Robust multi-target tracking method based on gaussian assumption probability density filter

Abstract

The application provides a robust multi-target tracking method based on a Gaussian hypothesis probability density filter, belongs to the technical field of robust multi-target tracking, and solves the problem that a traditional GF method is difficult to stably estimate target states when measurement is abnormal; the application increases Student's t distribution with heavy tail noise on the basis of original Gaussian measurement by modifying a measurement model; meanwhile, in order to overcome the limitation of the traditional GF on the measurement model, an affine function is applied to construct a pseudo measurement model, and a posterior probability density function is calculated by minimizing KL divergence, a prediction result is updated, weights in the prediction result are corrected, and a robust multi-target tracking process is completed; compared with the traditional GF method, the application improves the robustness of the algorithm in an environment with abnormal value measurement, and the finally obtained target state information is more reasonable.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of robust multi-target tracking, and is applied to the process of estimating the state of multiple targets under abnormal measurement environment, and particularly relates to a robust multi-target tracking method based on a Gaussian hypothesis probability density filter. BACKGROUND

[0002] Multi-target tracking problem is concerned due to its application value in civil field, and the problem needs to estimate the state and number of multiple targets. In traditional multi-target tracking method, data association is the core idea, but when the number of targets is large and there are a large number of clutters and false alarms, association will bring problems such as combination explosion and sharp increase in calculation amount.

[0003] Multi-target tracking method based on random finite set (RFS) is a non-associated multi-target tracking method. Multi-target tracking under RFS framework is to represent the target state and measurement as random sets, and through set integration and set differentiation operations, the estimation of target number and the estimation of target state at each time are obtained to realize joint detection and tracking of targets. However, due to the involvement of complex high-dimensional integral operation, the framework is difficult to be directly executed in actual application, so various approximation algorithms are derived. For example, probability hypothesis density (PHD) filter solves the practical executable problem of RFS to a certain extent, and then the filter of PHD is realized through sequential Monte Carlo (SMC) method and Gaussian mixture (GM) method.

[0004] Gaussian distribution of measurement noise is a kind of assumption condition, which has been widely applied to multi-target tracking problem. However, in some actual applications, there are some outliers in measurement, for example, irregular reflection of electromagnetic wave may cause significant change of radar reflection, and then cause outliers in target tracking process. The measurement noise under this condition no longer satisfies Gaussian distribution. Therefore, the traditional Gaussian filter (GF) is based on the assumption of Gaussian noise, and when the measurement is abnormal, it is difficult to realize stable target state estimation. SUMMARY

[0005] The object of the present application is to overcome the problem that the traditional GF-based multi-target tracking method is difficult to stably estimate the target state when the measurement is abnormal, and a robust multi-target tracking method based on Gaussian hypothesis probability density filter is proposed; by modifying the measurement model, the Student's t distribution with heavy-tailed noise is added on the basis of the original Gaussian measurement; at the same time, in order to overcome the limitation of the traditional GF for the measurement model, the affine function is applied to establish the pseudo measurement, and the updated target state is calculated by minimizing the KL divergence. Compared with the traditional GF method, the target state information obtained by the method of the present application is more reasonable.

[0006] The present application adopts the following technical solutions to achieve the object:

[0007] A robust multi-target tracking method based on Gaussian hypothesis probability density filter, which uses the multi-target intensity characteristic function in the multi-target tracking process to construct a pseudo measurement model, and then calculates the posterior probability density function by minimizing the KL divergence, updates the prediction result, and corrects the weight in the prediction result, to complete the robust multi-target tracking process.

[0008] Specifically, the method comprises the following steps:

[0009] S1, initializing the Gaussian component to determine the multi-target intensity function at the initial time;

[0010] S2, predicting the multi-target intensity function at the current time according to the multi-target intensity function at the previous time;

[0011] S3, updating the prediction result of the multi-target intensity function at the current time according to the prediction information and the Gaussian component information in the prediction process, to obtain the updated multi-target state and error covariance;

[0012] S4, calculating the corresponding weight of each Gaussian component after the prediction result is updated;

[0013] S5, performing pruning, merging and state extraction operations on the Gaussian component to obtain the multi-target intensity function result at the current time.

[0014] As described above, due to the adoption of the present technical solution, the present application has the following beneficial effects:

[0015] In view of the abnormal measurement noise in the traditional GF method, the measurement model is modified, the robustness of the algorithm in the environment with abnormal value measurement is improved by increasing the Student's t distribution, when the target state is estimated, the pseudo measurement model is constructed by the characteristic function, the optimal state calculation expression is obtained by minimizing the Kullback-Leibler (KL) divergence, and the weight calculation is adjusted correspondingly and sufficiently, finally more reasonable target state information is obtained, and the robust multi-target tracking process with better effect is realized. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 A step flowchart of the method of the present application is shown in the figure.

[0017] Figure 2 A comparison diagram of target track and corresponding measurement information in the embodiment of the present application is shown in the figure.

[0018] Figure 3 A tracking performance comparison diagram of the method of the present application and the standard GM-PHD algorithm is shown in the figure. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0020] Therefore, the detailed description of the embodiments of the present application provided in the drawings below is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0021] Embodiment 1

[0022] A robust multi-target tracking method based on Gaussian hypothesis probability density filter, uses the multi-target intensity characteristic function in the multi-target tracking process to construct a pseudo measurement model, then calculates the posterior probability density function by minimizing the KL divergence, updates the prediction result, and corrects the weight in the prediction result, to complete the robust multi-target tracking process.

[0023] This embodiment will detail the content of each step in the method according to the specific calculation process and the formula involved, which can be simultaneously referred to as Figure 1 The step flowchart is shown in the figure.

[0024] The method in this embodiment specifically includes the following steps:

[0025] S1. Initialize the Gaussian components and determine the multi-objective intensity function at the initial time.

[0026] In step S1, the multi-objective intensity function at the initial moment is as follows:

[0027]

[0028] In the formula, Represents the first time step at the initial moment. The weights of each Gaussian component; The Gaussian component of the initial target.

[0029] S2. Based on the multi-objective intensity function of the previous moment, predict the multi-objective intensity function of the current moment.

[0030] In step S2, The multi-target intensity function at time t is as follows:

[0031]

[0032] right The Gaussian components at time t are predicted to obtain... Multi-target intensity prediction function at time step.

[0033] The multi-target intensity prediction function at time t is as follows:

[0034]

[0035] In the formula, The probability of the target surviving; Weighting of new student targets; The Gaussian component of the new target; and It can be calculated as follows:

[0036]

[0037]

[0038] In the formula, The target transition matrix; Let be the process noise covariance.

[0039] S3. Based on the prediction information and Gaussian component information in the prediction process, update the prediction results of the multi-objective intensity function at the current moment to obtain the updated multi-objective state and error covariance.

[0040] In step S3, according to The multi-target intensity prediction function at time t is updated The multi-target intensity function at time t is given by

[0041]

[0042] where, is the detection probability; thus the first term represents the missed detection Gaussian component, and the second term represents the false alarm is the measurement update component, which is given by

[0043]

[0044] where, is the measurement The likelihood function for the th prior Gaussian component; is the th prior Gaussian component; is the corresponding weight;

[0045] is given by

[0046]

[0047] The calculation formula of is as follows:

[0048]

[0049] where, is the clutter intensity function;

[0050] The updated multi-target intensity function is further given by

[0051]

[0052] where, is the characteristic function; is the affine function;

[0053] The pseudo-measurement model is constructed as follows:

[0054]

[0055] where, is the Gaussian measurement model; is the Student t model.

[0056] After the pseudo-measurement model is constructed, the calculation results of the characteristic function and the affine function are obtained by minimizing the KL divergence, as follows:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] In the formula, Let be the degrees of freedom of the Student t model distribution;

[0063] The updated error covariance can be calculated as follows:

[0064]

[0065] This is the error covariance matrix.

[0066] S4. After the prediction results are updated, calculate the corresponding weight of each Gaussian component.

[0067] In step S4, the updated Gaussian component weights can be expressed as:

[0068]

[0069] In the formula, The calculation is as follows:

[0070]

[0071] This completes the calculation of the corresponding weights for the Gaussian components.

[0072] S5. Perform pruning, merging, and state extraction operations on the Gaussian components to obtain the multi-objective intensity function results at the current time.

[0073] In step S5, Gaussian components with weights less than the pruning threshold are deleted; Gaussian components with distances less than the merging threshold are merged; and Gaussian components with weights greater than the target state extraction threshold are extracted.

[0074] After completing the pruning, merging, and state extraction operations, the following formula is obtained:

[0075]

[0076] This formula is... The results of the multi-target intensity function at each time step are used to complete the robust multi-target tracking process.

[0077] Example 2

[0078] On the basis of Embodiment 1, this embodiment simulates the method in Embodiment 1 to illustrate the technical effect of the method in the field of multi-target tracking and state estimation in the presence of abnormal measurement.

[0079] The simulation environment of this embodiment is constructed in a two-dimensional plane, in which the number of targets varies with time. In order to simplify the processing, the derived targets are not considered in the simulation. The target state in the simulation includes x the position and velocity in the direction, y the position and velocity in the direction, which is specifically expressed as The transition process of the target state is expressed as:

[0080]

[0081]

[0082]

[0083]

[0084] In the formula, is the simulation period; is the standard deviation of the process noise; the target survival probability ; after the method content of Embodiment 1 is applied, the pseudo-measurement model obtained is:

[0085]

[0086] Among them:

[0087]

[0088]

[0089] The target detection probability ; the clutter distribution detected by the sensor at each time is independent, and the number satisfies the Poisson distribution, and the average number of clutters per unit area is , and the average value of the detected clutters per period is 10.

[0090] In the method of this embodiment, the pruning threshold ; the merging threshold ; the target state extraction threshold ; the maximum number of allowed Gaussian distributions is . The OSPA distance is used as the performance evaluation index of the multi-target tracking method in this embodiment, in which the truncation parameter , and the order .

[0091] According to the simulation settings and parameters, the standard GM-PHD method and the RGM-PHD method of the embodiment are compared, and the average OSPA value is calculated through 100 times of Monte Carlo simulation.

[0092] Figure 2 For the comparison chart of the target trajectory and the measurement information in the simulation, it can be seen from the chart that there are obvious outliers in the measurement process.

[0093] Figure 3 For the comparison result of the OSPA values of the standard method and the method of the embodiment, it can be seen that the RGM-PHD method of the embodiment is obviously better than the standard GM-PHD method, which shows that the application has robustness in the abnormal measurement environment and can obtain better multi-target tracking and state estimation effect.

Claims

1. A robust multi-target tracking method based on Gaussian hypothesis probability density filter, characterized in that: The robust multi-target tracking process is completed by using a multi-target intensity characteristic function in a multi-target tracking process, constructing a pseudo measurement model, calculating a posterior probability density function by minimizing KL divergence, updating a prediction result, and correcting a weight in the prediction result. The method comprises the following steps: S1, initializing a Gaussian component to determine a multi-target intensity function at an initial time; S2, predicting a multi-target intensity function at a current time according to a multi-target intensity function at a previous time; S3, updating a prediction result of the multi-target intensity function at the current time according to prediction information and Gaussian component information in the prediction process to obtain an updated multi-target state and error covariance; S4, calculating a corresponding weight of each Gaussian component after the prediction result is updated; S5, performing pruning, merging and state extraction operations on the Gaussian components to obtain a multi-target intensity function result at the current time; In step S1, the multi-target intensity function at the initial time is as follows: wherein represents the weight of the initial moment of the Gaussian component; Gaussian component of the initial target; In step S2, The multi-target intensity function at time t is given by right The Gaussian components at time t are predicted to obtain... Multi-target intensity prediction function at time step; The multi-objective strength prediction function at time instant t is given by wherein is the target survival probability; is the newborn target weight; is the Gaussian component of the newborn target; and is calculated as: In the formula, is the target transition matrix; is the process noise covariance.

2. The robust multi-target tracking method based on Gaussian hypothesis probability density filter according to claim 1, characterized in that: In step S3, the multi-objective intensity prediction function is updated according to the multi-objective intensity function at the time instant, as follows: the multi-objective intensity function at the time instant, as follows: wherein is the detection probability; is the measurement update component, which is expressed as follows: wherein is a measure of the likelihood function for the th prior Gaussian component; is the th prior Gaussian component; is the corresponding weight; As follows: The calculation formula is as follows: wherein is a clutter intensity function; The updated multi-target intensity function is further expressed as: wherein is a characteristic function; is an affine function; The pseudo measurement model is constructed as follows: wherein is a Gaussian measurement model; is a Student t model.

3. The robust multi-target tracking method based on Gaussian hypothesis probability density filter according to claim 2, characterized in that: After the pseudo measurement model is constructed, the calculation result of the characteristic function and the affine function is obtained by minimizing the KL divergence as follows: wherein is the degrees of freedom for the Student t model distribution; The updated error covariance is calculated as: i.e. the error covariance matrix.

4. The robust multi-target tracking method based on Gaussian hypothesis probability density filter according to claim 3, characterized in that: In step S4, the updated Gaussian component weight is expressed as: In the formula, The calculation is as follows: Thus, the corresponding weight calculation of the Gaussian component is completed.

5. The robust multi-target tracking method based on Gaussian hypothesis probability density filters according to claim 4, characterized in that: In step S5, for the Gaussian component with a weight less than a pruning threshold, a deletion operation is performed; for the Gaussian components with a distance less than a merging threshold, a merging operation is performed; and for the Gaussian component with a weight greater than a target state extraction threshold, a state extraction operation is performed.

6. The robust multi-target tracking method based on Gaussian hypothesis probability density filters according to claim 5, characterized in that: After the pruning, merging and state extraction operations are completed, the following formula is obtained: This is the formula The multi-objective intensity function results at the time instant.

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