Irregular target tracking method based on Gaussian process and variational Bayesian inference

Abstract

This invention discloses an irregular target tracking method based on Gaussian processes and variational Bayesian inference. A Gaussian process model is used to describe the radial function of the tracked target's contour, modeling the target shape. A variational Bayesian inference method is employed to jointly estimate the target's shape and measurement noise, deriving the posterior distribution forms of unknown measurement noise and the tracked target's shape. A square root capillary Kalman filter is used to handle the nonlinear filtering problem in tracking irregularly shaped targets, achieving simultaneous estimation of complex shape information and unknown measurement noise. This invention effectively overcomes the limitations of traditional tracking algorithms in handling complex target shapes when dealing with unknown measurement noise, significantly improving the accuracy and robustness of target tracking.

Description

Technical Field

[0001] This invention belongs to the technical field of signal processing and target tracking, and mainly relates to an irregular target tracking method based on Gaussian process and variational Bayesian inference. Background Technology

[0002] Target tracking is a core problem in many application fields, including military, civilian, and scientific research. In the civilian sector, this technology can be applied to security monitoring, autonomous driving, and traffic management. For example, tracking pedestrians and non-motorized vehicles in urban surveillance systems can improve public safety, and autonomous vehicles need to accurately identify and track complex targets in their surroundings to ensure safe driving. In scientific research, this technology also has wide applications in areas such as animal behavior research and environmental monitoring. For example, biologists can use this technology to classify and track the movement patterns of wild animals, and environmental scientists can monitor the dynamic changes of natural disasters. However, for targets with irregular shapes, such as people, animals, and complex mechanical equipment, traditional tracking algorithms often struggle to effectively handle their variable shapes.

[0003] In practical applications, methods for tracking irregularly shaped targets face numerous challenges. First, the shape of the target may be highly complex and uncertain, requiring algorithms to possess high adaptability and flexibility. Second, numerous environmental interference factors, such as occlusion, lighting variations, and complex backgrounds, can introduce changes in the statistical characteristics of unknown measurement noise, increasing the difficulty of target tracking. Therefore, algorithms need to comprehensively consider these issues to improve the accuracy and robustness of target tracking.

[0004] Gaussian process models are non-parametric Bayesian methods adept at handling complex function approximation problems. By defining a multivariate normal distribution in a high-dimensional space, they can flexibly fit various complex target shapes and motion patterns. Variational Bayesian inference is an approximate inference method that provides an efficient solution path when computing complex probabilistic models. It makes computation more feasible by approximating a complex posterior distribution to a simple set of distributions. Combining these two methods enables accurate tracking of irregularly shaped targets in dynamic and uncertain environments.

[0005] However, research in this field still faces many technical challenges. How to ensure the accuracy and stability of Gaussian process models in complex environments, and how to improve the computational efficiency of variational Bayesian inference, require further in-depth study. Although research institutions both domestically and internationally have made some progress, many challenges remain in practical applications, necessitating continuous innovation and algorithm optimization to achieve efficient tracking of irregularly shaped targets. Summary of the Invention

[0006] This invention addresses the problem in existing technologies that cannot effectively track irregularly shaped targets while adapting to the statistical characteristics of unknown measurement noise. It provides a method for tracking irregularly shaped targets based on Gaussian processes and variational Bayesian inference. The method employs a Gaussian process (GP) model to describe the radial function of the target's contour, thus modeling the target shape. A variational Bayesian (VB) inference method is used to jointly estimate the target's shape and measurement noise, deriving the posterior distribution of the unknown measurement noise and the target's shape. A square-root cumulative Kalman filter (SCKF) is used to handle the nonlinear filtering problem in tracking irregularly shaped targets, achieving simultaneous estimation of complex shape information and unknown measurement noise. This method effectively overcomes the limitations of traditional tracking algorithms in handling complex target shapes when dealing with unknown measurement noise, significantly improving the accuracy and robustness of target tracking.

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: an irregular target tracking method based on Gaussian process and variational Bayesian inference. A Gaussian process model is used to describe the radial function of the tracked target's contour, thus modeling the target shape. A variational Bayesian inference method is used to jointly estimate the target's shape state and measurement noise, deriving the posterior distribution of unknown measurement noise and the tracked target's shape state. A square root capacitive Kalman filter is used to handle the nonlinear filtering problem in tracking irregularly shaped targets, achieving simultaneous estimation of complex shape information and unknown measurement noise.

[0008] As an improvement to the present invention, an irregular target tracking method based on Gaussian process and variational Bayesian inference includes the following steps:

[0009] S1: Provides the target shape estimate at the initial time or at time t-1. and its square root covariance S t-1 The volume point is calculated using square root volume Kalman filtering. One-step prediction of volume points And the estimated parameters of the unknown measurement noise covariance matrix are initialized to obtain and

[0010] S2: Using the results obtained in step S1 One-step prediction based on the state and the square root covariance and S t|t-1 Based on this, the volume points are updated to obtain...

[0011] S3: Using the values ​​obtained in steps S1 and S2, initialize the variables before iterative measurement updates;

[0012] S4: Perform iterative measurement updates. Using the measurement equation obtained from shape modeling based on the Gaussian process model, and the estimated target state and measurement noise covariance obtained from the current iteration, calculate the predicted measurement value z. t|t-1 ;

[0013] S5: Calculate the state square root covariance S through the measurement update step in the square root volume Kalman filter. zz,t|t-1 And the cross-covariance P of state and measurement xz,t|t-1 Finally, update the state estimated in the j-th iteration. Sum of square roots and covariance

[0014] S6: Recalculate the new volume points and predicted measurements, calculate the measurement covariance, and update the estimated parameters of the measurement noise covariance. Obtain its estimated value

[0015] S7: When the difference between the measurement noise covariance estimated in two consecutive iterations is less than a set threshold, the iteration ends and the estimated state is output. Square root covariance and parameters

[0016] As an improvement of the present invention, the volume point in step S1 One-step prediction of volume points The specific calculation method is as follows:

[0017]

[0018] in, The transition matrix represents the shape state of the target. N equals dimensionality Represents matrix E N×2N The List,

[0019]

[0020] The parameters for estimating the unknown measurement noise covariance matrix are initialized as follows:

[0021]

[0022] Where ρ∈(0,1).

[0023] As another improvement of the present invention, in step S2, the volume point is updated. Specifically:

[0024]

[0025] in, and S t|t-1 A one-step prediction representing the state and the square root covariance.

[0026] As another improvement of the present invention, in step S4, the measured value z t|t-1 The calculation method is as follows:

[0027]

[0028] in, The measurement update z at time t is obtained by modeling the shape based on the Gaussian process model. i,t The representation of: τ=n t This represents the number of measurements taken at time t.

[0029] As another improvement of the present invention, in step S5, the state square root covariance S zz,t|t-1 And the cross-covariance P of state and measurement xz,t|t-1 The calculation method is as follows:

[0030]

[0031] in,

[0032]

[0033] Finally, update the estimated state in the j-th iteration. Sum of square roots and covariance

[0034]

[0035] Among them, z t It is the measurement set at time t.

[0036]

[0037] As a further improvement of the present invention, the estimated parameters of the measurement noise covariance are updated in step S6. Obtain its estimated value The calculation method is as follows:

[0038]

[0039] Among them, P zz Indicates the measured covariance. It is the predicted measurement value estimated in the j-th iteration.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] (1) By accurately modeling the target shape and motion pattern using the Gaussian process model, the error caused by the simplified assumptions about the target shape in traditional methods is avoided, which can significantly improve the initial estimation accuracy of the target position and achieve higher accuracy in tracking irregular targets.

[0042] (2) Variational Bayesian inference provides an efficient solution approach by approximating a complex posterior distribution as a set of simple distributions. It can perform multiple iterative estimations of the target's shape and measurement noise, gradually reducing the estimation error until the predetermined accuracy requirements are met.

[0043] (3) Compared with the existing popular extended target tracking algorithms, it innovatively combines the Gaussian process model with variational Bayesian inference, which shows superior performance in handling dynamic environments and complex-shaped targets. It can effectively handle the complexity of target shape and measurement noise uncertainty in the environment, and significantly improve the stability and robustness of the system.

[0044] (4) The method of the present invention has low computational complexity and is suitable for real-time processing, especially for application scenarios that require fast response. For example, it is highly practical for scenarios such as autonomous driving and drone navigation. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the steps of the method of the present invention;

[0046] Figure 2 This is a comparison chart of the estimation results of three different methods in the test examples of this invention;

[0047] Figure 3 This is a comparison chart of the average IOU values ​​of three different methods in 100 MC experiments in the test examples of this invention;

[0048] Figure 4 This is a comparison chart of three different methods for tracking pedestrian-bicycle targets in the test examples of this invention;

[0049] Figure 5 This is a comparison chart of three different methods for tracking car targets in the test examples of this invention. Detailed Implementation

[0050] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0051] Example 1

[0052] This invention presents an irregular target tracking method based on Gaussian processes and variational Bayesian inference, aiming to address the challenge of accurately tracking targets with irregular contours in complex environments, especially when faced with unknown statistical characteristics of measurement noise. The method utilizes a Gaussian process model to accurately model the target's shape and combines this with variational Bayesian inference to accurately estimate the statistical characteristics of the unknown measurement noise. Specifically, the method employs a Gaussian process model to describe the radial function of the tracked target's contour, thus modeling the target's shape. It then uses variational Bayesian inference to jointly estimate the target's shape and measurement noise, deriving the posterior distributions of the unknown measurement noise and the tracked target's shape. Finally, it employs square-root capillary Kalman filtering to handle the nonlinear filtering problem in tracking irregularly shaped targets, achieving simultaneous estimation of complex shape information and unknown measurement noise.

[0053] Specifically, the process begins by obtaining estimates of the target state and measurement noise covariance from the previous time step. Then, the volume point and its one-step prediction are calculated to obtain the predicted state value. Using these variables, the parameters required for estimation are initialized before the iteration begins. Based on this, the iteration starts, and the target's measurement equation is written by modeling the shape using a Gaussian process model. The square root covariance of the state and the cross-covariance of the state and measurement are calculated, and the state and square root covariance estimated in the current iteration are updated accordingly. New volume points and measurement predictions are then calculated, and the measurement noise covariance parameters are updated to obtain the estimated measurement noise covariance. The iteration ends when the difference between two consecutive iteration estimates is less than the set convergence threshold, and the estimated value is output.

[0054] An irregular target tracking method based on Gaussian processes and variational Bayesian inference, such as... Figure 1 As shown, it includes the following steps:

[0055] Step S1: First, give the estimated target shape value at the initial time or the previous time. and its square root covariance S t-1 The volume point is calculated using the steps in SCKF. One-step prediction of volume points

[0056]

[0057] in, The transition matrix represents the shape state of the target. N equals dimensionality Represents matrix E N×2N The List,

[0058]

[0059] The parameters for estimating the unknown measurement noise covariance matrix are initialized as follows:

[0060]

[0061] Where ρ∈(0,1];

[0062] Step S2: Using the information obtained in step S1 One-step prediction based on the state and the square root covariance and S t|t-1 As shown below:

[0063]

[0064]

[0065] Where Tria(·) denotes the QR decomposition of the matrix.

[0066]

[0067] It is the process noise covariance. Then new predicted volume points are generated:

[0068]

[0069] Step S3: Using the values ​​obtained in steps S1 and S2, initialize the variables before iterative measurement updates, as shown below:

[0070]

[0071] Step S4: Perform iterative measurement updates. First, based on the Gaussian process model, the measurement equation obtained by shape modeling is used. The i-th measurement z at time t... i,t It can be represented as:

[0072]

[0073] in, It is the position of the center of mass at the current moment, ψ t It is the direction angle of the target at the current moment.

[0074]

[0075] Where K(·,·) represents the kernel function, which is usually taken as... It is usually set to 1. Usually, 2 is taken, and d is usually taken as... θ i ,θ j ∈{θ1,…,θ N} represents N angular base points uniformly selected on the interval [0, 2π]. This is the vector describing the radial contour of the target at this base point, i.e., the target shape state. R t This represents the measurement noise covariance.

[0076] Will Substituting into the above measurement equation, we get τ=n t This represents the number of measurements taken at time t, and the final measurement z. t|t-1 The predicted value is calculated as follows:

[0077]

[0078] Step S5: Then calculate the root square covariance S of the state through the measurement update step in SCKF. zz,t|t-1 And the cross-covariance P of state and measurement xz,t|t-1 As shown below:

[0079]

[0080] in,

[0081]

[0082] Finally, update the estimated state in the j-th iteration. Sum of square roots and covariance

[0083]

[0084]

[0085] Among them, z t It is the measurement set at time t.

[0086]

[0087] Step S6: Recalculate the new volume points and predicted measurements, as shown below:

[0088]

[0089] The definition of variables in the measurement equation is described in detail in step S4. Substitute.

[0090] Then, the measurement covariance P is calculated. zz And update the estimated parameters of the measurement noise covariance. Obtain its estimated value The formula is shown below:

[0091]

[0092] Step S7: Finally, when the difference between the measurement noise covariance estimated in two adjacent iterations is less than a set threshold, that is:

[0093]

[0094] When the time is up, end the iteration and output the estimated state:

[0095]

[0096]

[0097] Where J equals the iteration number at the end.

[0098] Test case

[0099] The method proposed in this patent is used to track a single irregularly shaped target, and the measurement noise is unknown.

[0100] Assuming the target moves at a constant velocity [0.3 m / s; 0.2 m / s], the target shape state transition matrix is ​​defined as follows: Process noise covariance Sampling time Δt = 1s, forgetting factor α = 0.0001.

[0101] Figure 2 This image compares the estimation results of double-rectangular targets of different sizes under different measurement noise conditions using the method of this patented invention (VB-GP-SCKF) and the existing popular random matrix extended target tracking method (EM-ETT), and the GP-EKF algorithm assuming known measurement noise. The measurement noise covariance is set from left to right as follows: R = 0.1 2 I², R = 0.2 2 I², R = 0.4 2 I2, with target widths of 5m, 8m, and 13m respectively. The figure shows that the target shape estimated by the method of this invention is closer to the true target contour than the estimation results of the other two algorithms, and it exhibits better adaptability and robustness to different target sizes and measurement noise levels.

[0102] Figure 3 For 100 independent and repeated experiments, this invention's patented method (VB-GP-SCKF) was compared with existing popular methods such as the Stochastic Matrix Extended Target Tracking (EM-ETT) and the GP-EKF method assuming known measurement noise. Figure 2 A comparison chart of the average IOU values ​​of the target estimation results under the set simulation conditions. The formula for calculating the IOU value is: Where X0 and The figures represent the actual target region and the estimated target region, respectively. A higher IOU value (closer to 1) indicates a closer approximation between the estimated and actual values. As shown in the figure, the IOU value of the method described in this patent is significantly higher than the other two methods, indicating that the method described in this patent can achieve more accurate shape estimation results.

[0103] Figure 4 and Figure 5 This image compares algorithms for tracking pedestrian-bicycle and car targets, using scenes provided in the KITTI dataset and data collected by a Velodyne 64-line 3D LiDAR mounted on a vehicle roof. The green line represents the multi-ellipse extended target tracking algorithm, the blue line represents the GP-EKF method with preset measurement noise, and the magenta line represents the method using this patented invention (VB-GP-SCKF). As can be seen from the image, the contour lines estimated by this patented method are closer to the real target contour and better reflect the target contour details. Compared with currently popular target shape tracking methods, this patented method can achieve more accurate shape estimation results.

[0104] In summary, the method of this invention utilizes a Gaussian process model to accurately model the shape of the target and combines it with variational Bayesian inference techniques to accurately estimate the statistical characteristics of unknown measurement noise. This method effectively overcomes the limitations of traditional tracking algorithms in handling complex target shapes when dealing with unknown measurement noise, significantly improving the accuracy and robustness of target tracking. Experimental results based on simulation and real radar data demonstrate that this invention exhibits superior performance in both accuracy and robustness for tracking irregularly shaped targets.

[0105] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. An irregular target tracking method based on Gaussian processes and variational Bayesian inference, characterized in that: A Gaussian process model is used to describe the radial function of the tracked target contour, thereby modeling the target shape; A variational Bayesian inference method is used to jointly estimate the target's shape and measurement noise, deriving the posterior distribution of unknown measurement noise and the tracked target's shape. A square root capillary Kalman filter is employed to handle the nonlinear filtering problem in tracking irregularly shaped targets, achieving simultaneous estimation of complex shape information and unknown measurement noise. The process includes the following steps: S1: Give the initial time or Target shape estimate at time and its square root covariance The volume point is calculated using square root volume Kalman filtering. One-step prediction of volume points And initialize the estimation parameters of the unknown measurement noise covariance matrix to obtain and ; S2: Using the results obtained in step S1 One-step prediction based on the state and the square root covariance and Based on this, the volume points are updated to obtain... ; S3: Using the values ​​obtained in steps S1 and S2, initialize the variables before iterative measurement updates; S4: Perform iterative measurement updates. Using the measurement equation obtained from shape modeling based on the Gaussian process model, and the target state and measurement noise covariance estimate obtained from the current iteration, calculate the predicted measurement value. ; S5: Calculate the square root covariance of the state through the measurement update step in the square root volume Kalman filter. and the cross-covariance of states and measurements. Final update The state estimated in the next iteration Sum of square roots and covariance ; S6 Recalculate the new volume points and predicted measurements, calculate the measurement covariance, and update the estimated parameters of the measurement noise covariance. To obtain its estimated value ; S7: When the difference between the measurement noise covariance estimated in two consecutive iterations is less than a set threshold, the iteration ends and the estimated state is output. Square root covariance and parameters .

2. The irregular target tracking method based on Gaussian process and variational Bayesian inference as described in claim 1, characterized in that: The volume point in step S1 One-step prediction of volume points The specific calculation method is as follows: ； ； in, The transition matrix represents the shape state of the target. , equal dimensionality Representation matrix The List, ； The parameters for estimating the unknown measurement noise covariance matrix are initialized as follows: ； in .

3. The irregular target tracking method based on Gaussian process and variational Bayesian inference as described in claim 2, characterized in that: In step S2, the volume points are updated. Specifically: ； in A one-step prediction representing the state and the square root covariance.

4. The irregular target tracking method based on Gaussian process and variational Bayesian inference as described in claim 3, characterized in that: In step S4, the measured value The calculation method is as follows: ； in, The measurement equation obtained by shape modeling based on the Gaussian process model is in Time measurement update The representation of: , express The number of times measured.

5. The irregular target tracking method based on Gaussian process and variational Bayesian inference as described in claim 4, characterized in that: In step S5, the state square root covariance and the cross-covariance of states and measurements. The calculation method is as follows: ； ； in, This indicates performing a QR decomposition on the matrix; ； ； ； Final Update The state estimated in the next iteration Sum of square roots and covariance : ； ; in, It is the current Time measurement set , 。 6. The irregular target tracking method based on Gaussian process and variational Bayesian inference as described in claim 5, characterized in that: In step S6, the estimated parameters of the measurement noise covariance are updated. To obtain its estimated value The calculation method is as follows: ； ； ； in, Indicates the measured covariance. It is the first The predicted measurement value estimated in the next iteration.

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