A method for underwater multi-target tracking before detection based on auxiliary particle filtering
By using auxiliary particle filtering and point diffusion function models in underwater target tracking, the problems of low signal-to-noise ratio, multi-objective coincidence and complex association are solved, and more efficient target detection and tracking are achieved.
Patent Information
- Application Number
- CN202211024520.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-25
- Publication Date
- 2025-06-06
- Estimated Expiration
- 2042-08-25
AI Technical Summary
The existing underwater target tracking algorithm is prone to missed detection under low signal-to-noise ratio conditions. The overlapping of measurement values of multiple adjacent targets leads to detection failure, and the increase in the number of targets makes the target correlation complex and increases the computing power requirement.
The underwater multi-object detection pre-tracking method based on auxiliary particle filtering is adopted. The particle distribution is optimized through particle swarming, auxiliary variable sampling and resampling, and the influence of adjacent targets is considered, and the point diffusion function model is constructed to improve the computational efficiency of the likelihood function.
It effectively improves the accuracy of object detection under low signal-to-noise ratio conditions, reduces the correlation complexity in multi-objective situations, and reduces the computational complexity and resource requirements of the algorithm.
Smart Images
Figure CN115356739B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of underwater target tracking, and specifically relates to an underwater multi-target pre-detection tracking method based on auxiliary particle filtering. Background Art
[0002] Underwater target tracking obtains batch information of targets by associating data of sonar detection results. It is a key step in subsequent processing such as target positioning and target recognition, and can provide important target information for command decision-making systems. In the field of underwater target tracking, the Bayesian framework is widely used. Many existing underwater target tracking algorithms are implemented using the classic Detect-Before-Track (DBT) method. In this method, the input of the tracking method is the measurement value of the signal detection algorithm after threshold judgment. Target tracking is achieved through Measurement-to-track Association (MTA) and filtering processing. This model brings several serious problems:
[0003] 1) Target signals with low signal-to-noise ratio may not pass the detection threshold, resulting in missed target detection.
[0004] 2) When the measurement values of multiple adjacent targets overlap, only one measurement value can be obtained after detection processing.
[0005] 3) The increase in the number of targets makes target association more complex.
[0006] Another alternative underwater multi-target tracking method is the Tracking Before Detect (TBD) method, which directly detects and tracks the threshold-free sensor data. In addition, the TBD algorithm avoids the MTA problem and reduces the complexity of the algorithm; however, the problem becomes more difficult when there are adjacent targets and maneuvering targets in the sensor observation space. Summary of the invention
[0007] The present invention discloses an underwater multi-target pre-detection tracking method based on auxiliary particle filtering, which is used to solve the problem that target signals with low signal-to-noise ratio may not pass the detection threshold, resulting in missed target detection; when the measurement values of multiple adjacent targets overlap, only one measurement value can be obtained after detection processing; the increase in the number of targets makes target association more complicated, increasing the computing power.
[0008] The present invention is achieved through the following technical solutions:
[0009] A method for tracking underwater multiple targets before detection based on auxiliary particle filtering, the method comprising the following steps:
[0010] Step 1: Collecting data of sonar detection of underwater targets;
[0011] Step 2: Initialize the data particles and the weights corresponding to them;
[0012] Step 3: Use the particles in step 1 and their corresponding weights to group the targets using the predicted target state;
[0013] Step 4: Sample the auxiliary variables and calculate their corresponding first-order weights;
[0014] Step 5: Use the first-order weights of the auxiliary variables in step 4 to resample the particles and select high-quality particle numbers;
[0015] Step 7: Based on the first-order weights of the high-quality particle states in step 6, calculate the particle weights and estimate the target state.
[0016] An underwater multi-target pre-detection tracking method based on auxiliary particle filtering, the step 2 is specifically as follows: assuming that each target moves independently, the states of multiple targets at time k are represented by a multi-target state vector:
[0017]
[0018] in,() T represents matrix transpose, r represents the target number, represents the state vector of target j at time k, and d represents the dimension of the state vector of a single target;
[0019] The motion equation and measurement equation of target j at time k are described as:
[0020] x k,j =f(x k-1,j ,w k-1,j ) (2)
[0021] z k =h(X k ,v k ) (3)
[0022] Among them, w k-1,j represents the process noise vector of target j at time k-1, v k represents the measurement noise vector at time k, z k represents the measurement value at time k;
[0023] The state of the nth particle at time k It can be expressed as
[0024]
[0025] A method for underwater multi-target tracking before detection based on auxiliary particle filtering. is the parent particle, is a sub-particle; each parent particle is composed of r sub-particles; the sub-particles contain the kinematic characteristics and intensity information of the target;
[0026]
[0027] in represents the intensity information of the beamforming output of target j, Indicates target motion information
[0028]
[0029] and represents the direction and direction change rate of target j;
[0030] Assume that the initial prior probability density function p(X 0 ) can be approximated by the particle states and their weights
[0031]
[0032] n p is the number of particles required, is the prior weight of the nth particle at the initial time 0. When initialized, the prior weights of all particles are δ(·) is the Dirichlet function, is the prior state of the nth parent particle, is the prior state of the nth sub-particle of target j.
[0033] An underwater multi-target pre-detection tracking method based on auxiliary particle filtering, each sub-particle is initialized as follows:
[0034] The position of the target relative to the observer is uniformly distributed in [β 0,j -Δβ,β 0,j +Δβ];
[0035] The target's position change rate relative to the observer is uniformly distributed in
[0036] The intensity of the target output after beamforming is evenly distributed in [E k,j -ΔE,E k,j +ΔE];
[0037] β 0,j is the initial azimuth of target j estimated by the observer, and the deviation Δβ of the initial azimuth is a variable parameter that can be selected according to the performance of the sonar system; is the maximum value of the target azimuth change rate; E k,j is the orientation β 0,jThe intensity of the beamforming output at the corresponding resolution unit, ΔE describes the fluctuation of the received signal intensity.
[0038] A detection-before-tracking method based on auxiliary particle filtering. In step 3, the targets are grouped using the predicted target state. The predicted target state is
[0039]
[0040] in is the predicted target state corresponding to the nth sub-particle of target j, is the weight of this particle, n p Indicates the number of particles; all targets are grouped according to the predicted target position, where the predicted target position is one of the predicted target states and can be directly obtained from Get;
[0041] The specific grouping principle is as follows: neighboring targets are divided into a group, each group has at least one target, and each target can only belong to one group:
[0042]
[0043] Λ θ is the preset grouping threshold, H 1 Indicates that target j and target m belong to the same group, H 0 Indicates that target j and target m belong to different groups, and represents the predicted positions of targets j and m.
[0044] A detection-pre-tracking method based on auxiliary particle filtering. In step 4, in order to optimize particle sampling using measurement information, the auxiliary variables are first sampled and their corresponding first-order weights are calculated; wherein the auxiliary variables Indicated in under conditions The characteristics of the predicted particle state are selected as the auxiliary particle variable.
[0045]
[0046] Using the constant angular velocity motion model, the motion equation is expressed as
[0047]
[0048] where w k represents the process noise at time k, F represents the state transfer matrix, and the covariance matrix during the target motion is Q:
[0049]
[0050] Where τ represents the observation period, q represents the power spectral density of process noise;
[0051] According to the predicted direction, the target is associated with the beamforming output maximum based on the neighbor correlation criterion; if there is no neighboring target, the received signal sampling is performed through formula (13)
[0052]
[0053] Where E k,j represents the maximum value of the beamforming output corresponding to target j; rand represents a random number between [0,1] that is uniformly distributed; if there is a neighboring target, the received signal sampling is performed by formula (14)
[0054]
[0055] in Indicates the history window length w e The mean of the inner target maxima.
[0056] A detection-before-tracking method based on auxiliary particle filtering, assuming that after grouping, the number of groups is G, G < r, and each group is a set of targets belonging to the group; definition represents the predicted target state of all targets in group g except target j; if target j belongs to group g, then the likelihood function of target j at time k can be written as definition is the first-order weight;
[0057] If the beamforming scans M angles each time, corresponding to the M resolution units of the beamforming output; let is the measurement value corresponding to the i-th resolution unit at time k; redefine the point spread function
[0058] h i =e k,j ×exp(-(θ i -θ k,j ) 2 ×L(θ k,j ))+b (15)
[0059] where h i represents the target response of resolution unit i, e k,j represents the strength of the received signal after beamforming, b represents the noise intensity, θ k,j represents the target direction, L(θ k,j ) is the orientation θ k,j The corresponding L value at the position represents the attenuation degree of the target response, which is determined by the beamforming algorithm and the sonar system performance.
[0060] L(θ k,j )=L(floor(θ k,j / Δθ)+1) (16)
[0061] Where floor() represents the rounding down function, Δθ is the waveform forming scan width;
[0062] When there are adjacent targets, the joint target response is the superposition of the adjacent target responses; accordingly, the estimated joint target response is described as the superposition of the estimated adjacent target responses:
[0063]
[0064] N represents the number of neighboring targets;
[0065] According to the above point spread function model, the likelihood function of target j at time k is expressed as
[0066]
[0067] Where i represents θ i The corresponding resolution unit
[0068] i=floor(θ i / Δθ)+1 (19).
[0069] A detection-before-tracking method based on auxiliary particle filtering. If the target exists, u i =h i If the target does not exist, u i =b,
[0070] If the target exists, u i =h i -s×b, if the target does not exist, u i =(1-s)×b; Considering m adjacent measurement points, the likelihood function can be further written as:
[0071]
[0072] The likelihood ratio of target presence to target absence is
[0073]
[0074] Where E k =1 means the target exists, E k =0 means the target does not exist. d Under the condition of , the likelihood function is expressed as:
[0075]
[0076] For auxiliary variables Its first-order weight is expressed as
[0077] A detection-pre-tracking method based on auxiliary particle filtering, in step 6, specifically, defines a j,n ∈{1,2,…,n p} represents the particle number obtained by sampling the nth sub-particle of target j, n p is the number of particles required by the algorithm, then the state of the nth high-quality sub-particle at time k is
[0078]
[0079] To use the equation, and for the particle The corresponding first-order weight is
[0080] A detection-pre-tracking method based on auxiliary particle filtering, in step 7, the weight of the particle is expressed as
[0081]
[0082] The minimum mean square error (MMSE) criterion is used to estimate the target state.
[0083]
[0084] The beneficial effects of the present invention are:
[0085] The present invention proposes a likelihood function taking into account the influence of neighboring targets based on the point spread function.
[0086] The present invention uses auxiliary variables to optimize particle sampling using measurement information to make particle distribution more reasonable. This strategy has great advantages when the algorithm motion model does not match the actual motion state of the target.
[0087] The present invention divides neighboring targets into a group, and uses the predicted states of the neighboring targets to calculate the likelihood of the target, with high calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0088] Attached Figure 1 It is a flow chart of the method of the present invention.
[0089] Attached Figure 2 It is the motion situation diagram of the target and the observer.
[0090] Attached Figure 3 It is the target's position track diagram relative to the observer.
[0091] Attached Figure 4 It is the measurement data diagram generated by simulation.
[0092] Attached Figure 5This is the tracking result graph.
[0093] Attached Figure 6 Schematic diagram of OSPA positioning error, where parameters p = 1, c = 7000m. DETAILED DESCRIPTION
[0094] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0095] A method for tracking underwater multiple targets before detection based on auxiliary particle filtering, the method comprising the following steps:
[0096] Step 1: Collecting data of sonar detection of underwater targets;
[0097] Step 2: Initialize the data particles and the weights corresponding to them;
[0098] Step 3: Use the particles in step 1 and their corresponding weights to group the targets using the predicted target state;
[0099] Step 4: Sample the auxiliary variables and calculate their corresponding first-order weights;
[0100] Step 5: Use the first-order weights of the auxiliary variables in step 4 to resample the particles and select high-quality particle numbers;
[0101] Step 7: Based on the first-order weights of the high-quality particle states in step 6, calculate the particle weights and estimate the target state.
[0102] An underwater multi-target pre-detection tracking method based on auxiliary particle filtering, the step 2 is specifically as follows: assuming that each target moves independently, the states of multiple targets at time k are represented by a multi-target state vector:
[0103]
[0104] in,() T represents matrix transpose, r represents the target number, represents the state vector of target j at time k, and d represents the dimension of the state vector of a single target;
[0105] The motion equation and measurement equation of target j at time k are described as:
[0106] x k,j =f(x k-1,j ,w k-1,j) (2)
[0107] z k =h(X k ,v k ) (3)
[0108] Among them, w k-1,j represents the process noise vector of target j at time k-1, v k represents the measurement noise vector at time k, z k represents the measurement value at time k;
[0109] The particle filter uses the importance density function to sample particles in the state space, and uses the particles and their corresponding weights to approximate the posterior probability density of the target state to estimate the target state.
[0110] The state of the nth particle at time k It can be expressed as
[0111]
[0112] A method for underwater multi-target tracking before detection based on auxiliary particle filtering. To describe the proposed algorithm, we define is the parent particle, is a sub-particle; each parent particle is composed of r sub-particles; the sub-particles contain the kinematic characteristics and intensity information of the target;
[0113]
[0114] in represents the intensity information of the beamforming output of target j, Indicates target motion information
[0115]
[0116] and represents the direction and direction change rate of target j;
[0117] Assume that the initial prior probability density function p(X 0 ) can be approximated by the particle states and their weights
[0118]
[0119] n p is the number of particles required, is the prior weight of the nth particle at the initial time 0. When initialized, the prior weights of all particles are δ(·) is the Dirichlet function, is the prior state of the nth parent particle, is the prior state of the nth sub-particle of target j.
[0120] An underwater multi-target pre-detection tracking method based on auxiliary particle filtering, each sub-particle is initialized as follows:
[0121] The position of the target relative to the observer is uniformly distributed in [β 0,j -Δβ,β 0,j +Δβ];
[0122] The target's position change rate relative to the observer is uniformly distributed in
[0123] The intensity of the target output after beamforming is evenly distributed in [E k,j -ΔE,E k,j +ΔE];
[0124] β 0,j is the initial azimuth of target j estimated by the observer, and the deviation Δβ of the initial azimuth is a variable parameter that can be selected according to the performance of the sonar system; is the maximum value of the target azimuth change rate; E k,j is the orientation β 0,j The intensity of the beamforming output at the corresponding resolution unit, ΔE describes the fluctuation of the received signal intensity.
[0125] A detection-before-tracking method based on auxiliary particle filtering. In step 3, the targets are grouped using the predicted target state. The predicted target state is
[0126]
[0127] in is the predicted target state corresponding to the nth sub-particle of target j, is the weight of this particle, n p Indicates the number of particles; all targets are grouped according to the predicted target position, where the predicted target position is one of the predicted target states and can be directly obtained from Get;
[0128] The specific grouping principle is as follows: neighboring targets are divided into a group, each group has at least one target, and each target can only belong to one group:
[0129]
[0130] Λ θ is the preset grouping threshold, H 1 Indicates that target j and target m belong to the same group, H 0 Indicates that target j and target m belong to different groups, and represents the predicted positions of targets j and m.
[0131] A detection-pre-tracking method based on auxiliary particle filtering, in step 4, in order to optimize particle sampling using measurement information, i.e., step 4-6, the present invention first samples auxiliary variables and calculates their corresponding first-order weights; wherein the auxiliary variables Indicated in under conditions The present invention selects the predicted particle state as the auxiliary particle variable, Auxiliary variables also contain the target's kinematic characteristics and strength information.
[0132]
[0133] The present invention adopts a constant angular velocity motion model, and the motion equation is expressed as
[0134]
[0135] where w k represents the process noise at time k, F represents the state transfer matrix, and the covariance matrix during the target motion is Q:
[0136]
[0137] Where τ represents the observation period, q represents the power spectral density of process noise;
[0138] In actual sonar systems, due to environmental interference or signal fluctuations, the signal strength after beamforming output is random. This work combines historical observation information to sample the intensity state, as follows: According to the predicted direction, based on the proximity correlation criterion, the target is associated with the beamforming output maximum value; if this target has no neighboring targets, the received signal is sampled through formula (13)
[0139]
[0140] Where E k,j represents the maximum value of the beamforming output corresponding to target j; rand represents a random number between [0,1] that is uniformly distributed; if there is a neighboring target, the received signal sampling is performed by formula (14)
[0141]
[0142] in Indicates the history window length w e The mean of the inner target maxima.
[0143] A pre-detection tracking method based on auxiliary particle filtering. The present invention considers the influence of neighboring targets in the first-order weight. Assuming that after grouping, the number of groups is G, G < r, and each group is a set of targets belonging to the group; definition represents the predicted target state of all targets in group g except target j; if target j belongs to group g, then the likelihood function of target j at time k can be written as definition is the first-order weight;
[0144] The present invention defines the target response as the contribution of the target to the measured value in the observation area, uses the point spread function to describe the target response, and constructs the likelihood function. If the beamforming scans M angles each time, corresponding to the M resolution units of the beamforming output; let is the measured value corresponding to the i-th resolution unit at time k; the present invention redefines the point spread function
[0145] h i =e k,j ×exp(-(θ i -θ k,j ) 2 ×L(θ k,j ))+b (15)
[0146] where h i represents the target response of resolution unit i, e k,j represents the strength of the received signal after beamforming, b represents the noise intensity, θ k,j represents the target direction, L(θ k,j ) is the orientation θ k,j The corresponding L value at the location represents the attenuation degree of the target response, which is determined by the beamforming algorithm and the sonar system performance. In the present invention, L is preset, but it should be noted that beamforming has directionality, and resolution units with different directivities have different L values.
[0147] L(θ k,j )=L(floor(θ k,j / Δθ)+1) (16)
[0148] Where floor() represents the rounding down function, Δθ is the waveform forming scan width;
[0149] When there are adjacent targets, the joint target response is the superposition of the adjacent target responses; accordingly, the estimated joint target response is described as the superposition of the estimated adjacent target responses:
[0150]
[0151] N represents the number of neighboring targets;
[0152] According to the above point spread function model, the likelihood function of target j at time k is expressed as
[0153]
[0154] Where i represents θ i The corresponding resolution unit
[0155] i=floor(θ i / Δθ)+1 (19).
[0156] A detection-before-tracking method based on auxiliary particle filtering. If the target exists, u i =h i If the target does not exist, u i = b, but if the underwater background noise intensity is high, h i The value of u is similar to that of b, which makes the weights of the particles very close, resulting in a decrease in algorithm performance. In order to reduce the impact of background noise, a noise suppression factor s is introduced: if the target exists, u i =h i -s×b, if the target does not exist, u i =(1-s)×b; Considering m adjacent measurement points, the likelihood function can be further written as:
[0157]
[0158] The likelihood ratio of target presence to target absence is
[0159]
[0160] Where E k =1 means the target exists, E k =0 means the target does not exist. d Under the condition of , the likelihood function is expressed as:
[0161]
[0162] For auxiliary variables Its first-order weight is expressed as
[0163] A detection-pre-tracking method based on auxiliary particle filtering, in step 6, specifically, defines a j,n ∈{1,2,…,n p} represents the particle number obtained by sampling the nth sub-particle of target j, n p is the number of particles required by the algorithm, then the state of the nth high-quality sub-particle at time k is
[0164]
[0165] To use the equation, and for the particle The corresponding first-order weight is
[0166] A detection-pre-tracking method based on auxiliary particle filtering, in step 7, the weight of the particle is expressed as
[0167]
[0168] The minimum mean square error (MMSE) criterion is used to estimate the target state.
[0169]
[0170] First, construct the motion trajectories of the target and the observer. This example contains four targets. The motion trajectories of the observer and the target are as follows: Figure 2 The target's azimuth track relative to the observer is shown in Figure 3 As shown in Figure 1, there are two groups of targets that intersect. The azimuth tracks of target 1 and target 4 are close to each other for a long time, including the intersection point where the angular velocities of the two targets are similar, which is prone to association errors. Figure 3 The simulation data generated according to the target motion state is shown in Figure 4 shown.
[0171] Initialization parameters: number of particles n p =200, period τ = 10s, time window w d =0, grouping threshold Λ θ = 10°, and the Monte Carlo experiment was performed 1000 times. The tracking results are as follows Figure 5 As shown, even if target 1 and target 4 are in proximity in orientation for a long time and have similar angular velocities, the present invention can still maintain correct association and has good multi-target tracking performance. Figure 6 is the OSPA tracking error (parameters p=1, c=50°). The OSPA error of the present invention is relatively low (less than 2°) during the entire tracking process.
Claims
1. A method for underwater multi-target tracking before detection based on auxiliary particle filtering, It is characterized in that The pre-detection tracking method comprises the following steps: Step 1: Collecting data of sonar detection of underwater targets; Step 2: Initialize the data particles and the weights corresponding to them; Step 3: Use the particles in step 1 and their corresponding weights to group the targets using the predicted target state; Step 4: Sample the auxiliary variables and calculate their corresponding first-order weights; Select the predicted particle state as the auxiliary particle variable, The auxiliary variables also contain the kinematic characteristics and strength information of the target. The first-order weights take into account the influence of neighboring targets. Its first-order weight is expressed as in represents the predicted target state of all targets in group g except target j; Step 5: Use the first-order weights of the auxiliary variables in step 4 to resample the particles and select high-quality particle numbers; Step 6: Sample the high-quality particle states screened in step 5 and calculate the first-order weights of the high-quality particle states; Step 7: Based on the first-order weights of the high-quality particle states in step 6, calculate the particle weights and estimate the target state.
2. According to claim 1, a method for underwater multi-target tracking before detection based on auxiliary particle filtering, It is characterized in that Specifically, step 2 is to assume that each target moves independently, and the states of multiple targets at time k are represented by a multi-target state vector: in,() T represents the matrix transpose, r Indicates the number of targets, represents the state vector of target j at time k, and d represents the dimension of the state vector of a single target; The motion equation and measurement equation of target j at time k are described as: x k,j =f(x k-1,j ,w k-1,j ) (2) z k =h(X k ,v k ) (3) Among them, w k-1,j represents the process noise vector of target j at time k-1, v k represents the measurement noise vector at time k, z k represents the measurement value at time k; The state of the nth particle at time k It can be expressed as 3. According to claim 2, a method for underwater multi-target tracking before detection based on auxiliary particle filtering, It is characterized in that definition is the parent particle, is a sub-particle; each parent particle is composed of r sub-particles; the sub-particles contain the kinematic characteristics and intensity information of the target; in represents the intensity information of the beamforming output of target j, Indicates target motion information and represents the direction and direction change rate of target j; Assume that the initial prior probability density function p(X 0 ) can be approximated by the particle state and its weights n p is the number of particles required, is the prior weight of the nth particle at the initial time 0. When initialized, the prior weights of all particles are δ(·) is the Dirichlet function, is the prior state of the nth parent particle, is the prior state of the nth sub-particle of target j.
4. According to claim 3, a method for underwater multi-target tracking before detection based on auxiliary particle filtering, It is characterized in that Initialize each sub-particle as follows: The position of the target relative to the observer is uniformly distributed in [β 0,j -Δβ,β 0,j +Δβ]; The target's position change rate relative to the observer is uniformly distributed in The intensity of the target output after beamforming is evenly distributed in [E k,j -ΔE,E k,j +ΔE]; β 0,j is the initial azimuth of target j estimated by the observer, and the deviation Δβ of the initial azimuth is a variable parameter that can be selected according to the performance of the sonar system; is the maximum value of the target azimuth change rate; E k,j is the orientation β 0,j The intensity of the beamforming output at the corresponding resolution unit, ΔE describes the fluctuation of the received signal intensity.
5. The method for tracking before detection based on auxiliary particle filtering according to claim 1, It is characterized in that In step 3, the targets are grouped using the predicted target state. The predicted target state is in is the predicted target state corresponding to the nth sub-particle of target j, is the weight of this particle, n p Indicates the number of particles; all targets are grouped according to the predicted target position, where the predicted target position is one of the predicted target states and can be directly obtained from Get; The specific grouping principle is as follows: neighboring targets are divided into a group, each group has at least one target, and each target can only belong to one group: Λ θ is the preset grouping threshold, H 1 Indicates that target j and target m belong to the same group, H 0 Indicates that target j and target m belong to different groups, and represents the predicted positions of targets j and m.
6. A method for tracking before detection based on auxiliary particle filtering according to claim 1, It is characterized in that In step 4, in order to optimize particle sampling using measurement information, the auxiliary variables are first sampled and their corresponding first-order weights are calculated; the auxiliary variables Indicated in under conditions Features, Using the constant angular velocity motion model, the motion equation is expressed as where w k represents the process noise at time k, F represents the state transfer matrix, and the covariance matrix during the target motion is Q: Where τ represents the observation period, q represents the power spectral density of process noise; According to the predicted direction, the target is associated with the beamforming output maximum based on the neighbor correlation criterion; if there is no neighboring target, the received signal sampling is performed through formula (13) Where E k,j represents the maximum value of the beamforming output corresponding to target j; rand represents a random number between [0,1] that is uniformly distributed; if there is a neighboring target, the received signal sampling is performed by formula (14) in Indicates the history window length w e The mean of the inner target maxima.
7. A method for tracking before detection based on auxiliary particle filtering according to claim 6, It is characterized in that Assume that after grouping, the number of groups is G, G<r, and each group is a set of targets belonging to the group; define represents the predicted target state of all targets in group g except target j; If target j belongs to group g, then the likelihood function of target j at time k can be written as definition is the first-order weight; If the beamforming scans M angles each time, corresponding to the M resolution units of the beamforming output; let is the measurement value corresponding to the i-th resolution unit at time k; redefine the point spread function where h i represents the target response of resolution unit i, e k,j represents the strength of the received signal after beamforming, b represents the noise intensity, θ k,j represents the target direction, L(θ k,j ) is the orientation θ k,j The corresponding L value at the position represents the attenuation degree of the target response, which is determined by the beamforming algorithm and the sonar system performance. Where floor() represents the rounding down function, Δθ is the waveform forming scan width; When there are adjacent targets, the joint target response is the superposition of the adjacent target responses; accordingly, the estimated joint target response is described as the superposition of the estimated adjacent target responses: N represents the number of neighboring targets; According to the above point spread function model, the likelihood function of target j at time k is expressed as Where i represents θ i The corresponding resolution unit i=floor(θ i / Δθ)+1 (19).
8. A method for tracking before detection based on auxiliary particle filtering according to claim 7, It is characterized in that If the target exists, u i =h i -s×b, where s represents the noise suppression factor. If the target does not exist, u i =(1-s)×b; Considering m adjacent measurement points, the likelihood function can be further written as: The likelihood ratio of target presence to target absence is: Where E k =1 means the target exists, E k =0 means the target does not exist. d Under the condition of , the likelihood function is expressed as: For auxiliary variables Its first-order weight is expressed as 9. The method for tracking before detection based on auxiliary particle filtering according to claim 1, It is characterized in that Specifically, in step 6, define a j,n ∈{1,2,…,n p } represents the particle number obtained by sampling the nth sub-particle of target j, n p is the number of particles required by the algorithm, then the state of the nth high-quality sub-particle at time k is To use the equation, and for the particle It is obtained by sampling; its corresponding first-order weight is 10. The method for tracking before detection based on auxiliary particle filtering according to claim 1, It is characterized in that Specifically, in step 7, the weight of the particle is expressed as: The minimum mean square error (MMSE) criterion is used to estimate the target state: