A confidence propagation-based underwater weak target bearing detection pre-tracking method

Abstract

The application relates to a weak underwater target azimuth detection pre-tracking method based on belief propagation, which comprises the following steps: converting a weak target tracking problem into solving a joint posterior probability density function (pdf) based on a Bayesian rule; factorizing the joint posterior pdf, constructing a corresponding factor graph through a graph model; solving the transmitted information in the factor graph by using a belief propagation (BP) algorithm, and converting multiple integrals into ordinary integrals by using a Goodman variable substitution principle; constructing a likelihood function by using a complex Wishart distribution to describe the relationship between original sonar data and target states, and simplifying the remaining pdf by using a Gaussian distribution to obtain a confidence approximation of a target state edge posterior pdf; and calculating the number of weak targets and corresponding states by using a minimum mean square error (MMSE) estimator. The application can simultaneously track multiple weak targets without a complex clustering algorithm, has fewer preset parameters, and can accurately and efficiently track target state information including an azimuth, an azimuth angular velocity and target intensity.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of weak target detection and tracking, in particular to a confidence propagation-based underwater weak target bearing detection and tracking method. BACKGROUND

[0002] Sonar arrays are widely used in underwater target detection and tracking. With the progress of submarine stealth technology and the development of unmanned devices, the sound source level of these targets is continuously reduced, which are typical low signal-to-noise ratio targets (weak targets). Traditional detection and tracking algorithms are limited by the setting of the threshold value. When the threshold value is high, weak targets cannot be detected. When the threshold value is low, a large amount of clutter will be introduced, which brings great challenges to the accurate and efficient tracking of weak targets. The track-before-detect (TBD) algorithm takes the original sonar array data as input and can extract the implicit weak target information from it, providing a new solution for weak target detection and tracking.

[0003] Currently, the single target detection and tracking method in the sonar field is relatively mature, mainly including the Baum-Welsh filter or smoother of hidden Markov model, the Viterbi algorithm, and the particle filter. These methods cannot track multiple targets and describe the dynamic change of the target number, and the application scenarios are limited. The TBD algorithm based on random finite set can effectively solve the problem of tracking multiple weak targets, mainly including the probability hypothesis density (PHD) filter and the cardinal probability hypothesis density (CPHD) filter. These methods have a relatively complex derivation process, and the tracking accuracy of weak targets depends largely on the clustering algorithm and clustering strategy. The tracking accuracy of the method is low, the stability is poor, and the computational efficiency is also low. SUMMARY

[0004] In view of the above technical deficiencies, the present application provides a confidence propagation-based underwater weak target bearing detection and tracking method. The method can quickly and accurately derive the marginal posterior pdf of the target state from the joint posterior pdf through the belief propagation (BP) algorithm, and each target is maintained by a separate marginal posterior pdf, without the need for complex clustering algorithms and clustering strategies, greatly improving the estimation accuracy of the weak target state. In addition, the Goodman variable substitution principle is used to simplify the calculation of multiple integrals in the derivation process, the covariance-based likelihood function is constructed using the complex Wishart distribution, the sampling data of multiple pins are accumulated in time to improve the tracking accuracy and stability of the weak target, and the remaining distribution is approximated as a Gaussian distribution to further simplify the derivation process and improve the computational efficiency of the method.

[0005] The technical solution adopted by the present application to achieve the above-mentioned purposes is as follows:

[0006] A confidence propagation-based underwater weak target bearing detection and tracking method, comprising the following steps:

[0007] 1) Based on Bayesian rules, the weak target tracking problem is described using the joint posterior probability density function pdf;

[0008] 2) Factorize the joint posterior PDF and construct the corresponding factor graph using a graphical model;

[0009] 3) The confidence propagation backpropagation algorithm is used to calculate the prediction information, measurement estimation information and measurement update information in the factor map in sequence to realize tracking before weak target orientation detection.

[0010] Step 1) specifically refers to:

[0011] By combining the sonar measurement information at all time points with the state information of the weak target to be solved, the joint posterior PDF expression is obtained:

[0012] f(y 0:k |z 0:k )

[0013] Among them, y 0:k This represents all target states from time 0 to time k. N k Represents the number of targets at time k, and each augmented state Where the binary variable r k,n ∈{0,1} is used to indicate whether the target n exists, r k,n =1 indicates existence. The target state information represents the azimuth θ. k,n azimuth angular velocity With target strength z 0:k z represents all sonar measurement information from time 0 to time k. k This indicates the measurement at time k.

[0014] In step 2), the factorized joint posterior PDF expression is:

[0015]

[0016] Wherein, the target state y at time k k It consists of two parts, one part being the existence of target y at time k-1. k-1 Through the state transition equation f(y) k,n |y k-1,m The calculated number of targets is N. k-1 The other part consists of newly generated targets at time k, which follow a pre-defined probability distribution, and the number of these targets is N. k -N k-1 ,f(z k |y k) is the sonar likelihood function used to describe the relationship between sonar measurements and target state.

[0017] Step 3) includes the following steps:

[0018] 3.1) Based on confidence Calculate the prediction information α k,n ;

[0019] 3.2) Based on prediction information α k,n The BP algorithm is used to calculate the measurement estimation information β. n ;

[0020] 3.3) Based on measurement estimation information β n Input the measurement z at the current time. k Calculate measurement update information κ n ;

[0021] 3.4) Based on prediction information α k,n Measurement update information κ n Calculate the approximate confidence of the posterior pdf of the target state edge.

[0022] 3.5) Based on confidence The number of targets and their corresponding states are calculated using the MMSE estimator.

[0023] 3.6) Complete the calculation process for the current moment, and... Return to step 3.1) to begin the calculation for the next time step.

[0024] Step 3.1) specifically refers to:

[0025] For each objective n∈{1,…,N k-1}, prediction information α at time k k,n for:

[0026]

[0027] α k,n (x k,n ,r k,n =0)=1-α k,n (x k,n ,r k,n =1)

[0028] Where, p s Indicates the probability of the target's survival. Represents the marginal posterior pdff(x) of the target state at the previous time step. k-1,n ,r k-1,n =1|z 0:k-1 Approximate confidence level;

[0029] For each new target n′∈{N k-1 +1,…,N k Predicted information α of newborn targets at time k k,n′ for:

[0030] α k,n′ (x k,n′ ,r k,n′ =1)=p b f(x k,n′ )

[0031] α k,n′ (x k,n′ ,r k,n′ =0)=1-α k,n′ (x k,n′ ,r k,n′ =1)

[0032] Where, p b f(x) represents the target newborn probability. k,n′ (This is the pre-set target status pdf for newborns.)

[0033] Step 3.2) specifically refers to:

[0034] β n (x k,n ,r k,n )=α k,n (x k,n ,r k,n ).

[0035] Step 3.3) specifically refers to:

[0036] κ n (x k,n ,r k,n ;z k )=∫f(z k -r k,n g(x k,n )|ξ k,n )f(ξ k,n )dξ k,n

[0037] Where, f(ξ) k,n (This is about user-defined variables) The probability density function, y k\n This indicates that the target state y is not included at time k. k,n The set of remaining target states for n∈{1,…,N k}, g(y k,n ) represents starting from the target state x k,n Nonlinear mapping between sonar measurements, Where a(θ)k,n ) represents the array manifold vector, and H represents the conjugate transpose of the matrix.

[0038] Step 3.4) specifically refers to:

[0039] The likelihood function f(z) is described using the complex Wishart distribution. k -r k,n g(x k,n )|ξ k,n ), measure z at time k k Transform into complex sampling covariance matrix

[0040]

[0041] Where v represents the number of samples, z k,i This indicates that the array data is obtained from the i-th sample of the sonar at time k, and the likelihood function expression is:

[0042]

[0043] in, Let R represent a p-dimensional Wyshat distribution with matrix variable Y, degrees of freedom r, and scaling matrix A. σ The complex covariance matrix representing the environmental background noise.

[0044] Approximating pdff(ξ) using a Gaussian distribution k,n To simplify the calculation, we get:

[0045]

[0046] in Let Y be a Gaussian distribution with mean μ and covariance C, where μ is the mean. Covariance Specifically:

[0047]

[0048] Rewrite information κ n The expression is:

[0049]

[0050]

[0051] Based on the BP algorithm, the posterior pdff(y) of the target state edge is obtained. k,n |z 0:k The approximate confidence level of ) is:

[0052]

[0053] in, This is the normalization factor.

[0054] Step 3.5) specifically refers to:

[0055] For n∈{1,…,N k} Calculate the probability of the target's existence.

[0056]

[0057] like The value exceeds the preset target threshold. It is assumed that target n exists at time k, and the target state is calculated using the MMSE estimator.

[0058]

[0059] Statistics in n∈{1,…,N k The probability of the target existing in} is greater than The number of weak targets in the region is estimated by counting the number of weak targets.

[0060] The present invention has the following beneficial effects and advantages:

[0061] 1. The method of the present invention derives a confidence approximation of the target state edge posterior pdf by employing a confidence propagation algorithm, which has a concise and clear derivation process and improves the estimation accuracy of the underwater weak target state.

[0062] 2. The method of this invention uses the Goodman variable substitution principle to simplify multiple integrals into ordinary integrals, which simplifies the calculation process of measurement update information in the BP algorithm and improves computational efficiency.

[0063] 3. The method of this invention uses a complex Wishart distribution to describe the relationship between sonar array measurements and target state, and calculates the sampling covariance matrix by accumulating sampled values ​​over a period of time, so that the tracking results are accurate and stable.

[0064] 4. The method of the present invention uses the Gaussian distribution to approximate the measurement update of the residual distribution after removing the likelihood function calculation, and extracts the mean of the Gaussian distribution as the scaling matrix when calculating the complex Wishart distribution, which further improves the computational efficiency.

[0065] 5. The method of this invention is a general target tracking algorithm. For different application scenarios, it is only necessary to analyze the relationship between sensor measurements and target state and construct a suitable likelihood function, which has strong applicability. Attached Figure Description

[0066] Figure 1This is a structural diagram of the method of the present invention;

[0067] Figure 2 The method of this invention is a factor graph constructed based on a graph model;

[0068] Figure 3 This is a flowchart of the information calculation process for the belief propagation algorithm of the present invention. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0070] The basic idea of ​​this invention is to transform the underwater weak target tracking problem into solving a joint posterior PDF based on Bayesian rules, and to calculate the marginal posterior PDF of the target state under the condition that the measurement is from a sonar array. Since it is difficult to give an explicit expression for the joint posterior PDF, directly solving for the marginal posterior PDF through integration is impractical. This invention factorizes the joint posterior PDF, constructs a factor graph for the weak target tracking problem using a graphical model, and uses the BP algorithm to solve for the information transmitted between nodes in the graph, thereby deriving a confidence approximation of the marginal posterior PDF of the target state. The number of weak targets and their corresponding state estimates can then be calculated using the MMSE estimator. In the information derivation process, the Goodman variable substitution principle is used to simplify multiple integrals into ordinary integrals to simplify the derivation process. The sonar array measurement is transformed into a sampling covariance matrix, and a likelihood function is constructed using a complex Wishart distribution to describe the relationship between the measurement and the target state. A Gaussian distribution is used to simplify the remaining PDF. This invention's method can accurately, quickly, and stably track the dynamically changing states (azimuth, azimuth angular velocity, and target intensity) of multiple weak targets when the input is sonar array data.

[0071] like Figure 1 As shown, this embodiment designs an underwater weak target azimuth detection-before-tracking method based on confidence propagation. The method input is sonar array data, and the output is the number of targets and their corresponding states. The proposed method is divided into three steps: Step 1 uses joint posterior PDF to describe the weak target tracking problem; Step 2 uses a graphical model to construct a factor graph of the target tracking problem; Step 3 details the information derivation process and calculation flow of the confidence propagation method.

[0072] The weak target tracking problem is described using mathematical expressions. By combining sonar measurement information at all time points with the state information of the weak target to be solved, the following joint posterior PDF expression is obtained:

[0073] f(y 0:k |z 0:k )

[0074] Where y 0:k This represents all target states from time 0 to time k. N k This represents the number of targets at time k. Each augmented state... Where the binary variable r n,k ∈{0,1} is used to indicate whether the target n exists, r n,k =1 indicates that it exists. The target state information is represented by azimuth, azimuth angular velocity, and target intensity, respectively. Taking the logarithm of the target intensity is for computational convenience. 0:k z represents all sonar measurement information from time 0 to time k. k This indicates the measurement at time k.

[0075] Based on Bayesian rules, the target state edge posterior PDF expression f(y) is extracted from the above expression. k,n |z 0:k This allows us to estimate the number of weak targets and their corresponding states.

[0076] like Figure 2 As shown, this embodiment factorizes the joint posterior PDF, extracts the variable nodes (represented by circles in the figure) and factor nodes (represented by rectangles in the figure) to construct a factor graph, and derives an approximate expression of the marginal posterior PDF of the target state by calculating the information transmitted between the nodes in the factor graph. The factorized joint posterior PDF expression is as follows:

[0077]

[0078] Where the target state y at time k k It consists of two parts, one part being the existence of target y at time k-1. k-1 Through the state transition equation f(y) k,n |y k-1,n The calculated number of targets is N. k-1 The other part consists of newly generated targets at time k, which follow a pre-defined probability distribution, and the number of these targets is N. k -N k-1 f(z) k |y k α is the sonar likelihood function, used to describe the relationship between sonar measurements and the target state. The information transmitted between nodes is named, and the information to be solved includes α. k,n β n and κ n .

[0079] like Figure 3 As shown, this embodiment divides the belief propagation algorithm into the following steps according to the calculation order: prediction step, calculating prediction information α. k,n Measurement estimation step, calculate measurement estimation information β n Measurement update steps, calculate measurement update information κn The confidence update step calculates a confidence approximation of the posterior pdf of the target state edge. The current sonar measurement is incorporated into the measurement update step using a likelihood function constructed from the Wishart distribution, with confidence... By inputting the MMSE estimator, an estimate of the target state can be obtained; by counting targets greater than the birth threshold, the number of targets can be estimated. At this point, the entire calculation process for the current time step is complete. Returning to the prediction step allows for iterative solving of the underwater weak target tracking problem at the next time step.

[0080] For each N∈{1,…,n k-1}, prediction information α at time k k,n The expression is as follows:

[0081]

[0082] α k,n (x k,n ,r k,n =0)=1-α k,n (x k,n ,1)

[0083] Where p s Indicates the probability of the target's survival. The marginal posterior pdff(x) of the target state at the previous time step k-1,n ,r k-1,n =1|z 0:k-1 The confidence approximation of ). For each N ′ ∈{n k-1 +1,…,n k Predicted information α of newborn targets at time k k,n′ The expression is as follows:

[0084] α k,n′ (x k,n′ ,r k,n′ =1)=p b f(x k,n′ )

[0085] α k,n′ (x k,n′ ,r k,n′ =0)=1-α k,n′ (x k,n′ ,1)

[0086] Where p b f(x) represents the target newborn probability. k,n′ (This refers to the pre-defined target state pdf.) Prediction information α k,n ,n∈{1,…,N kThe sum of the pdf integrals still satisfies the definition that the sum of the pdf integrals is 1.

[0087] Based on the BP algorithm, the estimated information β is measured. n The calculation expression is as follows:

[0088] β n (x k,n ,r k,n )=α k,n (x k,n ,r k,n )

[0089] Similarly, the measurement update information κ can be obtained. n The expression is as follows:

[0090]

[0091] Where y k\n This indicates that the target state y is not included at time k. k,n The remaining target state set, Represents the target state y k\n The multiple integrals are then transformed into ordinary integrals using Goodman's substitution principle, yielding information κ. n The simplified expression is as follows:

[0092] κ n (x k,n ,r k,n ;z k )=∫f(z k -r k,n g(x k,n )|ξ k,n )f(ξ k,n )dξ k,n

[0093] Where f(ξ) k,n ) is about The probability density function, g(x) k,n ) represents starting from the target state x k,n Nonlinear mapping between sonar measurements and sonar measurements.

[0094] To obtain accurate and stable tracking results, considering the significant randomness of sonar measurements at individual sampling times, a complex Wishart distribution is used to describe the likelihood function f(z). k -r k,n g(x k,n )|ξ k,n By utilizing sampled values ​​over a period of time, this randomness can be effectively reduced. The z value measured at time k is used as an example. k Transforming it into a complex sampling covariance matrix yields the following expression:

[0095]

[0096] Where v represents the number of samples, assuming that the samples are independent and identically distributed, and v also represents the degrees of freedom in the Wishart distribution. k,i This indicates that the array data is obtained from the i-th sample of the sonar at time k, and the likelihood function expression is as follows:

[0097]

[0098] in Let R represent a complex p×p-dimensional symmetric Wieshard distribution with matrix variable Y, degrees of freedom r, and symmetric positive definite scaling matrix A. σ This represents the complex covariance matrix that the environmental background noise satisfies.

[0099] Complex Wishart distribution scaling matrix and sampling covariance matrix Having a similar form, construct g(x) k,n From the target state The nonlinear mapping to the complex covariance matrix is ​​shown below:

[0100]

[0101] Where a(θ) k,n ) is the array manifold vector, which is uniquely determined by the actual physical form of the sonar array, and H represents the conjugate transpose of the matrix.

[0102] Approximating pdff(ξ) using a Gaussian distribution k,n To simplify the calculation, we obtain the following expression:

[0103]

[0104] in Let Y be a Gaussian distribution with mean μ and covariance C. The relevant calculations are expressed as follows:

[0105]

[0106] Rewrite information k n The expression is as follows:

[0107]

[0108] Among them, the use of Replace ξ k,n This is to simplify the derivation process. Based on the obtained information and the BP algorithm, the marginal posterior pdff(y) of the target state is obtained. k,n |z 0:k The approximate confidence expression for ) is shown below:

[0109]

[0110] in The normalization factor ensures that the confidence sum satisfies the requirement that the integral sum of the probability density function is 1.

[0111] Based on the calculated confidence Use MMSE to estimate the number of weak targets and their corresponding states. For n∈{1,…,N k First, calculate the probability of the target's existence:

[0112]

[0113] like The value exceeds the preset target threshold. That is, assuming that target n exists at time k, the target state is calculated using the MMSE estimator. as follows:

[0114]

[0115] Statistics in n∈{1,…,N k The probability of the target existing in} is greater than The number of weak targets in the region is estimated by the number of targets.

[0116] The calculation process of the method of the present invention is as follows: Figure 3 As shown, it consists of the following steps.

[0117] (1) Based on confidence Information α is calculated through the prediction step. k,n ;

[0118] (2) Based on prediction information α k,n Information β is calculated through a measurement estimation step. n ;

[0119] (3) Based on measurement estimation information β n Input the measurement z at the current time. k Information k is calculated through measurement update steps. n ;

[0120] (4) Based on prediction information α k,n Measurement update information κ n Calculate confidence through confidence update steps

[0121]

[0122] (5) Based on confidence The number of targets and their corresponding states are calculated using the MMSE estimator.

[0123] (6) Complete the calculation process for the current time moment. Return to step (1) to start the calculation for the next time step.

Claims

1. A method for tracking underwater weak targets before azimuth detection based on confidence propagation, characterized in that, Includes the following steps: 1) Based on Bayesian rules, the weak target tracking problem is described using the joint posterior probability density function pdf; 2) Factorize the joint posterior PDF and construct the corresponding factor graph using a graphical model; 3) The belief propagation backpropagation algorithm is used to calculate the prediction information, measurement estimation information and measurement update information in the factor map in sequence to realize tracking before weak target orientation detection; Step 3) includes the following steps: 3.1) Based on confidence Calculate prediction information ; 3.2) Based on prediction information The BP algorithm is used to calculate measurement estimation information. ; 3.3) Based on measurement estimation information Input the current measurement time Calculate measurement update information ; 3.4) Based on prediction information Measurement update information Calculate the approximate confidence of the posterior pdf of the target state edge. ; 3.5) Based on confidence The number of targets and their corresponding states are calculated using the MMSE estimator. 3.6) Complete the calculation process for the current moment, and... Return to step 3.1) Start the calculation for the next time step; Step 3.1) specifically refers to: For each goal , Time prediction information for: ； ； in, Indicates the probability of the target's survival. This represents the marginal posterior pdf of the target state at the previous time step. Approximate confidence level; For each new goal , Real-time new target prediction information for: ； ； in, Indicates the probability of a target newborn. PDF of the pre-set target status for newborns; Step 3.2) specifically refers to: ； Step 3.3) specifically refers to: ； in, It's about user-defined variables. The probability density function, express The time does not include the target state The remaining set of target states, for , Indicates starting from the target state Nonlinear mapping between sonar measurements, ,in, Represents the array manifold vector. This indicates finding the conjugate transpose of a matrix; Step 3.4) specifically refers to: The likelihood function is described using the complex Wishart distribution. ,Will Time measurement Transform into complex sampling covariance matrix : ； in, Indicates the number of samples. Indicates in Time Sonar The matrix data is obtained through sampling, and the likelihood function expression is obtained as follows: ； in, Represent a matrix variable as The degrees of freedom are The scale matrix is of Vrije Utah distribution, The complex covariance matrix representing the environmental background noise. Approximating PDF using a Gaussian distribution To simplify the calculation, we get: ； in , indicating that the variable is The mean is covariance is The Gaussian distribution, where the mean is... Covariance Specifically: ； ； ； Rewrite information The expression is: ； Based on the BP algorithm, the posterior pdf of the target state edge is obtained. The approximate confidence level is: ； ； in, Normalization factor; Step 3.5) specifically refers to: for Calculate the probability of the target's existence. : ； like The value exceeds the preset target threshold. Then the target is considered exist The target state is always present and is calculated using the MMSE estimator. : ； Statistics in The probability of the target existing in the middle is greater than The number of weak targets in the region is estimated by counting the number of weak targets.

2. The underwater weak target orientation detection and tracking method based on confidence propagation according to claim 1, characterized in that, Step 1) specifically refers to: By combining the sonar measurement information at all time points with the state information of the weak target to be solved, the joint posterior PDF expression is obtained: ； in, Indicates from 0 to All target states at any given time, target state , express Number of targets at any given time, for each augmented state binary variables Used to indicate the target Does it exist? This indicates that it exists. The target status information represents the orientation. azimuth angular velocity With target strength , Indicates from 0 to All sonar measurement information at all times. express Time measurement.

3. The underwater weak target orientation detection and tracking method based on confidence propagation according to claim 1, characterized in that, In step 2), the factorized joint posterior PDF expression is: ； in, target status at any time It consists of two parts, one part is Always have a goal Through the state transition equation The calculated target number is: The other part is New targets are generated at each moment, following a pre-defined probability distribution, and the number of targets is... , This is the sonar likelihood function used to describe the relationship between sonar measurements and target state.

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