Three-dimensional extended target tracking method based on adaptive gaussian process under unknown measurement noise

Abstract

The application relates to a three-dimensional extended target tracking method of an adaptive Gaussian process under unknown measurement noise. Firstly, a forgetting factor is adaptively updated by recursively calculating the change rate of the Cramer-Rao lower bound trace, so that the dynamic optimization of filter parameters is realized; then, a projection method based on GP is used to represent a three-dimensional cross-shaped target, three-dimensional point clouds acquired by a sensor are projected to three orthogonal planes, and the three-dimensional extended shape of the target is reconstructed by using two-dimensional contour information; finally, a robust state estimator is constructed by fusing variational Bayesian inference and MCC, the joint posterior distribution of unknown measurement noise and system state is solved by variational approximation, and a cost function is constructed based on the maximum correlation entropy criterion, so that the influence of abnormal values is inhibited in a reweighted manner. The tracking method provided by the application can significantly improve the tracking precision and robustness of a three-dimensional extended target under unknown strong non-Gaussian measurement noise.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional extended target tracking technology, specifically to a three-dimensional extended target tracking method based on an adaptive Gaussian process hyperparameter improved by the Cramer-Rao lower bound under unknown measurement noise. Background Technology

[0002] Radar target tracking technology has made significant progress over the past few decades. When sensor resolution is low, a target returns only one measurement point per scan. Based on this, radar tracking algorithms treat the target as a point target and use this measurement point to estimate the target's motion state. As sensor resolution improves, targets occupy multiple resolution cells, allowing multiple measurement points to be acquired from the target surface at the same sampling time. This enables the target to be modeled as an extended target, and the measurement points are used to estimate the target's motion and profile. In modern anti-missile and air defense, stable tracking and precise interception of high-speed, highly maneuverable incoming targets require tracking algorithms that can effectively handle the complex characteristics of such targets as extended targets. This makes extended target tracking technology an important research direction.

[0003] 3D extended target tracking is a process that improves system situational awareness and target recognition capabilities by simultaneously estimating the target's motion state and 3D structure. Because there is a close coupling between the target's motion state and 3D structure, accurate motion state estimation leads to a more precise 3D structure, and vice versa. Since any target tracking algorithm is built upon a motion model and a target model, establishing an effective model is crucial for the performance of 3D extended target tracking algorithms.

[0004] However, compared to the rapid development of target tracking technology in two-dimensional scenes, research and exploration in the field of three-dimensional extended target tracking lags behind, with only a handful of relevant technical solutions. Most studies remain at the stage of simple three-dimensional extension of basic geometric models, generally using regular geometries such as ellipsoids and cubic bounding boxes to approximate the target's spatial range, which is difficult to accurately characterize targets with obvious directional features, such as aircraft. Kumru and Özkan pioneered the systematic application of GP models for surface learning and state estimation in their recursive three-dimensional Gaussian process (GP) tracking framework. Subsequently, Ebert and Wuensche introduced a squared exponential covariance function with periodic characteristics, significantly enhancing the GP model's ability to characterize complex surface structures. Building on this, Kumru and Özkan proposed a more complete three-dimensional GP morphological learning and tracking model and introduced an efficient projection approximation algorithm, improving computational practicality. Although this unconstrained modeling strategy can estimate targets with irregular shapes, existing GP-based methods usually assume that the statistical characteristics of measurement noise are known. Only when this assumption matches the actual noise environment can the expected tracking performance be achieved. However, in the real physical world, dynamic noise characteristics cause time-varying fluctuations in the noise covariance matrix, resulting in a significant deviation between this assumption and reality, which in turn reduces the performance of the tracking algorithm.

[0005] To overcome the drawback of fixed noise assumptions in existing Gaussian Proof-of-Sight (GP) methods, current techniques focus on adaptive noise filtering, aiming to address the unknown and time-varying characteristics of measurement noise. Unlike GP methods with fixed noise assumptions, these methods can dynamically estimate or correct the noise covariance matrix based on real-time measurement data, thereby maintaining tracking performance in environments with unknown or time-varying noise characteristics. The core lies in how to effectively infer the statistical characteristics of noise online from measurement data. Among them, the Variational Bayesian (VB) method, as a representative adaptive noise estimation method, can dynamically compensate for noise uncertainty by recursively estimating noise parameters through incorporating them into a state-space model.

[0006] However, even joint estimation methods like VB still implicitly assume that the noise follows a Gaussian distribution. This assumption often fails in actual observations such as lidar point clouds—sensor noise often exhibits heavy-tailed non-Gaussian characteristics, making the VB estimator susceptible to abnormal measurement interference, resulting in biased or even divergent results. To achieve better tracking performance in 3D extended target tracking using noise adaptive methods, the following problems still need to be addressed: (1) Existing adaptive filtering methods mostly use fixed hyperparameter settings, making it difficult to dynamically adjust according to changes in the noise environment and lacking theoretical guidance on the lower limit of estimation accuracy. (2) Current methods mainly follow the 2D extended target modeling approach, failing to establish an accurate 3D target geometric representation model, making it difficult to effectively characterize targets with complex spatial structures such as aircraft. (3) Existing estimators lack sufficient ability to suppress non-Gaussian heavy-tailed noise, and are prone to accuracy degradation or even divergence under abnormal measurement interference. Therefore, how to break through the constraints of the Gaussian assumption and develop a robust estimation framework that can simultaneously cope with unknown time-varying noise and non-Gaussian interference has become a key scientific challenge for improving the actual performance of 3D extended target tracking.

[0007] The technical problem that urgently needs to be solved by those skilled in the art is: how to break through the dependence of existing methods on the Gaussian noise assumption, achieve accurate characterization of the geometric structure of three-dimensional extended targets and robust adaptive estimation of unknown time-varying noise, so as to further improve the tracking accuracy and robustness of three-dimensional extended targets under unknown measurement noise conditions. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the present invention aims to provide a three-dimensional extended target tracking method based on an adaptive Gaussian process under unknown measurement noise. Specifically, it is a three-dimensional extended target tracking method based on an adaptive Gaussian process hyperparameter improved by Cramer-Rao lower bound (VB-MCC-PCRLB) under unknown measurement noise. This method can achieve dynamic adaptive adjustment of the forgetting factor, accurate characterization of the target's three-dimensional geometry, and robust suppression of non-Gaussian heavy-tailed noise, thereby improving the tracking accuracy and robustness of three-dimensional extended targets under unknown measurement noise conditions.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A three-dimensional extended target tracking method using an adaptive Gaussian process under unknown measurement noise includes the following steps: S1. Initialize the filter parameters; S2. The calculation of the posterior Cramer-Rao lower bound (PCRLB) is embedded into each round of filtering iteration. The posterior Fisher information matrix is ​​updated in real time according to the current state estimate. The theoretical lower bound of the state estimation accuracy, PCRLB, is obtained by inverting the information matrix. S3. Calculate the trace of PCRLB at each time step, adjust the hyperparameter forgetting factor based on the rate of change of the trace using a progressive strategy, and adaptively update the transition probability matrix and process noise covariance accordingly. S4. Introduce the Variational Bayesian (VB) algorithm to incorporate the covariance of the target state and measurement noise into the joint estimation framework. By minimizing the KL divergence, the approximate posterior probability distribution of the two is calculated online recursively, thereby achieving joint adaptive estimation of the state and noise. S5. For each filtering cycle, execute the VB iterative loop to recursively update the measurement noise covariance. S6. For the multi-measurement characteristics of 3D point clouds, the sample correlation entropy is calculated by Gaussian kernel weighted average of finite projection measurement samples, and the sample average correlation entropy estimation is used to replace the traditional covariance to complete the similarity measurement. S7. For Gaussian noise, the minimum mean square error (MMSE) criterion is used for processing; for non-Gaussian measurement noise, a cost function is constructed based on the maximum correlation entropy (MCC) criterion to achieve robust suppression of non-Gaussian noise. S8. Use the adjusted model parameters as input for the next round of filtering, and repeat S2-S7 to complete a new round of filtering estimation.

[0010] Further, in step S1, the initialization of the filtering parameters includes: setting the initial contour of each plane to a 50-dimensional all-one vector representation, predefining the initial translational and rotational states of the target, defining the initial information matrix and the initial forgetting factor in sequence, and completing the initialization of the prior degree of freedom parameters; the projection planes are selected from three orthogonal planes, and the projection matrices are set accordingly.

[0011] Furthermore, in step S1, for the three-dimensional cross-shaped measurement, the three-dimensional cross-shaped measurement point cloud is projected onto three orthogonal planes respectively. After extracting the two-dimensional contour information of each plane, the original three-dimensional target extended shape is reconstructed using the two-dimensional contour information, which reduces the computational complexity of three-dimensional modeling while preserving the spatial distribution characteristics of the target.

[0012] Further, in step S2, the dynamic calculation of the PCRLB value specifically includes: defining a three-dimensional extended target Fisher information matrix based on partial derivatives and expectations; constructing a joint distribution of target state and measurement according to Bayesian filtering; calculating the target state prediction and prediction covariance at the current time; calculating the Jacobian matrix of the nonlinear measurement function to derive the recursive equation of the Fisher information matrix; after recursively obtaining the Fisher information matrix of the target state at the current time, inverting the matrix to obtain the lower bound of the mean square error of the target state estimation, i.e., PCRLB.

[0013] Further, step S3 specifically includes: the trace of PCRLB reflects the overall accuracy of the current state estimation, and the relative rate of change of the PCRLB trace at adjacent time points is calculated; the forgetting factor is adjusted according to the changing trend of the PCRLB trace using a gradual adjustment strategy: when the PCRLB trace increases, the forgetting factor is increased to accelerate the decay of historical information, and when the PCRLB trace decreases, the forgetting factor is decreased to enhance the weight of historical information; after the forgetting factor adjustment is completed, the transition probability matrix and the process noise covariance matrix are updated accordingly.

[0014] Furthermore, a dead zone adjustment mechanism is introduced in step S3: the forgetting factor is only updated when the absolute value of the relative change rate of the PCRLB trace exceeds a preset threshold, so as to avoid over-responding to random noise fluctuations.

[0015] Furthermore, the target state and measurement noise covariance are jointly estimated, and their posterior probabilities are solved by Bayesian filtering. The approximate distribution of the posterior probability is decomposed into the product of two independent approximate probability densities of the target state and the measurement noise covariance using the VB method. The problem is transformed into minimizing the KL divergence between the approximate distribution and the true posterior. By minimizing the KL divergence, it is found that the posterior of the target state follows a Gaussian distribution, and the posterior of the measurement noise covariance follows an inverse gamma distribution.

[0016] Furthermore, the iterative update of the measurement noise covariance specifically includes: updating the shape and scale parameters of the inverse gamma distribution corresponding to the measurement noise covariance according to the rules of fusing prior information and current measurement; within each filtering cycle, executing the VB iterative loop according to the preset number of iterations, and deriving the measurement noise covariance expression based on 3D projection modeling.

[0017] Furthermore, in step S6, calculating the sample correlation entropy specifically includes: using a Gaussian kernel function to measure the generalized similarity between the state estimation error and the measurement error; and, for the multi-measurement characteristics of the 3D point cloud, calculating the sample correlation entropy by weighted averaging of Gaussian kernels of finite projection measurement samples to obtain the sample average correlation entropy estimate, which adapts to the multi-measurement calculation requirements of three orthogonal projection planes.

[0018] Furthermore, for non-Gaussian measurement noise, a cost function is constructed based on the maximum correlation entropy criterion. The optimal state estimate is derived by differentiating the cost function. An adaptive weight is introduced based on the innovation Mahalanobis distance calculation. The weight of abnormal measurements is reduced through an adaptive reweighting mechanism to suppress the impact of outliers on tracking accuracy. Then, Kalman gain correction, target state update, covariance matrix update, and inverse gamma distribution parameter update are completed in sequence to achieve target state estimation and covariance update.

[0019] Beneficial Effects: This invention proposes a 3D extended target tracking method based on an improved Cramer-Rao lower bound adaptive Gaussian process hyperparameter under unknown measurement noise within an improved 3D projection modeling framework. First, the 3D cross-shaped measurement is projected onto three orthogonal planes. The original 3D shape is reconstructed using the 2D contour information on each plane, establishing a projection model of the target's extended morphology. This accurately represents the spatial distribution characteristics of the target while reducing computational complexity. Then, the rate of change of the PCRLB at each time step and the trace of the lower bound between the current and previous time steps is recursively calculated. This rate of change is used to dynamically adjust the forgetting factor, adaptively balancing the weights of historical information and current measurements in state estimation, thereby improving the response capability to changes in the target's motion state. Finally, the VB method is used to solve the joint posterior distribution of unknown measurement noise and system state through variational approximation, achieving iterative updates of the noise covariance during filtering. A cost function is constructed based on MCC to suppress the influence of abnormal measurement values ​​through reweighting, enhancing the algorithm's robustness in complex environments. The method of the present invention can effectively solve the problem that the tracking accuracy of existing three-dimensional extended target tracking methods is prone to decline under unknown measurement noise conditions, and significantly improve the stability and accuracy of tracking. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of an extended object comparing the existing 2D approximation with the 3D approximation of this invention.

[0021] Figure 2 It is a three-dimensional cross-shaped target projection image.

[0022] Figure 3 These are magnified images of the motion trajectories and morphological estimations of the four algorithms in Simulation Experiment 1.

[0023] Figure 4 This is a comparison chart of the root mean square error and crossover ratio of the four algorithms in simulation experiment 1.

[0024] Figure 5 These are magnified images of the motion trajectory and shape estimation of the four algorithms in Simulation Experiment 2.

[0025] Figure 6 This is a comparison chart of the root mean square error and crossover ratio of the four algorithms in simulation experiment 2.

[0026] Note: Root mean square error (RMSE) and intersection-over-union ratio (IoU) are used to evaluate the accuracy of target motion state estimation and shape estimation, respectively. The smaller the RMSE and the larger the IoU, the higher the tracking accuracy of the algorithm. Detailed Implementation

[0027] 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 a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0028] A three-dimensional extended target tracking method based on an adaptive Gaussian process hyperparameter improved by the Cramer-Rao lower bound under unknown measurement noise is proposed. First, the Cramer-Rao lower bound at each time step and the rate of change of the trace of the lower bound value between the current and previous time steps are recursively calculated. This rate of change is used to characterize the matching degree between the current transition probability matrix and the actual target maneuver, and the forgetting factor is dynamically adjusted based on this to update the transition probability matrix. Then, a three-dimensional cross shape is projected onto three orthogonal planes, and the original three-dimensional shape is reconstructed using the two-dimensional contours on these planes. Finally, a variational Bayesian method is used to solve the joint posterior distribution of the unknown measurement noise and the system state through variational approximation, achieving iterative updating of the noise covariance during the filtering process. Simultaneously, a cost function is constructed based on the maximum correlation entropy criterion to suppress the influence of outliers through reweighting. Specifically, the method includes the following steps S1 to S8.

[0029] Step S1: First, initialize key parameters such as the filter state vector, measurement noise parameters, Gaussian process hyperparameters, and forgetting factor. Set the initial value of the state vector to zero; set the Gaussian process hyperparameters (including signal variance, noise variance, and length scale) to... The initial value of the forgetting factor is set to... The standard deviation of process noise is set to Standard deviation of measurement noise when measurements originate from the target contour Each scan cycle generates 40 measurement points following a Poisson distribution, and the noise covariance matrix... Sampling interval Second.

[0030] like Figure 1 As shown, Figure 1 The upper middle section shows the traditional two-dimensional modeling method, which simplifies the target to a planar outline; the lower section shows the three-dimensional modeling method used in this invention, which fully represents the target's geometric shape in three-dimensional space through cross-shaped measurement point clouds. Based on this, as... Figure 2 As shown, the 3D cross-shaped measurement point cloud acquired by the sensor is projected onto three orthogonal planes (XY plane, XZ plane, and YZ plane). Two-dimensional contour information is extracted on each plane, and these two-dimensional contours are used to reconstruct the original 3D extended shape of the target. This projection modeling method reduces computational complexity while accurately representing the spatial distribution characteristics of the target, providing a foundation for subsequent shape estimation.

[0031] The initial contours of each plane are represented by a 50-dimensional all-one vector, and the initial translational and rotational states of the target are represented as follows: and Projection plane selection Three orthogonal planes are used, and the projection matrix is ​​set accordingly: Set the initial calculation parameters for the Posterior Cramér-Rao Lower Bound (PCRLB). The initial forgetting factor is... Initialize the prior degrees of freedom parameters. Define the initial information matrix required for the PCRLB recursion. The rate of change of its trace is initialized to zero so that the forgetting factor can be dynamically adjusted in subsequent filtering processes to achieve an adaptive response to changes in the target's motion state.

[0032] Step S2: Embed the calculation of PCRLB into the filtering iteration process at each time step, update the Fisher information matrix in real time based on the current state estimate, and then dynamically calculate the PCRLB value at each time step.

[0033] At each filtering time step, the posterior Fisher information matrix of the previous time step is first calculated by combining the system state transition matrix and the process noise covariance matrix. Then, in the measurement update phase, the information increment contributed by the measurement is calculated based on the current measurement value and measurement function, and this increment is added to the Fisher information matrix of the prediction step to obtain the posterior Fisher information matrix of the current time step. The information matrix of the three-dimensional extended target is defined as follows: ; in, and Let the first and second partial derivatives be represented respectively. It is the expectation of state and measurement.

[0034] According to Bayesian filtering, the joint distribution of the target state and the measurement can be expressed as the product of the prior state distribution and the measurement likelihood function, specifically as follows: ; in, for Constant target status, From the initial moment to The sequence of measurements at time points.

[0035] In the filtering prediction stage, the target state prediction at the current time step is first calculated using the state estimate and state transition matrix from the previous time step. Target state prediction at time step and predicted covariance for: ; ; Because of the nonlinear functional relationship between the target state and the measurement, traditional linear Kalman filtering methods cannot be directly applied. To solve this problem, the nonlinear measurement function needs to be linearized and approximated. This is typically achieved using a first-order Taylor expansion, expanding the nonlinear function at the current state prediction value and taking its partial derivatives to construct the Jacobian matrix. The specific expression for this Jacobian matrix is ​​as follows: .

[0036] According to Bayesian estimation theory, the Fisher information matrix is ​​an important metric for measuring the information content of unknown state parameters, characterizing the contribution of measurement data to state estimation. Within a recursive filtering framework, the Fisher information matrix can be recursively calculated through two steps: time update and measurement update, thus reflecting changes in system state uncertainty in real time.

[0037] Based on the joint distribution of the states and measurements described above, the Fisher information matrix can be obtained by calculating the second moment of the logarithmic joint distribution with respect to the state vector. The inverse of this matrix is ​​PCRLB, which provides a quantitative assessment basis for the theoretical lower bound of the filtering accuracy.

[0038] The recursive equation for the Fisher information matrix is: ; Among them, , , and These are the block matrices in the recursive equation of the Fisher information matrix. It is dynamic model information determined by state transitions and process noise. and It is a coupling term between state and noise, used to compensate for the uncertainty of prediction information in the recursion. This refers to the new measurement information determined by the measurement model and measurement noise, and its specific expression is as follows: ; ; ; .

[0039] in for Information matrix of target state at any given time. It is a Jacobian matrix. yes The number of measurements acquired at each time step, according to the Cramer-Rao lower bound theory, dictates that for any unbiased estimator, its estimation error covariance matrix, in a matrix sense, is no less than the inverse of the Fisher information matrix. That is, the inverse of the Fisher information matrix constitutes the theoretical lower bound for the performance of all unbiased estimation methods; the estimation accuracy of any practical filtering algorithm cannot exceed this limit. This lower bound reflects the optimal accuracy achievable for target state estimation under given measurement data conditions and is an important benchmark for evaluating the performance of filtering algorithms. After recursive calculation, the lower bound of the mean squared error of the target state estimation, i.e., the PCRLB value, can be obtained by inverting the information matrix: .

[0040] This value can be used to quantitatively evaluate the theoretical optimal performance of the filtering algorithm, and can also provide guidance for the adaptive adjustment of filter parameters.

[0041] Step S3: Calculate the trace of PCRLB at each time step, make a decision on the adjustment direction and step size of the hyperparameter forgetting factor based on the rate of change of the trace, and adaptively update the transition probability matrix accordingly.

[0042] To dynamically evaluate the changing trend of the theoretical lower bound of the filter estimation accuracy over time, and thus provide a basis for the adaptive adjustment of filter parameters, the relative rate of change of the PCRLB trace at adjacent time points is defined as follows: .

[0043] Based on the changing trend of the PCRLB trace, the forgetting factor λ is adaptively adjusted. To enhance system robustness and avoid over-responding to noise or small fluctuations, a dead-zone adjustment mechanism is introduced: only when the absolute value of the rate of change of the PCRLB trace exceeds a set threshold (in this embodiment, the set threshold is 1.5%)... Parameter updates are only triggered when the system is in a state of flux. This mechanism effectively suppresses random fluctuations while responding promptly to real changes in the system. Furthermore, a gradual adjustment strategy is employed, with the following specific rules: when PCRLB shows a significant upward trend (indicating increased estimation error and a dynamic mismatch between the current model and the target), the forgetting factor is appropriately increased to accelerate the decay of historical information, enabling the filter to adapt to dynamic changes more quickly; when PCRLB shows a downward trend, the forgetting factor is decreased to enhance the weight of historical information, thereby obtaining a smoother shape estimate.

[0044] The update rule for the forgetting factor is designed as follows: .

[0045] In the recursive filtering framework, the forgetting factor controls the fusion weights between historical and current observation data, serving as a core parameter balancing the smoothness and adaptability of the estimation. The magnitude of the forgetting factor not only affects the evolution rate of the transition probability matrix over time but also directly determines the magnitude estimate of the process noise covariance matrix. The transition probability matrix and process noise covariance matrix are updated based on the forgetting factor: ; .

[0046] Step S4: Introduce the Variational Bayesian (VB) algorithm to incorporate the covariance of the target state and measurement noise into the joint estimation framework. By minimizing the KL divergence, the approximate posterior probability distribution of the two is calculated online recursively, thereby achieving joint adaptive estimation of the state and noise.

[0047] Assuming the target's motion state In the filtering process, the variable to be estimated is known, and its dynamic evolution model is known. This is achieved using given measurement data. The measurement includes an unknown covariance matrix. The noise, in other words, requires the system state to be considered. With unknown noise parameters Perform joint estimation, i.e., solve for the posterior probability distribution. The joint estimation problem can be recursively implemented using the following Bayesian filtering framework: .

[0048] However, due to the highly nonlinear characteristics of the system, including nonlinear measurement functions and non-Gaussian noise distribution, it is difficult to directly derive the joint posterior probability. The closed analytical expression is given. To effectively overcome this challenge, the VB algorithm is introduced, which decomposes the complex joint posterior into several independent factors through variational approximation, thereby achieving joint estimation of the target state, shape information, and measurement noise covariance.

[0049] Using the VB method, the approximate distribution of the posterior probability can be expressed as: ; in, and These are the target states. Measurement noise covariance The relevant, yet-to-be-determined, approximate probability density function. The core idea of ​​the VB method is to approximate the true posterior distribution by finding a solvable optimal approximate distribution. This solution process is equivalent to minimizing the KL divergence between the two. The specific definition of KL divergence is as follows: .

[0050] According to VB theory, the optimal approximate distribution is obtained by minimizing the KL divergence between the true posterior and the approximate distribution. Specifically, by fixing one factor and performing variational optimization on the other factor and setting the variation to zero, the iterative update equation satisfied by each approximate factor can be derived as follows: ; .

[0051] Based on the derivation results under the VB framework, the posterior distribution type of each variable can be further inferred. Specifically, the target state... The posterior approximate distribution is a Gaussian distribution, while the measurement noise covariance... The posterior approximate distribution is the inverse gamma distribution: ; .

[0052] Step S5: For each filtering cycle, execute the VB iterative loop to recursively update the measurement noise covariance.

[0053] In each variational iteration, the parameters of the inverse gamma distribution are updated by fusing prior information and measurement residuals. Specifically, the update rules for the shape and scale parameters are as follows: ; .

[0054] in, The dimension of the measurement is represented by the number of units of measurement. (S is the loop number), execute the VB iterative loop. In each iteration: First, fix the current state estimate, and use the projection modeling method to project the 3D cross-shaped measurement point cloud onto three orthogonal planes. Extract the 2D contour information on each plane, and then calculate the measurement noise covariance matrix of the current iteration step based on the projection model. The expression for the measurement noise covariance matrix can be derived as follows: .

[0055] Step S6: For the multi-measurement characteristics of 3D point clouds, calculate the sample correlation entropy by Gaussian kernel weighted average of finite projection measurement samples, and use the sample average correlation entropy estimate to replace the traditional covariance measure.

[0056] In non-Gaussian noise environments, the traditional mean squared error (MSE) criterion is insufficient to accurately characterize the similarity relationship between state estimation error and measurement error. Therefore, this invention introduces correlation entropy as a generalized similarity measure. The generalized similarity between state estimation error A and measurement error B is quantified using correlation entropy. The specific definition of the correlation entropy between A and B is as follows: ; in, It is the joint probability density function between two random variables.

[0057] Correlation entropy is a local similarity measure developed based on the Information Theory Learning (ITL) framework. It not only considers the magnitude of the error but also controls the contribution weights of different error samples through a kernel function, thus effectively suppressing the impact of large errors (outliers) on the estimation results. Ideally, if the joint distribution is known, the correlation entropy can be calculated directly. However, in practical applications, due to interference from unknown non-Gaussian noise in sensor measurements, the joint probability density... Typically, the prior knowledge is unknown. Therefore, this invention employs a Gaussian kernel function to estimate the relevant entropy, mapping error samples to a high-dimensional feature space for similarity measurement. The specific form of the Gaussian kernel function is as follows: ; in, This represents the innovation vector (i.e., the difference between the actual measurement and the predicted measurement). The kernel width controls the local scope of the kernel function. Since the joint probability density function between random variables is often unknown in practical engineering, the theoretical correlation entropy cannot be directly calculated. Therefore, this invention employs a sample-based kernel density estimation method. It calculates the sample correlation entropy by weighted averaging of the Gaussian kernel functions of a finite number of projected measurement samples, and uses the average of the samples to estimate the true statistical correlation entropy. This estimation method effectively adapts to the characteristic of multiple measurements at each time step in 3D point cloud data.

[0058] The formula for calculating the sample correlation entropy is as follows: ; in, for The total number of 3D point cloud measurements at any given time. These are the three orthogonal planes corresponding to the projection of the three-dimensional target. yes Time, Number The measurement was taken at the first Two-dimensional projection measurement of a projection plane yes Time, Number The measurement was taken at the first The predicted measurements of each projection plane are calculated from the target state estimate at the current moment through the projection function.

[0059] Step S7: For Gaussian noise, the minimum mean square error (MMSE) criterion is used for processing; for non-Gaussian measurement noise, a cost function is constructed based on the maximum correlation entropy (MCC) criterion to achieve robust suppression of non-Gaussian noise.

[0060] To effectively address the prevalent non-Gaussian measurement noise (such as heavy-tailed distributions and impulse noise) in practical engineering, traditional minimum mean square error (MMC) criteria struggle to achieve ideal estimation results. Therefore, this invention introduces the MCC criterion to process non-Gaussian noise. MCC, by maximizing the similarity measure of error signals in a high-dimensional feature space, adaptively reduces the weight of large error samples, thereby enhancing the robustness of the filtering algorithm. Based on the MCC criterion, the cost function used in this invention is specifically described as follows: ; in, This represents the cost function constructed based on MCC. This represents the square of the weighted Mahalanobis distance. To obtain the optimal estimate of the state, it is necessary to differentiate the cost function with respect to the state to be estimated, and then set the derivative equal to zero, thereby finding the point where the cost function reaches its extremum. This is achieved by... The optimal estimate is obtained by taking the derivative. The following equation must be satisfied: ; .

[0061] in, This represents the adaptive weights calculated based on the innovation Mahalanobis distance. These weights can be dynamically adjusted according to the statistical characteristics of the innovation. When the innovation is abnormal (such as the appearance of outliers), the weights are automatically reduced, thereby suppressing the influence of outliers on the estimation results.

[0062] Based on this adaptive weight First, calculate the corrected Kalman gain: .

[0063] Then, the target state estimate and state covariance matrix are updated using Kalman gain: ; .

[0064] Finally, the parameters of the inverse gamma distribution are updated according to the VB iteration mechanism. The specific update formula is as follows: .

[0065] Step S8: After completing the above update, output the updated version. The adjusted model parameters (including state estimation, covariance matrix, noise parameters, and GP hyperparameters) are used as the initial input values ​​for the filter at the next time step. Then, the process returns to step S2 and repeats the iterative process from S2 to S7 to complete a new round of filter estimation. The above steps are repeated iteratively to achieve continuous three-dimensional extended target tracking.

[0066] The innovation of this invention is mainly reflected in: (1) An adaptive forgetting factor algorithm based on PCRLB is proposed. By recursively calculating PCRLB online, the filter parameters are embedded into the adaptive control loop to achieve dynamic optimization, which solves the problem that the smoothness and agility of static parameters are difficult to balance in dynamic environments.

[0067] (2) In order to overcome the geometric limitations of traditional models, a GP-based projection method is used to represent the three-dimensional cross-shaped target. The original three-dimensional range of the target is reconstructed by multiple projections of the target, thereby transforming the tracking problem into simultaneously estimating the target state and its projected contour.

[0068] (3) A robust state estimator was constructed by combining VB inference and MCC. This combined strategy effectively improved the tracking accuracy, significantly enhanced the robustness of the algorithm, and effectively suppressed the influence of unknown measurement noise and measurement outliers on state estimation.

[0069] The effectiveness of this invention is verified through simulation experiments. A single three-dimensional cross-shaped maneuvering extended object is used as the experimental tracking object, and the Monte Carlo method is used for the experiment, without involving clutter and missed detection issues. The program executes 300 steps at a time, and the sampling time is set to... .

[0070] In Experiment 1, the target's maneuvering process was set as follows: uniform motion from 0 to 2.5 s, and turning at a rate of [missing information] from 2.5 to 30 s. The turning motion. In Experiment 2, the target's maneuvering process was set as follows: uniform motion from 0 to 5 seconds, and turning motion with a turning rate of 0% from 5 to 17.5 seconds. The turning motion has a turning rate of 17.5~30s. .

[0071] In the above simulation scenario, the tracking performance of the proposed method (VB-MCC-PCRLB) was comprehensively verified by integrating and comparing various algorithms with the original GP model. The algorithms used in the experiment included: (1) VB-MCC-PCRLB: A three-dimensional extended target tracking method based on PCRLB adaptive Gaussian process hyperparameters is proposed under unknown measurement noise.

[0072] (2) PCRLB-EKF: A three-dimensional extended target tracking method based on Gaussian process of PCRLB adaptive forgetting factor is proposed.

[0073] (3) VB-MCC-EKF: A three-dimensional extended target tracking method based on VB and MCC under unknown measurement noise is proposed.

[0074] (4) GP-EKF: Three-dimensional extended target tracking based on extended Kalman filter under unknown measurement noise.

[0075] Reference Appendix Figure 3 , Figure 3 The comparison of the 2D projection tracking performance of the four algorithms in Experiment 1 is presented. Figure 3 (a) shows the tracking performance of the GP-EKF algorithm; Figure 3 (b) shows the tracking performance of the PCRLB-EKF algorithm; Figure 3 (c) shows the tracking performance of the VB-MCC-EKF algorithm; Figure 3 (d) shows the tracking performance of the algorithm (VB-MCC-PCRLB) of this invention; Figure 3 (e) to Figure 3 (h) are magnified views of the corresponding algorithms.

[0076] Reference Appendix Figure 5 , Figure 5 The comparison of the 2D projection tracking performance of the four algorithms in Experiment 2 is presented. Figure 5 (a) shows the tracking performance of the GP-EKF algorithm; Figure 5 (b) shows the tracking performance of the PCRLB-EKF algorithm; Figure 5 (c) shows the tracking performance of the VB-MCC-EKF algorithm; Figure 5 (d) shows the tracking performance of the VB-MCC-PCRLB algorithm of this invention; Figure 5 (e) to Figure 5 (h) are magnified views of the corresponding algorithms.

[0077] Figure 3 and Figure 5 The trajectory of the target in three-dimensional space is shown, where the x, y, and z axes represent the X, Y, and Z axes of a Cartesian coordinate system, respectively. The superior performance of this invention is demonstrated by comparing the shape estimation results of four algorithms with the actual expanded shape of the target at different time periods.

[0078] Furthermore, such as Figure 4 and Figure 6 As shown, where, Figure 4 and Figure 6The red dotted line represents the GP-EKF algorithm, the blue dotted line represents the VB-MCC-EKF algorithm, the green dotted line represents the PCRLB-EKF algorithm, and the purple dotted line represents the VB-MCC-PCRLB algorithm of this invention.

[0079] Figure 4 The experiment demonstrates a comparison of the target tracking performance of four algorithms in Experiment 1. Figure 4 (a) is a comparison chart of the root mean square error of position (RMSE). Figure 4 (b) is a comparison chart of the root mean square error of velocity (Velocity RMSE). Figure 4 (c) is a comparison chart of shape estimation accuracy (IoU). Root mean square error (RMSE) and intersection-over-union (IoU) ratio are used to evaluate the accuracy of target motion state estimation and shape estimation, respectively. A smaller RMSE and a larger IoU ratio indicate higher tracking accuracy. As shown in the chart, the VB-MCC-PCRLB algorithm proposed in this invention outperforms the other three comparative algorithms in all three metrics: position estimation, velocity estimation, and shape estimation. Specifically, in terms of position and velocity estimation, the algorithm of this invention has the lowest RMSE, demonstrating higher motion state tracking accuracy; in terms of shape estimation, the algorithm of this invention has the highest IoU, enabling more accurate estimation of the 3D target.

[0080] Figure 6 Experiment 2 presents a comparison of the target tracking performance of four algorithms. Figure 6 (a) is a comparison chart of the root mean square error of position (RMSE). Figure 6 (b) is a comparison chart of the root mean square error of velocity (Velocity RMSE). Figure 6 (c) is a comparison chart of shape estimation accuracy (IoU). As can be seen from the figure, the VB-MCC-PCRLB algorithm proposed in this invention also outperforms the comparison algorithms in all indicators, further verifying the effectiveness and robustness of the method under different experimental scenarios.

[0081] In summary, this invention proposes a 3D extended target tracking method based on an adaptive hyperparameter Gaussian process improved by PCRLB under unknown measurement noise. It establishes a dynamic hyperparameter adjustment mechanism by combining PCRLB and adaptively updates the forgetting factor through recursive calculation of the rate of change of the PCRLB trace, achieving dynamic optimization of filter parameters and effectively solving the inherent limitation of static parameters in balancing smoothness and agility. A GP-based projection method is used to characterize the 3D cross-shaped target, projecting the 3D point cloud acquired by the sensor onto three orthogonal planes. The 3D extended shape of the target is reconstructed using 2D contour information, which can more accurately approximate the geometry of the real aircraft. A robust state estimator is constructed by integrating VB inference and MCC, solving the joint posterior distribution of unknown measurement noise and system state through variational approximation, and suppressing the influence of abnormal measurement values ​​based on the MCC criterion, effectively improving the estimation accuracy and robustness of the algorithm under non-Gaussian noise environments. Simulation results show that the proposed algorithm can significantly improve the estimation accuracy of the motion state and extended shape of the 3D extended target under unknown strong non-Gaussian measurement noise conditions.

[0082] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A three-dimensional extended target tracking method using an adaptive Gaussian process under unknown measurement noise, characterized in that, Includes the following steps: S1. Initialize the filter parameters; S2. The calculation of the posterior Cramer-Rao lower bound (PCRLB) is embedded into each round of filtering iteration. The posterior Fisher information matrix is ​​updated in real time according to the current state estimate. The theoretical lower bound of the state estimation accuracy, PCRLB, is obtained by inverting the information matrix. S3. Calculate the trace of PCRLB at each time step, adjust the hyperparameter forgetting factor based on the rate of change of the trace using a progressive strategy, and adaptively update the transition probability matrix and process noise covariance accordingly. S4. Introduce the Variational Bayesian (VB) algorithm to incorporate the covariance of the target state and measurement noise into the joint estimation framework. By minimizing the KL divergence, the approximate posterior probability distribution of the two is calculated online recursively, thereby achieving joint adaptive estimation of the state and noise. S5. For each filtering cycle, execute the VB iterative loop to recursively update the measurement noise covariance. S6. For the multi-measurement characteristics of 3D point clouds, the sample correlation entropy is calculated by Gaussian kernel weighted average of finite projection measurement samples, and the sample average correlation entropy estimation is used to replace the traditional covariance to complete the similarity measurement. S7. For Gaussian noise, the minimum mean square error (MMSE) criterion is used for processing; for non-Gaussian measurement noise, a cost function is constructed based on the maximum correlation entropy (MCC) criterion to achieve robust suppression of non-Gaussian noise. S8. Use the adjusted model parameters as input for the next round of filtering, and repeat S2-S7 to complete a new round of filtering estimation.

2. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S1, the initialization of the filtering parameters includes: setting the initial contour of each plane to a 50-dimensional all-one vector representation, predefining the initial translation and rotation states of the target, defining the initial information matrix and the initial forgetting factor in sequence, and completing the initialization of the prior degree of freedom parameters; three orthogonal planes are selected for the projection plane, and the projection matrix is ​​set accordingly.

3. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S1, for the three-dimensional cross-shaped measurement, the three-dimensional cross-shaped measurement point cloud is projected onto three orthogonal planes respectively. After extracting the two-dimensional contour information of each plane, the original three-dimensional target extended shape is reconstructed using the two-dimensional contour information, which reduces the computational complexity of three-dimensional modeling while preserving the spatial distribution characteristics of the target.

4. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S2, the dynamic calculation of the PCRLB value specifically includes: defining a three-dimensional extended target Fisher information matrix based on partial derivatives and expectations; constructing a joint distribution of target state and measurement according to Bayesian filtering; calculating the target state prediction and prediction covariance at the current time; calculating the Jacobian matrix of the nonlinear measurement function to derive the recursive equation of the Fisher information matrix; after recursively obtaining the Fisher information matrix of the target state at the current time, inverting the matrix to obtain the lower bound of the mean square error of the target state estimation, i.e., PCRLB.

5. The three-dimensional extended target tracking method according to claim 1, characterized in that, Step S3 specifically includes: the trace of PCRLB reflects the overall accuracy of the current state estimation, and the relative rate of change of the PCRLB trace at adjacent time points is calculated; the forgetting factor is adjusted according to the trend of the PCRLB trace using a gradual adjustment strategy: when the PCRLB trace increases, the forgetting factor is increased to accelerate the decay of historical information, and when the PCRLB trace decreases, the forgetting factor is decreased to enhance the weight of historical information; after the forgetting factor adjustment is completed, the transition probability matrix and the process noise covariance matrix are updated accordingly.

6. The three-dimensional extended target tracking method according to claim 5, characterized in that, Step S3 also introduces a dead zone adjustment mechanism: the forgetting factor is only updated when the absolute value of the relative change rate of the PCRLB trace exceeds a preset threshold, thus avoiding over-response to random noise fluctuations.

7. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S4, the target state and measurement noise covariance are jointly estimated, and their posterior probabilities are solved by Bayesian filtering. The approximate distribution of the posterior probability is decomposed into the product of two independent approximate probability densities of the target state and the measurement noise covariance using the VB method. The problem is transformed into minimizing the KL divergence between the approximate distribution and the true posterior. By minimizing the KL divergence, it is found that the posterior of the target state follows a Gaussian distribution, and the posterior of the measurement noise covariance follows an inverse gamma distribution.

8. The three-dimensional extended target tracking method according to claim 7, characterized in that, In step S5, the iterative update of the measurement noise covariance specifically includes: updating the shape and scale parameters of the inverse gamma distribution corresponding to the measurement noise covariance according to the rules of fusing prior information and current measurement; within each filtering cycle, executing the VB iterative loop according to the preset number of iterations, and deriving the measurement noise covariance expression based on three-dimensional projection modeling.

9. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S6, calculating the sample correlation entropy specifically includes: using a Gaussian kernel function to measure the generalized similarity between the state estimation error and the measurement error; and, for the multi-measurement characteristics of 3D point clouds, calculating the sample correlation entropy by weighted averaging of Gaussian kernels of finite projection measurement samples to obtain the sample average correlation entropy estimate, which adapts to the multi-measurement calculation requirements of three orthogonal projection planes.

10. The three-dimensional extended target tracking method according to claim 1, characterized in that, In step S7, for non-Gaussian measurement noise, a cost function is constructed based on the maximum correlation entropy criterion. The optimal state estimate is derived by taking the derivative of the cost function. An adaptive weight is introduced based on the innovation Mahalanobis distance calculation. The weight of abnormal measurements is reduced through an adaptive reweighting mechanism to suppress the influence of outliers on tracking accuracy. Then, Kalman gain correction, target state update, covariance matrix update and inverse gamma distribution parameter update are completed in sequence to complete the target state estimation and covariance update.

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