A multi-target tracking method based on background-pulse Kalman filtering algorithm
By applying Gaussian mixture processing to the observation noise and combining it with the input-output interaction of the JPDA algorithm, the problem of large tracking error and divergence in multi-target tracking under non-Gaussian noise environment is solved, achieving stronger tracking capability and robustness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2023-07-03
- Publication Date
- 2026-06-30
AI Technical Summary
Existing multi-target tracking algorithms are prone to large tracking errors and divergence when faced with non-Gaussian noise, especially in dense clutter environments.
A background-pulse Kalman filter-based algorithm is adopted. By performing Gaussian mixture processing on the observation noise, input and output interaction are carried out, and target fusion is performed in combination with the JPDA algorithm to achieve effective processing of non-Gaussian noise.
It improves the robustness and accuracy of multi-target tracking, reduces tracking errors, maintains good tracking performance in non-Gaussian noise environments, and avoids divergence.
Smart Images
Figure CN117008119B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of multi-target tracking technology, and more specifically, to a multi-target tracking method based on the background-pulse Kalman filter algorithm. Background Technology
[0002] Multi-target tracking refers to the simultaneous observation and prediction of the kinematic states of multiple targets. This patent studies the problem of tracking multiple targets using a single sensor. The topic of multi-target tracking has wide applications in practice, such as underwater unmanned vehicles using their built-in sonar to track schools of fish, and ground robots using lidar to track pedestrian trajectories in the environment.
[0003] Existing multi-target tracking algorithms often assume that the sensor observation noise is Gaussian noise. However, in real-world environments, due to the interference of electromagnetic signals from noise sources and the multiple superpositions of noise propagation, the superimposed signal often exhibits non-uniformity, manifesting as non-Gaussian noise in the time-domain statistics. This type of noise is more prone to extreme error values than Gaussian noise. Traditional multi-target tracking algorithms, such as those combining joint probabilistic data association and Kalman filtering, are prone to large tracking errors or even divergence under non-Gaussian noise, resulting in a "failure to keep up" problem. While methods using maximum correlation entropy (MCC) and minimum error entropy (MEE) have improved upon this, the degree of performance improvement is limited.
[0004] Therefore, conventional multi-target tracking methods need to be improved so that they have stronger tracking capabilities, smaller tracking errors, are less prone to divergence, and have good robustness when facing non-Gaussian noise with unknown distribution. Summary of the Invention
[0005] The purpose of this invention is to provide a multi-target tracking method based on the background-pulse Kalman filter algorithm. The aim is to achieve stronger tracking ability, smaller tracking error, less divergence, and good robustness when the multi-target tracking method faces non-Gaussian noise.
[0006] The embodiments of the present invention are achieved through the following technical solutions:
[0007] A multi-target tracking method based on the background-pulse Kalman filter algorithm includes the following steps for target tracking at time k:
[0008] Acquire the static noise distribution of the sensor when there is no input, and obtain the Gaussian mixing ratio β of this static noise. i and covariance matrix
[0009] Perform input interaction to obtain the fusion state of target r at time k-1. The mixture covariance matrix of the target r at time k-1
[0010] according to and Perform the state of model j of target r at time k. Covariance The prediction;
[0011] according to and Calculate the association probability β mr (k), to obtain the innovation matrix The m-th measurement Z of the Gaussian component j of the target r m The residual corresponding to (k)
[0012] according to and β mr (k) Perform a state update, updating the state of the Gaussian component j of the target r at time k.
[0013] according to Update model probabilities;
[0014] according to and Perform target fusion output;
[0015] Repeat the above steps to proceed to the next moment of target tracking.
[0016] Preferably, the method for performing input interaction is as follows:
[0017]
[0018]
[0019] in,
[0020]
[0021]
[0022] In the above formula, It is the state of model i of target r at time k-1. It is the mixture covariance matrix of model i of target r at time k-1. π is the probability that target r is model i at time k-1. ij Let i be the probability of switching to model j.
[0023] Preferably, the state of model j for target r at time k is... Covariance The prediction method is as follows:
[0024]
[0025]
[0026] Where F is the state transition matrix and Q is the state noise covariance matrix.
[0027] Preferably, the according to and Calculate the association probability β mr (k), to obtain the innovation matrix The m-th measurement Z of the Gaussian component j of the target r m The residual corresponding to (k) The method is as follows:
[0028]
[0029] If the above formula is satisfied, it means Z m (k) is the m-th measurement of the Gaussian component j of the target r. The correlation probability β between the two is obtained through the JPDA algorithm. mr (k);
[0030] in, For the associated threshold, and:
[0031]
[0032]
[0033] Where H is the observation matrix and R is the covariance matrix.
[0034] Preferably, the according to and β mr (k) The method for updating the state is as follows:
[0035] according to Obtain the fused residual of the Gaussian component j of target r at time k.
[0036]
[0037] according to Obtain the Kalman gain of the Gaussian component j of target r at time k.
[0038]
[0039] according to and Update the state of the Gaussian component j of target r at time k.
[0040]
[0041] Obtain the covariance of the Gaussian component j of the target r at time k.
[0042]
[0043] Preferably, the according to The method for updating model probabilities is as follows:
[0044]
[0045]
[0046] Where c is the normalization coefficient, and its value is π is the probability that target r is model i at time k-1. ij Let i be the probability of switching to model j.
[0047] Preferably, the according to and The method for achieving target fusion output is as follows:
[0048] Obtain the fusion state vector of target r at time k.
[0049]
[0050] Obtain the fusion covariance matrix P of target r at time k. r (k|k):
[0051]
[0052] in, Let r be the probability that the target r is model j at time k.
[0053] The technical solutions of the embodiments of the present invention have at least the following advantages and beneficial effects:
[0054] The present invention first performs Gaussian mixture calculation on the observation noise, and then performs input interaction, output interaction and other operations. Compared with the existing technical solutions, the method used in the present invention is less likely to discard the deviation value.
[0055] Under the scheme of the present invention, since it is not easy to discard the deviation value, the multi-target tracking results obtained by the present invention have stronger tracking ability and smaller tracking error, and the prediction results under dense clutter and non-Gaussian observation noise are closer to the real trajectory.
[0056] This invention associates non-Gaussian noise with JPDA in an interactive manner, thus exhibiting better target tracking capability, easier convergence, and good robustness against divergence when dealing with non-Gaussian noise.
[0057] This invention is rationally designed, and its logical construction process has a high cost-performance ratio in terms of computing power, making it easy to promote and apply. Attached Figure Description
[0058] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0059] Figure 1 Provided for embodiments of the present invention;
[0060] Figure 2 The trajectory diagram shows the experimental results of the multi-target tracking method provided in Embodiment 1 of the present invention.
[0061] Figure 3 A comparison of the root mean square errors of the tracking results in the X and Y directions of the multi-target tracking method based on the background-pulse Kalman filter algorithm provided in Embodiment 1 of the present invention and the traditional scheme;
[0062] Figure 4 A detailed representation of the position error in the X and Y directions of the tracking result of the multi-target tracking method based on the background-pulse Kalman filter algorithm is provided for Embodiment 1 of the invention.
[0063] Figure 5 The diagram shows a comparison between the root mean square error of the tracking results of the multi-target tracking method based on the background-pulse Kalman filter algorithm under Gaussian noise and existing methods, as provided in Embodiment 1 of the invention. Detailed Implementation
[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.
[0065] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0066] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.
[0067] Example 1
[0068] See Figures 1-2 A multi-target tracking method based on the background-pulse Kalman filter algorithm, which includes the following steps for target tracking at time k:
[0069] Step S1: Acquire the static noise distribution of the sensor when there is no input, and obtain the Gaussian mixing ratio β of the static noise. i and covariance matrix
[0070] Step S2: Perform input interaction to obtain the fusion state of target r at time k-1. The mixture covariance matrix of the target r at time k-1
[0071] Step S3: According to and Perform the state of model j of target r at time k. Covariance The prediction;
[0072] Step S4: According to and Calculate the association probability β mr (k), to obtain the innovation matrix The m-th measurement Z of the Gaussian component j of the target r m The residual corresponding to (k)
[0073] Step S5: According to and β mr (k) Perform a state update, updating the state of the Gaussian component j of the target r at time k.
[0074] Step S6: According to Update model probabilities;
[0075] Step S7: According to and Perform target fusion output;
[0076] Step S8: Proceed to the next moment of target tracking, that is, update the value of k to k = k + 1, and then return to step S1 and repeat the above steps S1-S7 to continue the complete multi-target tracking.
[0077] In the proposed scheme of this embodiment, Gaussian mixture analysis is first performed on the observation noise, followed by input and output interaction operations. Compared with existing algorithms, this method is less likely to discard bias values; at the same time, through interaction, non-Gaussian noise is associated with JPDA, so when dealing with non-Gaussian noise, this algorithm has better target tracking ability and good robustness that is less prone to divergence.
[0078] The following are the simulation results of two uniform velocity trajectory tracking models:
[0079] Use X i (k) = [x(m), vx(m / s), y(m), vy(m / s)] represents the state information of target i at time k. Assume that the initial states of the two moving targets, namely target 1 and target 2, are X1 and X2, respectively:
[0080] X1=[3000m,20m / s,3000m,-20m / s];
[0081] X2=[5000m,-20m / s,3000m,-20m / s];
[0082] Their state equations and observation equations are as follows:
[0083]
[0084]
[0085] Among them, w i (k) is the covariance Q t (k)=10 -2 Zero-mean Gaussian noise, v i (k) is the covariance. Non-Gaussian noise, denoted as v i (k)~0.9N(0,0.1 2 )+0.1N(0,10 2 Set the sampling time T = 1s and associate the threshold. The detection probability is 16.
[0086] The trajectory diagram of the experimental results of the multi-target tracking method in this embodiment, based on 300 Monte Carlo experiments, is shown in the attached diagram. Figure 2 , Figure 2 The point cloud in the image represents cluttered measurements. The two dashed lines represent the trajectories of target 1 and target 2 obtained using the tracking method in this embodiment, while the two dashed lines represent the actual trajectories of target 1 and target 2, respectively. Figure 2 It can be seen that the prediction results obtained by the method in this embodiment are very close to the actual trajectory.
[0087] To compare with traditional methods, we compared the tracking results of the same target 1 and target 2 using the scheme of this embodiment and the JPDA-KF method. The comparison results, namely the root mean square error comparison chart in the X and Y directions, are shown in the figure. Figure 3 , Figure 3 In the upper part of Figure a, the vertical axis represents the root mean square error of position in the X direction, and in the lower part of Figure b, the vertical axis represents the root mean square error of position in the Y direction. The horizontal axis in the figures represents time. In the upper and lower figures, the two dashed lines represent the root mean square errors of position of target 1 and target 2 under the tracking of the JPDA-KF method, and the two solid lines represent the root mean square errors of position of target 1 and target 2 under the tracking of the method in this embodiment.
[0088] Detailed representations of the positional errors of the trajectory in the X and Y directions obtained based on the scheme of this embodiment can be found in the following diagrams. Figure 4 Similarly, Figure 4 In the upper left figure a, the vertical axis represents the position error in the X direction, and in the lower figure b, the vertical axis represents the position error in the Y direction. The horizontal axis in the figures represents time, and the two lines in the upper and lower figures represent target 1 and target 2, respectively.
[0089] A detailed representation of the root mean square error of the trajectory obtained based on the scheme in this embodiment can be found in [reference needed]. Figure 5 , Figure 5 The results are compared with those of existing algorithms under Gaussian noise. Figure 5 In the upper graph (a), the vertical axis represents the root mean square error of position under the method of this embodiment, and the vertical axis of the lower graph (b) represents the root mean square error of position of the existing algorithm. The horizontal axis in the graphs represents time, and the implementation and dashed line in the upper and lower graphs represent target 1 and target 2, respectively. Under Gaussian noise, the algorithm of this patent performs similarly to the existing algorithm, both performing very well; under non-Gaussian noise, the algorithm of this patent outperforms the existing algorithm.
[0090] In summary, the comparison shows that when Gaussian noise is present in the observations, both the method in this embodiment and existing algorithms perform well. However, when non-Gaussian noise is present, existing techniques struggle to converge and exhibit significant measurement errors. Conversely, the method in this embodiment effectively handles non-Gaussian noise, exhibiting smaller errors and minimal deviation between the measured and actual positions. Therefore, when non-Gaussian noise is present in the observations, this algorithm demonstrates smaller errors and better robustness, significantly outperforming existing solutions.
[0091] In summary, this embodiment first performs Gaussian mixture analysis on the non-Gaussian observation noise, and then incorporates the solution results through an interactive input method. Finally, the JPDA algorithm and output fusion are used to obtain the final result. Compared with existing methods, this method has good robustness with small tracking errors and low divergence for non-Gaussian observation noise.
[0092] Example 2
[0093] This embodiment is based on the technical solution of embodiment 1, and further explains the method of input interaction in step S2.
[0094] In this embodiment, the method for performing input interaction is as follows:
[0095]
[0096]
[0097] in,
[0098]
[0099]
[0100] In the above formula, It is the state of model i of target r at time k-1. It is the mixture covariance matrix of model i of target r at time k-1. π is the probability that target r is model i at time k-1. ij Let i be the probability of switching to model j.
[0101] Example 3
[0102] This embodiment is based on the technical solution of implementation 1, and describes the state of model j of target r at time k in step S3. Covariance The prediction method will be further explained.
[0103] As a preferred embodiment, the state of model j of target r at time k is... Covariance The prediction method is as follows:
[0104]
[0105]
[0106] Where F is the state transition matrix and Q is the state noise covariance matrix.
[0107] Example 4
[0108] This embodiment is based on the technical solution of Implementation 1, and calculates the association probability β in step S4. mr (k), to obtain the innovation matrix The m-th measurement Z of the Gaussian component j of the target r m The residual corresponding to (k) The method will be further explained.
[0109] In this embodiment, the method according to and Calculate the association probability β mr (k), to obtain the innovation matrix The m-th measurement Z of the Gaussian component j of the target r m The residual corresponding to (k) The method is as follows:
[0110]
[0111] If the above formula is satisfied, it means Z m (k) is the m-th measurement of the Gaussian component j of the target r. The correlation probability β between the two is obtained through the JPDA algorithm. mr (k);
[0112] in, For the associated threshold, and:
[0113]
[0114]
[0115] Where H is the observation matrix and R is the covariance matrix.
[0116] Example 5
[0117] This embodiment is based on the technical solution of implementation 1, and further explains the method of state update in step S5.
[0118] As a preferred embodiment, the following is based on and β mr (k) The method for updating the state is as follows:
[0119] according to Obtain the fused residual of the Gaussian component j of target r at time k.
[0120]
[0121] according to Obtain the Kalman gain of the Gaussian component j of target r at time k.
[0122]
[0123] according to and Update the state of the Gaussian component j of target r at time k.
[0124]
[0125] Obtain the covariance of the Gaussian component j of the target r at time k.
[0126]
[0127] Example 6
[0128] This embodiment is based on the technical solution of implementation 1, and further describes step S6 according to... The method for updating the model probabilities will be further explained.
[0129] As a preferred embodiment of this solution, the method based on The method for updating model probabilities is as follows:
[0130]
[0131]
[0132] Where c is the normalization coefficient, and its value is π is the probability that target r is model i at time k-1. ij Let i be the probability of switching to model j.
[0133] Example 7
[0134] This embodiment is based on the technical solution of implementation 1, and addresses the issue in step S7 according to... and The method for performing target fusion output will be further explained.
[0135] In this embodiment, the method according to and The method for achieving target fusion output is as follows:
[0136] Obtain the fusion state vector of target r at time k.
[0137]
[0138] Obtain the fusion covariance matrix P of target r at time k. r (k|k):
[0139]
[0140] in, Let r be the probability that the target r is model j at time k.
[0141] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A multi-target tracking method based on a background-pulse Kalman filtering algorithm, characterized in that, The target tracking at the kth moment comprises the following steps: The static noise distribution of the acquisition sensor at no input is collected, and the Gaussian mixed proportion of the static noise is obtained and a covariance matrix , a number representing a model component of the Gaussian mixed model; Perform input interaction, get the fusion state of target r at the k-1 moment And the mixed covariance matrix of target r at the k-1 moment ; According to and , the state and covariance of the model j of the target r at the kth moment are predicted; According to and calculate the association probability , obtain the innovation matrix and the mth measurement of the target r Gaussian component j the corresponding residual ; According to The state update, the Gaussian component j of the update target r at the kth moment ; According to updating the model probabilities; According to and perform target fusion output; Repeat the above steps to enter the target tracking of the next moment.
2. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 1, characterized in that, The method for performing input interaction is: ； ； Wherein, ； ； In the above formula, is the state of model i of target r at time k-1, is the mixed covariance matrix of model i of target r at time k-1, is the probability of target r being model i at time k-1, is the probability of model i switching to model j.
3. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 1, characterized in that, said performing a prediction of the state of the model j of the target r at the kth time instant and the covariance of the prediction is a method comprising: ； ； Wherein, F is a state transition matrix, and Q is a state noise covariance matrix.
4. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 1, characterized in that, The method according to And Calculate the correlation probability , Obtain the innovation matrix And the mth measurement of the target r Gaussian component j The corresponding residual The method is: ； If the above formula is satisfied, it is represented is the mth measurement of the target r Gaussian component j, and the association probability of the two is obtained by the JPDA algorithm ; wherein is a correlation threshold, and: ； ； Wherein, H is an observation matrix, and R is a covariance matrix.
5. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 4, characterized in that, The method according to The method for updating the state is: According to Obtaining the fusion residual of the Gaussian component j of the target r at the kth moment : ； According to Obtaining the Kalman gain of the Gaussian component j of the target r at the kth moment : ； According to and , the state of the Gaussian component j of the update target r at the k-th time point : ； obtaining the covariance of the Gaussian component j of the target r at the kth moment : 。 6. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 5, characterized in that, The method according to The method for updating the model probability is: ； ； where c is a normalization coefficient, and its value is , is the probability that the target r is model i at time k-1, is the probability that model i switches to model j.
7. The multi-target tracking method based on the background-pulse Kalman filtering algorithm according to claim 1, characterized in that, The method according to and The method for target fusion output is: acquiring a fusion state vector of the target r at the kth moment : ； acquiring a fusion covariance matrix of the target r at the kth moment : ， where, P (r, k | j) is the probability that the target r is in state k at time t for model j.