Target passive tracking trajectory division method based on azimuth-frequency

Abstract

The invention discloses a target passive tracking trajectory division method based on azimuth-frequency, and belongs to the technical field of passive sonar underwater multi-target tracking. The objective of the invention is to solve the problem of poor tracking effect of an existing method in a scene that a target has track intersection. According to the method, aiming at a scene that underwater multi-target tracking trajectories are crossed, under the condition of passive tracking of a single observation platform, a frequency measurement value is introduced into a target state to obtain an azimuth-frequency augmented state vector, and azimuth-frequency joint information can improve the discrimination degree of posterior probability solution of a target corresponding to the measurement value, so that the target tracking precision is improved. Therefore, the accuracy of batch division of the targets under the condition of track intersection is improved. And an RB particle filter, a multi-hypothesis tracking technology and a Kalman smoothing filtering technology are combined, so that a good target tracking effect is realized, and the correctness of a tracking result is ensured. The method can be applied to the technical field of underwater multi-target tracking.

Description

Technical Field

[0001] The invention belongs to the technical field of passive sonar underwater multi-target tracking, and in particular relates to a target passive tracking trajectory division method based on azimuth-frequency. Background Art

[0002] Passive sonar systems rely on capturing noise signals continuously released by ships to achieve target detection. In traditional passive target tracking, target positioning and tracking mainly rely on a single information source (such as pure bearing information). However, pure bearing tracking is easily restricted by factors such as noise, interference, and measurement errors. Especially in the case of multiple targets and intersecting target trajectories, pure bearing tracking is difficult to distinguish signals generated by different sound sources, resulting in mutual interference between targets, which in turn affects the accurate assessment of key information such as target status and quantity, and may eventually cause errors in the batch division of target trajectories, leading to tracking errors.

[0003] With the continuous advancement of sensor technology and signal processing technology, multi-dimensional information fusion technology has gradually become a research focus in the field of target detection and tracking. By fusing azimuth-frequency multi-dimensional information, a more detailed description of target characteristics can be provided, which can significantly improve the performance of target detection and tracking and effectively combat interference. Combined with the fused target azimuth frequency information, appropriate tracking algorithms and data association algorithms are used to track the target in real time.

[0004] The underwater multi-target tracking algorithm focuses on the Kalman filter model supported by Bayesian theory. The model accurately predicts and updates the future state of the target and obtains the target path based on the historical state of the target and the current observation data. Under the conditions of linear state model and Gaussian white noise, the classic Kalman filter is the optimal filter; under the conditions of nonlinear state model and non-Gaussian white noise, the generalized Kalman filter is the suboptimal filter. When the number of targets is unknown or variable, both the classic Kalman filter and the generalized Kalman filter have poor tracking performance. In contrast, the particle filter can not only effectively reduce the amount of Monte Carlo calculations, but also can track unknown numbers of multiple targets well under the conditions of nonlinear state model and non-Gaussian white noise.

[0005] Data association is the core link to achieve multi-dimensional information fusion. It requires accurate matching of measurement data of different time frames with targets, aiming to establish the corresponding relationship between measurement data and noise, surviving targets and new targets. In actual tracking scenarios, there are mainly the following two problems:

[0006] First, there are false alarms and missed detections during the detection process, and the measurement data contains a lot of noise, making the correspondence between the target and the observation unclear;

[0007] Second, the time points of target appearance and disappearance as well as the number of targets are unknown a priori.

[0008] To solve the above problems, scholars from various countries have explored a variety of data association algorithms, such as nearest neighbor association, probabilistic data association, joint probabilistic data association, and multi-hypothesis tracking. However, the first two association methods are difficult to solve the problem of multi-target birth and death, and the latter association method faces the problem of combinatorial explosion in computational complexity.

[0009] The Rao-Blackwellized Monte Carlo data association algorithm is based on the RB particle filter and is combined with the multi-hypothesis tracking algorithm to track targets. It can achieve batch division of targets while reducing the amount of calculation. However, in the scenario where the target trajectories intersect, due to the similar states of each target, the Rao-Blackwellized Monte Carlo data association algorithm still finds it difficult to accurately divide particles, resulting in errors in the judgment of the birth and disappearance of targets, batch division errors, and algorithm failure. Limited by the lack of prior information, the tracking effect of existing algorithms when dealing with the problem of target trajectory intersection is still not ideal, and various batch division errors are prone to occur. Summary of the invention

[0010] The purpose of the present invention is to solve the problem of poor tracking effect of existing methods in the scenario where the target trajectories intersect, and propose a target passive tracking trajectory division method based on azimuth-frequency to improve the passive tracking performance of underwater multi-targets in the scenario where the target trajectories intersect.

[0011] The technical solution adopted by the present invention to solve the above technical problems is: a target passive tracking trajectory division method based on azimuth-frequency, the method specifically comprising the following steps:

[0012] Step 1: Initialize a particle set containing N particles, initialize the weight of each particle in the particle set to 1 / N, and record the initialization weight of the i-th particle as Initialize the particle set structure array S 0 , S 0 ={S{1} 0 ,S{2} 0 ,...,S{N} 0};

[0013] Among them, S{1} 0 represents the target data in the first particle, wherein the target data includes a target state and a target number corresponding to the target state;

[0014] Step 2: Initialization time k=1;

[0015] Step 3, initialize particle count i=1;

[0016] Step 4: Based on the measurement data collected at time k and the states of the targets at time k-1 in the i-th particle, the states of the targets at time k are predicted and updated;

[0017] Step 5: Calculate the probability of each target disappearing at time k, and calculate the posterior probability that the measurement data collected at time k comes from the new target, the posterior probability that it comes from clutter, and the posterior probability that it comes from each target existing at time k-1;

[0018] Sampling is performed based on the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined based on the sampling results;

[0019] Then, according to the source of the measurement value at time k, the extinction of the target at time k, and the prediction and update results of step 4, the target data in the i-th particle at time k is updated;

[0020] Step 6: whether i=N is satisfied;

[0021] If satisfied, proceed to step seven;

[0022] If not satisfied, set i=i+1 and return to step 4;

[0023] Step 7: According to the posterior probability of the target being born from the measurement data collected at time k, the posterior probability of the clutter being derived from the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k, the weight of each particle is updated respectively, and the updated weights are normalized respectively to obtain the weight of each particle after normalization;

[0024] Calculate the effective number of particles at time k according to the weight of each particle after normalization And compare the effective particle number and the size of the threshold η;

[0025] If the effective number of particles If it is less than the threshold η, the particles are resampled and step eight is executed again;

[0026] If the effective number of particles If it is greater than or equal to the threshold η, then directly execute step eight;

[0027] Step 8: Determine whether the tracking process is completed;

[0028] If the tracking process is finished, the normalized weights of each particle at the last moment are compared, and the particle corresponding to the maximum normalized weight at the last moment is selected. The target data of the selected particle at each moment is smoothed and filtered to obtain the target data after smoothing and filtering, that is, the final target tracking trajectory is obtained.

[0029] If the tracking process is not finished, set k=k+1 and return to step three.

[0030] Furthermore, in the ith particle, the target state of the jth target at time k-1 is Defined as:

[0031]

[0032] in, represents the position of the jth target at time k-1 in the i-th particle, yes The first derivative of represents the frequency of the jth target in the i-th particle at time k-1, yes The first-order derivative of . The superscript T indicates the transpose.

[0033] Furthermore, the state of each target existing at time k-1 is predicted and updated at time k, specifically:

[0034] The Kalman filter method is used to predict the state of the jth target at time k in the i-th particle at time k-1:

[0035]

[0036] In the formula, represents the target state prediction result of the jth target at time k in the i-th particle at time k-1, F k-1 is the system state transfer matrix at time k-1, represents the covariance matrix of the jth target at time k-1 in the i-th particle, represents the covariance matrix prediction result of the jth target at time k in the i-th particle at time k-1, Q k-1 Represents the covariance matrix of the state transition process noise;

[0037] The Kalman filter method is used to update the state of the jth target at time k in the i-th particle at time k-1:

[0038]

[0039] Among them, Η kis the system observation matrix at time k, represents the intermediate variable, R k represents the variance of the observation noise at time k, is the updated covariance of the ith particle at time k, express The inverse, is the Kalman gain of the ith particle at time k, z k represents the measurement collected at time k, represents the target state update result of the jth target at time k-1 in the i-th particle at time k, represents the updated covariance matrix of the jth target at time k in the i-th particle at time k-1, j = 1, 2, ..., J k-1 , J k-1 is the target number at time k-1 in the ith particle.

[0040] Furthermore, the specific process of step five is as follows:

[0041] Step 5. Calculate the probability of each target existing at time k-1 disappearing at time k, and record the probability of the jth target existing at time k-1 disappearing at time k as

[0042] Step 52: Calculate the prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) and the likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ); specifically:

[0043] (1) When the measurement value collected at time k comes from the target newborn:

[0044] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is the target birth probability pb, that is, p(e k ,c k |e 1:k-1 ,c 1；k-1 )=p b =0.04;

[0045] Likelihood Among them, m 00 is the initial state of the new target, P 00 is the initial covariance matrix of the new target;

[0046] (2) When the measurement value collected at time k comes from clutter:

[0047] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is (1-p b )·p c , p c is the probability that the measured value is caused by noise;

[0048] Likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ) is 1 / 360;

[0049] (3) When the measurement value collected at time k comes from the jth target existing at time k-1:

[0050] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 )for

[0051] Likelihood Where I is the identity matrix;

[0052] Step 53: Based on the prior transfer probability and likelihood probability calculated in step 52, calculate the posterior probability that the k-time measurement value comes from the target, the posterior probability that it comes from the clutter, and the posterior probability that it comes from each target existing at k-1 time; where: the posterior probability that the k-time measurement value comes from the target is simply recorded as The posterior probability that the measured value at time k comes from the clutter is simply written as The posterior probability that the k-time measurement value is derived from the j-th target existing at k-1 time is simply written as

[0053] Step 54: Sampling is performed according to the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined according to the sampling results;

[0054] Step 55: Update the target data in the i-th particle at time k according to the source of the measurement value at time k, the target extinction status, and the prediction and update results of step 4.

[0055] Furthermore, the specific process of step 54 is as follows:

[0056] Step 541: Calculate the probability p i ′,′ j+2 :

[0057]

[0058] Among them, j′≠j;

[0059] Calculate the probability p i ″:

[0060]

[0061] Step 542: Calculate the probability

[0062]

[0063] Among them, j′≠j;

[0064] Calculating Probability

[0065]

[0066] Step 543: Calculate the probability

[0067]

[0068] Among them, j′≠j;

[0069] Calculate the probability p i ' , ″ j+2 :

[0070]

[0071] Step 544: Sample all the probabilities calculated in steps 541 to 543, and determine the source of the measurement value at time k and whether the target has disappeared based on the sampling results.

[0072] Furthermore, the specific process of step 55 is as follows:

[0073] If it is determined that the measurement value collected at time k comes from the new target and there is a target extinction, then the state prediction result of the jth target at time k-1 that has not disappeared is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle;

[0074] If it is determined that the measurement value collected at time k comes from the new target and no target disappears, then the state prediction result of the jth target at time k-1 is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle;

[0075] If it is determined that the measurement value collected at time k comes from clutter and a target disappears, then the state prediction result of the jth target at time k-1 that has not disappeared is Stored in the i-th particle at time k;

[0076] If it is determined that the measurement value collected at time k comes from clutter and no target disappears, then the state prediction result of the jth target at time k-1 is Stored in the i-th particle at time k;

[0077] If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and a target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 that have not disappeared are stored in the ith particle at time k;

[0078] If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and no target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 are stored in the ith particle at time k.

[0079] Furthermore, the weight of each particle is updated respectively based on the posterior probability of the target being born, the posterior probability of clutter, the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k. The specific process is:

[0080]

[0081] Among them, p i ' ,m is the mth probability calculated in step 541 to step 543, m = 1, 2, ..., M, M represents the total number of probabilities calculated in step 541 to step 543, represents the weight of the i-th particle at time k after update, represents the weight of the i-th particle at time k-1.

[0082] Furthermore, the updated weights are normalized to obtain the weight of each particle after normalization. The specific process is:

[0083]

[0084] in, Represents the weight of the i-th particle at time k after normalization.

[0085] Furthermore, the effective number of particles at time k is calculated according to the weight of each particle after normalization, specifically:

[0086]

[0087] in, Indicates the number of effective particles.

[0088] The beneficial effects of the present invention are:

[0089] The present invention aims at the scenario where there are intersections in underwater multi-target tracking trajectories. Under the condition of passive tracking by a single observation platform, the frequency measurement value is introduced into the target state to obtain the azimuth-frequency augmented state vector. The azimuth-frequency joint information can improve the discrimination of the posterior probability solution of the measured value corresponding to the target, thereby improving the accuracy of batch division of targets in the case of intersection of trajectories. In addition, the RB particle filter, multi-hypothesis tracking technology and Kalman smoothing filter technology are combined to achieve a good target tracking effect and ensure the accuracy of the tracking results. Compared with conventional multi-target tracking methods, the method of the present invention can still significantly reduce batch division errors in the case of intersection of target trajectories, and the tracking performance of the method of the present invention is proved by experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a flow chart of a method for dividing target passive tracking trajectories based on azimuth-frequency of the present invention;

[0091] Figure 2 Case a where batch division is wrong when target trajectories intersect;

[0092] In the figure, the color curves other than the black line represent the tracking trajectory after smoothing;

[0093] Figure 3 b is the case where batch division is wrong when the target track crosses;

[0094] In the figure, the color curves other than the black line represent the tracking trajectory after smoothing;

[0095] Figure 4 It is the measured value and the real trajectory diagram when the target trajectory crosses;

[0096] Figure 5 The target tracking result of the algorithm of the present invention when the target trajectories intersect;

[0097] In the figure, the other colored curves except the black line represent the tracking trajectories obtained by the method of the present invention;

[0098] Figure 6 The target tracking result after smoothing by the algorithm of the present invention when the target trajectories intersect;

[0099] In the figure, the other colored curves except the black line represent the tracking trajectories obtained by the method of the present invention;

[0100] Figure 7 This is a comparison chart between the estimated and actual number of targets of the improved algorithm when the target trajectories intersect. DETAILED DESCRIPTION

[0101] Specific implementation method 1: Combination Figure 1 The present embodiment describes a method for dividing target passive tracking trajectories based on azimuth-frequency, and the method specifically comprises the following steps:

[0102] Step 1: Initialize a particle set containing N particles, initialize the weight of each particle in the particle set to 1 / N, and record the initialization weight of the i-th particle as Initialize the particle set structure array S 0 , S 0 ={S{1} 0 ,S{2} 0 ,...,S{N} 0};

[0103] Among them, S{1} 0 represents the target data in the first particle, wherein the target data includes a target state and a target number corresponding to the target state (i.e., includes the azimuth, azimuth derivative, frequency and frequency derivative corresponding to each numbered target, and the target state and target number are stored together);

[0104] Step 2: Initialization time k=1;

[0105] Step 3, initialize particle count i=1;

[0106] Step 4: Based on the measurement data collected at time k and the states of the targets at time k-1 in the i-th particle, the states of the targets at time k are predicted and updated;

[0107] Step 5: Calculate the probability of each target disappearing at time k, and calculate the posterior probability that the measurement data collected at time k comes from the new target, the posterior probability that it comes from clutter, and the posterior probability that it comes from each target existing at time k-1;

[0108] Sampling is performed based on the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined based on the sampling results;

[0109] Then, according to the source of the measurement value at time k, the extinction of the target at time k, and the prediction and update results of step 4, the target data in the i-th particle at time k is updated;

[0110] Step 6: whether i=N is satisfied;

[0111] If satisfied, proceed to step seven;

[0112] If not satisfied, set i=i+1 and return to step 4;

[0113] Step 7: According to the posterior probability of the target being born from the measurement data collected at time k, the posterior probability of the clutter being derived from the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k, the weight of each particle is updated respectively, and the updated weights are normalized respectively to obtain the weight of each particle after normalization;

[0114] Calculate the effective number of particles at time k according to the weight of each particle after normalization And compare the effective particle number and the size of the threshold η;

[0115] If the effective number of particles If it is less than the threshold η, the particles are resampled and step eight is executed again;

[0116] If the effective number of particles If it is greater than or equal to the threshold η, then directly execute step eight;

[0117] Step 8: Determine whether the tracking process is finished (i.e., whether new measurements are collected);

[0118] If the tracking process is finished, the normalized weights of each particle at the last moment are compared, and the particle corresponding to the maximum normalized weight at the last moment is selected. The target data of the selected particle at each moment is processed by Kalman smoothing filter to obtain the target data after smoothing filter processing, that is, the final target tracking trajectory is obtained;

[0119] If the tracking process is not finished, set k=k+1 and return to step three.

[0120] Add the target data of each particle at each moment to the set SS:

[0121]

[0122] By comparison, the maximum weight after normalization at the last moment is obtained, and then the particle i′ corresponding to the maximum weight is obtained. The target data of particle i′ at each moment is smoothed and filtered, and the target data of particle i′ after smoothing and filtering at each moment is recorded as S′{i′} 1 , S′{i′} 2 ,…,S′{i′} k , for any target in the tracking process, according to the target in S′{i′} 1 , S′{i′} 2 ,…,S′{i′} k The state data in is used to obtain the tracking trajectory of the target.

[0123] The method of the present invention can be implemented using only a small number of particles (the number of particles is set to 10 in the present invention), thus avoiding the "dimensionality disaster" problem of the amount of calculation.

[0124] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that: in the i-th particle, the target state of the j-th target at time k-1 Defined as:

[0125]

[0126] in, represents the position of the jth target at time k-1 in the i-th particle, yes The first derivative of represents the frequency of the jth target in the i-th particle at time k-1, yes The first-order derivative of . The superscript T indicates the transpose.

[0127] The other steps and parameters are the same as those in the first embodiment.

[0128] This implementation expands the traditional pure bearing target state vector into a bearing-frequency augmented state vector. The continuous-time state equation of the target motion is:

[0129]

[0130] Where t represents time, θ(t) represents the target position at time t, is the first-order derivative of θ(t), f(t) represents the target frequency at time t, is the first-order derivative of f(t), w(t) represents the state process noise at time t;

[0131] According to the continuous time state equation of target motion, the discrete time state equation is obtained as follows:

[0132]

[0133] In the formula, θ k-1 represents the position of the target at time k-1, is θ k-1 The first derivative of k-1 represents the frequency of the target at time k-1, Yes k-1 The first derivative of k-1 is the system state transfer matrix at time k-1 (the system state transfer matrix at each time is ), w k-1 is the state process noise at time k-1, wk- 1 ~N(0,Qk- 1 ), Q k-1 represents the state transition process noise w k-1 The covariance matrix of (the covariance matrix is ​​the same at each moment), and Q k-1 is a Gaussian white noise with a mean of 0 and a variance of q. dt represents the sampling period (i.e., the time interval for data collection. In simulation, dt = 0.1 seconds is taken, indicating that the real state of the target is sampled once every 0.1 seconds). The covariance matrix Q k-1 for:

[0134]

[0135] Measurement equation z k Described as:

[0136]

[0137] Where, H k-1 is the system observation matrix at time k-1 (the system observation matrix at each time is the same and is obtained through initialization), v k-1 is the observation noise at time k-1 (the observation noise at each time is the same and is obtained by initialization), v k-1 ~N(0,R k-1 ).

[0138] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that: the state of each target existing at time k-1 is predicted and updated at time k, specifically:

[0139] The Kalman filter method is used to predict the state of the jth target at time k in the i-th particle at time k-1:

[0140]

[0141] In the formula, represents the target state prediction result of the jth target at time k in the i-th particle at time k-1, F k-1 is the system state transfer matrix at time k-1, represents the covariance matrix of the jth target at time k-1 in the i-th particle (covariance matrix Obtained by initialization), represents the covariance matrix prediction result of the jth target at time k in the i-th particle at time k-1, Q k-1 Represents the covariance matrix of the state transition process noise;

[0142] The Kalman filter method is used to update the state of the jth target at time k in the i-th particle at time k-1:

[0143]

[0144] Among them, Η k is the system observation matrix at time k, represents the intermediate variable, R k represents the variance of the observation noise at time k, is the updated covariance of the ith particle at time k, express The inverse, is the Kalman gain of the ith particle at time k, z k represents the measurement collected at time k, represents the target state update result of the jth target at time k-1 in the i-th particle at time k, represents the updated covariance matrix of the jth target at time k in the i-th particle at time k-1, j = 1, 2, ..., J k-1 , J k-1 is the target number at time k-1 in the ith particle.

[0145] The other steps and parameters are the same as those in the first or second embodiment.

[0146] Specific implementation method 4: This implementation method is different from the specific implementation methods 1 to 3 in that the specific process of step 5 is:

[0147] The extinction and rebirth of the target exist independently of each other. According to the Markov characteristics of the three indicators:

[0148]

[0149] Therefore, the target tracking problem is related to whether the target disappears and the source of the measurement value, so the following process needs to be performed:

[0150] Step 5. Calculate the probability of each target existing at time k-1 disappearing at time k, and record the probability of the jth target existing at time k-1 disappearing at time k as

[0151] If the probability distribution of the target's life span is known, the probability of the target's extinction can be calculated. For example, if the target's survival time satisfies the gamma distribution, the probability of the target's disappearance under the gamma distribution can be obtained, that is, assuming that the time when the jth target was last associated with the measurement value is t last,j , and it is not judged to be extinct at time k-1 (the target still exists), then at time k, the probability of the jth target disappearing is:

[0152] p(d k =jt k ,t k-1 ,t last,j )=p(t d ∈[t k-1 -t last,j ,t k -t last,j ]t d >t k-1 -t last,j ) (9)

[0153] Step 52: Calculate the prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) and the likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ); specifically:

[0154] Assume that the measurement value comes from the target newborn as a hypothesis, that the measurement value comes from each target at time k-1 as a hypothesis, and that the measurement value comes from clutter as a hypothesis, for a total of M hypotheses;

[0155] (1) When the measurement value collected at time k comes from the target newborn:

[0156] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is the target newborn probability pb set by the system (the target newborn probability in the present invention is 0.4), that is, p(e k ,c k |e 1:k-1 ,c 1；k-1 )=pb =0.04;

[0157] Likelihood Among them, m 00 is the initial state of the new target, P 00 is the initial covariance matrix of the new target, m 00 and P 00 All are initialized to 0;

[0158] That is, p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ) is equal to the likelihood probability between the actual measurement value and the expected measurement value obtained after the Kalman filter update process of the new target initial state;

[0159] (2) When the measurement value collected at time k comes from clutter:

[0160] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is (1-p b )·p c , p c is the probability that the measured value is caused by noise;

[0161] The clutter is evenly distributed in the measurement space, and the likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ) is 1 / 360;

[0162] (3) When the measurement value collected at time k comes from the jth target existing at time k-1 (i.e., the target trajectory is maintained):

[0163] Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 )for

[0164] Likelihood Where I is the identity matrix;

[0165] Based on Bayes' rule, it can be deduced that the prior transfer probability, likelihood probability and posterior probability have the relationship of formula (10);

[0166]

[0167] Among them, p(e k ,c k |z 1:k ,e 1:k-1 ,c 1:k-1 ) represents the posterior probability of the measured value at time k, and ∝ represents that the value of the posterior probability is related to the product of the prior transition probability and the likelihood probability. Therefore, the product of the prior transition probability and the likelihood probability can be approximated as the posterior probability;

[0168] c k is the data association index, which indicates the measurement association under the current assumption. If the current assumption is that the measurement value comes from the target newborn, then c k Indicates that a measurement is newly associated with a target; target visibility indicator k ={d k ,b k}, d k and b k They respectively indicate the birth and extinction of the target at time k;

[0169] Step 53: Based on the prior transfer probability and likelihood probability calculated in step 52, calculate the posterior probability that the k-time measurement value comes from the target, the posterior probability that it comes from the clutter, and the posterior probability that it comes from each target existing at k-1 time; where: the posterior probability that the k-time measurement value comes from the target is simply recorded as The posterior probability that the measured value at time k comes from the clutter is simply written as The posterior probability that the k-time measurement value is derived from the j-th target existing at k-1 time is simply written as

[0170] Step 54: Sampling is performed according to the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined according to the sampling results;

[0171] Step 55: Update the target data in the i-th particle at time k according to the source of the measurement value at time k, the target extinction status, and the prediction and update results of step 4.

[0172] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0173] By executing the process of this embodiment on each of the N particles in the particle set, N updated new particles at the current moment can be obtained: k ={S{1} k ,S{2} k ,...S{N} k}.

[0174] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the specific process of step 54 is:

[0175] Step 541: Calculate the probability p i ' , ' j+2 :

[0176]

[0177] Among them, j′≠j;

[0178] Calculate the probability p i ″:

[0179]

[0180] Step 542: Calculate the probability

[0181]

[0182] Among them, j′≠j;

[0183] Calculating Probability

[0184]

[0185] Step 543: Calculate the probability

[0186]

[0187] Among them, j′≠j;

[0188] Calculate the probability p i ' , ″ j+2 :

[0189]

[0190] Step 544: Use the Monte Carlo method to sample all the probabilities calculated in steps 541 to 543 (simulating the hypothesis selection process), and determine the source of the measurement value at time k based on the sampling results (through sampling, a value can be sampled from all the probabilities. The larger the value, the greater the probability of being sampled during sampling. According to the sampled value, determine whether the measurement value at time k comes from a new target, clutter, or a target existing at time k-1) and whether there is a target extinction (that is, if the sampled value is obtained by multiplying the posterior probability that the measurement value comes from the new target by the probability of the second target extinction, then the measurement value comes from the new target and the second target extincts; if the sampled value is the posterior probability that the measurement value comes from the new target, then the measurement value comes from the new target and no target extincts).

[0191] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0192] Specific implementation method 6: This implementation method is different from specific implementation methods 1 to 5 in that the specific process of step 55 is:

[0193] If it is determined that the measurement value collected at time k comes from the new target and there is a target extinction, then the state prediction result of the jth target at time k-1 that has not disappeared is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle. The i-th particle no longer stores the state of the target that is determined to be extinct.

[0194] If it is determined that the measurement value collected at time k comes from the new target and no target disappears, then the state prediction result of the jth target at time k-1 is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle;

[0195] If it is determined that the measurement value collected at time k comes from clutter and a target disappears, then the state prediction result of the jth target at time k-1 that has not disappeared is Stored in the i-th particle at time k, the i-th particle no longer stores the state determined as the extinction target;

[0196] If it is determined that the measurement value collected at time k comes from clutter and no target disappears, then the state prediction result of the jth target at time k-1 is Stored in the i-th particle at time k;

[0197] If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and a target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 that have not disappeared are stored in the ith particle at time k as the latest state of other targets at time k at time k-1;

[0198] If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and no target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 are stored in the ith particle at time k as the latest states of other targets at time k at time k-1.

[0199] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0200] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that: the weight of each particle is updated separately according to the posterior probability of the target being born, the posterior probability of clutter, the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k; the specific process is:

[0201]

[0202] Among them, p i ' ,m is the mth probability calculated in step 541 to step 543 (that is, each probability calculated in step 541 to step 543 is abbreviated as p i ' ,m In the form of, m = 1, 2, ..., M, M represents the total number of probabilities calculated in step 541 to step 543, represents the weight of the i-th particle at time k after update, represents the weight of the i-th particle at time k-1.

[0203] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0204] Each hypothesis corresponds to a priori transition probability and likelihood probability. Therefore, the weight of the particle can be updated by combining the priori transition probability and likelihood probability of all M groups of hypotheses.

[0205] Specific implementation eight: This implementation differs from specific implementations one to seven in that: the updated weights are normalized to obtain the weight of each particle after normalization; the specific process is:

[0206]

[0207] in, Represents the weight of the i-th particle at time k after normalization.

[0208] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0209] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that: the effective number of particles at time k is calculated based on the weight of each particle after normalization, specifically:

[0210]

[0211] in, Indicates the number of effective particles.

[0212] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0213] Experimental Section

[0214] Figure 2 and Figure 3 There are two cases where batch division is wrong when the target tracks cross. Figure 4 is the measured value and the actual trajectory diagram when the target trajectory crosses. Figure 5 is the target tracking result of the algorithm of the present invention when the target trajectories intersect. Figure 6 is the target tracking result after smoothing by the algorithm of the present invention when the target trajectories intersect. Figure 7 The figure is a comparison chart of the target number estimation and the actual number of the algorithm of the present invention when the target trajectories intersect. It can be seen that the algorithm of the present invention can significantly improve the tracking performance when the target trajectories intersect.

[0215] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A target passive tracking trajectory division method based on azimuth-frequency, characterized in that: The method specifically comprises the following steps: Step 1: Initialize a particle set containing N particles, initialize the weight of each particle in the particle set to 1 / N, and record the initialization weight of the i-th particle as Initialize the particle set structure array S0, S0 = {S{1}0, S{2}0, ..., S{N}0}; Wherein, S{1}0 represents the target data in the first particle, and the target data includes the target state and the target number corresponding to the target state; Step 2: Initialization time k=1; Step 3, initialize particle count i=1; Step 4: Based on the measurement data collected at time k and the states of the targets at time k-1 in the i-th particle, the states of the targets at time k are predicted and updated; Step 5: Calculate the probability of each target disappearing at time k, and calculate the posterior probability that the measurement data collected at time k comes from the new target, the posterior probability that it comes from clutter, and the posterior probability that it comes from each target existing at time k-1; Sampling is performed based on the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined based on the sampling results; Then, according to the source of the measurement value at time k, the extinction of the target at time k, and the prediction and update results of step 4, the target data in the i-th particle at time k is updated; Step 6: whether i=N is satisfied; If satisfied, proceed to step seven; If not satisfied, set i=i+1 and return to step 4; Step 7: According to the posterior probability of the target being born from the measurement data collected at time k, the posterior probability of the clutter being derived from the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k, the weight of each particle is updated respectively, and the updated weights are normalized respectively to obtain the weight of each particle after normalization; Calculate the effective number of particles at time k according to the weight of each particle after normalization And compare the effective particle number and the size of the threshold η; If the effective number of particles If it is less than the threshold η, the particles are resampled and step eight is executed again; If the effective number of particles If it is greater than or equal to the threshold η, then directly execute step eight; Step 8: Determine whether the tracking process is completed; If the tracking process is finished, the normalized weights of each particle at the last moment are compared, and the particle corresponding to the maximum normalized weight at the last moment is selected. The target data of the selected particle at each moment is smoothed and filtered to obtain the target data after smoothing and filtering, that is, the final target tracking trajectory is obtained. If the tracking process is not finished, set k=k+1 and return to step three.

2. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 1, characterized in that: The target state of the jth target at time k-1 in the i-th particle Defined as: in, represents the position of the jth target at time k-1 in the i-th particle, yes The first derivative of represents the frequency of the jth target in the i-th particle at time k-1, yes The first-order derivative of . The superscript T indicates the transpose.

3. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 2, characterized in that: The state of each target existing at time k-1 is predicted and updated at time k, specifically: The Kalman filter method is used to predict the state of the jth target at time k in the i-th particle at time k-1: In the formula, represents the target state prediction result of the jth target at time k in the i-th particle at time k-1, F k-1 is the system state transfer matrix at time k-1, represents the covariance matrix of the jth target at time k-1 in the i-th particle, represents the covariance matrix prediction result of the jth target at time k in the i-th particle at time k-1, Q k-1 Represents the covariance matrix of the state transition process noise; The Kalman filter method is used to update the state of the jth target at time k in the i-th particle at time k-1: Among them, Η k is the system observation matrix at time k, represents the intermediate variable, R k represents the variance of the observation noise at time k, is the updated covariance of the ith particle at time k, express The inverse, is the Kalman gain of the ith particle at time k, z k represents the measurement collected at time k, represents the target state update result of the jth target at time k-1 in the i-th particle at time k, represents the updated covariance matrix of the jth target at time k in the i-th particle at time k-1, j = 1, 2, ..., J k-1 , J k-1 is the target number at time k-1 in the ith particle.

4. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 3, characterized in that: The specific process of step five is as follows: Step 5. Calculate the probability of each target existing at time k-1 disappearing at time k, and record the probability of the jth target existing at time k-1 disappearing at time k as Step 52: Calculate the prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) and the likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ); specifically: (1) When the measurement value collected at time k comes from the target newborn: Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is the target birth probability pb, that is, p(e k ,c k |e 1:k-1 ,c 1；k-1 )=p b =0.04; Likelihood Among them, m 0|0 is the initial state of the new target, P 0|0 is the initial covariance matrix of the new target; (2) When the measurement value collected at time k comes from clutter: Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is (1-p b )·p c , p c is the probability that the measured value is caused by noise; Likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ) is 1 / 360; (3) When the measurement value collected at time k comes from the jth target existing at time k-1: Prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 )for Likelihood Where I is the identity matrix; Step 53: Based on the prior transfer probability and likelihood probability calculated in step 52, calculate the posterior probability that the k-time measurement value comes from the target, the posterior probability that it comes from the clutter, and the posterior probability that it comes from each target existing at k-1 time; where: the posterior probability that the k-time measurement value comes from the target is simply recorded as The posterior probability that the measured value at time k comes from the clutter is simply written as The posterior probability that the k-time measurement value is derived from the j-th target existing at k-1 time is simply written as Step 54: Sampling is performed according to the extinction probability and the posterior probability, and the source of the measurement value at time k and the extinction of the target at time k are determined according to the sampling results; Step 55: Update the target data in the i-th particle at time k according to the source of the measurement value at time k, the target extinction status, and the prediction and update results of step 4.

5. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 4, characterized in that: The specific process of step 54 is as follows: Step 541: Calculate the probability p″ i,j+2 : Among them, j′≠j; Calculate the probability p″ i : Step 542: Calculate the probability Among them, j′≠j; Calculating Probability Step 543: Calculate the probability Among them, j′≠j; Calculate the probability p″′ i,j+2 : Step 544: Sample all the probabilities calculated in steps 541 to 543, and determine the source of the measurement value at time k and whether the target has disappeared based on the sampling results.

6. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 5, characterized in that: The specific process of step 55 is as follows: If it is determined that the measurement value collected at time k comes from the birth of a target and a target disappears, then the state prediction result of the jth target at time k-1 that has not disappeared is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle; If it is determined that the measurement value collected at time k comes from the new target and no target disappears, then the state prediction result of the jth target at time k-1 is Store it in the i-th particle at time k, and add the number of the new target and the initial state of the new target to the i-th particle; If it is determined that the measurement value collected at time k comes from clutter and a target disappears, then the state prediction result of the jth target at time k-1 that has not disappeared is Stored in the i-th particle at time k; If it is determined that the measurement value collected at time k comes from clutter and no target disappears, then the state prediction result of the jth target at time k-1 is Stored in the i-th particle at time k; If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and a target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 that have not disappeared are stored in the ith particle at time k; If it is determined that the measurement value collected at time k comes from a target j′ at time k-1 and no target disappears, then The state of target j′ at time k is stored in the ith particle, and the state prediction results of other targets at time k-1 are stored in the ith particle at time k.

7. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 6, characterized in that: The weight of each particle is updated according to the posterior probability of the target being born, the posterior probability of the clutter, the posterior probability of each target existing at time k-1, and the probability of each target existing at time k-1 disappearing at time k. The specific process is: Among them, p i ' ,m is the mth probability calculated in step 541 to step 543, m = 1, 2, ..., M, M represents the total number of probabilities calculated in step 541 to step 543, represents the weight of the i-th particle at time k after update, represents the weight of the i-th particle at time k-1.

8. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 7, characterized in that: The updated weights are normalized respectively to obtain the weight of each particle after normalization. The specific process is: in, Represents the weight of the i-th particle at time k after normalization.

9. The method for dividing target passive tracking trajectories based on azimuth-frequency according to claim 8, characterized in that: The effective number of particles at time k is calculated according to the weight of each particle after normalization, specifically: in, Indicates the number of effective particles.

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