An azimuth-frequency-based target passive tracking trajectory division method

Abstract

The application discloses a bearing-frequency-based target passive tracking trajectory division method, and belongs to the technical field of underwater multi-target tracking of passive sonar.The application aims to solve the problem of poor tracking effect of the existing method in the presence of target trajectory intersection scenes.The application introduces a frequency measurement value into a target state to obtain a bearing-frequency augmented state vector under the condition of passive tracking of a single observation platform in the presence of the underwater multi-target tracking trajectory intersection scenes.Bearing-frequency joint information can improve the discrimination degree of the solution of the posterior probability of the measurement value corresponding to the target, so that the correctness of batch division of the target in the trajectory intersection case is improved.Combining with an RB particle filter, a multi-hypothesis tracking technology and a Kalman smoothing filter technology, good target tracking effect is achieved, and the correctness of the tracking result is ensured.The method can be applied to the technical field of underwater multi-target tracking.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of underwater multi-target passive sonar tracking, and particularly relates to a target passive tracking trajectory division method based on bearing-frequency. BACKGROUND

[0002] The passive sonar system relies on capturing the noise signals continuously released by ships to realize target detection. In the traditional target passive tracking, the target positioning and tracking mainly rely on a single information source (such as pure bearing information). However, the pure bearing tracking is easily restricted by noise, interference and measurement errors, etc. Especially in the case of multiple targets and target trajectory intersection, the pure bearing tracking is difficult to distinguish the signals generated by different sound sources, leading to mutual interference between targets, and further affecting the accurate evaluation of the key information such as target state and number, and finally causing the error in target trajectory batch division and leading to tracking error.

[0003] With the continuous progress of sensor technology and signal processing technology, multi-dimensional information fusion technology has gradually become the research focus in the field of target detection and tracking. By fusing the bearing-frequency multi-dimensional information, more detailed target feature description can be provided, which significantly improves the performance of target detection and tracking, and effectively counteracts the interference. Combined with the fused target bearing-frequency information, a suitable tracking algorithm and data association algorithm are used to track the target in real time.

[0004] The underwater multi-target tracking algorithm focuses on the Kalman filter model supported by the Bayesian theory. According to the historical state of the target and the current observation data, the future state of the target is accurately predicted and updated, and the target path is obtained. Under the condition of linear state model and Gaussian white noise, the classical Kalman filter is the optimal filter; under the condition of nonlinear state model and non-Gaussian white noise, the extended Kalman filter is a suboptimal filter. However, in the case of unknown or variable number of targets, the tracking performance of both the classical Kalman filter and the extended Kalman filter is poor. In contrast, the particle filter can not only effectively reduce the Monte Carlo calculation amount, but also can track the unknown number of multi-targets under the condition of nonlinear state model and non-Gaussian white noise state noise.

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

[0006] 1. False alarm and missed detection exist in the detection process, and the measurement data contain a large amount of noise, making the corresponding relationship between the target and the observation unclear;

[0007] 2. The time points of target appearance and disappearance and the number of targets are unknown a priori.

[0008] To solve the above problems, scholars in various countries have explored various 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 multiple target birth and death, and the latter association method faces the problem of combinatorial explosion of calculation amount.

[0009] The Rao-Blackwellized Monte Carlo data association algorithm is based on the RB particle filter, and the joint multi-hypothesis tracking algorithm can realize batch division of targets while reducing the calculation amount. However, in the scene of target trajectory intersection, due to the similar state of each target, the Rao-Blackwellized Monte Carlo data association algorithm still cannot accurately divide the particles, resulting in incorrect judgment of target birth and death, batch division error, and algorithm failure. Limited by the lack of prior information, the tracking effect of the existing algorithm in dealing with the problem of target trajectory intersection is still not ideal, and various batch division errors are prone to occur. SUMMARY

[0010] The purpose of the present application is to solve the problem of poor tracking effect of the existing method in the scene of target trajectory intersection, and a bearing-frequency-based target passive tracking trajectory division method is proposed to improve the performance of underwater multi-target passive tracking in the scene of target trajectory intersection.

[0011] The technical scheme adopted by the present application to solve the above technical problems is: a bearing-frequency-based target passive tracking trajectory division method, which specifically comprises the following steps:

[0012] Step one, initialize a particle set containing N particles, initialize the weight of each particle in the particle set to 1 / N, and record the initialized weight of the i th particle as Initialize the particle set structure array S0, S0={S{1}0,S{2}0,...,S{N}0};

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

[0014] Step two, initialize the time k=1;

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

[0016] Step four, according to the measurement data collected at time k and the state of each target at time k-1 in the i th particle, the state of each target existing at time k-1 is predicted and updated;

[0017] Step five, calculate the probability of each target at k-1 time disappearing at k time, respectively, calculate the posterior probability of the measurement data collected at k time being derived from target birth, the posterior probability being derived from clutter, and the posterior probability being derived from each target existing at k-1 time;

[0018] According to the disappearance probability and the posterior probability, sampling is performed, and the source of the measurement value at k time and the disappearance of the target at k time are determined according to the sampling result;

[0019] According to the source of the measurement value at k time, the disappearance of the target at k time, and the prediction and update results of step four, the target data in the i th particle at k time is updated;

[0020] Step six, whether i=N is satisfied;

[0021] If satisfied, step seven is continuously executed;

[0022] If not satisfied, i is set as i+1, and step four is returned to be executed;

[0023] Step seven, the weight of each particle is updated according to the posterior probability of the measurement data collected at k time being derived from target birth, the posterior probability being derived from clutter, the posterior probability being derived from each target existing at k-1 time, and the probability of each target existing at k-1 time disappearing at k time, and the normalized weight of each particle after normalization processing is obtained;

[0024] The effective particle number at k time is calculated according to the normalized weight of each particle The effective particle number is compared with the size of threshold η;

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

[0026] If the effective particle number is greater than or equal to the threshold η, step eight is directly executed;

[0027] Step eight, whether the tracking process is ended is judged;

[0028] If the tracking process is ended, the normalized weight of each particle at the last time is compared, the particle corresponding to the maximum normalized weight at the last time is selected, the target data of the selected particle at each time is subjected to smoothing filtering processing, the target data after smoothing filtering processing is obtained, and the final target tracking trajectory is obtained;

[0029] If the tracking process is not ended, k is set as k+1, and step three is returned to be executed.

[0030] Further, the target state of the jth target at the k-1th moment in the ith particle is defined as

[0031]

[0032] wherein, denotes the position of the jth target at the k-1th moment in the ith particle, is the first derivative of , and the upper index T denotes transposition. denotes the frequency of the jth target at the k-1th moment in the ith particle, is the first derivative of , and the upper index T denotes transposition.

[0033] Further, the state of each target existing at the k-1th moment is predicted and updated at the kth moment, specifically:

[0034] The state of the jth target existing at the k-1th moment in the ith particle is predicted at the kth moment by using the Kalman filtering method:

[0035]

[0036] wherein, denotes the prediction result of the target state of the jth target at the kth moment at the k-1th moment in the ith particle, F k-1 is the system state transition matrix at the k-1th moment, denotes the covariance matrix of the jth target at the k-1th moment in the ith particle, denotes the prediction result of the covariance matrix of the jth target at the kth moment at the k-1th moment in the ith particle, Q k-1 denotes the covariance matrix of the state transition process noise;

[0037] The state of the jth target existing at the k-1th moment in the ith particle is updated at the kth moment by using the Kalman filtering method:

[0038]

[0039] wherein, H k is the system observation matrix at the kth moment, denotes an intermediate variable, R k denotes the variance of the observation noise at the kth moment, is the update covariance of the ith particle at the kth moment, denotes the inverse of , and the upper index T denotes transposition. is the Kalman gain of the ith particle at the kth moment, z k denotes the measurement collected at the kth moment,​ This represents the target state update result of the j-th target in the i-th particle at time k-1. This represents the update result of the covariance matrix of the j-th target at time k in the i-th particle at time k-1, where j = 1, 2, ..., J. k-1 J k-1 It is the number of targets in the i-th particle at time k-1.

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

[0041] Step 51: Calculate the probability that each target existing at time k-1 will disappear at time k. Let the probability that the j-th target existing at time k-1 will disappear at time k be denoted as...

[0042] Step 5.2: Calculate the prior transition probability p(e) respectively. k ,c k |e 1:k-1 ,c 1；k-1 ) and 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 Let p(e) be the target newborn probability pb, i.e., p(e) k ,c k |e 1:k-1 ,c 1；k-1 ) = p b =0.04;

[0045] Likelihood probability Where, m 00 This is the initial state of the new target, P. 00 It is the initial covariance matrix of the new target;

[0046] (2) When the measurement value collected at time k originates 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 pc the probability of the measurement value caused by noise;

[0048] the 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 k time is from the jth target existing at k-1 time:

[0050] the prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) is

[0051] the likelihood probability wherein I is a unit matrix;

[0052] Step five three, according to the prior transition probability and the likelihood probability calculated in step five two, the posterior probability of the measurement value at k time being from target birth, the posterior probability of the measurement value at k time being from clutter, and the posterior probability of the measurement value at k time being from each target existing at k-1 time are calculated respectively; wherein: the posterior probability of the measurement value at k time being from target birth is simply denoted as the posterior probability of the measurement value at k time being from clutter is simply denoted as the posterior probability of the measurement value at k time being from the jth target existing at k-1 time is simply denoted as

[0053] Step five four, sampling is performed according to the extinction probability and the posterior probability, and the source of the measurement value at k time and the extinction of the target at k time are determined according to the sampling result;

[0054] Step five five, target data in the ith particle at k time is updated according to the source of the measurement value at k time, the extinction of the target, and the prediction and updating result of step four.

[0055] Further, the specific process of step five four is as follows:

[0056] Step five four one, the probability p i ′,′ j+2 is calculated:

[0057]

[0058] wherein j'≠j;

[0059] the probability p i ″ is calculated:

[0060]

[0061] Step five four two, calculating the probability

[0062]

[0063] wherein j'≠j;

[0064] calculating the probability

[0065]

[0066] Step five four three, calculating the probability

[0067]

[0068] wherein j'≠j;

[0069] calculating the probability p i ′ , ″ j+2 :

[0070]

[0071] Step five four four, sampling all the probabilities calculated in step five four one to step five four three, and determining the source of the measurement value at time k and whether there is target extinction according to the sampling result.

[0072] Further, the specific process of step five five is as follows:

[0073] If it is determined that the measurement value collected at time k is from target birth and there is target extinction, the state prediction result of the jth target at time k-1 which has not been extinguished is stored in the ith particle at time k, and the number of the born target and the initial state of the born target are added in the ith particle; If it is determined that the measurement value collected at time k is from target birth and there is no target extinction, the state prediction result of the jth target at time k-1 is stored in the ith particle at time k, and the number of the born target and the initial state of the born target are added in the ith particle;

[0074] If it is determined that the measurement value collected at time k is from clutter and there is target extinction, the state prediction result of the jth target at time k-1 which has not been extinguished is stored in the ith particle at time k;

[0075] If it is determined that the measurement value collected at time k is from clutter and there is target extinction, the state prediction result of the jth target at time k-1 which has not been extinguished is stored in the ith particle at time k;

[0076] ​​If it is determined that the measurement value collected at the kth moment is derived from clutter and no target is eliminated, the state prediction result of the jth target at the (k-1)th moment is stored in the ith particle at the kth moment is stored in the ith particle at the kth moment;

[0077] If it is determined that the measurement value collected at the kth moment is derived from a certain target j' at the (k-1)th moment and a target is eliminated, the state of the target j' at the kth moment is stored in the ith particle, and the state prediction result of the other target at the (k-1)th moment which is not eliminated is stored in the ith particle at the kth moment; is stored in the ith particle at the kth moment;

[0078] If it is determined that the measurement value collected at the kth moment is derived from a certain target j' at the (k-1)th moment and no target is eliminated, the state of the target j' at the kth moment is stored in the ith particle, and the state prediction result of the other target at the (k-1)th moment is stored in the ith particle at the kth moment.

[0079] Further, the weight of each particle is updated according to the posterior probability that the measurement data collected at the kth moment is derived from target birth, the posterior probability that the measurement data is derived from clutter, the posterior probability that each target existing at the (k-1)th moment, and the probability that each target existing at the (k-1)th moment is eliminated at the kth moment. The specific process is as follows:

[0080]

[0081] wherein p i ′ ,m is the mth probability calculated in steps 541 to 543, m = 1, 2, …, M, M represents the total number of probabilities calculated in steps 541 to 543, represents the weight of the ith particle at the kth moment after updating, represents the weight of the ith particle at the (k-1)th moment.

[0082] Further, the updated weight is normalized to obtain the weight of each particle after normalization. The specific process is as follows:

[0083]

[0084] wherein, represents the weight of the ith particle at the kth moment after normalization.

[0085] Further, the number of effective particles at the kth moment is calculated according to the weight of each particle after normalization. The specific process is as follows:

[0086]

[0087] wherein, ​represents the effective particle number.

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

[0089] The present application is aimed at the scene of underwater multi-target tracking trajectory intersection, under the condition of passive tracking of 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 discriminability of the posterior probability solution of the measurement value corresponding to the target, so as to improve the correctness of batch division under the condition of trajectory intersection. Combined with the RB particle filter, multi-hypothesis tracking technology and Kalman smoothing filter technology, good target tracking effect is realized, and the correctness of the tracking result is ensured. Compared with the conventional multi-target tracking method, the present application method can still significantly reduce the batch division error under the condition of target trajectory intersection, and the tracking performance of the present application method is proved by experiments. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 The flow chart of the target passive tracking trajectory division method based on azimuth-frequency of the present application;

[0091] Figure 2 The batch division error condition a when the target trajectory intersects;

[0092] In the figure, the curves of other colors except the black line represent the tracking trajectories after smoothing;

[0093] Figure 3 The batch division error condition b when the target trajectory intersects;

[0094] In the figure, the curves of other colors except the black line represent the tracking trajectories after smoothing;

[0095] Figure 4 The measurement value and the real trajectory under the condition of target trajectory intersection;

[0096] Figure 5 The target tracking result of the algorithm of the present application under the condition of target trajectory intersection;

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

[0098] Figure 6 The target tracking result of the algorithm of the present application after smoothing under the condition of target trajectory intersection;

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

[0100] Figure 7 The target number estimation of the improved algorithm under the condition of target trajectory intersection and the actual number comparison diagram. Detailed Implementation

[0101] Specific implementation method one: Combining Figure 1 This embodiment describes a target passive tracking trajectory segmentation method based on azimuth-frequency. The method specifically includes the following steps:

[0102] Step 1: Initialize a particle set containing N particles. Initialize the weight of each particle in the set to 1 / N, and denote the initial weight of the i-th particle as . Initialize the particle set structure array S0, S0 = {S{1}0,S{2}0,...,S{N}0};

[0103] Where S{1}0 represents the target data in the first particle, the target data includes the target state and the target number corresponding to the target state (i.e., the orientation, orientation derivative, frequency and frequency derivative of each target number are included, and the target state and target number are stored together).

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

[0105] Step 3: Initialize the particle count i = 1;

[0106] Step 4: Based on the measurement data collected at time k and the states of each target in the i-th particle at time k-1, predict and update the states of each target existing at time k-1 at time k.

[0107] Step 5: Calculate the probability of each target disappearing at time k for each target at time k-1, and calculate the posterior probability of the measurement data collected at time k originating from the newly formed target, the posterior probability of originating from clutter, and the posterior probability of originating from each target existing at time k-1.

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

[0109] Then, based on the source of the measurement value at time k, the disappearance of the target at time k, and the prediction and update results of step four, the target data in the i-th particle at time k is updated.

[0110] Step 6: Does i = N satisfy the condition?

[0111] If satisfied, proceed to step seven;

[0112] If the condition is not met, then let i = i + 1 and return to step four.

[0113] Step seven, according to the posterior probability of the target new generation, the posterior probability of the clutter, the posterior probability of each target existing at k-1 time and the probability of each target existing at k-1 time disappearing at k time, the weight of each particle is updated respectively, and the updated weight is normalized respectively to obtain the weight of each particle after normalization;

[0114] The effective particle number at k time is calculated according to the weight of each particle after normalization And compare the effective particle number With the size of threshold η;

[0115] If the effective particle number Is less than the threshold η, the particles are resampled, and then step eight is executed;

[0116] If the effective particle number Is greater than or equal to the threshold η, step eight is directly executed;

[0117] Step eight, judge whether the tracking process is ended (i.e. whether there is new measurement collected) or not;

[0118] If the tracking process is ended, the normalized weight of each particle at the last time is compared, the particle corresponding to the maximum normalized weight at the last time is selected, the target data of the selected particle at each time is subjected to Kalman smoothing filter processing, and the target data after smoothing filter processing is obtained, i.e. the final target tracking trajectory is obtained;

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

[0120] The target data of each particle at each time is added to the set SS:

[0121]

[0122] The maximum weight at the last time after normalization is obtained by comparison, and the particle i' corresponding to the maximum weight is obtained, the target data of the particle i' at each time is subjected to smoothing filter processing, and the target data of the particle i' at each time after smoothing filter processing is recorded as S'{i'}1, S'{i'}2, …, S'{i'} k For any target in the tracking process, the tracking trajectory of the target is obtained according to the state data of the target in S'{i'}1, S'{i'}2, …, S'{i'} k

[0123] The method of the application can be realized by using a small amount of particles (the number of particles is set to 10 in the application), which avoids the "dimension disaster" problem of calculation amount.​

[0124] Specific implementation two: the difference between this embodiment and specific implementation one is that in the ith particle, the target state of the jth target at k-1 moment is defined as:

[0125]

[0126] wherein, denotes the orientation of the jth target at k-1 moment in the ith particle, is the first derivative of , and denotes the frequency of the jth target at k-1 moment in the ith particle, is the first derivative of , and the upper index T represents transposition.

[0127] The other steps and parameters are the same as those in specific implementation one.

[0128] This embodiment extends the traditional pure-orientation target state vector to an orientation-frequency augmented state vector. The continuous-time state equation of target motion is:

[0129]

[0130] wherein, t represents time, θ(t) represents the target orientation at t, is the first derivative of θ(t), f(t) represents the target frequency at t, is the first derivative of f(t), and w(t) represents the state process noise at t;

[0131] The discrete-time state equation obtained according to the continuous-time state equation of target motion is:

[0132]

[0133] In the formula, θ k-1 denotes the orientation of the target at k-1 moment, is the first derivative of θ k-1 , f k-1 denotes the frequency of the target at k-1 moment, is the first derivative of f k-1 , F k-1 is the system state transition matrix at k-1 moment (the system state transition matrix at each moment is ), w k-1 is the state process noise at k-1 moment, wk-1 ~ N(0, Qk-1), Q k-1 denotes the covariance matrix of the state transition process noise w k-1 (the covariance matrix at each moment is the same), and Qk-1 is Gaussian white noise with mean 0 and variance q, dt represents the sampling period (i.e. the time interval of data collection, in simulation, dt = 0.1 s, which means that the real state of the target is sampled once every 0.1 s), the covariance matrix Q k-1 is:

[0134]

[0135] The measurement equation z k is 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, which is obtained by initialization), v k-1 is the observation noise at time k-1 (the observation noise at each time is the same, which is obtained by initialization), v k-1 ~ N(0, R k-1 ).

[0138] Specific implementation three: the difference between this embodiment and specific implementation one or two is that the state of each target existing at time k-1 at time k is predicted and updated, specifically:

[0139] The state of the jth target existing at time k-1 in the ith particle at time k is predicted by using the Kalman filtering method:

[0140]

[0141] wherein, represents the target state prediction result of the jth target at time k-1 in the ith particle at time k, F k-1 is the system state transition matrix at time k-1, represents the covariance matrix of the jth target at time k-1 in the ith particle (the covariance matrix is obtained by initialization), represents the covariance matrix prediction result of the jth target at time k-1 in the ith particle at time k, Q k-1 represents the covariance matrix of the state transition process noise;

[0142] The state of the jth target existing at time k-1 in the ith particle at time k is updated by using the Kalman filtering method:

[0143]

[0144] wherein, H k is the system observation matrix at time k, denotes the intermediate variable, R k denotes the variance of the observation noise at time k, is the update covariance of the i-th particle at time k, denotes the inverse of is the Kalman gain of the i-th particle at time k, z k denotes the measurement collected at time k, denotes the target state update result of the j-th target at time k in the i-th particle at time k-1, denotes the covariance matrix update result of the j-th target at time k in the i-th particle at time k-1, j = 1, 2, …, J k-1 , J k-1 is the number of targets at time k-1 in the i-th particle.

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

[0146] The fourth embodiment is different from any one of the first to third embodiments in that the specific process of the step five is as follows:

[0147] The death and birth of the targets exist independently, and according to the Markov characteristics of the three indexes, it is known that:

[0148]

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

[0150] Step five one, the probability of death of each target existing at time k-1 at time k is calculated respectively, and the probability of death of the j-th target existing at time k-1 at time k is denoted as

[0151] If the lifetime probability distribution of the target is known, the death probability of the target can be calculated, for example, it is assumed that the lifetime of the target satisfies the gamma distribution, and then the death probability of the target under the gamma distribution can be obtained, that is, it is assumed that the last time when the j-th target is associated with the measurement value is t last,j , and at time k-1, it is not determined to die (the target still exists), then at time k, the probability of death of the j-th target 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 five, respectively calculate prior transition probability p(e k ,c k |e 1:k-1 ,c 1；k-1 ) and likelihood probability p(z k |e k ,c k ,z 1:k ,e 1；k-1 ,c 1；k-1 ), specifically:

[0154] The measurement value is derived from the target new generation as a hypothetical case, the measurement value is derived from each target at k-1 moment as a hypothetical case, and the measurement value is derived from clutter as a hypothetical case, a total of M hypothetical cases;

[0155] (1) When the measurement value collected at k moment is derived from target new generation:

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

[0157] Likelihood probability Where 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 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 filtering update process of the new target initial state;

[0159] (2) When the measurement value collected at k moment is derived 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 of the measurement value caused by noise;

[0161] The clutter is uniformly 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 ) of the measurement value and the clutter is 1 / 360;

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

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

[0164] Likelihood probability where I is a unit matrix;

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

[0166]

[0167] where p(e k ,c k |z 1:k ,e 1:k-1 ,c 1:k-1 ) represents the posterior probability of the measurement value at the k time, 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 a data association index, and the data association index represents the measurement association under the current hypothesis. If the current hypothesis is that the measurement value is from target birth, c k represents that the measurement is associated with target birth; the target visibility indicator e k ={d k ,b k}, d k and b krespectively indicate the birth and death of the target at time k;

[0169] Step five three, according to the prior transition probability and the likelihood probability calculated in step five two, calculate the posterior probability of the measurement value at time k being from target birth, the posterior probability of the measurement value at time k being from clutter, and the posterior probability of the measurement value at time k being from each target existing at time k-1 respectively; wherein: the posterior probability of the measurement value at time k being from target birth is denoted as the posterior probability of the measurement value at time k being from clutter is denoted as the posterior probability of the measurement value at time k being from the jth target existing at time k-1 is denoted as

[0170] Step five four, sample according to the death probability and the posterior probability, and determine the source of the measurement value at time k and the death of the target at time k according to the sampling result;

[0171] Step five five, update the target data in the ith particle at time k according to the source of the measurement value at time k, the death of the target, and the prediction and update result of step four.

[0172] The other steps and parameters are the same as one of the first to third embodiments.

[0173] Perform the process of the embodiment on the N particles in the particle set respectively, and N updated new particles at the current time S k = {S{1} k ,S{2} k ,...S{N} k} are obtained.

[0174] The fifth embodiment is different from one of the first to fourth embodiments in that the specific process of step five four is as follows:

[0175] Step five four one, calculate the probability p i ′ , ′ j+2 :

[0176]

[0177] Wherein, j'≠j;

[0178] Calculate the probability p i ″:

[0179]

[0180] Step five four two, calculate the probability

[0181]

[0182] Where, j′≠j;

[0183] Calculate probability

[0184]

[0185] Step 543: Calculate the probability

[0186]

[0187] Where, j′≠j;

[0188] Calculate 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). Based on the sampling results, determine the source of the measurement value at time k (by sampling, a value can be sampled from all probabilities; the larger the value, the greater the probability of it being sampled. Based on the sampled value, determine whether the measurement value at time k originates from a newly formed target, clutter, or a target existing at time k-1) and whether a target has disappeared (i.e., if the sampled value is obtained by multiplying the posterior probability that the measurement value originates from a newly formed target by the probability that the second target has disappeared, then the measurement value originates from a newly formed target and the second target has disappeared; if the sampled value is the posterior probability that the measurement value originates from a newly formed target, then the measurement value originates from a newly formed target and no target has disappeared).

[0191] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0192] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One through Five in that the specific process of step five is as follows:

[0193] If it is determined that the measurement value collected at time k originates from the emergence of new targets and the disappearance of some targets, then the state prediction result of the j-th target at time k-1 that has not disappeared will be used. Store the target 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 has been determined to be eliminated.

[0194] If it is determined that the measurement value collected at time k originates from the emergence of new targets and no targets have disappeared, then the state prediction result of the j-th target at time k-1 is... The number of the new target and the initial state of the new target are stored in the ith particle at the kth moment, and are added in the ith particle;

[0195] If it is determined that the measurement value collected at the kth moment is from clutter and there is target extinction, the state prediction result of the jth target at the k-1th moment which has not been extinguished is stored in the ith particle at the kth moment; The number of the new target and the initial state of the new target are stored in the ith particle at the kth moment, and are added in the ith particle;

[0196] If it is determined that the measurement value collected at the kth moment is from clutter and there is target extinction, the state prediction result of the jth target at the k-1th moment which has not been extinguished is stored in the ith particle at the kth moment; The number of the new target and the initial state of the new target are stored in the ith particle at the kth moment, and are added in the ith particle;

[0197] If it is determined that the measurement value collected at the kth moment is from clutter and there is target extinction, the state prediction result of the jth target at the k-1th moment which has not been extinguished is stored in the ith particle at the kth moment; The number of the new target and the initial state of the new target are stored in the ith particle at the kth moment, and are added in the ith particle;

[0198] If it is determined that the measurement value collected at the kth moment is from clutter and there is target extinction, the state prediction result of the jth target at the k-1th moment which has not been extinguished is stored in the ith particle at the kth moment; The number of the new target and the initial state of the new target are stored in the ith particle at the kth moment, and are added in the ith particle;

[0199] The other steps and parameters are the same as one of the first to fifth embodiments.

[0200] The seventh embodiment is different from one of the first to sixth embodiments in that the weight of each particle is updated according to the posterior probability of the measurement data collected at the kth moment, the posterior probability of clutter, the posterior probability of each target existing at the k-1th moment, and the probability of each target existing at the k-1th moment being extinguished at the kth moment.

[0201]

[0202] Wherein, p i ′ ,m is the form of the mth probability calculated in steps 54-1 to 54-3 (i.e. each probability calculated in steps 54-1 to 54-3 is simply denoted as p i ′ ,m ), m = 1, 2, …, M, M represents the total number of probabilities calculated in steps 54-1 to 54-3, wi(k) represents the weight value of the i th particle at the k th moment after updating, wi(k-1) represents the weight value of the i th particle at the k-1 th moment.

[0203] The other steps and parameters are the same as one of the first to sixth embodiments.

[0204] The prior transition probability and the likelihood probability correspond to each hypothesis, and therefore, the weight value of the particle can be updated in combination with the prior transition probability and the likelihood probability of all M groups of hypotheses.

[0205] The eighth embodiment is different from one of the first to seventh embodiments in that the updated weight value is normalized to obtain the weight value of each particle after normalization, and the specific process is as follows:

[0206]

[0207] wi(k) represents the weight value of the i th particle at the k th moment after normalization. wi(k) represents the weight value of the i th particle at the k th moment after normalization.

[0208] The other steps and parameters are the same as one of the first to seventh embodiments.

[0209] The ninth embodiment is different from one of the first to eighth embodiments in that the effective particle number at the k th moment is calculated according to the weight value of each particle after normalization, and the specific process is as follows:

[0210]

[0211] wi(k) represents the weight value of the i th particle at the k th moment after normalization. wi(k) represents the weight value of the i th particle at the k th moment after normalization.

[0212] The other steps and parameters are the same as one of the first to eighth embodiments.

[0213] Experimental part

[0214] Figure 2 and Figure 3 Two cases of batch division error when the target trajectory intersects, Figure 4 The measured value and the real trajectory graph in the case of target trajectory intersection, Figure 5 The target tracking result of the algorithm of the application in the case of target trajectory intersection, Figure 6 The target tracking result of the algorithm of the application in the case of target trajectory intersection, Figure 7 The target tracking result of the algorithm of the application in the case of target trajectory intersection,

[0215] The above calculation examples of the present application are only used to illustrate the calculation model and calculation process of the present application, and are not used to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and all the embodiments cannot be exhausted here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A target passive tracking trajectory segmentation method based on azimuth-frequency, characterized in that, The method specifically includes the following steps: Step 1: Initialize a container A particle set of particles, where the weight of each particle in the set is initialized to 0. and will the The initial weights of each particle are denoted as: Initialize the particle set structure array , ; in, This represents the target data in the first particle, which includes the target state and the target number corresponding to the target state. Step 2: Initialization ; Step 3: Initialize particle count ; Step 4, according to Measurement data collected at each moment and the first Among the particles At any given time, the state of each target is... Various goals that exist at all times Predict and update the state at any given moment; No. Among the particles, The first moment The target state of each objective Defined as: (1) in, Indicates the first Among the particles The first moment The location of the target. yes The first derivative, Indicates the first Among the particles The first moment The frequency of each target yes The first derivative of , where the superscript T indicates the transpose; Step 5: Calculate separately Every goal at any moment The probability of extinction at each moment is calculated separately. The measurement data collected at any given time comes from the posterior probability of the target's newborn, the posterior probability of clutter, and the posterior probability of... The posterior probability of each target existing at any given time; Sampling is performed based on the extinction probability and the posterior probability, and the results are used to determine... The source and target of time measurement values The disappearance of time; Then according to Source of time measurement values The status of the target's disappearance at any given moment, along with the prediction and update results from step four, are used to update... Time of the first Target data in each particle; Step Six: Is it satisfied? ; If satisfied, proceed to step seven; If not satisfied, then let Return to step four; Step 7, according to The measurement data collected at any given time comes from the posterior probability of the target's newborn, the posterior probability of clutter, and the posterior probability of... The posterior probability of each target existing at any given time and Every goal that exists at all times The probability of extinction at any given time is used to update the weight of each particle, and the updated weights are then normalized to obtain the normalized weight of each particle. Calculate based on the weights of each particle after normalization. Effective particle count at time 1 And compare the number of effective particles. With threshold Size; If the number of effective particles Less than the threshold If so, the particles are resampled before proceeding to step eight; If the number of effective particles Greater than or equal to the threshold If so, proceed directly to step eight; Step 8: Determine if the tracking process has ended; If the tracking process ends, compare the normalized weights of each particle at the last moment, select the particle with the maximum normalized weight at the last moment, and perform smoothing filtering on the target data of the selected particle at each moment to obtain the smoothed target data, which is the final target tracking trajectory. If the tracking process is not finished, then let Return to step three.

2. The target passive tracking trajectory division method based on azimuth-frequency as described in claim 1, characterized in that, The pair Various goals that exist at all times The state at any given time is predicted and updated, specifically as follows: Using the Kalman filter method to analyze the first Among the particles, The first moment that exists at all times One goal is Predicting the state at any given time: (6) In the formula, Indicates the first Among the particles The first moment One goal is The target state prediction result at time 10:

00. for The system state transition matrix at time t. Indicates the first Among the particles The first moment The covariance matrix of each objective. Indicates the first Among the particles The first moment One goal is The predicted results of the covariance matrix at time t. The covariance matrix representing the noise during the state transition process; Using the Kalman filter method to analyze the first Among the particles, The first moment that exists at all times One goal is The status is updated in real time: (7) in, for Time-based system observation matrix Indicates intermediate variables. express Observe the variance of the noise at all times. For the first Individual particles The updated covariance at each moment, express The reverse, For the first Individual particles Kalman gain at time step express Measurements collected at all times Indicates the first Among the particles The first moment One goal is The result of updating the target state at any given time. Indicates the first Among the particles The first moment One goal is The result of updating the covariance matrix at time step [time]. , It is the first Among the particles The number of targets at any given time.

3. The target passive tracking trajectory division method based on azimuth-frequency as described in claim 2, characterized in that, The specific process of step five is as follows: Step 51: Calculate separately Every goal that exists at all times The probability of instantaneous extinction will The first moment that exists at all times One goal is The probability of extinction at any given time is denoted as . , ; Step 52: Calculate the prior transition probabilities separately. and likelihood probability Specifically: (1) When The measurements collected at each moment are derived from the target's neonatal time: Prior transition probability Target newborn probability ,Right now ; Likelihood probability ,in, This is the initial state of the new goal. It is the initial covariance matrix of the new target; (2) When The measurements collected at each moment are derived from clutter time: Prior transition probability for , The probability that the measured value is caused by noise; Likelihood probability for ; (3) When The measurements collected at any time come from The first moment that exists at all times When there are multiple goals: Prior transition probability for ; Likelihood probability ,in, It is the identity matrix; Step 53: Based on the prior transition probability and likelihood probability calculated in Step 52, calculate the following respectively: The time-based measurements are derived from the posterior probability of target emergence, the posterior probability from clutter, and the posterior probability from... The posterior probability of each target existing at any given time; where: The time-based measurement value is derived from the posterior probability of the target newborn, which is abbreviated as: ,Will The posterior probability of a time measurement originating from clutter is abbreviated as: ,Will Time measurement values ​​come from The posterior probability of the j-th target existing at time j is denoted as: ; Step 54: Sampling is performed based on the extinction probability and posterior probability, and the results are used to determine... The source and target of time measurement values The disappearance of time; Step 55, according to The source of the time measurement value, the target's disappearance status, and the prediction and update results from step four are used to update the data. Time of the first Target data in each particle.

4. The target passive tracking trajectory division method based on azimuth-frequency according to claim 3, characterized in that, The specific process of step five-four is as follows: Step 541: Calculate the probability : (11) in, ; Calculate probability : (12) Step 542: Calculate the probability : (13) in, ; Calculate probability : (14) Step 543: Calculate the probability : (15) in, ; Calculate probability : (16) Step 544: Sample all the probabilities calculated in Steps 541 to 543, and determine the probability based on the sampling results. The source of the time measurement and whether the target has disappeared.

5. The target passive tracking trajectory segmentation method based on azimuth-frequency according to claim 4, characterized in that, The specific process of step 55 is as follows: If determined The constantly collected measurement values ​​originate from both target creation and target destruction; therefore, the values ​​of those that have not been destroyed will be... Time of the first State prediction results for each target exist The first moment Stored in the particle, and in the ... Add the target number and initial state of the new target to each particle; If determined If the collected measurements are from target creation and no target destruction, then... Time of the first State prediction results for each target exist The first moment Stored in the particle, and in the ... Add the target number and initial state of the new target to each particle; If determined If the collected measurements originate from clutter and some targets disappear, then the remaining targets will be... Time of the first State prediction results for each target exist The first moment Stored in individual particles; If determined If the measurements collected at any given time originate from clutter and no target disappears, then... Time of the first State prediction results for each target exist The first moment Stored in individual particles; If determined The measurements collected at any time come from A certain goal at a certain moment And if a target is eliminated, then... In the Stored in each particle as Momentary Goal The state, and the undying The state prediction results of other targets at time 1 The first moment Stored in individual particles; If determined The measurements collected at any time come from A certain goal at a certain moment And if no target is eliminated, then... In the Stored in each particle as Momentary Goal The state, and The state prediction results of other targets at time 1 The first moment Stored in individual particles.

6. The target passive tracking trajectory segmentation method based on azimuth-frequency according to claim 5, characterized in that, According to The measurement data collected at any given time comes from the posterior probability of the target's newborn, the posterior probability of clutter, and the posterior probability of... The posterior probability of each target existing at any given time and Every goal that exists at all times The probability of extinction at any given time is used to update the weights of each particle; the specific process is as follows: (17) in, It is the first one calculated in steps 541 to 543. A probability, , This represents the total number of probabilities calculated in steps 541 to 543. Indicates the updated number Individual particles Weights at time points Indicates the first Individual particles The weight of time.

7. The target passive tracking trajectory division method based on azimuth-frequency according to claim 6, characterized in that, The updated weights are then normalized to obtain the normalized weights for each particle; the specific process is as follows: (18) in, Indicates the number of digits after normalization. Individual particles The weight of time.

8. The target passive tracking trajectory division method based on azimuth-frequency according to claim 7, characterized in that, The calculation is based on the weights of each particle after normalization. The effective number of particles at time t is as follows: (19) in, This indicates the number of effective particles.

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