An adaptive track initiation method based on GLMB

Abstract

The present invention belongs to the technical field of multi-target tracking, and specifically relates to an adaptive track initiation method based on GLMB. The present invention traverses all possible tracks based on measurement data at two consecutive moments, and preliminarily screens the measurement data to remove most clutter using speed screening rules and Doppler information screening rules. The target measurement probability is calculated based on the posterior probability to distinguish the measurement source. The target measurement probability can be used to distinguish whether the measurement originates from a new target or a surviving target. The speed information implicit in the Doppler measurement is used to calculate the initial operating state of the new target and enter the next prediction process, thereby completing the track initiation function.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-target tracking, and in particular relates to an adaptive track initiation method based on GLMB (Generalized Labeled Multi-Bernoulli). Background Art

[0002] After decades of development, multi-target tracking (MTT) technology has formed two sets of algorithm systems. One is the traditional MTT algorithm, which decomposes the multi-target tracking problem into multiple single-target tracking problems through the data association (DA) algorithm. Due to the combinatorial explosion characteristic of the DA algorithm, as the number of targets increases, the matching combinations required to be enumerated will increase exponentially, making the algorithm lose real-time performance; the other is a multi-target tracking algorithm based on random finite modeling. By modeling multi-target states and multi-target measurements as random finite sets (RFS), it can naturally describe the mechanisms such as track start and termination, and can completely avoid the measurement-track association process. Due to the systematic and scientific nature of the RFS theory, it has attracted widespread attention and research from scholars.

[0003] In multi-target tracking, measurement is the only source of information. However, in RFS-based MTT algorithms, the density of new targets is generally determined by prior information. New targets are typically located at a few locations, and their transfer parameters are also determined by prior information. In real-world detection scenarios, the required prior information for new targets is unknown, and they may appear anywhere within the detection area. Standard GLMB filters cannot correctly initiate tracks in such situations.

[0004] To solve the above problems, the present invention proposes a track adaptive initiation algorithm suitable for GLMB filter, which can complete the track initiation process based only on measurement information when the position of the new target is uncertain. Summary of the Invention

[0005] In order to overcome the problems in the prior art, the present invention proposes an adaptive track initiation method based on GLMB.

[0006] The technical solution of the present invention to solve the above technical problems is as follows:

[0007] The present invention provides a GLMB-based adaptive track initiation method, comprising the following steps:

[0008] Convert the polar coordinate system measurement data received by the radar into the rectangular coordinate system measurement data;

[0009] According to the prior information, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density;

[0010] Filter out clutter in the measurement data through velocity screening rules and Doppler information screening rules;

[0011] Adopting the sequential filtering method to update the multi-target posterior probability density;

[0012] The probability of target measurement is calculated through the posterior probability density in the updating process, and the surviving targets and new targets are distinguished by the probability of target measurement. The measurements related to the new targets are retained for the new trajectory at the next moment.

[0013] Furthermore, based on the prior information, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density, which specifically includes the following steps:

[0014] According to the new component calculated at the previous moment, the single target density of the new target is calculated;

[0015] According to the posterior information transmitted at the previous moment, the single target density of the surviving target is calculated;

[0016] The single target density of the new target and the single target density of the surviving target are connected in parallel to obtain the multi-target prediction probability density.

[0017] Furthermore, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density, which also includes: and calculating the initial operating state of the new target based on the speed information hidden in the Doppler information.

[0018] Furthermore, the multi-target posterior probability density is:

[0019]

[0020] Where, represents the mean, variance, and weight of the missing measurement; represents the mean, variance, and weight of the position measurement; θ(l) represents the track association mapping with label l; δ(θ(l)) is the De Kotta function. When θ(l) = 0, δ(θ(l)) = 1, indicating that the measurement and track are not associated, indicating that the track has been missed; conversely, when θ(l) ≠ 0, δ(θ(l)) = 0, indicating that the track and measurement information have been updated, indicating that the track is normal.

[0021] Furthermore, the probability ρ(z) of the target measurement is:

[0022]

[0023] in, Denotes the k-time measurement set Z k The probability of association between the surviving target i and the measurement, otherwise, 1-p i Denotes the k-time measurement set Z k The association probability of the new target and the clutter in p D,k is the sensor detection probability; z k is the measurement point at time k, represents the Gaussian density with mean m and variance P, H k is the observation matrix, R is the position measurement noise covariance, and h(·) is defined as follows:

[0024]

[0025] In the above formula, (x, y) represents the target position, (x s ,y s ) indicates the sensor position.

[0026] Compared with the prior art, the present invention has the following technical effects:

[0027] The present invention traverses all possible tracks based on measurement data from two consecutive moments, and performs preliminary screening of the measurement data to remove most clutter using speed screening rules and Doppler information screening rules. The target measurement probability is calculated based on the posterior probability to distinguish the measurement source. The target measurement probability can be used to distinguish whether the measurement originates from a new target or a surviving target. The speed information implicit in the Doppler measurement is used to calculate the initial operating state of the new target and enter the next prediction process, completing the track initiation function. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions and advantages of the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0029] Figure 1 This is a flowchart of the adaptive track initiation GLMB algorithm of the present invention;

[0030] Figure 2 The actual motion trajectory diagram of the invented target;

[0031] Figure 3 A schematic diagram of the invented sensor measurement;

[0032] Figure 4 GLMB tracking effect diagram for inventing track adaptive initiation;

[0033] Figure 5 To invent the GLMB tracking effect diagram;

[0034] Figure 6 Schematic diagram of OSPA distance of the present invention. DETAILED DESCRIPTION

[0035] To further illustrate the technical means and effects employed by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, describes in detail the specific implementations, structures, features, and effects of the technical solutions proposed by the present invention. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable manner. Unless otherwise defined, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention pertains.

[0036] Reference Figures 1-6 In order to solve the problems existing in the prior art, the present invention proposes an adaptive track initiation method based on GLMB, which only requires the measurement information of the previous moment to estimate the motion state of the target and incorporates it into the prediction process of the filtering algorithm. In addition, the unreasonable new components are removed during the branch pruning process, which can effectively reduce the probability of false short tracks and improve the tracker performance.

[0037] A GLMB-based adaptive track initiation method specifically includes the following steps:

[0038] Step 1. Convert the radar measurement data into coordinates.

[0039] The polar coordinate measurement data of the radar is [r z ,θ z ],r z is the distance measured in polar coordinates, θ z is the azimuth angle in polar coordinates; the measured distance r z =r+v r , the azimuth angle is θ z =θ+v θ , where r represents the actual distance between the sensor and the tracked target, v r represents the distance noise, θ represents the true azimuth, v θ represents angular noise.

[0040] The classic measurement conversion is:

[0041]

[0042] Among them, x z Represents the x-axis coordinate of the converted rectangular coordinate system; y z Represents the transformed y-axis coordinate.

[0043] Due to the presence of noise, an erroneous estimation result will be given after nonlinear transformation. The precise compensation procedure of these errors depends on the angle noise v θ , assuming the angle noise v θ It can be explained by using a symmetric probability density function. Since the symmetric probability density function of angle noise is symmetric, we can get the expectation:

[0044] E(sin v θ )=0

[0045] E represents expectation, the Sin function is an odd function, and the theorem states that the expected value of an odd function with a probability density is 0. This formula describes the above theorem.

[0046] Through the expectation of the above formula, we can get:

[0047]

[0048] Among them, ε θ is the azimuth compensation factor, when ε θ ≠1, the expectation is biased, when ε θ ≠0 can give an unbiased transformation:

[0049]

[0050] Among them, x m Represents the x-axis coordinate in the rectangular coordinate system, y m Represents the y-axis coordinate in the rectangular coordinate system.

[0051] The position component covariance corresponding to the measurement point is as follows:

[0052]

[0053] Rm is the covariance of the position component. Rm is a 2*2 matrix. In order to conveniently represent the calculation process of these four position values, the specific parameters are as follows:

[0054]

[0055] Among them, the compensation factor ε θ =E(cosv θ ), ε′ θ =E(cos2v θ ).

[0056] Step 2. Based on the prior information, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density.

[0057] Since the value of the new component is calculated from the measurement value at the previous moment, the new component cannot be directly connected in parallel with the surviving component, and additional state prediction of the new component is required.

[0058] The multi-target prediction probability density is obtained based on prior information:

[0059]

[0060]

[0061]

[0062] Where X represents the set of target states, and Δ(X) represents the label difference indicator, which is defined as

[0063] That is, when the labels of the elements in the set X are different, Δ(X) = 1; otherwise, Δ(X) = 0. δ(·) represents the Dirac delta function, which is defined as: L(X + ) represents the label projection function, Indicates survival tag The weight of Indicates a new label The weight of . and p +，B (·, l) represent the density of surviving targets and the density of new targets respectively. For a given label set L, p S represents the survival probability of the target at the next moment.

[0064] Among them, the single target density of the surviving target is:

[0065]

[0066] in,

[0067]

[0068]

[0069]

[0070] In the above formula, represents the Gaussian density with mean m and variance P, is the Gaussian component weight of the surviving target; F is the state transfer matrix, Q is the covariance of the noise; is the scaling factor.

[0071] The single target density of the new target is:

[0072]

[0073]

[0074]

[0075]

[0076] In the above formula, represents the Gaussian density with mean m and variance P, is the Gaussian component weight of the new target. F is the state transfer matrix, Q is the covariance of the noise; Assign existence probabilities to new targets.

[0077] The motion state of the new target needs to be estimated using the new target parameters calculated in step 3 at the previous moment.

[0078] Step 3. Filter out the clutter in the measurement data of two consecutive moments using the velocity screening rule and the Doppler information screening rule; and calculate the initial operating state of the new target based on the velocity information hidden in the Doppler information.

[0079] Assume that the target estimated state at time k is m is the target estimated state mean, and the measurement set at the corresponding moment is Z k ={Y k ,D k}, where the position measurement set Doppler measurement collection Represents the Doppler measurement. Since the position measurement set is in polar coordinate form, it needs to be converted into rectangular coordinates, and and are the radial distance and azimuth measured by the radar, and They are the x-axis and y-axis coordinates after coordinate conversion.

[0080] Here we take one measurement value from each of the conversion measurement sets at two consecutive moments k-1 and k Velocity information and Doppler information are used to filter the measurements. The filtering rules are as follows:

[0081] The speed information filtering rules are:

[0082]

[0083] The Doppler information filtering rules are:

[0084]

[0085] Where ||·||2 represents the 2-norm of the vector, Δt represents the time interval between moments k-1 and k, v1 and v2 represent the minimum and maximum speeds of the detected target, respectively; σ d is the measurement noise of the Doppler information.

[0086] The motion speed during the Doppler information screening process can be calculated by the following formula:

[0087]

[0088]

[0089] After measurement and screening, the state vector and covariance of the new trajectory at time k are calculated through the subsequent algorithm. The calculation process is as follows:

[0090] The mean required for the new target and covariance They are:

[0091]

[0092]

[0093] The position component of the mean is directly measured as:

[0094]

[0095] The corresponding position component covariance is:

[0096]

[0097] The velocity component of the mean is The corresponding covariance is:

[0098]

[0099] The Doppler measurement equation is:

[0100]

[0101] By observation, the above formula can be reconstructed as:

[0102]

[0103] in,

[0104]

[0105] In the above formula, n d,k represents the Doppler observation noise,

[0106] Velocity component estimation using linear minimum mean square error criterion and velocity component covariance You can get:

[0107]

[0108] The velocity component covariance is:

[0109]

[0110] in, is the location of the Doppler radar.

[0111] The required weights of the new components at the prediction step are set as:

[0112] Step 4: Introduce Doppler measurement and use sequential filtering to update the posterior probability density.

[0113] Since Doppler radar has unique Doppler measurement (radial velocity) compared to conventional radar measurement data, a sequential filtering approach is used to introduce Doppler measurement into the δ-GLMB update process.

[0114] The specific implementation steps are as follows:

[0115] The updated posterior probability density of δ-GLMB is:

[0116]

[0117]

[0118] Where θ(l) represents the track association mapping with label l; δ(θ(l)) is the De Kotta function, which is used to distinguish between missed detection targets and normal detections. When θ(l) = 0, δ(θ(l)) = 1, indicating that the measurement and track are not associated, indicating that the track has been missed. Conversely, when θ(l) ≠ 0, δ(θ(l)) = 0, indicating that the track and measurement information have been updated, indicating that the track is normal. represents the Gaussian density with mean m and variance P, is the Gaussian component weight of the target, l represents the label information corresponding to the component, Indicates the measurement point corresponding to the component.

[0119] Update the branch weight to:

[0120]

[0121] The single target normalization constant is:

[0122]

[0123] When θ(l)=0, the track is missed and the measurement is lost. The parameters of are given by the following formula:

[0124]

[0125]

[0126]

[0127] When θ(l)≠0, position measurement The parameters are obtained by processing the position measurement and Doppler measurement as follows:

[0128] First, use position measurement to update the status:

[0129]

[0130]

[0131]

[0132]

[0133] Among them, H c represents the target observation matrix, represents the likelihood function, p D is the detection probability of the radar, K yp and S yp They represent the gain and innovation covariance of position measurement respectively, and the corresponding calculation process is as follows:

[0134]

[0135]

[0136] Compared with traditional filters, in order to effectively utilize Doppler information, a sequential filtering method is adopted, that is, the position information is first used to update the state, and then the Doppler measurement is used to further update the transition state. After obtaining a more accurate state estimate and likelihood function, the position and Doppler measurement information are finally used to calculate the weights.

[0137] Next, we use the Doppler information y d Perform sequential updates. The specific steps are as follows:

[0138] Use Doppler information to sequentially update the target state:

[0139]

[0140]

[0141]

[0142] The weight of the position component is:

[0143]

[0144]

[0145] in, They are expressed as the clutter intensity of the position component and the Doppler component respectively. for:

[0146]

[0147] The Doppler measurement gain and covariance are:

[0148]

[0149]

[0150] Among them, R c and σ d are the standard deviations of the position measurement and Doppler measurement noise respectively. The Jacobian matrix of the Doppler measurement is:

[0151] H d (m) = [h1,h2,h3,h4]

[0152] The parameters in the formula are:

[0153]

[0154] Step 5. Calculate the probability of target measurement through the posterior probability density in the update process, distinguish surviving targets from new targets through the probability of target measurement, and retain the measurement related to the new target for the new track at the next moment.

[0155] After the above calculations, a birth trajectory is established based on each measurement value. These measurements include clutter that has not been eliminated by the measurement filtering rules, measurements of currently surviving targets, and measurements generated by the new targets we are interested in. Although most of the clutter is eliminated by measurement filtering before calculation, there will still be some clutter that cannot be eliminated by simple filtering rules, which can often be corrected by subsequent filtering algorithms. The very few clutter that is retained will fall near the surviving target measurement, which will cause the filter to think that this is a measurement point generated by the current surviving target, which will lead to divergence of the filtering results. In response to the above phenomenon, we also need to group the measurement set and divide the measurement set into surviving target-related points and new target-related points. The steps for measurement division are as follows:

[0156] At time k, the measurement set Z k By the survival target related point Z B,k Points related to new goals Z S,k Composition, here we define the measurement set Z k The probability ρ(z) from the target measurement is:

[0157]

[0158] in, represents Z at time k k The probability of association between target i surviving and measurement, otherwise, 1-p i Represents the measurement Z at time k k The association probability of the new target i and the clutter is p. D,k is the sensor detection probability, z k is the measurement point at time k, represents the Gaussian density with mean m and variance P, H k is the observation matrix, R is the position measurement noise covariance, and h(·) is defined as follows:

[0159]

[0160] In the above formula, (x, y) represents the state vector of the target, (x s ,y s ) indicates the sensor position.

[0161] If ρ(z k )>0.5, it is considered that the measurement comes from the current survival target. On the contrary, when ρ(z k )≤0.5 indicates that the measurement originates from a new target or clutter. According to the above rules, the measurement set is divided into Z B,k , Z S,k Two parts, and Z B,k Used to generate new target components at the next moment, Z S,k Used in the subsequent GLMB update process.

[0162] The experimental conditions in this application are: the new positions appear at different times and in different locations, respectively (-750, 20), (-750, -750), (750, -750), (750, 750), (-750, 750), and the survival probability of the target is p S =0.99, the detection probability of the sensor is p D = 0.98, the total number of targets is 9, each object moves with a constant speed and state vector, the state vector is in and represents the position component, and represents the velocity component. The initial states, birth times, and extinction times of these nine tracking objects are shown in Table 1. Figure 2 represents the motion trajectory of each target, Figure 3 The data measured by the sensor includes the measurement generated by the target and clutter.

[0163] Table 1 Tracking target running status table

[0164]

[0165]

[0166] The standard state transfer matrix is ​​set as:

[0167]

[0168] The covariance matrix is:

[0169]

[0170] Where v represents the process noise with covariance Q and mean 0, σ v =10m / s. The target's prior velocity standard deviation is σ s =17m / s, the standard deviation of Doppler observation noise is σ d =0.5m / s. In the experiment, the clutter density follows the Poisson distribution, and the number of clutter points in each cycle follows the mean value λ c = 20 Poisson distribution, the position of each clutter point is evenly distributed within the measurement range, λ c Indicates the average amount of clutter per unit volume. The Doppler radar position is set to The observation noise covariance matrix is ​​R = diag([(π / 180) 2 ,100]). For the convenience of comparison, the pruning parameter T of all filters is T=10 -5 , the merging threshold U = 4, and the maximum number of Gaussian components is J max =100, and the multi-target extraction threshold is 0.5.

[0171] In order to verify the effectiveness of the algorithm, we compared Figure 4 、 5 It can be seen that without the track adaptive initiation algorithm, GLMB cannot effectively track the target. Targets appearing at unknown positions are completely undetectable, and even incorrect tracking results are given when the target tracks intersect. Figure 6 The performance of the filtering algorithm is shown in Figure 2. Fluctuations occur at moments 0, 10, 30, 40, and 50 because new targets are generated at these moments. However, the algorithm can converge within 2 seconds, which indicates the effectiveness of the track initiation algorithm.

[0172] In summary, the method of this embodiment can calculate the parameters required for the initiation of a new track in one step based on Doppler measurements. By means of measurement screening and grouping, the influence of clutter and the measurement points of surviving targets on the new track can be effectively reduced. The method can quickly complete the goal of track initiation by using only measurement points at two consecutive moments, and the filter performance can converge quickly.

[0173] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. An adaptive track initiation method based on GLMB, characterized in that: The following steps are involved: Convert the polar coordinate system measurement data received by the radar into the rectangular coordinate system measurement data; According to the prior information, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density; Filter out clutter in the measurement data through velocity screening rules and Doppler information screening rules; Adopting the sequential filtering method to update the multi-target posterior probability density; The probability of target measurement is calculated through the posterior probability density in the updating process, and the surviving targets and new targets are distinguished by the probability of target measurement. The measurements related to the new targets are retained for the new trajectory at the next moment.

2. The GLMB-based adaptive track initiation method according to claim 1, characterized in that: According to the prior information, the single target density of the new target and the single target density of the surviving target are correlated to obtain the multi-target prediction probability density, which specifically includes the following steps: According to the new component calculated at the previous moment, the single target density of the new target is calculated; According to the posterior information transmitted at the previous moment, the single target density of the surviving target is calculated; The single target density of the new target and the single target density of the surviving target are connected in parallel to obtain the multi-target prediction probability density.

3. The GLMB-based adaptive track initiation method according to claim 2, characterized in that: The single target density of the new target and the single target density of the surviving target are associated to obtain the multi-target prediction probability density, which also includes: and calculating the initial operating state of the new target based on the speed information hidden in the Doppler information, and the initial operating state includes the mean, covariance and weight of the new target.

4. The GLMB-based adaptive track initiation method according to claim 3, characterized in that: The multi-target posterior probability density: Where, represents the mean, variance, and weight of the missing measurement; represents the mean, variance, and weight of the position measurement; θ(l) represents the track association mapping with label l; δ(θ(l)) is the De Kotta function. When θ(l) = 0, δ(θ(l)) = 1, indicating that the measurement and track are not associated, which means that the track is missed. On the contrary, when θ(l) ≠ 0, δ(θ(l)) = 0, indicating that the track and measurement information are updated, indicating that the track is normal; l represents the label information corresponding to the component, Indicates the measurement point corresponding to the component.

5. The GLMB-based adaptive track initiation method according to claim 4, characterized in that: The probability ρ(z) of the target measurement is: in, Denotes the k-time measurement set Z k The probability of association between the surviving target i and the measurement, otherwise, 1-p i Denotes the k-time measurement set Z k The association probability of the new target and the clutter in ; p D,k is the sensor detection probability; z k is the measurement point at time k, represents the Gaussian density with mean m and variance P, H k is the observation matrix, R is the position measurement noise covariance, and h(·) is defined as follows: In the above formula, (x, y) represents the target position, (x s ,y s ) indicates the sensor position.

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