Intra-group target number estimation method based on potential probability hypothesis density filter

Abstract

The invention provides an intra-group target number estimation method based on a potential probability hypothesis density filter, which utilizes the characteristic that the potential probability hypothesis density filter can track unknown targets in a complex environment to construct multiple hypotheses of the unknown target number corresponding to indistinguishable measurement through amplitude information. The method is introduced into a potential probability hypothesis density updating step so as to improve the accuracy of intra-group target number estimation, real targets and clutters are further distinguished through an elliptical gating technology, and the calculation amount is reduced. When the resolution of the sensor is limited, accurate estimation of the number of the intra-group targets of the dense group targets can be realized, and the estimation precision of the number of the group targets is obviously improved; the method is suitable for a dense clutter environment. When the number of the targets in the group is accurately estimated, the motion state of the group targets can be effectively estimated.

Description

Technical Field

[0001] The present invention relates to the field of group target tracking, and in particular to a method for estimating the number of targets in a group based on a potential probability hypothesis filter when a sensor resolution is limited under clutter conditions. Background Art

[0002] Target tracking holds significant applications in both military and civilian sectors. In modern intelligent warfare, drone swarm warfare has become a new combat mode. While countries are intensively researching drone swarm warfare, they are also vigorously developing the counter-drone industry to achieve an integrated offensive and defensive strategy. Given limited firepower, achieving precise strikes against drone swarms requires accurate tracking of the entire group. Therefore, tracking dense swarms of targets is crucial. Traditional target tracking algorithms often assume moving targets are point targets, performing state estimation by assigning measurements to targets one-to-one. However, with the increasing complexity of target tracking scenarios, traditional multi-target tracking algorithms are struggling to meet these requirements. For swarms of targets, due to their dense density and mutual occlusion, it is difficult to distinguish between clutter and true target measurements within a measurement set. Therefore, it is impossible to directly determine the number of true targets within a swarm. Furthermore, due to limited sensor resolution, measurements often fall short of the true number of targets, making it difficult to correlate data between targets and measurements.

[0003] The problem of tracking indistinguishable groups of targets is a hot topic of research both domestically and internationally. Research on extended targets has been used to analyze group target tracking performance. Specifically, the measurements generated by the group are modeled as extended targets, while the group's centroid and its extended shape are estimated. These algorithms offer low computational complexity, simple structure, and strong real-time performance. However, in complex environments, they can only capture the overall motion trend of the group and fail to accurately estimate the number of targets within the group. In recent years, a class of algorithms based on random finite sets (RFSs) has provided new insights for multi-target tracking. The most representative of these are the probability hypothesis density filter and the potential probability hypothesis density filter. While these filters and their improved algorithms can effectively track unknown targets and estimate their number, they are designed for multi-target or resolvable groups of targets and struggle to accurately estimate the number of targets within dense groups. Therefore, this paper considers incorporating amplitude information into group target tracking. By establishing an indistinguishable group target measurement model and incorporating amplitude information into a potential probability hypothesis density filter, an amplitude likelihood function is constructed. This information is fully utilized to distinguish the number of targets and clutter within each resolution unit, thereby improving the accuracy of both the number of group targets and the state of the group targets. Summary of the Invention

[0004] To overcome the shortcomings of the existing technology, the present invention provides a method for estimating the number of targets within a group based on a potential probability hypothesis density filter. This method aims to address the existing difficulty in accurately estimating the number of targets within a dense group of targets when the sensor resolution is limited. The method provides a method for estimating the number of targets within a group based on a potential probability hypothesis density filter using target amplitude information. This method can provide a high-precision strategy for estimating the number of targets within a dense group of targets in clutter conditions, even for sensors with limited resolution.

[0005] This invention discloses a method for estimating the number of targets within a group based on a cardinalized probability hypothesis density (CPHD) filter. This method leverages the ability of the CPHD filter to track unknown targets in complex environments. It constructs multiple hypotheses about the number of unknown targets corresponding to indistinguishable measurements using amplitude information, and incorporates these hypotheses into the CPHD update step to improve the accuracy of the estimation. Elliptical gating technology is used to further distinguish between real targets and clutter, reducing the computational complexity. This invention enables high-precision estimation of the number of targets within a dense group of targets even when sensor resolution is limited and clutter is present.

[0006] The technical solution adopted by the present invention to solve the technical problem includes the following steps:

[0007] Step 1: For the k-time cluster target, a state transition model of the cluster target is established. The measurement information of the dense cluster target is obtained through sensors. The measurement information includes position information, speed information and amplitude information. The single target measurement likelihood function and clutter likelihood function are also established.

[0008] Step 2: Based on the target state transfer equation, the group target intensity function is predicted through the potential probability hypothesis density filter;

[0009] Step 3: Use elliptical gating technology to distinguish real targets from clutter, and construct multiple hypotheses based on target amplitude information. Introduce the measurement likelihood function into the potential probability hypothesis density filter update step to achieve the update of the group target intensity function.

[0010] Step 4: Use the EAP (Expected A Posterior) method to extract the state of the group target intensity function and obtain an accurate estimate of the number of targets in the group.

[0011] In step 1, a state transition model of dense group targets under clutter conditions and a group target measurement model with limited sensor resolution are constructed, and a single target measurement likelihood function and a clutter likelihood function are established. The specific steps are:

[0012] Assume that at time k, a subgroup contains Nk targets, and the target states are is a single target state space, where the target state of the i-th individual is represents the target position, Represents the target speed. Assuming that the motion models of individual targets in the group are all linear Gaussian, the state transition probability density function of individual target i is expressed as follows:

[0013]

[0014] Where, represents the state of the i-th target at time k-1, N(·; m, P) represents a Gaussian probability density function with mean m and covariance P; F k-1 is the state transfer matrix; Q is the covariance matrix of process noise;

[0015] Considering the limited resolution of the sensor, the measurement space It is divided into a set of non-overlapping resolution units, and the resolution unit is recorded as U = {u1,u2,…u n},satisfy and make represents the position measurement function, X is the target state space, The target measurement space, Indicates that it falls into the resolution unit u j The set of individual target states in represents the state of the i-th target in the group target at time k, X k represents the set of group target states at time k, then the position measurements in each resolution unit are combined as follows:

[0016]

[0017] In the formula Representation unit u j The number of individual targets in is the measurement noise that obeys Gaussian distribution, represents the empty set, represents the target position measurement obtained by each resolution unit after the combined measurement; assuming that the detection probability of the measurement set in each resolution unit is but The probability of

[0018] Rayleigh distribution is used to describe the amplitude variation of target and clutter, so the probability distribution of target measurement amplitude is and the probability distribution of clutter amplitude It is expressed as follows:

[0019]

[0020] in, is the known individual target signal-to-noise ratio, represents the amplitude information of the jth measurement at time k;

[0021] Assuming that the amplitude measurement and position measurement of the same target set or clutter are independent of each other, the single measurement likelihood function is As shown in formula (5), the clutter likelihood function As shown in formula (6):

[0022]

[0023] Where, For single target measurement with amplitude information, For single target measurement without amplitude information,

[0024] is the clutter measurement with amplitude information, z (0) For clutter measurement without amplitude information,

[0025] c(z (0) ) are the target position measurement likelihood function and the clutter position measurement likelihood function, respectively.

[0026] with c a (a) Single target amplitude likelihood function and clutter amplitude likelihood function respectively.

[0027] In step 2, the target intensity function of the group at the previous sampling moment is predicted based on the target state transfer equation to obtain the predicted intensity function of the group at the current moment. The specific steps include:

[0028] Assume that the posterior strength v at time k-1 is given k-1 and the posterior potential distribution ρ k-1 , and v k-1 is a Gaussian mixture, that is:

[0029]

[0030] Where, are the weight, mean and covariance of the i-th Gaussian component at time k-1, respectively, then the predicted potential distribution ρ k|k-1 (n) and intensity v k|k-1 (x) are as follows:

[0031]

[0032] In the formula

[0033]

[0034] Among them, v S,k|k-1 (x) represents the predicted strength function of the survival target, γ k (x) is the new target intensity function, is the survival probability of the jth target, is the binomial coefficient, ρ Γ,k (n) represents the potential distribution of new targets at time k,

[0035] is the potential distribution function at time k-1, Represent the weight, mean and covariance of the i-th predicted Gaussian component at time k, respectively, F k-1 With Q k-1 are the target state transition matrix and the covariance matrix of process noise, respectively.

[0036] In step 3, the elliptical gating technique is used to distinguish real targets from clutter, and multiple hypotheses are constructed based on the amplitude information to measure the number of corresponding targets. The measurement likelihood function is introduced and the group target intensity function is updated at the current moment. The specific steps include:

[0037] Elliptical gating technology is used to remove most of the clutter measurements, effectively simplifying the calculation of the filter update step. The formula is as follows:

[0038]

[0039] In the formula For effective measurement, T g is the threshold value, z k,m is the mth measurement at time k, is the predicted mean of the j-th Gaussian component, is the inverse matrix of the innovation covariance matrix;

[0040] Let S = {1, ..., n} represent the set of all hypotheses of the number of target sources corresponding to a measurement. The sth element in the set represents that the measurement contains s targets. Since each indistinguishable measurement in the measurement set comes from s targets, each measurement is used to update the target state s times. Assume that the predicted strength v at time k is given. k|k-1 and the predicted potential distribution ρ k|k-1 , from formula (7), we can know that v k|k-1 It is in the form of Gaussian mixture and is expressed as:

[0041]

[0042] Then, update the potential distribution ρ k (n) and intensity vk (x) are respectively expressed as:

[0043]

[0044] In the formula

[0045]

[0046] in, represents the measurement set at time k, Z is the measurement set without amplitude information, is a single target measurement with amplitude information, and z is a single target measurement without amplitude information; For a given measurement set The possibility that there are n targets under the condition is the normalization constant; g(a k |s) represents the individual target amplitude likelihood function at time k; c a (a k )c z (z) represents the clutter likelihood function, w T is the weight of the predicted Gaussian component corresponding to each target, that is, w in formula (19) k|k-1 ;p D,k (x) represents the target detection probability; e j (·) represents the j-order elementary symmetric function, is a transition parameter used to calculate the potential distribution, is the permutation coefficient, p K,k is the potential distribution of clutter at time k. k ) is the known amplitude information a k The probability of assuming s under the condition of , s is the number of targets that may be included in the measurement in this hypothesis, is the target intensity function under the assumption s, q k (z) is the temporary weight of each Gaussian component after Kalman filtering, is the measurement prediction of the i-th target, is the innovation covariance matrix of the i-th target, is the Kalman gain matrix of the i-th target, I is the identity matrix, H k is the observation matrix at time k, is the transposed matrix of the observation matrix at time k, R k is the sensor measurement noise covariance matrix. is the weight, mean and covariance of the i-th prediction component at time k, is the weight, mean and covariance of the i-th updated component at time k.

[0047] In step 4, the EAP (Expected A Posterior) method is used to extract the group target intensity function to obtain an accurate estimate of the number of targets in the group. The specific steps are:

[0048] Since the mean of each Gaussian term corresponds to a local extreme point of the posterior intensity, the weight represents the contribution of the Gaussian term to the target number, and the intensity function after pruning and fusion is recorded as The target number is estimated Arrange the Gaussian items in v(x) in descending order of weight, and select the top Gaussian items in v(x) according to the number of targets obtained. A Gaussian term with a larger weight, The mean and covariance of the Gaussian terms are used as the group target state estimates.

[0049] An electronic device comprises: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method described above.

[0050] A computer-readable storage medium stores program code, which can be called by a processor to execute the method described above.

[0051] The beneficial effects of the present invention are:

[0052] (1) When the sensor resolution is limited, the number of targets in a dense group can be accurately estimated, and the accuracy of the target number estimation is significantly improved;

[0053] (2) The proposed method can be applied to dense clutter environments;

[0054] (3) While obtaining an accurate estimate of the number of targets in the group, the motion state of the group targets can also be effectively estimated. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of a method for estimating the number of targets within a group based on a potential probability hypothesis density (CPHD) filter according to the present invention.

[0056] Figure 2 This is the real trajectory diagram of the two-dimensional plane group target of the present invention.

[0057] Figure 3 This is the group target motion state estimation diagram of the present invention.

[0058] Figure 4 This is a comparison diagram of the estimated number of targets within a group of targets in an embodiment of the present invention.

[0059] Figure 5Graph showing the error in group target state estimation and quantity estimation in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be further described below with reference to the accompanying drawings and examples.

[0061] This paper discloses a method for estimating the number of targets within a group based on a cardinalized probability hypothesis density (CPHD) filter. This method leverages the ability of the CPHD filter to track unknown targets in complex environments. It constructs multiple hypotheses about the number of unknown targets corresponding to indistinguishable measurements using amplitude information, and incorporates these hypotheses into the CPHD update step to improve the accuracy of the estimation. Elliptical gating technology is used to further distinguish between real targets and clutter, reducing computational effort and enabling high-precision estimation of the number of targets within densely packed groups.

[0062] Step 1: For the k-time cluster target, a state transition model of the cluster target is established. The measurement information of the dense cluster target is obtained through sensors. The measurement information includes position information, speed information and amplitude information. The single target measurement likelihood function and clutter likelihood function are also established.

[0063] Step 2: According to the target state transfer equation, the group target intensity function is predicted through the potential probability hypothesis density filter;

[0064] Step 3: Use elliptical gating technology to distinguish real targets from clutter, and construct multiple hypotheses based on target amplitude information. Introduce the measurement likelihood function into the potential probability hypothesis density filter update step to achieve the update of the group target intensity function.

[0065] Step 4: Use the EAP (Expected A Posterior) method to extract the state of the group target intensity function and obtain an accurate estimate of the number of targets in the group.

[0066] In step 1, a state transition model for dense group targets under clutter conditions and a group target measurement model with limited sensor resolution are constructed, and a single target measurement likelihood function and a clutter likelihood function are established, including:

[0067] Assume that at time k, a subgroup contains N k targets, and the target states are is a single target state space, where the target state of the i-th individual is represents the target position, Represents the target speed. Assuming that the motion models of individual targets in the group are all linear Gaussian, the state transition probability density function of individual target i can be expressed as follows:

[0068]

[0069] Where, represents the state of the i-th target at time k-1, N(·; m, P) represents a Gaussian probability density function with mean m and covariance P; F k-1 is the state transfer matrix; Q is the covariance matrix of process noise.

[0070] Considering the limited resolution of the sensor, the measurement space It is divided into a set of non-overlapping resolution units, and this set of resolution units is recorded as U = {u1,u2,…u n}, which satisfies and make represents the position measurement function, X is the target state space, is the target measurement space, Indicates that it falls into the resolution unit u j The set of individual target states in represents the state of the i-th target in the group target at time k, X k represents the set of group target states at time k, then the position measurements in each resolution unit are combined as follows:

[0071]

[0072] In the formula Representation unit u j The number of individual targets in is the measurement noise that obeys Gaussian distribution, represents the empty set, represents the target position measurement obtained by each resolution unit after the combined measurement. Assume that the detection probability of the measurement set in each resolution unit is but The probability of

[0073] Rayleigh distribution is used to describe the amplitude variation of target and clutter, then the probability distribution of target measurement amplitude is and the probability distribution of clutter amplitude It is expressed as follows:

[0074]

[0075] in, is the known individual target signal-to-noise ratio, represents the amplitude information of the jth measurement at time k.

[0076] Assuming that the amplitude measurement and position measurement of the same target set or clutter are independent of each other, the single measurement likelihood function is and clutter likelihood function As shown in formula (5) and formula (6) respectively:

[0077]

[0078] Where, For single target measurement with amplitude information, For single target measurement without amplitude information, is the clutter measurement with amplitude information, z (0) For clutter measurement without amplitude information, c(z (0) ) are the target position measurement likelihood function and the clutter position measurement likelihood function, respectively. with c a (a) Single target amplitude likelihood function and clutter amplitude likelihood function respectively.

[0079] In step 2, the target intensity function of the group at the previous sampling moment is predicted based on the target state transfer equation to obtain the predicted intensity function of the group at the current moment, including:

[0080] Assume that the posterior strength v at time k-1 is given k-1 and the posterior potential distribution ρ k-1 , and v k-1 is a Gaussian mixture, that is

[0081]

[0082] Where, The predicted potential distribution ρ is the weight, mean and covariance of the i-th Gaussian component at time k-1 respectively. k|k-1 (n) and intensity v k|k-1 (x) are as follows:

[0083]

[0084] In the formula

[0085]

[0086] Among them, v S,k|k-1 (x) represents the predicted strength function of the survival target, γ k (x) is the new target intensity function, is the survival probability of the jth target, is the binomial coefficient, ρ Γ,k(n) represents the potential distribution of new targets at time k, is the potential distribution function at time k-1, Represent the weight, mean and covariance of the i-th predicted Gaussian component at time k, respectively, F k-1 With Q k-1 are the target state transition matrix and the covariance matrix of process noise, respectively.

[0087] In step 3, the elliptical gating technique is used to distinguish real targets from clutter, and multiple hypotheses are constructed based on the amplitude information to measure the number of corresponding targets. The measurement likelihood function is introduced and the group target intensity function is updated at the current moment, including:

[0088] Using elliptical gating technology to remove most of the clutter measurements can effectively simplify the calculation of the filter update step. The formula is as follows:

[0089]

[0090] In the formula For effective measurement, T g is the threshold value, z k,m is the mth measurement at time k, is the predicted mean of the j-th Gaussian component, is the inverse matrix of the innovation covariance matrix.

[0091] Let S = {1, ..., n} represent the set of all hypotheses about the number of target sources corresponding to a measurement. The sth element in the set represents the number of targets in the measurement. Since each indistinguishable measurement in the measurement set comes from s targets, each measurement is used to update the target state s times. Assume that the predicted strength v at time k is given k|k-1 and the predicted potential distribution ρ k|k-1 , from formula (7), we can know that v k|k-1 It is in the form of Gaussian mixture, expressed as

[0092]

[0093] Then, update the potential distribution ρ k (n) and intensity v k (x) are respectively expressed as:

[0094]

[0095] In the formula

[0096]

[0097]

[0098] in, represents the measurement set at time k, Z is the measurement set without amplitude information, is a single target measurement with amplitude information, and z is a single target measurement without amplitude information; For a given measurement set The possibility that there are n targets under the condition is the normalization constant; g(a k |s) represents the individual target amplitude likelihood function at time k; c a (a k )c z (z) represents the clutter likelihood function, w T is the weight of the predicted Gaussian component corresponding to each target, that is, w in formula (19) k|k-1 ;p D,k (x) represents the target detection probability; e j (·) represents the j-order elementary symmetric function, is a transition parameter used to calculate the potential distribution, is the permutation coefficient, p K,k is the potential distribution of clutter at time k. k ) is the known amplitude information a k The probability of assuming s under the condition of , s is the number of targets that may be included in the measurement in this hypothesis, is the target intensity function under assumption s. k (z) is the temporary weight of each Gaussian component after Kalman filtering, is the measurement prediction of the i-th target, is the innovation covariance matrix of the i-th target, is the Kalman gain matrix of the i-th target, I is the identity matrix, H k is the observation matrix at time k, is the transposed matrix of the observation matrix at time k, R k is the sensor measurement noise covariance matrix. is the weight, mean and covariance of the i-th prediction component at time k, is the weight, mean and covariance of the i-th updated component at time k.

[0099] In step 4, the EAP (Expected A Posterior) method is used to extract the group target intensity function to obtain an accurate estimate of the number of targets in the group, including:

[0100] Since the mean of each Gaussian term corresponds to a local extreme point of the posterior intensity, the weight represents the contribution of the Gaussian term to the target number. Therefore, the intensity function after pruning and fusion is recorded as The target number is estimated Arrange the Gaussian items in v(x) in descending order of weight, and select the top Gaussian items in v(x) according to the number of targets obtained. A Gaussian term with a larger weight, The mean and covariance of the Gaussian terms are used as the group target state estimates.

[0101] Example

[0102] The method provided by the present application is described below in conjunction with specific embodiments. This embodiment is described for the following environment. Assuming a two-dimensional linear group target tracking scenario, the observation area is set to [-1000m, 1000m] × [-1000m, 1000m]. The simulation scenario contains two group targets. The first group target contains 30 individual targets, which are born at the 5th second and die at the 95th second. The second group target contains 40 individual targets, which are born at the 20th second and die at the 80th second. The center of mass positions of the two group targets at the initial moment are respectively located at [-800m, 800m] T ,[200m,600m] T , with a radius of 30m. Assume that the relevant parameters of the tracking method are as follows, is the state transition matrix, is the process noise matrix, is the Kronecker product, T=1s is the sampling period, σ w =5m is the standard deviation of process noise; is a linear observation function, v k is the measurement noise, and σ v =10m is the standard deviation of measurement noise; target survival probability p S,k =0.99. The position resolution of the sensor is set to λ m =10m, individual target signal-to-noise ratio Each unresolvable measurement consists of at most 4 individual targets. The clutter model is a signal with a strength of κ k Poisson finite set, i.e. κ k =λ c Vu(z), where the Poisson process parameter λ c =50, V is the area of ​​the monitoring area, and u(·) represents the uniform probability distribution within the monitoring area. The traditional CPHD filtering method (denoted as GM-CPHD) and the CPHD-based target number estimation method given in this paper (denoted as GM-S-CPHD) are used to estimate the target state in this case. The target state estimation of the group is obtained. Figure 3 shown.

[0103] Depend on Figure 3It can be seen that the estimated points are consistent with the true trajectory of the group targets, indicating that the method proposed in this paper can effectively track the state of the group targets. Under the tracking of two different methods, the number of targets in the group is estimated as follows: Figure 4 As shown in the figure, the OSPA (Optimal Subpattern Assignment) distance of the group target tracking result and the positioning error and potential error of the OSPA distance are compared. Figure 5 As shown. Figure 4 、 Figure 5 It can be seen that the method given in this paper can track multiple groups of targets under dense clutter conditions and accurately estimate the number of targets in the group.

[0104] Compared with the prior art, the present application has the following significant advantages:

[0105] (1) When the sensor resolution is limited, the number of targets in a dense group can be accurately estimated, and the accuracy of the target number estimation is significantly improved;

[0106] (2) The proposed method can be applied to dense clutter environments;

[0107] (3) While obtaining an accurate estimate of the number of targets in the group, the motion state of the group targets can also be effectively estimated.

Claims

1. A method for estimating the number of targets in a group based on a potential probability hypothesis density filter, characterized in that The steps include: Step 1: For the k-time cluster target, a state transition model of the cluster target is established. The measurement information of the dense cluster target is obtained through sensors. The measurement information includes position information, speed information and amplitude information. The single target measurement likelihood function and clutter likelihood function are also established. Step 2: Based on the target state transfer equation, the group target intensity function is predicted through the potential probability hypothesis density filter; Step 3: Use elliptical gating technology to distinguish real targets from clutter, and construct multiple hypotheses based on target amplitude information. Introduce the measurement likelihood function into the potential probability hypothesis density filter update step to achieve the update of the group target intensity function. Step 4: Use the EAP method to extract the state of the group target intensity function and obtain an accurate estimate of the number of targets in the group.

2. The method for estimating the number of targets within a group based on a potential probability hypothesis density filter according to claim 1, wherein: In step 1, a state transition model of dense group targets under clutter conditions and a group target measurement model with limited sensor resolution are constructed, and a single target measurement likelihood function and a clutter likelihood function are established. The specific steps are: Assume that at time k, a subgroup contains N k targets, and the target states are is a single target state space, where the target state of the i-th individual is represents the target position, Represents the target speed. Assuming that the motion models of individual targets in the group are all linear Gaussian, the state transition probability density function of individual target i is expressed as follows: Where, represents the state of the i-th target at time k-1, N(·; m, P) represents a Gaussian probability density function with mean m and covariance P; F k-1 is the state transfer matrix; Q is the covariance matrix of process noise; Considering the limited resolution of the sensor, the measurement space It is divided into a set of non-overlapping resolution units, and the resolution unit is recorded as U = {u1,u2,…u n },satisfy and make represents the position measurement function, X is the target state space, The target measurement space, Indicates that it falls into the resolution unit u j The set of individual target states in represents the state of the i-th target in the group target at time k, X k represents the set of group target states at time k, then the position measurements in each resolution unit are combined as follows: In the formula Representation unit u j The number of individual targets in is the measurement noise that obeys Gaussian distribution, represents the empty set, represents the target position measurement obtained by each resolution unit after the combined measurement; assuming that the detection probability of the measurement set in each resolution unit is but The probability of Rayleigh distribution is used to describe the amplitude variation of target and clutter, so the probability distribution of target measurement amplitude is and the probability distribution of clutter amplitude It is expressed as follows: Where θ is the known signal-to-noise ratio of the individual target, represents the amplitude information of the jth measurement at time k; Assuming that the amplitude measurement and position measurement of the same target set or clutter are independent of each other, the single measurement likelihood function is As shown in formula (5), the clutter likelihood function As shown in formula (6): Where, For single target measurement with amplitude information, For single target measurement without amplitude information, is the clutter measurement with amplitude information, z (0) For clutter measurement without amplitude information, c(z (0) ) are the target position measurement likelihood function and the clutter position measurement likelihood function, respectively. with c a (a) Single target amplitude likelihood function and clutter amplitude likelihood function respectively.

3. The method for estimating the number of targets within a group based on a potential probability hypothesis density filter according to claim 1, wherein: In step 2, the target intensity function of the group at the previous sampling moment is predicted based on the target state transfer equation to obtain the predicted intensity function of the group at the current moment. The specific steps include: Assume that the posterior strength v at time k-1 is given k-1 and the posterior potential distribution ρ k-1 , and v k-1 is a Gaussian mixture, Right now: Where, are the weight, mean and covariance of the i-th Gaussian component at time k-1, respectively, then the predicted potential distribution ρ k|k-1 (n) and intensity v k|k-1 (x) are as follows: In the formula Among them, v S,k|k-1 (x) represents the predicted strength function of the survival target, γ k (x) is the new target intensity function, is the survival probability of the jth target, is the binomial coefficient, ρ Γ,k (n) represents the potential distribution of the new target at time k, p k-1 (l) is the potential distribution function at time k-1, Represent the weight, mean and covariance of the i-th predicted Gaussian component at time k, respectively, F k-1 With Q k-1 are the target state transition matrix and the covariance matrix of process noise, respectively.

4. The method for estimating the number of targets within a group based on a potential probability hypothesis density filter according to claim 1, wherein: In step 3, the elliptical gating technique is used to distinguish real targets from clutter, and multiple hypotheses are constructed based on the amplitude information to measure the number of corresponding targets. The measurement likelihood function is introduced and the group target intensity function is updated at the current moment. The specific steps include: Elliptical gating technology is used to remove most of the clutter measurements, effectively simplifying the calculation of the filter update step. The formula is as follows: In the formula For effective measurement, T g is the threshold value, z k,m is the mth measurement at time k, is the predicted mean of the j-th Gaussian component, is the inverse matrix of the innovation covariance matrix; Let S = {1, ..., n} represent the set of all hypotheses of the number of target sources corresponding to a measurement. The sth element in the set represents that the measurement contains s targets. Since each indistinguishable measurement in the measurement set comes from s targets, each measurement is used to update the target state s times. Assume that the predicted strength v at time k is given. k|k-1 and the predicted potential distribution ρ k|k-1 , from formula (7), we can know that v k|k-1 It is in the form of Gaussian mixture and is expressed as: Then, update the potential distribution ρ k (n) and intensity v k (x) are respectively expressed as: In the formula in, represents the measurement set at time k, Z is the measurement set without amplitude information, is a single target measurement with amplitude information, and z is a single target measurement without amplitude information; For a given measurement set The possibility that there are n targets under the condition is the normalization constant; g(a k |s) represents the individual target amplitude likelihood function at time k; c a (a k )c z (z) represents the clutter likelihood function, w T is the weight of the predicted Gaussian component corresponding to each target, that is, w in formula (19) k|k-1 ;p D,k (x) represents the target detection probability; e j (·) represents the j-order elementary symmetric function, is a transition parameter used to calculate the potential distribution, is the permutation coefficient, p K,k is the potential distribution of clutter at time k; P(s|a k ) is the known amplitude information a k The probability of assuming s under the condition of , s is the number of targets that may be included in the measurement in this hypothesis, is the target intensity function under the assumption s, q k (z) is the temporary weight of each Gaussian component after Kalman filtering, is the measurement prediction of the i-th target, is the innovation covariance matrix of the i-th target, is the Kalman gain matrix of the i-th target, I is the identity matrix, H k is the observation matrix at time k, is the transposed matrix of the observation matrix at time k, R k is the sensor measurement noise covariance matrix; is the weight, mean and covariance of the i-th prediction component at time k, is the weight, mean and covariance of the i-th updated component at time k.

5. The method for estimating the number of targets within a group based on a potential probability hypothesis density filter according to claim 1, wherein: In step 4, the EAP method is used to extract the group target intensity function to obtain an accurate estimate of the number of targets in the group. The specific steps are: Since the mean of each Gaussian term corresponds to a local extreme point of the posterior intensity, the weight represents the contribution of the Gaussian term to the target number, and the intensity function after pruning and fusion is recorded as The target number is estimated Arrange the Gaussian items in v(x) in descending order of weight, and select the top Gaussian items in v(x) according to the number of targets obtained. A Gaussian term with a larger weight, The mean and covariance of the Gaussian terms are used as the group target state estimates.

6. An electronic device, characterized in that: include: one or more processors; Memory; One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to perform the method according to any one of claims 1.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores program code, and the program code can be called by a processor to execute the method according to any one of claims 1.

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