A tracking method based on interactive multiple model kernel Kalman filter

Abstract

The application discloses a tracking method based on an interactive multiple model kernel Kalman filter, which comprises the following steps: step one: embedding: extracting proposal particles at the n-1 moment, and calculating a kernel weight mean vector and a covariance matrix; step two: prediction: the proposal particles at the n-1 moment are propagated through a dynamic state-space model to obtain prior state particles at the n moment, and a predicted kernel mean and a covariance matrix are calculated based on a kernel Kalman rule; step three: updating: measurement state particles are generated by taking the proposal particles at the n moment as a measurement model, and the kernel weight mean vector and the covariance matrix are updated; and step four: model fusion output: the model confidence is updated, different model results are fused, and the output of an interactive multiple model kernel Kalman filter (IMM-KKF) algorithm is obtained. The application can obtain high-precision tracking of a target trajectory under the condition of a small amount of particle sampling, and can adapt to the maneuvering characteristics of the target switching between a straight-line constant velocity (CV) and a coordinated turn (CT) and other multiple motion models.

Description

Technical Field

[0001] This invention belongs to the field of sonar system technology, and in particular to a tracking method based on interactive multi-model kernel Kalman filtering. Background Technology

[0002] Pure azimuth tracking (BOT) refers to a technique that estimates the two-dimensional or three-dimensional position, velocity, and other state parameters of a target solely by observing its azimuth angle relative to a sensor. The core challenge of BOT systems stems from their inherent nonlinear observation characteristics—the observed value (azimuth angle) and the target state (position, velocity) have a nonlinear functional relationship.

[0003] To address the state estimation problem of nonlinear systems, existing known techniques mainly fall into three categories: First, the Extended Kalman Filter (EKF), which linearizes the nonlinear function through a first-order Taylor expansion, but suffers from significant linearization errors in strongly nonlinear scenarios; second, the Unscented Kalman Filter (UKF), which improves the accuracy of nonlinear processing by approximating the posterior probability distribution using Sigma points, but may still exhibit divergence in some nonlinear problems; and third, the Particle Filter (PF), which is suitable for highly nonlinear systems, but requires a large number of particles to ensure tracking accuracy, and the tracking accuracy decreases significantly when the number of particles decreases.

[0004] The kernel method refers to transforming the state estimation problem of a nonlinear dynamic system into a high-dimensional kernel feature space through kernel functions. This high-dimensional kernel feature space can then be solved using linear operations. Applying the kernel method can overcome the Gaussian distribution assumption and nonlinear approximation error problems inherent in traditional nonlinear filtering.

[0005] Existing techniques such as particle filtering are suitable for nonlinear systems, but require a large number of particle sampling and resampling operations, leading to an exponential increase in computational complexity, which cannot meet the requirements of real-time tracking. In addition, the filters in existing multi-model schemes all adopt traditional linear or nonlinear filtering frameworks and are not combined with kernel methods, making it difficult to achieve high-precision nonlinear estimation with low computational complexity. Summary of the Invention

[0006] To address the inherent nonlinearity of pure orientation tracking (BOT) systems, some nonlinear filtering algorithms rely on a large number of particle samples, resulting in high computational complexity and poor real-time performance. Furthermore, a single motion model cannot adapt to the target's maneuvering characteristics when switching between multiple motion modes, such as constant velocity in a straight line (CV) and coordinated turning (CT), leading to tracking inaccuracies. This invention designs a method that combines interactive multi-model (IMM) and kernel Kalman filter (KKF) algorithms to achieve high-precision tracking of the target trajectory with a small number of particle samples, and can adapt to the target's maneuvering characteristics when switching between multiple motion models, such as constant velocity in a straight line (CV) and coordinated turning (CT).

[0007] The technical solution of this invention is as follows:

[0008] A tracking method based on interactive multi-model kernel Kalman filtering includes:

[0009] Step 1: Embedding Step: Obtain the importance distribution from the posterior kernel mean estimate at time n-1, extract the proposal particles in the data space, and calculate the kernel weight mean vector and covariance matrix in the kernel feature space.

[0010] Step 2: Prediction Step: The proposed particle at time n-1 propagates in the data space through the process equations in the dynamic state-space model to obtain the prior state particle at time n; the predicted kernel mean and covariance matrix are calculated in the kernel feature space based on the kernel Kalman rule.

[0011] Step 3: Update Step: Substitute the proposed particle at time n into the measurement model in the dynamic state-space model to generate the measurement state particle. The information obtained from the new observation is used to update the kernel weight mean vector and covariance matrix. Based on the observation information, the posterior kernel mean embedding is obtained and mapped to the data space to obtain the state estimate.

[0012] Step 4: Model Fusion Output: Update the model confidence based on the estimated values ​​in the kernel feature space, fuse the results of different models, and obtain the output of the Interactive Multi-Model Kernel Kalman Filter (IMM-KKF) algorithm.

[0013] The beneficial effects of this invention are as follows:

[0014] 1. This invention proposes a joint framework of multi-model interaction and kernel Kalman filtering algorithm, which realizes high-precision tracking of maneuvering targets with different motion models;

[0015] 2. This invention combines a dynamic state-space model to adaptively generate particles, which significantly reduces the number of particles required while ensuring estimation accuracy;

[0016] 3. This invention leverages the combined advantages of data-driven and model-driven approaches. On one hand, it uses a dynamic state-space model to generate particles based on a model-driven framework. On the other hand, it utilizes the non-parametric properties of kernel methods to handle strong nonlinearity in the model, thus avoiding excessive reliance on model accuracy. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the workflow of the IMM-KKF algorithm of this invention.

[0018] Figure 2 This is a schematic diagram of the CV model of the present invention;

[0019] Figure 3 This is a schematic diagram of the CT model of the present invention;

[0020] Figure 4 This is a BOT result diagram of the KKF algorithm in the CV model of this invention;

[0021] Figure 5 This is a BOT result diagram of the KKF algorithm for the CT model in this invention;

[0022] Figure 6 This is a BOT result diagram of the IMM-KKF algorithm of this invention. Detailed Implementation

[0023] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0024] 1. Interactive Multiple Model (IMM)

[0025] Interactive Multiple Model (IMM) is a state estimation method for maneuvering targets. Its core principle is to describe different dynamic modes of the system (such as constant speed, acceleration, turning, etc.) in parallel using multiple sub-models. By leveraging the interaction and fusion of models and probabilistic weighting, it achieves accurate tracking of complex dynamic behaviors. It is primarily used in target tracking (such as radar and sonar tracking of maneuvering targets) and navigation systems (such as UAV flight state estimation), and is particularly suitable for systems with frequent mode switching or complex dynamic behaviors.

[0026] In pure orientation tracking (BOT), the maneuvering target state is characterized by a dynamic state-space model, where... These are the coordinates of the target on a two-dimensional horizontal plane. The goal is to The velocity component in the direction.

[0027] Assuming the target motion follows both a linear uniform velocity (CV) model and a nonlinear coordinated turning (CT) model, the state equation for the CV model is:

[0028] ,

[0029] Where T0 is the sampling interval. v is the angular velocity of the turning direction. n For random perturbations;

[0030] The state equation of the CT model is:

[0031] ,

[0032] Where T0 is the sampling interval. v is the angular velocity of the turning direction. n For random perturbations;

[0033] The measurement equations for both the CV and CT models are:

[0034] ,

[0035] Among them, u n For measuring noise.

[0036] This invention proposes a framework combining Interactive Multi-Model (IMM) and Kernel Kalman Filter (KKF) to adapt to the maneuvering characteristics of targets switching between multiple modes such as constant speed (CV) and coordinated turning (CT), thereby achieving high-precision real-time tracking.

[0037] Based on this, a tracking method based on interactive multi-model kernel Kalman filtering is provided, including:

[0038] Step 1: Embedding Steps:

[0039] The importance distribution is obtained from the posterior kernel mean estimate at time n-1. Proposal particles are extracted from the data space, and the kernel weight mean vector and covariance matrix are calculated in the kernel feature space.

[0040] Specifically, the particle and nuclear characteristic mapping at time n-1 is represented as: and Its empirical kernel mean and covariance matrix are

[0041] ,

[0042] ,

[0043] Wherein, the kernel feature map at time n-1 , For the weight vector, This is the weight matrix.

[0044] By choosing a suitable kernel function, one can... Extract the corresponding mean from the data space. Covariance Therefore, proposal particles are generated based on the importance distribution:

[0045] ,

[0046] .

[0047] Step Two: Prediction Steps

[0048] The proposed particle at time n-1 propagates through the process equations in various dynamic state-space models in the data space to obtain the prior state particle at time n; the predicted kernel mean and covariance matrix are calculated in the kernel feature space based on the kernel Kalman rule.

[0049] Specifically, the proposal particle at time n-1 Through propagation using the CV or CT model described above, the prior state particle at time n is obtained. .

[0050] The kernel feature map is represented as:

[0051] .

[0052] The calculated kernel mean and covariance matrix are as follows:

[0053] ,

[0054] .

[0055] Step 3: Update steps:

[0056] The proposed particle at time n is substituted into the measurement model in the dynamic state-space model to generate the measurement state particle. The information obtained from the new observation is used to update the kernel weight mean vector and covariance matrix. Based on the observation information, the posterior kernel mean embedding is obtained and mapped to the data space to obtain the state estimate.

[0057] Specifically, the prior state of the particle at time n... Substituting into the measurement equation described above, we obtain the measurement state particle. . The kernel feature map is represented as:

[0058] .

[0059] The posterior kernel mean and covariance matrix are calculated as follows:

[0060] ,

[0061] ,

[0062] ,

[0063] in, For the kernel Kalman gain operator, The kernel vector is measured at time n. Let be the Gram matrix at time n.

[0064] Step 4: Model Fusion Output:

[0065] The model confidence is updated based on the estimated values ​​in the kernel feature space. The results from different models are then fused to obtain the output of the Interactive Multi-Model Kelvin Kalman Filter (IMM-KKF) algorithm. The calculation formula is as follows:

[0066] ,

[0067] ,

[0068] Where J is the number of models, This represents the model confidence level.

[0069] Figure 1 This invention provides the workflow of the kernel Kalman filter algorithm, which mainly includes three modules: a constant velocity (CV) model prediction and update module, a coordinated turning (CT) model prediction and update module, and a model selection and fusion module. Prediction and updates for different models are performed simultaneously in the data space and the kernel feature space. Figure 1 In the diagram, rounded rectangles represent state estimates in the data space, and circles represent state estimates in the kernel feature space. Finally, the IMM algorithm fuses the kernel Kalman filter estimation results of different models into the final output of the system.

[0070] Figure 2 , Figure 3 The diagrams shown are the CV model and CT model of the present invention. The CV model describes a linearly maneuvering target with uniform linear motion, while the CT model describes a highly maneuvering target with normal acceleration, but the acceleration is unknown. The dynamic state space model is also nonlinear.

[0071] Figure 4 , Figure 5 The figures show the BOT results of the CV model and CT model KKF algorithm in this invention, respectively. KKF ​​and PF use the same number of particles. The results show that KKF can achieve continuous tracking of the target under both maneuvering models, while the tracking trajectory of particle filtering (PF) has errors. The errors increase the complexity of the random maneuvering model.

[0072] Figure 6 The BOT results of the IMM-KKF algorithm of this invention are provided, which show that the IMM-KKF algorithm can achieve continuous tracking of the target under the condition of changing motion model.

[0073] In summary, this invention addresses the shortcomings of existing nonlinear filtering in dynamic systems by combining interactive multi-model (EMB) and kernel Kalman filtering methods. First, the EMB framework enables the system to adapt to switching between CV and CT modes through model probability weighting, avoiding tracking inaccuracies inherent in single-model approaches. Meanwhile, linearization in the kernel feature space eliminates nonlinear approximation errors, and the combination of these two methods significantly improves estimation accuracy. Second, the kernel method greatly reduces the number of particles required while maintaining estimation accuracy, resulting in computational complexity far lower than particle filtering, thus meeting real-time tracking requirements. Therefore, this invention outperforms existing technologies in both estimation accuracy and real-time performance, making it suitable for pure orientation tracking scenarios under high-maneuverability conditions.

[0074] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

Claims

1. A tracking method based on interactive multi-model kernel Kalman filtering, characterized in that, include: Step 1: Embedding step: Obtain the importance distribution from the posterior kernel mean estimate at time n-1, extract the proposal particles in the data space, and calculate the kernel weight mean vector and covariance matrix in the kernel feature space; Step 2: Prediction Step: The proposed particle at time n-1 propagates in the data space through the process equations in the dynamic state-space model to obtain the prior state particle at time n; the prediction kernel mean and covariance matrix are calculated in the kernel feature space based on the kernel Kalman rule. Step 3: Update step: Substitute the proposed particle at time n into the measurement model in the dynamic state-space model to generate the measurement state particle. The information obtained from the new observation is used to update the kernel weight mean vector and covariance matrix. Based on the observation information, the posterior kernel mean embedding is obtained and mapped to the data space to obtain the state estimate. Step 4: Model Fusion Output: Update the model confidence based on the estimated values ​​in the kernel feature space, fuse the results of different models, and obtain the output of the Interactive Multi-Model Kernel Kalman Filter (IMM-KKF) algorithm.

2. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 1, characterized in that: In step one, the particle and nuclear feature mapping at time n-1 is represented as: and Its empirical kernel mean and covariance matrix are: ， ， Wherein, the kernel feature map at time n-1 , For the weight vector, This is the weight matrix.

3. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 2, characterized in that: In step one, the kernel function is selected from... Extract the corresponding mean from the data space. Covariance Therefore, proposal particles are generated based on the importance distribution: ， 。 4. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 3, characterized in that: In step two, the proposed particle at time n-1 Propagation is performed using either the CV model or the CT model to obtain the prior state of the particle at time n. , The kernel feature map is represented as: 。 5. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 4, characterized in that: In step two, the predicted kernel mean and covariance matrix are calculated as follows: ， 。 6. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 5, characterized in that: In step three, the prior state particle at time n... Substituting into the measurement equation, we obtain the particle in the measurement state. , The kernel feature map is represented as: 。 7. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 6, characterized in that: In step three, the posterior kernel mean and covariance matrix are calculated as follows: ， ， ， in, For the kernel Kalman gain operator, The kernel vector is measured at time n. Let be the Gram matrix at time n.

8. The tracking method based on interactive multi-model kernel Kalman filtering according to claim 7, characterized in that: In step four, the calculation formula for the interactive multi-model kernel Kalman filter (IMM-KKF) algorithm is as follows: ， ， Where J is the number of models, This represents the model confidence level.

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