A multi-target tracking method and system based on interactive multi-model of Gaussian process and adaptive noise

Abstract

The application discloses a multi-target tracking method and system based on a Gaussian process interactive multi-model and adaptive noise, and belongs to the technical field of multi-target tracking. In order to solve the problems of serious model mismatch, low tracking precision and easy loss of a track in a complex scene with strong sudden maneuvering, a heterogeneous motion model library containing a standard motion model, a Gaussian process GP-based motion model and an adaptive noise maneuvering model is constructed; each Gaussian component in a Gaussian mixture probability hypothesis density GM-PHD filter is extended and defined as an interactive multi-model IMM structure embedded with the heterogeneous motion model library; in a prediction and update cycle of the filter, the multiple motion models are subjected to probability interaction, parallel prediction, parallel update and fusion based on sensor measurement in the IMM structure of each Gaussian component, an updated Gaussian component set is obtained to perform pruning, merging and generation of a new target component, and multi-target tracking is completed.

Description

Technical Field

[0001] This invention belongs to the field of multi-target tracking technology, specifically relating to a multi-target tracking method and system based on Gaussian process interactive multi-model and adaptive noise. Background Technology

[0002] The task of a multi-target tracking system consists of three main stages: a perception stage, which uses sensors such as radar, lidar, or image sensors to scan the observation space and acquire measurement information; a filtering stage, which processes the measurement data returned by the sensors, containing the target's true signal and a large amount of clutter, to achieve target state estimation and trajectory management; and an application stage, which outputs stable and accurate tracking results to the decision-making system for path planning or threat assessment. Among these, tracking performance and tracking accuracy are directly determined by the multi-target tracking filter, which is the core and bottleneck of the entire system.

[0003] Among current mainstream multi-target tracking filters, probability hypothesis density (PHD) filters based on random finite set theory, especially their Gaussian mixture (GM-PHD) implementation, have been widely used due to their theoretical advantages in handling target number uncertainty and clutter environments. However, existing GM-PHD-based tracking methods still suffer from one or more of the following technical shortcomings when dealing with increasingly complex real-world scenarios:

[0004] First, traditional hypothesis management strategies have limitations. Standard GM-PHD filters typically employ fixed-threshold pruning and merging strategies to control the number of Gaussian components. This strategy is primarily designed for idealized scenarios where targets are sparse and far apart. In real-world applications such as autonomous driving and drone swarms, where there are high-density, near-multiple targets, the shortcomings of this strategy are amplified: 1) Merging criteria based on spatial distance may incorrectly merge Gaussian components representing different neighboring targets with similar states into one, directly leading to incorrect target number estimation and track loss; 2) Pruning criteria based on fixed weights may prematurely delete true target components whose weights are temporarily low due to temporary target occlusion or weak sensor signals, thus affecting the continuity of tracking.

[0005] Secondly, and more fundamentally, the problem lies in the inherent inadequacy of the motion model's capabilities. The aforementioned pruning and merging errors are often merely symptoms; the root cause lies in the overly simplistic motion model upon which the filter relies. Standard GM-PHD typically embeds linear models such as constant velocity (CV) and constant acceleration (CA). These models are completely incapable of describing the target's complex nonlinear maneuvers (such as sharp turns and S-shaped maneuvers). When the target performs such maneuvers, the model's predictions deviate significantly from the true trajectory, causing the Gaussian components to fail to correctly correlate with new measurements. Ultimately, these components are pruned or drifted due to insufficient weight and then incorrectly merged.

[0006] While Interactive Multi-Model (IMM-GM-PHD) improves tracking capabilities for known maneuvers by introducing a pre-defined, fixed model library (e.g., adding a cooperative turning model CT), its fundamental limitation lies in its inability to handle complex, unknown, and unpre-defined motion patterns outside the model library. It lacks the ability to learn unique target motion patterns from data, and IMM-GM-PHD also faces the risk of tracking failure when the target exhibits a completely new maneuver.

[0007] Third, there is a lack of real-time, fine-grained adaptive adjustment mechanisms. The parameters of existing filters, especially the process noise covariance (Q), which is crucial for maneuver compensation, are typically set offline or adjusted globally. In multi-target scenarios, different targets may be in different motion states (stationary, constant speed, maneuvering) at the same time. Using a uniform, fixed Q value cannot achieve differentiated processing, while global adjustment lacks real-time capability. Currently, there is a lack of an effective method that can detect the maneuvering intentions of specific targets in real time at the anonymous, grouped Gaussian component level and quickly and independently adjust their model uncertainty parameters.

[0008] In summary, existing technologies still have significant performance bottlenecks in handling multi-target tracking problems involving high mobility, unknown motion patterns, and dense scenes. Summary of the Invention

[0009] The problem this invention aims to solve is the technical difficulties such as severe model mismatch, low tracking accuracy, and easy loss of track in complex scenarios with sudden and strong maneuvers.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise includes the following steps:

[0012] S1. Construct a heterogeneous motion model library that includes a standard motion model, a motion model based on Gaussian process (GP), and an adaptive noise maneuver model;

[0013] S2. Each Gaussian component in the Gaussian mixture probability hypothesis density (GM-PHD) filter is extended and defined as an interactive multi-model (IMM) structure embedded in the heterogeneous motion model library;

[0014] S3. In the prediction and update loop of the filter, within the IMM structure of each Gaussian component, the multiple motion models are subjected to probabilistic interaction, parallel prediction, and parallel update and fusion based on sensor measurements to obtain an updated set of Gaussian components.

[0015] S4. Prune, merge, and generate new target components on the updated Gaussian component set obtained in step S3 to complete multi-target tracking.

[0016] Furthermore, the process noise in the adaptive noise maneuver model constructed in step S1 is time-varying, and the specific implementation method includes the following steps:

[0017] S1.1. Set the state equation of the adaptive noise maneuver model as follows:

[0018]

[0019] in, Let w represent the state vector of the target at time k, F represent the state transition matrix, and w represent the state vector of the target at time k. k-1 Represents the process noise vector;

[0020] S1.2. Assuming the process noise vector is zero-mean Gaussian white noise, the expression is:

[0021]

[0022] in, The process noise covariance matrix;

[0023] Set the process noise in the process noise covariance matrix. The calculation is dynamically adjusted using an adaptive excitation function Ψ, resulting in the expression:

[0024]

[0025] in, This is the baseline value for process noise. This represents the maximum dynamic value of the process noise; It is the weighted average energy of the normalized squared innovation over the past N time steps, which is associated with the Gaussian component spectrum. It is the energy reference threshold for motor detection; It is the gain coefficient used to control the response sensitivity.

[0026] Furthermore, in step S1.2, the adaptive activation function is designed as a logistic function. The resulting expression is:

[0027]

[0028] in, This represents the residual energy.

[0029] Furthermore, the statistical properties of the historical innovation sequence are obtained based on the calculation of the normalized innovation square (NIS); at each filter update time, the normalized innovation square is defined as the quadratic form of the innovation vector at time k and its innovation covariance matrix, and its expression is:

[0030]

[0031] in, Let the normalized squared innovation at time k be the value. Let k be the innovation vector at time k. Let be the new information covariance matrix at time k.

[0032] Furthermore, in step S2, the Gaussian components in the Gaussian mixture model are extended and defined to obtain the extended Gaussian components as follows:

[0033]

[0034] in, Let be the weight of the Gaussian component i at time k-1. Let i be the mean of the Gaussian components i after fusion at time k-1. Let i be the covariance of the Gaussian components i after fusion at time k-1. Let be the set of independent state estimates for each sub-model within the i-th Gaussian component. and Let be the mean and covariance of the j-th sub-model at time k-1, respectively. is the probability weight of the j-th model within Gaussian component i at time k-1; M is the total number of models;

[0035]

[0036] Set up independent state estimates for each sub-model within the Gaussian components. .

[0037] Furthermore, the specific implementation method of step S3 includes the following steps:

[0038] S3.1. In the prediction phase of the filter, probabilistic interaction is performed between motion models for each Gaussian component, and then parallel prediction is performed;

[0039] First, calculate the mixture probability of transitioning from model l to model j. The expression is:

[0040]

[0041] in, It is the inter-model transition probability from model l to model j. Normalization factor;

[0042]

[0043] Then, the initial state after mixing is calculated for each model j. ;

[0044] Parallel prediction involves using the dynamic equations of each model to predict the initial state of each model, resulting in the predicted state. ;

[0045] S3.2. In the measurement-based parallel update and fusion stage of the filter, construct the model fit factor modified standard likelihood, and obtain the modified likelihood for model update and fusion;

[0046] Then construct the modified likelihood. The product of the standard likelihood and the model fit factor is expressed as:

[0047]

[0048] in, For standard likelihood, This is the model fit factor;

[0049] S3.3. Based on the corrected likelihood obtained in step S3.2, the model probability is updated, the sub-model state is updated, the state is fused and the weight is updated using the standard IMM and Kalman filter equations to obtain the updated Gaussian component set.

[0050] A system for a multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise includes a processor, a memory, and a computer program stored in the memory and run on the processor. When the computer program runs, it implements the steps of the multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise as described above.

[0051] The beneficial effects of this invention are:

[0052] This invention presents a multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise, establishing a novel tracking paradigm from "passive following" to "active learning," fundamentally solving the problem of unknown complex maneuvers. Existing technologies, including standard IMM filters, essentially rely on a pre-defined, fixed library of motion models to passively match target behavior. The upper limit of this method is constrained by the designer's prior knowledge, making it unable to handle unique or entirely new maneuvering patterns outside the model library. This invention creatively embeds Gaussian process (GP) models into the IMM framework, achieving a cognitive leap from "following rules" to "learning patterns." The GP model, as a general non-parametric function approximator, can directly learn the target's inherent, unique "motion signature" from its real historical data without any pre-defined physical equations. Therefore, this invention can accurately predict and stably track complex nonlinear trajectories that existing technologies cannot handle, fundamentally solving the tracking failure problem caused by motion model mismatch and greatly expanding the capability boundaries of tracking systems.

[0053] This invention presents a multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise, introducing an online fast adaptive mechanism based on residuals to achieve instantaneous response and refined compensation for sudden maneuvers. When target behavior is highly unpredictable, even learned models may exhibit delays. Existing technologies typically use fixed model parameters, leading to sluggish responses to sudden maneuvers and resulting in target loss. The adaptive noise model introduced in this invention equips the system with a highly sensitive "tactical response unit." This mechanism independently monitors the residual between the "theoretical prediction" and the "harsh reality" in real time for each Gaussian component's spectrum. Once a sustained and significant increase in residuals is detected (a strong signal of maneuver), the system instantaneously and substantially increases the process noise Q of that component's spectrum. This is equivalent to immediately increasing the filter's "error tolerance," allowing it to "discard" old erroneous predictions and place greater weight on new sensor measurements. This technical feature enables this invention to achieve rapid locking and stable tracking capabilities in the face of sudden maneuvers, capabilities that are difficult to match with existing technologies.

[0054] This invention presents a multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise, achieving intelligent decision-making from "hard model switching" to "probabilistic dynamic fusion," greatly improving the algorithm's intelligence and robustness. Traditional multi-model methods are more like a "switching" mechanism among a few limited options. The GP-IMM (Gaussian process interactive multi-model) core constructed in this invention is a probabilistic fusion decision-making framework far more advanced than switching. At each moment, for each potential target, the system does not rigidly select the "optimal" model, but maintains a confidence distribution across all available models (standard, learned, and adaptive). Sensor measurements act as "votes," dynamically adjusting this confidence distribution. This design makes the system's decision-making extremely flexible and robust: when the target's behavior conforms to the learned mode, the weight of the GP model is high; when it suddenly maneuvers, the weight of the adaptive model rapidly increases. The system can always make the most reasonable judgment at the moment by integrating the wisdom of all models in a probabilistic weighted manner. This avoids the decision jitter and errors that may be caused by "hard switching," making the entire tracking system like a thoughtful expert who knows how to weigh various possibilities, and achieving a new level of intelligence and scene adaptability.

[0055] The present invention describes a multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise. By deeply and organically combining data-driven machine learning models, fast online adaptive mechanisms and advanced probabilistic fusion frameworks, it effectively overcomes the fundamental bottleneck of traditional GM-PHD filters when facing complex dynamic targets, and ultimately achieves a significant improvement in multi-target tracking accuracy, robustness and intelligence. Attached Figure Description

[0056] Figure 1 This is a flowchart of a multi-target tracking method based on Gaussian process interactive multiple models and adaptive noise, as described in this invention.

[0057] Figure 2 This is a structural block diagram of a multi-target tracking method based on Gaussian process interactive multiple models and adaptive noise, as described in this invention.

[0058] Figure 3 A schematic diagram of a typical multi-target tracking scenario that includes complex maneuvers and conventional motion, provided by the present invention;

[0059] Figure 4 This is a schematic diagram of a typical multi-target tracking scenario failure that includes complex maneuvers and conventional motion, provided by the present invention.

[0060] Figure 5 This is a schematic diagram of the GP-IMM (Gaussian Process Interactive Multi-Model) structure and adaptive adjustment logic within a single Gaussian component provided by the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0062] Therefore, the following detailed description of specific 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 specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0063] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 -Appendix Figure 5 Detailed explanation is as follows:

[0064] Example 1:

[0065] A multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise includes the following steps:

[0066] S1. Construct a heterogeneous motion model library that includes a standard motion model, a motion model based on Gaussian process (GP), and an adaptive noise maneuver model;

[0067] Furthermore, the process noise in the adaptive noise maneuver model constructed in step S1 is time-varying, and the specific implementation method includes the following steps:

[0068] S1.1. Set the state equation of the adaptive noise maneuver model as follows:

[0069]

[0070] in, Let w represent the state vector of the target at time k, F represent the state transition matrix, and w represent the state vector of the target at time k. k-1 Represents the process noise vector;

[0071] S1.2. Assuming the process noise vector is zero-mean Gaussian white noise, the expression is:

[0072]

[0073] in, The process noise covariance matrix;

[0074] Set the process noise in the process noise covariance matrix. The calculation is dynamically adjusted using an adaptive excitation function Ψ, resulting in the expression:

[0075]

[0076] in, This is the baseline value for process noise. This represents the maximum dynamic value of the process noise; It is the weighted average energy of the normalized squared innovation over the past N time steps, which is associated with the Gaussian component spectrum. It is the energy reference threshold for motor detection; It is the gain coefficient used to control the response sensitivity.

[0077] Furthermore, in step S1.2, the adaptive activation function is designed as a logistic function. The resulting expression is:

[0078]

[0079] in, The residual energy is the key innovation of this formula. It transforms the adjustment of process noise Q from a discrete "on / off" behavior into a smooth, continuous "throttle" behavior. When the residual energy... Slightly above the benchmark When the threshold is reached, Q increases gradually; when it far exceeds the baseline, Q rapidly approaches the maximum maneuver value. This non-linear response mechanism, compared to simple threshold switching, can adapt to different levels of maneuver more stably and precisely, which is something that existing technologies do not possess.

[0080] Furthermore, the statistical properties of the historical innovation sequence are obtained based on the calculation of the normalized innovation square (NIS); at each filter update time, the normalized innovation square is defined as the quadratic form of the innovation vector at time k and its innovation covariance matrix, and its expression is:

[0081]

[0082] in, Let the normalized squared innovation at time k be the value. Let k be the innovation vector at time k. Let be the new information covariance matrix at time k.

[0083] Furthermore, in step S1, the normalized squared innovation over the past N time steps associated with the Gaussian component spectrum is quantized using Mahalanobis distance.

[0084] S2. Each Gaussian component in the Gaussian mixture probability hypothesis density (GM-PHD) filter is extended and defined as an interactive multi-model (IMM) structure embedded in the heterogeneous motion model library;

[0085] Furthermore, in step S2, the Gaussian components in the Gaussian mixture model are extended and defined to obtain the extended Gaussian components as follows:

[0086]

[0087] in, Let be the weight of the Gaussian component i at time k-1. Let i be the mean of the Gaussian components i after fusion at time k-1. Let i be the covariance of the Gaussian components i after fusion at time k-1. Let be the set of independent state estimates for each sub-model within the i-th Gaussian component. and Let be the mean and covariance of the j-th sub-model at time k-1, respectively. is the probability weight of the j-th model within Gaussian component i at time k-1; M is the total number of models;

[0088]

[0089] Set up independent state estimates for each sub-model within the Gaussian components. .

[0090] Furthermore, the standard motion model, such as the uniform velocity (CV) model, has the following state transition equation: ,in Here is the state transition matrix. .

[0091] Gaussian process (GP) motion model: Its state transition is modeled as a Gaussian process, expressed as:

[0092] in, and These are the mean function and covariance kernel function of GP, respectively.

[0093] Furthermore, regarding multi-target tracking in complex scenarios, when studying scenarios such as autonomous driving and drone swarms, the motion patterns of multiple targets (target A, target B) may differ significantly. Target A might be performing simple uniform linear motion, while target B might be executing a complex S-shaped maneuver that is difficult to describe using existing physical models. Traditional methods, which use a single or fixed model library, cannot accurately track both behaviors simultaneously, and are prone to introducing large errors when target B begins its maneuver, ultimately leading to track loss, as will be discussed later. Figure 3 As shown, this invention provides a revolutionary extended definition of the Gaussian component in the traditional GM-PHD filter. At time k-1, a Gaussian component i is no longer solely determined by its weights, mean, and covariance. Instead of being defined as a single entity, it has been expanded into an interactive multi-model structure containing M motion models. In its specific implementation, to endow each Gaussian component with the ability to learn and adapt, its internal IMM model library is innovatively designed to contain at least three different types of motion models.

[0094] S3. In the prediction and update loop of the filter, within the interactive multi-model structure (IMM) containing multiple motion models in each Gaussian component, probabilistic interaction, parallel prediction, and measurement-based parallel update and fusion are performed between the motion models to obtain the updated set of Gaussian components.

[0095] Furthermore, the specific implementation method of step S3 includes the following steps:

[0096] S3.1. In the prediction phase of the filter, probabilistic interaction is performed between motion models for each Gaussian component, and then parallel prediction is performed;

[0097] First, calculate the mixture probability of transitioning from model l to model j. The expression is:

[0098]

[0099] in, It is the inter-model transition probability from model l to model j. Normalization factor;

[0100]

[0101] Then, the initial state after mixing is calculated for each model j. ;

[0102] Parallel prediction involves using the dynamic equations of each model to predict the initial state of each model, resulting in the predicted state. :

[0103] Standard model j: , ;

[0104] GP model g: , ;

[0105] Adaptive noise model: = +( - ) ( , , );

[0106] S3.2. In the measurement-based parallel update and fusion stage of the filter, construct the model fit factor modified standard likelihood, and obtain the modified likelihood for model update and fusion;

[0107] When the measurement set at time k Upon arrival, for each measurement ;

[0108] Then construct the modified likelihood. The product of the standard likelihood and the model fit factor is expressed as:

[0109]

[0110] in, For standard likelihood, This is the model fit factor;

[0111] Standard Likelihood :

[0112]

[0113] The innovation of this formula lies in the fact that it establishes a completely new standard for likelihood quantification. The factor measures the degree to which the statistical properties of the actual residuals deviate from the theoretical expectation. If a model's prediction is very close to the measurement (large L), but the statistical properties of the residuals it produces are significantly inconsistent with its claimed uncertainty S (e.g., a model that claims to be very accurate gives a large residual). The factor will become very small, thus "penalizing" the model's total likelihood. This elevates the evaluation of likelihood from simply "distance" to a higher dimension of "reliability of performance".

[0114] S3.3. Based on the corrected likelihood obtained in step S3.2, the model probability is updated, the sub-model state is updated, the state is fused and the weight is updated using the standard IMM and Kalman filter equations to obtain the updated Gaussian component set.

[0115] Furthermore, subsequent steps such as model probability update, sub-model state update, state fusion, and weight update all employ standard IMM and Kalman filter equations, but their core input—likelihood—has been replaced with our innovative modified likelihood. .

[0116] The model probability update formula becomes:

[0117]

[0118] In this way, the innovative ideas of the invention (adaptive Q and modified likelihood) are seamlessly and logically injected into the core decision loop of the entire filter, where the predicted model probabilities are... .

[0119] Sub-model state update: For each sub-model j, calculate its updated state using the standard Kalman update equation. :

[0120]

[0121] State fusion and weight update involve weighting and fusing all updated sub-model states according to their latest probabilities to obtain the final, single state of the Gaussian component i at time k. :

[0122]

[0123] And update its weight in the entire PhD based on the total likelihood. .

[0124] S4. Prune, merge, and generate new target components on the updated Gaussian component set obtained in step S3 to complete multi-target tracking.

[0125] Furthermore, step S4 is a standard step for the GM-PHD filter, but because the method of this invention can estimate the state more accurately, the subsequent pruning and merging decisions are more reliable. After the adaptive processing of this invention, the filter can better handle situations such as... Figure 3 In the complex scenarios shown, it exhibits the following characteristics: Figure 4The superior performance is demonstrated. For a target A moving at a constant speed, the "standard model" within the component will obtain a high probability; while for a target B performing an S-shaped maneuver, the probabilities of the "GP model" and "adaptive noise model" within its corresponding component will dynamically increase, dominating its state prediction, thus enabling its tracking trajectory to closely match the real trajectory and avoiding the divergence and loss of traditional methods.

[0126] In its implementation, the key parameters and calculations involved in this method are as follows: GP model: obtained through offline Gaussian process regression training on a large amount of typical maneuver trajectory data, its hyperparameters (such as kernel function type, length scale, etc.) are optimized by maximizing the marginal likelihood function. Under the method of this embodiment, a complete filtering cycle enables each Gaussian component to possess independent and intelligent "thinking" and "adapting" capabilities without the need for difficult pre-processing trajectory correlation.

[0127] Example 2:

[0128] A system for a multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise includes a processor, a memory, and a computer program stored in the memory and run on the processor. When the computer program runs, it implements the steps of the multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise as described in Example 1.

[0129] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0130] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise, characterized in that, Includes the following steps: S1. Construct a heterogeneous motion model library that includes a standard motion model, a motion model based on Gaussian process (GP), and an adaptive noise maneuver model; S2. Each Gaussian component in the Gaussian mixture probability hypothesis density (GM-PHD) filter is extended and defined as an interactive multi-model (IMM) structure embedded in the heterogeneous motion model library; S3. In the prediction and update loop of the filter, within the IMM structure of each Gaussian component, multiple motion models are subjected to probabilistic interaction, parallel prediction, and parallel update and fusion based on sensor measurements to obtain an updated set of Gaussian components. The multiple motion models include a standard motion model, a motion model based on Gaussian process (GP), and an adaptive noise maneuver model. S4. Prune, merge, and generate new target components on the updated Gaussian component set obtained in step S3 to complete multi-target tracking; In the adaptive noise maneuver model constructed in step S1, the process noise is time-varying. The specific implementation method includes the following steps: S1.

1. Set the state equation of the adaptive noise maneuver model as follows: in, Let q represent the state vector of the target at time k, F represent the state transition matrix, and q represent the state vector of the target at time k. k-1 Represents the process noise vector; S1.

2. Assuming the process noise vector is zero-mean Gaussian white noise, the expression is: in, The process noise covariance matrix; Set the process noise in the process noise covariance matrix. The calculation is dynamically adjusted using an adaptive excitation function Ψ, resulting in the expression: in, This is the baseline value for process noise. This represents the maximum dynamic value of the process noise; It is the weighted average energy of the normalized squared innovation over the past N time steps, which is associated with the Gaussian component spectrum. It is the energy reference threshold for motor detection; It is the gain coefficient used to control the response sensitivity.

2. The multi-target tracking method based on Gaussian process interactive multiple models and adaptive noise according to claim 1, characterized in that, In step S1.2, the adaptive activation function is designed as a logistic function. The resulting expression is: in, This represents the residual energy.

3. The multi-target tracking method based on Gaussian process interactive multiple models and adaptive noise according to claim 2, characterized in that, The statistical properties of the historical innovation sequence are obtained based on the calculation of the normalized innovation square (NIS). At each filter update time, the normalized squared innovation is defined as the quadratic form of the innovation vector at time k and its innovation covariance matrix, and its expression is: in, Let the normalized squared innovation at time k be the value. Let k be the innovation vector at time k. Let be the new information covariance matrix at time k.

4. The multi-target tracking method based on Gaussian process interactive multiple model and adaptive noise according to claim 1, characterized in that, In step S2, the Gaussian components in the Gaussian mixture model are extended and defined to obtain the extended Gaussian components as follows: in, Let be the weight of the Gaussian component i at time k-1. Let i be the mean of the Gaussian components i after fusion at time k-1. Let i be the covariance of the Gaussian components i after fusion at time k-1. Let be the set of independent state estimates for each sub-model within the i-th Gaussian component. and Let be the mean and covariance of the j-th sub-model at time k-1, respectively. is the probability weight of the j-th model within Gaussian component i at time k-1; M is the total number of models; ； Set up independent state estimates for each sub-model within the Gaussian components. .

5. A multi-target tracking method based on Gaussian process interactive multiple models and adaptive noise according to claim 1 or 4, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. In the prediction phase of the filter, probabilistic interaction is performed between motion models for each Gaussian component, and then parallel prediction is performed; First, calculate the mixture probability of transitioning from model l to model j. The expression is: in, It is the inter-model transition probability from model l to model j. Normalization factor; Then, the initial state after mixing is calculated for each model j. ; Parallel prediction involves using the dynamic equations of each model to predict the initial state of each model, resulting in the predicted state. ; S3.

2. In the measurement-based parallel update and fusion stage of the filter, construct the model fit factor modified standard likelihood, and obtain the modified likelihood for model update and fusion; Then construct the modified likelihood. The product of the standard likelihood and the model fit factor is expressed as: in, For standard likelihood, This is the model fit factor; S3.

3. Based on the corrected likelihood obtained in step S3.2, the model probability is updated, the sub-model state is updated, the state is fused and the weight is updated using the standard IMM and Kalman filter equations to obtain the updated Gaussian component set.

6. A system for multi-target tracking based on Gaussian process interactive multi-model and adaptive noise, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed, implements the steps of a multi-target tracking method based on Gaussian process interactive multi-model and adaptive noise as described in any one of claims 1-5.

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