-noise ratio test statistic function of distributed detection based on the Neyman-Pearson criterion

[0015]

[0016] Among them, μ n represents the noise power of the nth radar, λ m and ζ m,n is an unknown parameter;

[0017] (3c) Given the false alarm probability The Monte Carlo experiment method is used to determine the detection threshold -η that satisfies the false alarm probability;

[0018] (3d) According to the results of step (3b) and step (3c), the non-uniform signal-to-noise ratio fusion criterion is obtained, which is expressed as:

[0019] (4) According to the definition of detection probability and the result of step (3d), the decision area is calculated as The target detection probability Get the objective function:

[0020] (5) Using the CMA-ES algorithm to maximize the objective function And iteratively update to obtain two sets of parameters in the test statistic function: the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ;

[0021] (6) Substitute the two sets of parameters, the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ, obtained in step (5), into the non-identical signal-to-noise ratio test statistic function in step (3b) In the calculation, the actual value of the non-identical signal-to-noise ratio test statistic is obtained;

[0022] (7) According to the non-uniform signal-to-noise ratio fusion criterion, the test statistic Compare with the detection threshold -η to determine whether the target exists:

[0023] If the test statistic If it is greater than the detection threshold -η, then H1 is considered to be true and the target is determined to exist;

[0024] Otherwise, H0 is considered to be true and the target is judged to be non-existent.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] First, the present invention considers the differences in the signal-to-noise ratio distribution of networked radars and designs a non-uniform signal-to-noise ratio fusion criterion, which can effectively improve the performance of radar network fusion detection in scenarios with different signal-to-noise ratio distributions.

[0027] Second, since the present invention uses the CMA-ES algorithm to learn the support SNR matrix and the support SNR weight vector, it can balance the optimal detection performance of each local radar under multiple SNR distributions, and further improve the performance of radar network fusion detection in different SNR distribution scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is an implementation flow chart of the present invention;

[0029] Figure 2 1 is a comparison chart of the probability of target detection in three radar scenarios by the present invention and three existing detection methods;

[0030] Figure 3 3 is a comparison chart of the probability of target detection in five radar scenarios using the present invention and three existing detection methods. DETAILED DESCRIPTION

[0031] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0032] Reference Figure 1 , the implementation steps of this example are as follows:

[0033] Step 1: Select the probability density function p(S) of the expected observation target signal-to-noise ratio distribution.

[0034] The signal-to-noise ratio refers to the logarithm of the ratio of signal power to noise power. In practical applications, radar cannot obtain signal power information in advance.

[0035] Assume that the signal-to-noise ratio of each local radar observation of the target is random and obeys a probability distribution with a probability density function of p(S). Common probability distributions include uniform distribution, Gaussian distribution, Poisson distribution, exponential distribution, etc. This example uses but is not limited to the exponential distribution probability density function, which is expressed as follows:

[0036]

[0037] Where θ represents the parameter of the exponential distribution, and S represents the signal-to-noise ratio of the networked radar.

[0038] Step 2: Initialize unknown parameters.

[0039] Perform uniform sampling between 5dB and 20dB to generate M groups of signal-to-noise ratios ζ m , m=1,...,M, and obtain M groups of signal-to-noise ratios ζ corresponding to N radar stations m Support signal-to-noise ratio matrix composed of Each element in the matrix has a value between 5dB and 20dB, and the weight of each group of signal-to-noise ratio is set to Get the support signal-to-noise ratio weight vector

[0040] Where λ=[λ1,…,λ M ] T , T represents transpose, M represents the M groups of signal-to-noise ratios of each radar,

[0041] ζ m,n represents the mth signal-to-noise ratio distribution corresponding to the nth radar, n=1,...,N, m=1,...,M, and N represents the number of radars in the networked radar.

[0042] Step 3: Construct the fusion criteria of different signal-to-noise ratios.

[0043] (3.1) The Lagrange multiplier method is used to construct the optimization objective function of distributed fusion detection:

[0044] (3.1.1) Combine multi-objective optimization with the Neyman-Pearson criterion to model the multi-objective optimization problem:

[0045] The Neyman-Pearson criterion is to select the decision region under the condition that the false alarm probability is constrained within a certain constant range. Make the target detection probability P DThe multi-objective optimization problem is composed of multiple objective functions and related equations and inequality constraints. Therefore, under the condition that the false alarm probability does not exceed the tolerable range α, the decision region is selected. Let the detector signal-to-noise ratio distribution be ζ1,…,ζ M The detection probability of multiple targets is maximized, and the multi-objective optimization problem is modeled as:

[0046]

[0047] Among them, P FA represents the false alarm probability, ζ m represents the mth signal-to-noise ratio distribution, Denotes a given signal-to-noise ratio distribution ζ m The detection probability of the next target, m=1,...,M;

[0048] (3.1.2) Use linear weighting to transform the multi-objective optimization problem into a single-objective optimization problem. The formula is as follows:

[0049]

[0050] Among them, λ m represents the support SNR weight under the SNR distribution of group m, m = 1, ..., M;

[0051] (3.1.3) The target detection problem is considered as a binary hypothesis problem, where H0 indicates that the target does not exist and H1 indicates that the target exists.

[0052] (3.1.4) Assuming that each radar obtains the target observation value independently, define the target detection probability and false alarm probability P FA :

[0053] Let x=[x1,...,x N ] T Represents the observation value vector of the networked radar. The observation value of each local radar can be regarded as a point in the N-dimensional space. In order to obtain a complete fusion detection decision criterion, the networked radar system needs to make a judgment on each point in the space. The space composed of all observation values ​​x that meet the hypothesis H1 is expressed as According to the false alarm probability P FA and detection probability The definitions of , their formulas can be written as:

[0054]

[0055] in, represents the decision region, Denotes a given signal-to-noise ratio distribution ζ mThe probability density function of x when the target exists is: represents the probability density function of x when the target does not exist, x=[x1,...,x N ] T represents the observation value vector of the networked radar, N represents the number of networked radars, T represents the transpose, ζ m,n Indicates ζ m The nth element in p(x n |ζ m,n ,H1) represents the given signal-to-noise ratio distribution ζ m,n When the target exists, x n The probability density function, p(x n |H0) indicates that the target does not exist when x n The probability density function of

[0056] (3.1.5) According to the Lagrange multiplier method and the two definitions in step (3.1.4), we get the objective function

[0057] According to the two definitions in step (3.1.4), the false alarm probability P FA and detection probability It is the accumulation of joint probability density in N-dimensional space, and since the probability density function is non-negative, the false alarm probability P FA and detection probability Increase or decrease at the same time.

[0058] According to the Neyman-Pearson criterion, the false alarm probability needs to be constrained within a certain constant range, that is, the decision region is selected Maximize the detection probability. This type of problem can be solved using the Lagrange multiplier method. Let α be the maximum allowed false alarm probability and establish the optimization objective function:

[0059]

[0060] Substitute the two definitions of step (3.1.4) into the optimization objective function In the above equation, we can get:

[0061]

[0062] Among them, η represents the Lagrange coefficient, α is the maximum allowed false alarm probability, and x n is the observation value of the nth radar;

[0063] (3.2) Constructing the non-identical SNR test statistic function for distributed detection

[0064] (3.2.1) Assume that the interference affecting target detection in the radar network is complex Gaussian white noise, and the radar cross section of the target obeys the Swerling I type fluctuation model. For N radar stations, the observation value of the nth radar station is denoted as x n , get the radar observation value x n The probability density function p(x n |ζ m,n ,H1) and the probability density function p(x n |H0):

[0065]

[0066] (3.2.2) Based on the probability density function under the Swerling I model in step (3.2.1), the likelihood ratio expression of the non-identical signal-to-noise ratio test statistic is obtained

[0067]

[0068] Among them, p(x n |ζ m,n ,H1),p(x n |H0) represents the probability density function of the observation value in the case of target and the probability density function of the observation value in the case of no target;

[0069] (3.2.3) The probability density function p(x n |ζ m,n ,H1) and p(x n |H0) into the likelihood ratio expression of the non-identical SNR test statistic In the statistic function of the non-identical signal-to-noise ratio test, we can get

[0070]

[0071] Among them, μ n represents the noise power of the nth radar, λ m and ζ m,n is an unknown parameter, λ m represents the support SNR weight under the SNR distribution of group m, ζ m,n represents the mth signal-to-noise ratio distribution ζ m The nth element in ;

[0072] (3.2.4) Based on the non-identical signal-to-noise ratio test statistic function Design another permutation-invariant test statistic for different signal-to-noise ratios

[0073] Since the non-uniform SNR test statistic function The observation vector x of each local radar does not have permutation invariance, so two observation vectors x1 and x2 with the same elements but different orders can be considered different. It is not suitable for target detection scenarios that require real-time fusion of observation results. Therefore, based on the non-identical signal-to-noise ratio test statistic function Design another permutation-invariant test statistic function for different signal-to-noise ratios

[0074]

[0075] Among them, x n:N Indicates the network observations x1…,x N The nth largest observation value in ;

[0076] (3.3) Given the false alarm probability Determine the detection threshold -η that satisfies the false alarm probability:

[0077] According to the theoretical formula The detection threshold is set. However, due to the complexity of this formula, it is usually set through Monte Carlo experiments in simulations. In many cases, the relationship between the detection threshold and the false alarm probability is very complex or does not have a closed-form solution. In this example, a Monte Carlo experiment is used to determine the detection threshold -η that satisfies the false alarm probability.

[0078] (3.4) According to the results of steps (3.2.3) and (3.3), two different SNR fusion criteria are obtained:

[0079] (3.4.1) According to the non-identical signal-to-noise ratio test statistic function and the detection threshold -η, the non-identical signal-to-noise ratio test statistic function is obtained as Different signal-to-noise ratio fusion criteria:

[0080]

[0081] (3.4.2) According to the permutation-invariant non-identical SNR test statistic function and the detection threshold -η, we get the permutation-invariant fusion criterion for different signal-to-noise ratios:

[0082]

[0083] Step 4, calculate the decision area as The target detection probability Get the objective function.

[0084] (4.1) Perform N on the probability density function p(S) S Point sampling, get N SSNR sample value S (i) , i=1,...,N S ;

[0085] (4.2) for N S SNR sample value S (i) The decision region is calculated as The target detection probability

[0086]

[0087] Where -η represents the detection threshold, x=[x1,...,x N ] T represents the observation value vector of the networked radar, N represents the number of networked radars, T represents transposition, S (i) represents the i-th signal-to-noise ratio sample obtained from p(S), i = 1,...,N S , p(x|S (i) ,H1) represents the signal-to-noise ratio distribution S (i) The probability density function of x when the target exists;

[0088] (4.3) for N S Target detection probability Find the average and get the objective function

[0089]

[0090] Step 5: Use the CMA-ES algorithm to maximize the objective function And iteratively update to obtain two sets of parameters: the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ in the test statistic function.

[0091] For the two different SNR fusion criteria designed in step (3.4), their detection performance is affected by two sets of parameters: the support SNR weight vector λ and the support SNR matrix ζ. Therefore, the relevant parameters that need to be obtained through training are the support SNR weight vector λ and the support SNR matrix ζ. The specific implementation includes the following:

[0092] (5.1) The support signal-to-noise ratio matrix ζ is obtained by training with the CMA-ES algorithm:

[0093] (5.1.1) Set the multivariate normal distribution N(m ζ ,σ ζ C ζ ) in the initial values ​​of the parameters, where σ ζ It represents the search step size when iterative training is used to obtain the support signal-to-noise ratio matrix ζ, m ζDenotes the mean vector associated with the support signal-to-noise ratio matrix ζ, satisfying C ζ Denotes the covariance matrix associated with the support signal-to-noise ratio matrix ζ, and assumes that the initial mean vector m ζ is a zero vector, and the initial covariance matrix is ​​C ζ =I MN , where I MN represents the identity matrix of MN×MN dimensions;

[0094] (5.1.2) From the multivariate normal distribution N(m ζ ,σ ζ C ζ ) is randomly sampled to obtain the initial solution of the support signal-to-noise ratio weight vector λ ζ ;

[0095] (5.1.3) Calculate the objective function value corresponding to each solution According to the size of the objective function, sort the values ​​from high to low and intercept the first μ ζ solutions, used to update the parameters of the support signal-to-noise ratio matrix ζ in the multivariate normal distribution, where μ ζ represents the number of samples used to update the parameters of the multivariate normal distribution;

[0096] (5.1.4) Resample to generate a new solution, and iterate step (5.1.3) until the solution does not change after two iterations, and obtain the final support signal-to-noise ratio matrix ζ parameters;

[0097] (5.2) The support signal-to-noise ratio weight vector λ is obtained by training using the CMA-ES algorithm:

[0098] (5.2.1) Set the multivariate normal distribution N(m λ ,σ λ C λ ) in the initial values ​​of the parameters, where σ λ It represents the search step length when iterative training is used to obtain the support signal-to-noise ratio weight vector λ, m λ Represents the mean vector associated with the support signal-to-noise ratio weight vector λ, satisfying C λ Represents the covariance matrix associated with the support signal-to-noise ratio weight vector λ, and assumes the initial mean vector m λ is a zero vector, and the initial covariance matrix is ​​C λ =I M , where I M represents the M×M dimensional identity matrix;

[0099] (5.2.2) From the multivariate normal distribution N(m λ ,σ λ C λ) is randomly sampled to obtain the initial solution of the support signal-to-noise ratio weight vector λ λ :

[0100] (5.2.3) Calculate the objective function value corresponding to each solution According to the size of the objective function, sort the values ​​from high to low and intercept the first μ λ solutions, used to update the parameters of the support signal-to-noise ratio weight vector λ in the multivariate normal distribution, where μ λ represents the number of samples used to update the parameters of the multivariate normal distribution;

[0101] (5.2.4) Resample to generate a new solution, and iterate step (5.2.3) until the solution of two iterations does not change, and obtain the final support signal-to-noise ratio weight vector λ parameter.

[0102] Step 6: Calculate the non-identical SNR test statistics based on the support SNR weight vector λ and the support SNR matrix ζ parameters. and the permutation-invariant SNR test statistic function The actual value of .

[0103] (6.1) Substitute the two sets of parameters, support SNR weight vector λ and support SNR matrix ζ, into the non-identical SNR test statistic function in step (3.2.3) In the calculation, the non-identical signal-to-noise ratio test statistic is obtained The actual value of

[0104] (6.2) Substitute the two sets of parameters, the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ, into the permutation-invariant non-identical signal-to-noise ratio test statistic function in step (3.2.4) In the calculation, the non-identical signal-to-noise ratio test statistic with permutation invariance is obtained. The actual value of .

[0105] Step 7: Fusion criteria based on different signal-to-noise ratios and permutation-invariant fusion criteria for different signal-to-noise ratios Perform target detection.

[0106] (7.1) For target fusion detection scenarios where real-time requirements are not high, according to the non-uniform signal-to-noise ratio fusion criterion The non-identical signal-to-noise ratio test statistic Compare with the detection threshold -η to determine whether the target exists.

[0107] If the signal-to-noise ratio test statistic is different If it is greater than the detection threshold -η, then H1 is considered to be true and the target is determined to exist;

[0108] Otherwise, H0 is considered to be true and the target is judged to be non-existent;

[0109] (7.2) For target detection scenarios that require real-time fusion of observation results, the permutation-invariant fusion criterion of different signal-to-noise ratios is used. The permutation-invariant SNR test statistic Compare with the detection threshold -η to determine whether the target exists:

[0110] If the non-identical SNR test statistic is permutation invariant If it is greater than the detection threshold -η, then H1 is considered to be true and the target is determined to exist;

[0111] Otherwise, H0 is considered to be true and the target is judged to be non-existent.

[0112] The effect of the present invention is further illustrated by the following simulation test:

[0113] 1. Simulation conditions:

[0114] Assuming that the radar cross section of the target obeys the Swerling I type fluctuation model and the noise power of each local radar is the same, the false alarm probability P FA =10 -4 Under such conditions, L-band networked radar is used for target detection.

[0115] Simulation test scenario 1: In the three radar scenario, set the signal-to-noise ratio of the three radars to S1:S2:S3=100:1:1, designate the first radar as the main radar, and set the signal-to-noise ratio of the first radar to And the signal-to-noise ratios of the other two radars are set according to the signal-to-noise ratio of the first radar.

[0116] Simulation test scenario 2: In the five radar scenarios, set the signal-to-noise ratio of the five radars to S1:S2:S3:S4:S5 = 100:5:10:2:1, designate the first radar as the main radar, and set the signal-to-noise ratio of the first radar to And the signal-to-noise ratios of the other four radars are set according to the signal-to-noise ratio of the first radar.

[0117] 2. Simulation content:

[0118] Simulation 1: Under the conditions of the above simulation test scenario 1, the present invention and the existing Three detection methods are used for target detection, and the results are as follows Figure 2 As shown, the horizontal axis is the main radar signal-to-noise ratio and the vertical axis is the target detection probability.

[0119] described The detection method is a target detection method based on the optimal test statistic, which requires that the signal-to-noise ratio of each radar observed target is accurately known, and measures the upper bound of the detection performance that any detector can achieve in the corresponding scenario.

[0120] described The detection method is a target detection method based on the test statistic of the main radar information. The main radar can be selected according to the appearance position of the observed target and the layout configuration of each radar. The optimal fusion detection performance can only be obtained when the target signal energy is distributed only on the main radar.

[0121] described The detection method is a target detection method based on the incoherent accumulation test statistic. It is the most commonly used test statistic method in practical applications. It can only achieve the optimal fusion detection performance when the target signal energy is evenly distributed on each local radar.

[0122] from Figure 2 It can be seen that the simulation results under the three radar scenarios are as follows:

[0123] ① The present invention is based on the non-identical signal-to-noise ratio test statistic and the permutation-invariant SNR test statistic The fusion detection performance of the detection method is better than the existing Detection method.

[0124] ② The present invention is based on the non-identical signal-to-noise ratio test statistic The detection method is different from the existing The fusion detection performance of the detection methods is basically the same and close to Fusion detection performance of detection methods;

[0125] ③ The present invention is based on the non-identical signal-to-noise ratio test statistic The detection performance is better than the permutation-invariant non-identical signal-to-noise ratio test statistic of the present invention. This is because the non-uniform SNR test statistic It is necessary to know in advance which radar echo signal is stronger and set it as the main radar. Therefore, the non-identical SNR test statistic is Lower weights can be assigned to weaker observations from other radars, resulting in better fusion detection performance in situations with large differences in signal-to-noise ratios.

[0126] Simulation 2: Under the conditions of the above simulation test scenario 2, the present invention and the existing Three detection methods are used for target detection, and the results are as follows Figure 3 As shown, the horizontal axis is the main radar signal-to-noise ratio and the vertical axis is the target detection probability.

[0127] from Figure 3 It can be seen that the fusion detection performance of the present invention is better than the existing fusion target detection method based on incoherent accumulation in the five radar scenarios. The present invention is based on the non-identical signal-to-noise ratio test statistic The fusion detection performance is better than Detection method, close to Detection method.

[0128] from Figure 2 and Figure 3 From the comparison curves, it can be seen that when the signal-to-noise ratios of local radars are different, the present invention shows more significant improvement in fusion detection performance as the number of radar stations increases compared to the existing fusion target detection method based on incoherent accumulation.

[0129] In summary, compared with the existing detection method based on the incoherent accumulation fusion criterion, the present invention has a higher detection probability and better detection performance for target fusion detection in radar scenarios with different signal-to-noise ratio distributions. In addition, the fusion detection performance shows more significant improvement as the number of radar stations increases, indicating that the present invention can balance the optimal detection performance of each local radar under multiple signal-to-noise ratio distributions, and improve the performance of fusion detection of the radar network in scenarios with different signal-to-noise ratio distributions.

[0130] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and the order of the step numbers is not limited.

Claims

1. A networked radar target detection method based on a fusion criterion of different signal-to-noise ratios, characterized in that: The steps include: (1) Select the probability density function p(S) of the expected observation target signal-to-noise ratio distribution and randomly set the number of signal-to-noise ratio sampling points to N S ; (2) Initialize unknown parameters: support signal-to-noise ratio weight vector and M groups of signal-to-noise ratios ζ corresponding to N radar stations m Support signal-to-noise ratio matrix composed of (3) Constructing the fusion criteria of different signal-to-noise ratios: (3a) Using the Lagrange multiplier method to construct the optimization objective function of distributed fusion detection Among them, η represents the Lagrange coefficient, α is the maximum allowed false alarm probability, and x n is the observation value of the nth radar, represents the decision region, ζ m represents the mth signal-to-noise ratio distribution, Denotes a given signal-to-noise ratio distribution ζ m The detection probability of the target, m=1,...,M,P FA represents the false alarm probability, λ m Denotes a given signal-to-noise ratio distribution ζ m The supported signal-to-noise ratio weight of each radar, ζ m,n Indicates ζ m The nth element in p(x n |ζ m,n ,H1) represents the given signal-to-noise ratio distribution ζ m,n When the target exists, x n The probability density function, p(x n |H0) indicates that the target does not exist when x n The probability density function of , H1 means the target exists, H0 means the target does not exist; (3b) Based on the result of step (3a), construct the non-identical signal-to-noise ratio test statistic function of distributed detection based on the Neyman-Pearson criterion Among them, μ n represents the noise power of the nth radar, λ m and ζ m,n is an unknown parameter; (3c) Given the false alarm probability The Monte Carlo experiment method is used to determine the detection threshold -η that satisfies the false alarm probability; (3d) According to the results of step (3b) and step (3c), the non-uniform signal-to-noise ratio fusion criterion is obtained, which is expressed as: (4) According to the definition of detection probability and the result of step (3d), the decision area is calculated as The target detection probability Get the objective function: (5) Using the CMA-ES algorithm to maximize the objective function And iteratively update to obtain two sets of parameters in the test statistic function: the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ; (6) Substitute the two sets of parameters, the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ, obtained in step (5), into the non-identical signal-to-noise ratio test statistic function in step (3b) In the calculation, the actual value of the non-identical signal-to-noise ratio test statistic is obtained; (7) According to the non-uniform signal-to-noise ratio fusion criterion, the test statistic Compare with the detection threshold -η to determine whether the target exists: If the test statistic If it is greater than the detection threshold -η, then H1 is considered to be true and the target is determined to exist; Otherwise, H0 is considered to be true and the target is judged to be non-existent.

2. The method according to claim 1, characterized in that The probability density function p(S) of the expected observed target signal-to-noise ratio distribution selected in step (1) is expressed as follows: Where θ represents the parameter of the exponential distribution, and S represents the signal-to-noise ratio of the networked radar.

3. The method according to claim 1, characterized in that Initialization support signal-to-noise ratio weight vector in step (2) and the support signal-to-noise ratio matrix It is expressed as follows: λ=[λ1,…,λ M ] T Where T represents transpose, N represents the number of radars in the networked radar, and M represents the M groups of signal-to-noise ratios of each radar.

4. The method according to claim 1, wherein In step (3a), the Lagrange multiplier method is used to construct the optimization objective function of distributed fusion detection The implementation is as follows: (3a1) Combining multi-objective optimization with the Neyman-Pearson criterion, the multi-objective optimization problem is modeled as follows: (3a2) Use linear weighting to transform the multi-objective optimization problem into a single-objective optimization problem. The formula is as follows: subject to P FA ≤α Among them, among them, λ m represents the support SNR weight under the SNR distribution of group m, m = 1, ..., M; (3a3) Assuming that each radar obtains the target observation value independently, define the target detection probability and false alarm probability P FA They are represented as follows: in, Denotes a given signal-to-noise ratio distribution ζ m The probability density function of x when the target exists is: represents the probability density function of x when the target does not exist, x=[x1,...,x N ] T represents the observation value vector of the networked radar, N represents the number of radars in the networked radar, and T represents the transpose; (3a4) According to the Lagrange multiplier method and the two definitions in step (3a3), we get the objective function 5. The method according to claim 1, characterized in that In step (3b), we construct the non-identical SNR test statistic function for distributed detection. The implementation is as follows: (3b1) Assuming that the interference affecting target detection is complex Gaussian white noise and the radar cross section of the target obeys the Swerling I type fluctuation model, the radar observation value x is obtained n The probability density function p(x n |ζ m,n ,H1) and the probability density function p(x n |H0): (3b2) Based on the result of step (3b1), using the Neyman-Pearson criterion, we can get the non-identical signal-to-noise ratio test statistic function 6. The method according to claim 1, characterized in that The decision region calculated in step (4) is The target detection probability when , is as follows: Where -η represents the detection threshold, x=[x1,...,x N ] T represents the observation value vector of the networked radar, N represents the number of networked radars, T represents transposition, S (i) represents the i-th signal-to-noise ratio sample obtained from p(S), i = 1,...,N S , p(x|S (i) ,H1) represents the signal-to-noise ratio distribution S (i) The probability density function of x when the target exists.

7. The method according to claim 1, characterized in that In step (5), the CMA-ES algorithm is used to maximize the objective function And iteratively update, implemented as follows: (5a) Setting the initial values ​​of the multivariate normal distribution parameters and the conditions for stopping the iteration; (5b) Randomly sample the population of initial solutions from a multivariate normal distribution; (5c) Calculate the objective function value corresponding to each solution in step (5b) According to the objective function value, the first μ solutions are sorted from high to low and used to update the parameters of the multivariate normal distribution; (5d) Resample to generate a new solution, and iterate step (5c) until the solution of two iterations does not change, and obtain the final two sets of parameters: the support signal-to-noise ratio weight vector λ and the support signal-to-noise ratio matrix ζ.

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