Multi-target tracking based on joint probability association of number of observations with high probability association

Abstract

The application discloses a multi-target tracking method based on joint probability association of observation value number of high-probability association, which comprises the following steps: obtaining multiple observation values of different targets through a sensor; estimating the association probability of the observation values and the targets; setting an effective observation range; performing an exhaustive search on the possible association conditions of the observation values and each target to obtain all feasible joint events; obtaining the association probability density of the observation values to the targets for the feasible joint events in the effective observation range; and updating the posterior state quantity and covariance of each target through Kalman filtering according to the association probability density of the observation values to the targets to realize target tracking. Compared with the traditional JPDA method, the multi-target tracking method based on joint probability association of observation value number of high-probability association can greatly improve the real-time performance and better adapt to different engineering environment requirements, although the target tracking precision is slightly reduced.

Description

Technical Field

[0001] This invention relates to a multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association, belonging to the field of target tracking technology. Background Technology

[0002] Multi-target tracking has a wide range of applications, from military technologies such as air defense monitoring, military radar, and maritime surveillance to civilian fields such as civilian GPS navigation, traffic monitoring, underwater resource exploration, and drug testing.

[0003] Traditional JPDA (Performance-Related Target Analysis) methods for multi-target tracking require the following steps: First, they need to estimate the target state at the current time based on the posterior state value and error covariance of the target at the previous time step, obtaining the prior probability of the target state at the current time and calculating the estimated state variables. Second, based on the estimated state variables of each target, the target state information fed back by the sensor at the current time is verified to obtain measurement data with high correlation probabilities, aiming to reduce the computational complexity of the algorithm. Third, based on the assumptions, the possible correlations between the verified observations and each target are exhaustively enumerated to obtain all feasible joint events. Fourth, using Bayes' principle, the probability of each feasible joint event is calculated, and the marginal probabilities of each observation for each target are obtained. Finally, the posterior probability density of each target at the current time is updated, and the posterior state variables and error covariance of each target at the current time are solved.

[0004] The traditional JPDA method has a high computational complexity in exhaustively enumerating feasible joint events. If we consider good sensor performance and an infinitely large correlation gate, then any measurement value can be associated with any target. In this case, the number N of feasible joint events obtained by decomposition satisfies the following relationship:

[0005]

[0006] In the above formula, k represents the current sampling time, n(k) represents the number of trajectories at the current time, and m(k) represents the number of observations within the correlation gate at the current time. It is evident that the algorithm complexity increases dramatically as the number of targets or the corresponding number of observations increases. However, in some tracking scenarios, the probability of many feasible joint events occurring is very small, even close to zero. Decomposing and calculating these events obviously consumes a significant amount of computational resources.

[0007] Therefore, it is necessary to study and improve the existing JPDA law in order to solve the above problems. Summary of the Invention

[0008] To overcome the above problems, the inventors conducted in-depth research and proposed a multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association, including the following steps:

[0009] S1. Obtain multiple observations of different targets through sensors;

[0010] S2. Estimate the probability of association between the observed value and the target;

[0011] S3. Set the effective observation range;

[0012] S4. Exhaustively enumerate all possible associations between the observed values ​​and each target to obtain all feasible joint events. For feasible joint events within the effective observation range, obtain the association probability density between the observed values ​​and the targets.

[0013] S5. Based on the correlation probability density between the observed values ​​and the target, update the posterior state variables and covariance of each target through Kalman filtering to achieve target tracking.

[0014] In a preferred embodiment, in S2, the estimated probability of association between the measured value and the target can be expressed as:

[0015]

[0016] in, Let represent the probability of association between measurement value j and target i, and c be the normalization factor. B represents the Gaussian density of the measured value j with respect to the target i. j B i For process variables, h represents different target numbers, l represents different observation numbers, n(k) represents the number of targets at time k, and m(k) represents the number of observations at time k.

[0017] In a preferred embodiment, the measured value j corresponds to the Gaussian density B of target i. j i is represented as:

[0018]

[0019] in, The information vector representing the observations: that is, the difference between the observed values ​​and the expected observed values, S i (k) represents the observation covariance, T is the transpose sign, and k represents the scan time.

[0020] In a preferred embodiment, in S3, the effective observation range is used to characterize feasible joint events that approximate the true correlation situation.

[0021] In a preferred embodiment, the effective observation range is determined by the number of observations with a high probability of correlation with the target.

[0022] In a preferred embodiment, the number of observations with a high probability of correlation with the target is expressed as:

[0023]

[0024] Where m(k) represents the number of observations at time k, f i This indicates a flag used to determine if a target is associated with another target. If the estimated probability of association between the measured value and the target is greater than a threshold p... h ,Right now Then f j =1; otherwise, f j =0.

[0025] In a preferred embodiment, the effective observation range can be expressed as [n s ,n h ], where n s n represents the lower limit of the effective observation range. h Indicates the upper limit of the effective observation range;

[0026] n h =min(m,n) f +s l )

[0027] n s =max(1,n) f -s l )

[0028] Among them, s l These are preset range parameters.

[0029] In a preferred embodiment, in S5, the kinematic model of the target is set as follows:

[0030] x(k)=Fx(k-1)+Gw(k-1)

[0031] y(k)=Hx(k)+v(k)

[0032] Where x represents the target state vector, y represents the observation vector; w represents the Gaussian white noise in the system input part, and its corresponding covariance matrix is ​​Q; v represents the Gaussian white noise in the system observation part, and its corresponding covariance matrix is ​​R; F is the system state transition matrix, G is the noise driving matrix, H is the observation matrix; and k represents the discrete time.

[0033] The beneficial effects of this invention include:

[0034] (1) Based on the approximate correlation probability between each observation and the target, the number of observations with a high correlation probability is obtained. Feasible joint events are listed around this number, so as to list as many feasible joint events with high probability as possible, thereby ensuring the tracking accuracy.

[0035] (2) Although the target tracking accuracy is slightly reduced, the real-time performance is greatly improved, which can better adapt to different engineering environment requirements;

[0036] (3) By setting the range parameters and making appropriate adjustments, a large number of feasible joint events are reduced to a certain extent, and the real-time performance of the calculations during engineering applications is increased. Attached Figure Description

[0037] Figure 1 A flowchart illustrating a multi-target tracking method based on the joint probability association of the number of observations with high probability association, according to a preferred embodiment of the present invention, is shown.

[0038] Figure 2 The simulation results of Example 1 show s l The root mean square error of the tracked target when set to 0;

[0039] Figure 3 The simulation results of Example 1 show s l The mean square error of the tracked target when set to 0;

[0040] Figure 4 The simulation results of Example 1 show s l The root mean square error of the tracked target when set to 1;

[0041] Figure 5 The simulation results of Example 1 show s l The mean square error of the tracked target when set to 1;

[0042] Figure 6 A comparison chart of computation time in Example 1 and Comparative Example 1 is shown. Detailed Implementation

[0043] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0044] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0045] This invention provides a multi-target tracking method based on joint probabilistic association of the number of observations with high probability association, characterized by the following steps:

[0046] S1. Obtain multiple observations of different targets through sensors;

[0047] S2. Estimate the probability of association between the observed value and the target;

[0048] S3. Set the effective observation range;

[0049] S4. Exhaustively enumerate all possible associations between the observed values ​​and each target to obtain all feasible joint events. For feasible joint events within the effective observation range, obtain the association probability density between the observed values ​​and the targets.

[0050] S5. Based on the correlation probability density between the observed values ​​and the target, update the posterior state variables and covariance of each target through Kalman filtering to achieve target tracking.

[0051] In S1 of this invention, the type of sensor is not limited and can be any type of sensor, such as radar, camera, etc.

[0052] In S2, based on Kalman filtering, the association probability between the observation and the target is roughly estimated. The estimated association probability between the measurement and the target can be expressed as:

[0053]

[0054] in, Let represent the probability of association between measurement value j and target i, and c be the normalization factor. B represents the Gaussian density of the measured value j with respect to the target i. j B i For process variables, h represents different target numbers, l represents different observation numbers, n(k) represents the number of targets at time k, and m(k) represents the number of observations at time k.

[0055] Furthermore, the Gaussian density of the measured value j relative to target i Represented as:

[0056]

[0057] in, The information vector representing the observations: that is, the difference between the observed values ​​and the expected observed values, S i (k) represents the covariance of the observations, T is the transpose sign, and k represents the scan time.

[0058] The inventors discovered that in the traditional JPDA method, the closer the feasible joint event probability value is to the real-world correlation, the higher the probability value. Therefore, the real-time performance of multi-target tracking can be enhanced by removing feasible joint event probability values ​​that are far from the real-world correlation.

[0059] However, the challenge of this invention lies in how to minimize the impact on tracking accuracy while removing some feasible joint events.

[0060] In S3, the effective observation range is used to characterize feasible joint events that approximate the true correlation situation. Preferably, the effective observation range is determined by the number of observations with a high probability of correlation with the target.

[0061] Specifically, the number of observations with a high probability of being highly correlated with the target is expressed as:

[0062]

[0063] Where m(k) represents the number of observations at time k, f i This indicates a flag used to determine if a target is associated with another target. If the estimated probability of association between the measured value and the target is greater than a threshold p... h ,Right now Then f j =1; otherwise, f j =0.

[0064] threshold p h The specific value can be obtained by those skilled in the art through multiple experiments or set based on experience. In this invention, its specific value is not particularly limited.

[0065] Furthermore, the effective observation range can be expressed as [n s ,n h ], where n s n represents the lower limit of the effective observation range. h This indicates the upper limit of the effective observation range.

[0066] Preferably,

[0067] n h =min(m,n) f +s l )

[0068] n s =max(1,n) f -s l )

[0069] Among them, s l These are preset range parameters.

[0070] In S4, the method for obtaining the feasible joint events is the same as that of the traditional JPDA method, and will not be described in detail here.

[0071] Unlike the traditional JPDA method, after obtaining feasible joint events, the marginal probability of the target is not solved by the probability of all feasible joint events, but by the marginal probability of the target within the feasible joint events within the effective observation range.

[0072] In this invention, by setting an effective observation range, the amount of data computation during the tracking process is greatly reduced, thereby significantly improving the tracking speed and ensuring real-time tracking. The inventors discovered that although setting an effective observation range reduces target tracking accuracy to some extent, the impact on target tracking accuracy is minimal because the discarded feasible joint events are all data with low correlation.

[0073] S5 is essentially the same as the traditional JPDA method, the only difference being that, in this application, the kinematic model of the target is set as follows:

[0074] x(k)=Fx(k-1)+Gw(k-1)

[0075] y(k)=Hx(k)+v(k)

[0076] Where x represents the target state vector, y represents the observation vector; w represents the Gaussian white noise in the system input part, and its corresponding covariance matrix is ​​Q; v represents the Gaussian white noise in the system observation part, and its corresponding covariance matrix is ​​R; F is the system state transition matrix, G is the noise driving matrix, H is the observation matrix; and k represents the discrete time.

[0077] Example

[0078] Example 1

[0079] A simulation experiment was set up to perform 1000 Monte Carlo simulations and track 6 moving targets.

[0080] In the simulation experiment, the following steps are used to track...

[0081] S2. Estimate the probability of association between the observed value and the target;

[0082] S3. Set the effective observation range;

[0083] S4. Exhaustively enumerate all possible associations between the observed values ​​and each target to obtain all feasible joint events. For feasible joint events within the effective observation range, obtain the association probability density between the observed values ​​and the targets.

[0084] S5. Based on the correlation probability density between the observed values ​​and the target, update the posterior state variables and covariance of each target through Kalman filtering to achieve target tracking.

[0085] In S2, based on Kalman filtering, the association probability between the observation and the target is roughly estimated. The estimated association probability between the measurement and the target can be expressed as:

[0086]

[0087] In S3, the effective observation range is used to characterize feasible joint events with high probability, and the effective observation range is determined by the number of observations with high probability of correlation with the target.

[0088] Specifically, the number of observations with a high probability of being highly correlated with the target is expressed as:

[0089]

[0090] Among them, f i This indicates a flag used to determine if a target is associated with another target. If the estimated probability of association between the measured value and the target is greater than a threshold p... h ,Right now Then f j =1; otherwise, f j =0.

[0091] The effective observation range can be represented as [n] s ,n h ],

[0092] n h =min(m,n) f +s l )

[0093] n s =max(1,n) f -s l )

[0094] Among them, s l Set them to 0 and 1 respectively;

[0095] In S4, the feasible joint events are obtained in the same way as in the traditional JPDA method. S5 is basically the same as the traditional JPDA method, except that the kinematic model of the target is set as follows:

[0096] x(k)=Fx(k-1)+Gw(k-1)

[0097] y(k)=Hx(k)+v(k)

[0098] Comparative Example 1

[0099] The same simulation experiment as in Example 1 was conducted using the traditional JPDA method.

[0100] Simulation results of Example 1 are as follows Figures 2-5 As shown, where Figure 2 , 3 For s l When set to 0, the root mean square error (RMSE) and mean square error (MSE) of the tracked target are... Figure 4 , 5 For s lThe root mean square error (RMSE) and mean square error (MSE) of the tracked target when set to 1 are shown in the figure. Different values ​​of s... l Below, the root mean square error and mean square error of the tracked target are both less than 3, indicating that the method in Example 1 has high tracking accuracy, meaning it can guarantee high tracking accuracy. By adjusting s l It can also adjust the tracking accuracy;

[0101] Figure 6 A comparison chart of computation time in Example 1 and Comparative Example 1 is shown. The chart shows that the method in Example 1 has a faster computation time, thus improving tracking speed and exhibiting higher real-time performance. This can be achieved by adjusting the threshold s. l It can also adjust the relationship between tracking accuracy and computing speed, and can achieve a balance between computing speed and target tracking accuracy to a certain extent, reducing the complexity of computing while sacrificing target tracking accuracy to a small extent.

[0102] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0103] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0104] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A multi-target tracking method based on joint probabilistic association of the number of observations with high probability association, characterized in that, Includes the following steps: S1. Obtain multiple observations of different targets through sensors; S2. Estimate the probability of association between the observed value and the target; S3. Set the effective observation range; S4. Exhaustively enumerate all possible associations between the observed values ​​and each target to obtain all feasible joint events. For feasible joint events within the effective observation range, obtain the association probability density between the observed values ​​and the targets. S5. Based on the correlation probability density between the observed values ​​and the target, update the posterior state variables and covariance of each target through Kalman filtering to achieve target tracking; In S3, the effective observation range is used to characterize feasible joint events that approximate the true correlation situation, and the effective observation range is determined by the number of observations with a high probability of correlation with the target; Number of observations with high correlation to the target Represented as: ， in, express The number of observations at each time point This indicates a flag used to determine if a target is associated with another target. If the estimated probability of association between the measured value and the target is greater than a threshold... ,but ; otherwise, .

2. The multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association as described in claim 1, characterized in that, In S2, the estimated probability of association between the measured value and the target is expressed as: ， in, Indicates the measured value For the target The probability of association, As the normalization factor, Indicates the measured value For the target Gaussian density, , For process variables, , , Indicates different target numbers, Indicates the numbering of different observations, express The number of targets at any given time.

3. The multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association as described in claim 2, characterized in that... Measured values For the target Gaussian density Represented as: ， in, The information vector represents the difference between the observed value and the expected observed value. Represents the covariance of the observed values. This is the transpose symbol.

4. The multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association as described in claim 1, characterized in that... The effective observation range can be expressed as [ , ],in, This indicates the lower limit of the effective observation range. Indicates the upper limit of the effective observation range; ， in, These are preset range parameters.

5. The multi-target tracking method based on the joint probabilistic association of the number of observations with high probability association as described in claim 1, characterized in that, In S5, the kinematic model of the target is set as follows: ， in, Represents the target state vector. Represents the observation vector; The Gaussian white noise represents the input portion of the system, and its corresponding covariance matrix is: ; The Gaussian white noise in the system's observation part has the following covariance matrix: ; Here is the system state transition matrix. For noise driving matrix, This is the observation matrix.

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