A tracking method for high-speed high-mechanism moving targets

Abstract

The application provides a tracking method for high-speed high-maneuvering target, through adaptive adjustment of model parameters in time sequence by using adaptive fence division, each motion model in the interactive model set can spontaneously adapt and better match the current target maneuvering mode, the application can effectively reduce excessive dependence of the prior information of model parameters in the model set of the traditional maneuvering target tracking algorithm, realize more accurate tracking of the maneuvering target; and the application faces highly complex target maneuvering mode, adopts the more robust dangerous sensitive filtering estimation method for model type and target motion measurement noise uncertainty, therefore can effectively reduce excessive dependence of the prior information of model type in the model set of the traditional maneuvering target tracking algorithm, and meet the tracking demand of high-speed high-maneuvering target.

Description

Technical Field

[0001] This invention belongs to the field of maneuvering target tracking technology, specifically relating to a tracking method for high-speed, highly maneuverable targets. Background Technology

[0002] Maneuvering target tracking technology is a popular research topic in the field of target tracking, and it is commonly used in defense engineering such as UAV defense and radar detection. Compared with ordinary non-maneuvering target tracking, maneuvering target tracking is more difficult, mainly because the motion rules of maneuvering targets are complex, and it is difficult to accurately describe the motion patterns of maneuvering targets using a single motion model. Therefore, using single-model filtering algorithms (such as the Kalman filter algorithm) under the traditional Bayesian tracking theory framework to track maneuvering targets often results in large trajectory deviations, ultimately leading to non-convergence of tracking errors.

[0003] To address the issue of non-single motion models for maneuvering targets, maneuvering target tracking algorithms are often combined with the concept of multi-model adaptive control, resulting in an adaptive algorithm with a Markov transition probability structure—the Interacting Multiple Model (IMM) algorithm. The core idea of ​​the IMM algorithm is to use a set of parallel Kalman filters instead of a single Kalman filter. Each Kalman filter employs a different motion model to match different target motion states, and the transitions between various motion models utilize Markov chains. Through the parallel operation and dynamic weight adjustment of this set of Kalman filters, the final state estimation is achieved, thus enabling adaptive state filtering of the dynamic system when the statistical laws governing system noise and measurement noise change unknownly.

[0004] However, the traditional IMM algorithm also has limitations for high-speed, highly maneuverable targets. Specifically, high-speed, highly maneuverable targets exhibit undesirable motion patterns and highly uncertain speeds. Furthermore, the traditional IMM algorithm heavily relies on a prior set of interaction models; when the models in the prior set cannot adequately match the target's high-speed maneuvering, significant tracking errors still occur. To address this issue, researchers proposed combining the IMM algorithm with graph theory, resulting in the improved AG-IMM algorithm. This algorithm uses an adaptive fence partitioning method, selecting the covariance value estimated by the tracking filter as the basis for fence adjustment, adaptively adjusting the parameters of the target model (i.e., adaptively adjusting the model set) to obtain the model set that best describes the current maneuvering target's motion pattern. Experiments demonstrate that this algorithm achieves higher tracking accuracy than the IMM algorithm in high-speed maneuvering target tracking scenarios.

[0005] Because the filtering process in the AG-IMM algorithm uses standard Kalman filtering, it still has two drawbacks in high-speed, high-maneuverability target tracking scenarios:

[0006] On the one hand, the core idea of ​​the AG-IMM algorithm is to modify the model's parameters through adaptive fencing, but it cannot modify the model type. For high-speed maneuvering targets, their motion models are often advanced maneuvering models (such as Jerk models, Single models, etc.), and they exhibit complex and diverse changes at different times, making the target model's category unknown from the outset. Under these circumstances, the AG-IMM algorithm usually does not achieve good tracking results.

[0007] On the other hand, the AG-IMM algorithm requires specifying the measurement noise of the target motion for tracking. However, for high-speed maneuvering targets, prior information such as measurement noise is often unavailable. Therefore, when the measurement noise of the target motion is unknown, the tracking accuracy of the AG-IMM algorithm will be reduced. Summary of the Invention

[0008] To address the aforementioned problems in the existing technology, this invention provides a tracking method for high-speed, high-mobility moving targets. The technical problem to be solved by this invention is achieved through the following technical solution:

[0009] Step 1: Obtain target measurement information of the moving target detected by the detection device within the detection range at the previous moment, and extract the state vector of the moving target at the previous moment from the target measurement information;

[0010] Step 2: Using the unscented transformation method, based on the set of interaction models used when tracking the maneuvering target in the previous moment, the model-related parameters of each motion model, and the target-related parameters of the maneuvering target, solve the filtered information state at the current moment. Then, using the filtered information state at the current moment, solve the state vector of the target predicted by each motion model at the current moment and the prediction covariance matrix corresponding to each motion model.

[0011] The interaction model set includes multiple motion models, and the model-related parameters include: functional parameters that fully describe the motion model, model probabilities, error covariance matrix, and Markov chain transition probability matrix between each motion model; the target-related parameters of the maneuvering target include process noise matrix and measurement noise matrix.

[0012] Step 3: Based on the current state vector and the prediction covariance matrix corresponding to each motion model, calculate the innovation residual, residual covariance matrix, updated target state vector, and corresponding updated covariance matrix for each model at the current time.

[0013] Step 4: Calculate the model probability of each motion model at the current time based on the information residuals of each motion model at the current time, the updated covariance matrix, and the model probability of each motion model at the previous time.

[0014] Step 5: The model probabilities, updated target state vectors, and updated covariance matrices of each motion model at the current time are fused separately for each motion model, so as to obtain the model fusion probability, fusion state vector and fusion covariance matrix at the current time. The fusion state vector at the current time is used as the danger-sensitive filter estimation result at the current time.

[0015] Step 6: Using the information residuals and residual covariance matrices of each model at the current time, perform fence partitioning on each model to adjust the functional parameters of each model in the interactive model set.

[0016] Step 7: Using the adjusted set of interaction models, calculate the Markov chain transition probability matrix at the current time.

[0017] Step 8: When the next moment arrives, the process of steps 1 to 7 is repeated, taking the next moment as the current moment, to predict the state vector of the maneuvering target in the time series, thereby realizing the continuous tracking of the maneuvering target.

[0018] The beneficial effects of this invention are:

[0019] This invention provides a tracking method for high-speed, high-mobility moving targets. It proposes a technical concept combining adaptive fence partitioning and multi-model hazard-sensitive filtering. This invention improves the model set parameter determination method in the traditional IMM algorithm by utilizing an adaptive fence partitioning method, while simultaneously introducing multi-model hazard-sensitive filtering estimation to improve the filtering process in the traditional IMM algorithm. This effectively solves the shortcomings of the traditional IMM algorithm in tracking maneuvering targets, such as heavy reliance on prior information and significant limitations on the maneuvering modes of the targets that can be tracked. Specifically, this invention has the following advantages compared to existing maneuvering target tracking technologies:

[0020] First, by using adaptive fence partitioning to adaptively adjust the model parameters over time, the motion models in the interactive model set can spontaneously adapt and better match the current target's maneuvering mode. This invention can effectively reduce the excessive reliance of traditional maneuvering target tracking algorithms on the prior information of model parameters in the model set, and achieve more accurate tracking of maneuvering targets.

[0021] Second, this invention addresses highly complex target maneuvering patterns by employing a more robust danger-sensitive filtering estimation process that is less sensitive to uncertainties in model type and target motion measurement noise. Therefore, it can effectively reduce the heavy reliance of traditional maneuvering target tracking algorithms on prior information about model types in the model set, thus meeting the tracking requirements for high-speed, highly maneuverable targets.

[0022] Third, this invention combines the advantages of adaptive fence partitioning for tracking when the target model category can be determined, and the advantages of hazard-sensitive filtering estimation for tracking when the target model category cannot be determined, and achieves an effective combination of the two through model parameter integration and updating.

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating a tracking method for high-speed, high-mobility moving targets provided by an embodiment of the present invention;

[0025] Figure 2(a) is a schematic diagram of the trajectory of the maneuvering target in simulation experiment 1;

[0026] Figure 2(b) is a schematic diagram of the filtering trajectories of the three algorithms in simulation experiment 1;

[0027] Figure 2(c) is a comparative diagram of the RMSE algorithms of the three algorithms in simulation experiment 1;

[0028] Figure 2(d) is a schematic diagram comparing the time consumption of the three algorithms in simulation experiment 1;

[0029] Figure 3(a) is a schematic diagram of the trajectory of the maneuvering target in simulation experiment 2;

[0030] Figure 3(b) is a schematic diagram of the filtering trajectories of the three algorithms in simulation experiment 2;

[0031] Figure 3(c) is a comparative diagram of the RMSE algorithms of the three algorithms in simulation experiment 2;

[0032] Figure 3(d) is a schematic diagram comparing the time consumption of the three algorithms in simulation experiment 2. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0034] To address this problem, the IMM algorithm can be combined with graph theory to obtain the improved AG-IMM algorithm. This algorithm uses an adaptive fence partitioning method, selecting the covariance value estimated by the tracking filter as the basis for fence adjustment, and adaptively adjusting the parameters of the target model (i.e., adaptively adjusting the model set) to obtain the model set description that best matches the current maneuvering target motion pattern. Experiments show that this algorithm can achieve higher tracking accuracy than the IMM algorithm in high-speed maneuvering target tracking scenarios. The following is a detailed description of the tracking method for high-speed, high-mobility moving targets provided by this invention.

[0035] like Figure 1 As shown, the present invention provides a tracking method for high-speed, high-mobility moving targets, comprising:

[0036] Step 1: Obtain target measurement information of the moving target detected by the detection device within the detection range at the previous moment, and extract the state vector of the moving target at the previous moment from the target measurement information;

[0037] This step acquires target measurement information of a moving target detected by radar or other sensors within their detection range at the previous moment; extracts the state vector of the moving target at the previous moment from the target measurement information; the state vector includes the coordinate position and velocity of the moving target in the Cartesian coordinate system.

[0038] Let the current time be k, the previous time be k-1, and the state vector of the k-1 maneuvering target be [x(k-1), y(k-1), v]. x (k-1),v y (k-1)] T Where x(k-1) and y(k-1) represent the x-coordinate and y-coordinate of the maneuvering target in the Cartesian coordinate system at time k-1, respectively, and v x (k-1) and v y (k-1) represent the velocity components along the horizontal and vertical axes of the maneuvering target at time k-1 in the Cartesian coordinate system. At this point, the observation matrix used to extract the target coordinate information is: The extracted target coordinate information is [x(k-1), y(k-1)]. T It is worth noting that when the tracking scene is in a three-dimensional Cartesian coordinate system, the target's state vector consists of its coordinates and velocity information along the three axes [x(k-1), y(k-1), z(k-1), v]. x (k-1),v y (k-1),v z (k-1)] T At this point, the observation matrix used to extract target coordinate information is: The extracted target coordinate information is [x(k-1), y(k-1), z(k-1)]. T .

[0039] Step 2: Using the unscented transformation method, based on the set of interaction models used when tracking the maneuvering target in the previous moment, the model-related parameters of each motion model, and the target-related parameters of the maneuvering target, solve the filtered information state at the current moment. Then, using the filtered information state at the current moment, solve the state vector of the target predicted by each motion model at the current moment and the prediction covariance matrix corresponding to each motion model.

[0040] The interaction model set includes multiple motion models, and the model-related parameters include: functional parameters that fully describe the motion model, model probabilities, error covariance matrices, and Markov chain transition probability matrices between the motion models; the target-related parameters of the maneuvering target include the process noise matrix Q = λ*Q. c and measurement noise matrix;

[0041] Where λ is the density of process noise, Q c The measurement noise matrix is ​​a matrix compatible with the dimension of the state vector. Where m k Let δ be the dimension of the observed information. i Let n be the observation error of the i-th observation. The set of interaction models includes n. k For a given motion model, the CT [CT: uniform turning] model or an approximate CV model are typically chosen, and their model parameters are as follows: Among them, w n For the set n k Each motion model corresponds to a functional parameter that can fully describe the model.

[0042] This step utilizes the danger-sensitive filtering estimation results from the previous moment to solve for the filtering information state at the current moment; based on the filtering information state at the current moment, it calculates the state vector of the maneuvering target predicted by each motion model at the current moment and the prediction covariance matrix corresponding to each motion model.

[0043] It is worth noting that the models in the model set can be freely set in this step. For example, other advanced maneuvering models, such as the Jerk model or the Single model, can be added. At the same time, the process noise matrix and the measurement noise matrix can also be freely set.

[0044] For ease of explanation, this application defines k-1 as the initial time, where k-1 = 0. The Markov chain transition probability matrix between each motion model is as follows: The initial model probabilities for each model are: π ijLet represent the transition probability distribution among motion models, where ij is the index of each motion model in the interaction model set, and has . Generally speaking, the initial model probabilities should remain equal, that is... The initial state vector of the maneuvering target is represented as [x(0), y(0), v]. x (0),v y (0)] T The error covariance matrix is ​​Σ0 for all cases.

[0045] It is worth noting that: Let the filter estimate of the danger-sensitive filter at time k be... This value is the filter estimate from the danger-sensitive filter at time k-1. It is obtained through recursion in time sequence (i.e., prediction step → update step), let the intermediate quantity generated in the prediction step be represented as... This intermediate quantity is the predicted result of the state vector, and it is easy to see that this intermediate quantity depends on the motion model j. The key to this step is to obtain the state vector at time k. and its corresponding prediction covariance matrix The solution process is explained below:

[0046] In hazard-sensitive filtering, filter estimation With filter information status There are explicit conversion relationships, so you can generally directly... To obtain by recursion in time sequence This step can be specifically divided into the following two sub-steps:

[0047] Step 21: Estimate the danger sensitivity using time k-1. Determine the filter information state at time k. First, define the intermediate information state. The following equation (1) can be obtained:

[0048]

[0049] Among them, pure saturation This is called the danger sensitivity coefficient; k is the current time; k-1 is the previous time; W k The weight matrix is ​​positive definite; z k It is the measurement of the maneuvering target at time k; This represents a unit vector where the j-th position is 1 and the other positions are 0, used to represent the index of a model in the set of interaction models; This represents the danger-sensitive filter estimation result at the previous moment; Indicates intermediate information state; π ij Let represent the transition probability distribution between models, where i and j are the indices of each model in the interaction model set, and have . p(z) represents the Markov chain transition probability matrix at the previous time step. k ) indicates measurement z k The prior probability density of p(z); k |x,e j ) indicates measurement z k Likelihood probability density; W k-1 This represents a positive definite weight matrix; N represents the number of models in the interaction model set. Represents an n-dimensional real vector or space; r k Represents the model index at time k; Pr{·} represents the conditional probability;

[0050] In multi-model estimation, the computational complexity of the optimal solution grows exponentially. To overcome this problem, the classic IMM method is used for approximation in this sub-step. Specifically, assume the filtered information state at time k-1. It is approximated by a Gaussian distribution, that is:

[0051]

[0052] in Let be the model probability corresponding to the j-th model in the model set at time k-1, then the intermediate information state We also approximate it using a Gaussian term, that is...

[0053]

[0054] The parameters in the above formula are calculated as follows:

[0055]

[0056]

[0057]

[0058] Then we get:

[0059]

[0060] The parameters in the above formula are calculated as follows:

[0061]

[0062]

[0063]

[0064] Step 22: Based on the filtered information state at time k Obtain the target state prediction results under each model. and the corresponding prediction covariance matrix

[0065] Note that the system's state equation and measurement equation can be expressed as:

[0066]

[0067]

[0068] Where, f j (·) represents the parameter w j The state transition matrix g corresponding to model j j (·) represents the parameter w j The observation matrix corresponding to model j (generally, the observation matrices of all models should be consistent); Q k R k These are the process covariance matrix and the observation covariance matrix, respectively, with B and D being matrices of corresponding compatibility dimensions.

[0069] The status of the filtered information can be further obtained.

[0070]

[0071] To solve the high-dimensional integral in the above equation, the unscented transform technique can be used to give the closed-loop form of the expression. That is, based on the state mean and the corresponding covariance matrix, 2n+1 weighted σ points (n is the dimension of the state vector) are generated. The first unscented transform is then performed on the integral part contained in the filtered information at the current time to obtain the Gaussian density function of the filtered information. The process of the first unscented transform is as follows:

[0072]

[0073]

[0074]

[0075] Therefore, the Gaussian density function of the filtered information can be obtained:

[0076]

[0077] The parameters on the right-hand side of the above equation represent the predicted state vector of the maneuvering target at the current moment, which the model depends on. and the corresponding prediction covariance matrix The calculation formula is as follows:

[0078]

[0079]

[0080] in, s = 0, 1, ..., 2n s = n+1,…,2n represents the index of point σ, W s σ represents the weight of the selected σ point in the stepless transformation; 2n+1 represents the total number of selected σ points in the stepless transformation; κ represents the scaling factor, which is usually set to a positive number; f represents the state prediction that model j depends on at time k-1; j (·) represents the parameter w j The state transition matrix g corresponding to model j j (·) represents the parameter w j The observation matrix corresponding to model j; Q j B represents the process noise matrix of the j-th model; j Represents the process noise matrix Q j Dimensionally compatible process control matrix; (·) T This indicates finding the transpose of a matrix.

[0081] Combining formulas (13) and (17), the state of the filtered information at time k is... It can be represented as:

[0082]

[0083] in, For measuring z under hazardous sensitivity k The probability density function, Let be the residual covariance matrix that model j depends on at time k-1. Both are Gaussian probability density functions;

[0084] Step 3: Based on the current state vector and the prediction covariance matrix corresponding to each motion model, calculate the innovation residual, residual covariance matrix, updated target state vector, and corresponding updated covariance matrix for each model at the current time.

[0085] Step 3 includes:

[0086] Step 31: Apply the unscented transformation to the product of the Gaussian probability density functions in formula (20) again to obtain the output of the model-dependent unscented transformation.

[0087] Step 32: Based on the unscented transformation results in Step 31, calculate the innovation residual of each model, the residual covariance matrix of each model, and the state-measurement cross-covariance matrix of each model at the current moment, using the state vector of the maneuvering target and the corresponding prediction covariance matrix.

[0088] according to Find the residual covariance matrix of the model dependency at time k. and the model-dependent state-measure cross-covariance matrix The specific formula is as follows:

[0089]

[0090]

[0091]

[0092] The innovation residuals of each model at time k are obtained as follows:

[0093] Step 33: Based on the residual covariance matrix and the state-measurement cross-covariance matrix at the current time, calculate the updated target state vector and the updated covariance matrix at the current time.

[0094] Based on the obtained and Calculate the updated target state vector that the model depends on at time k. and the corresponding updated covariance matrix

[0095]

[0096]

[0097] in, Let represent the model probability of the j-th motion model at time k. Let g represent the model probability of the j-th motion model at time k. j {} represents the measurement function; R k D represents the measurement noise matrix; j Represents the measurement noise matrix R k Dimensionally compatible measurement control matrix; Let represent the residual covariance matrix of the i-th motion model at time k. Let represent the residual covariance matrix of the j-th motion model at time k. Let represent the residual covariance matrix of the i-th motion model at time k. Let the residual covariance matrix of the j-th motion model at time k be denoted as . Let represent the prediction covariance matrix at time k.

[0098] Step 4: Calculate the model probability of each motion model at the current time based on the information residuals of each motion model at the current time, the updated covariance matrix, and the model probability of each motion model at the previous time.

[0099] This step includes: Step 41: Calculate the likelihood value of each motion model at the current time based on the innovation residuals and updated covariance matrix of each motion model at the current time; Step 42: Calculate the model probability of each motion model at the current time based on the likelihood value of each motion model at the current time and the model probability of each motion model at the previous time.

[0100] The new residuals of each model at time k have been obtained. And the residual covariance matrix of each model is The likelihood values ​​for each model are:

[0101]

[0102] Based on the likelihood value and the probabilities of each model at time k-1 The model probabilities of each model at time k can be calculated:

[0103]

[0104] in, This represents the model probability at time k-1. This represents the model fusion probability at time k-1.

[0105] Step 5: The model probabilities, updated target state vectors, and updated covariance matrices of each motion model at the current time are fused separately for each motion model, so as to obtain the fused model probabilities, fused state vectors, and fused covariance matrices at the current time. The fused state vector at the current time is used as the danger-sensitive filtering estimation result at the current time.

[0106] From the transition probabilities of each model at time k-1 in the aforementioned steps, the state of the filtered information at time k can be obtained as follows:

[0107]

[0108] Therefore, the danger-sensitive filtering estimation result at time k can be obtained as follows:

[0109]

[0110] It is worth noting that the above equation involves higher-order integrals, so there is no explicit solution. To obtain an explicit solution to the optimization problem above, we further approximate the Gaussian mixture term in the integral on the right-hand side of the above equation with a Gaussian distribution. Right now:

[0111]

[0112] The model fusion probability in the above formula is expressed as:

[0113]

[0114] The state vector after model fusion is represented as:

[0115]

[0116] The covariance matrix after model fusion is expressed as:

[0117]

[0118] Where M represents the number of models.

[0119] Finally, the danger-sensitive filter estimation result and the corresponding covariance matrix at time k are obtained as follows:

[0120]

[0121]

[0122] Step 6: Using the information residuals and residual covariance matrices of each model at the current time, perform fence partitioning on each model to adjust the functional parameters of each model in the interactive model set.

[0123] The innovation residuals and residual covariance matrices of each model at time k are respectively expressed as follows: This step can be divided into the following four sub-steps:

[0124] Step 61: Calculate the distance function of each motion model based on the innovation residuals and residual covariance matrix of each motion model at the current time;

[0125] use and Find the distance function for each model at time k. The distance function is expressed as:

[0126] Step 62: Based on the likelihood values ​​of each motion model at the current time, calculate the cross-likelihood matrix among the motion models at the current time;

[0127] Based on the likelihood values ​​of each model at time k Find the model cross-likelihood matrix at time k. in Let the cross-likelihood matrix between model i and model j be expressed as:

[0128]

[0129] Step 63: For each motion model, determine whether the distance function of the motion model is greater than the threshold. If it is, adjust the functional parameters of the motion model adaptively according to the update formula that includes the adaptive fence step size.

[0130] If the setting is Where the scalar ◇ is the index value of the model with the highest transition probability in the model set, if (M is the threshold, usually a constant less than 10), then the fence step size is:

[0131]

[0132] Where G0 is the initial fence step size. Step size limit parameter ( The larger the step size G is, the smaller the step size G becomes. The step size is used to adjust the model set parameters. To perform adaptive adjustments, the update formula that includes the adaptive fence step size is as follows:

[0133]

[0134] Wherein, scalar◇ is the index value of the motion model with the highest transition probability in the Markov chain in the set of interaction models; α and β both represent the index value of the model.

[0135] Step 64: If the distance function is not greater than the threshold, then the functional parameters of the motion model are adaptively adjusted according to the update formula that does not include the adaptive fence step size;

[0136] Conversely if Then, by performing a probabilistic approximation on the interaction model set at time k, we have an update formula that does not include the adaptive fence step size:

[0137]

[0138] Among them, the set of functional parameters Indicates the nth k Functional parameters of a motion model.

[0139] This yields the model set parameters at time k. The model parameters will be used to represent the state equation and measurement equation at the next time step.

[0140] Step 7: Using the adjusted set of interaction models, calculate the Markov chain transition probability matrix at the current time.

[0141] This step includes:

[0142] Step 71: Calculate the merging probability of the motion models based on the model probability of each motion model at the current time and the fusion model probability;

[0143] Define the model merging probability:

[0144]

[0145] in, It is the model probability calculated in step 7.

[0146] Step 72: Based on the mutual likelihood matrix, merging interaction probability, and Markov chain transition probability matrix of the motion models at the current time, calculate the Markov chain transition probability matrix of each motion model at the current time.

[0147] Based on the model cross-likelihood matrix Φ at time k k and the model transition probability matrix П at time k-1 k Find the Markov chain transition probability matrix at time k.

[0148]

[0149] Among them, the probability intermediate quantity

[0150] Step 8: When the next moment arrives, the process of steps 1 to 7 is repeated, taking the next moment as the current moment, to predict the state vector of the maneuvering target in the time series, thereby realizing the continuous tracking of the maneuvering target.

[0151] It is worth noting that as time goes by, time k-1 passes and time k arrives, the algorithm recursively repeats steps 1 to 7 until the state filtering result and the corresponding filtering covariance matrix from the initial tracking time to the tracking termination time (i.e., the target stopping time) are obtained, thus achieving continuous tracking of the target.

[0152] The following two simulation experiments further illustrate the aforementioned beneficial effects of the present invention:

[0153] Simulation settings:

[0154] A high-speed, high-maneuverability target tracking method based on adaptive fence partitioning and multi-model hazard-sensitive filtering is adopted. It is assumed that the target moves in a two-dimensional plane, and the target's state vector is [x(k), y(k), v]. x (k),v y (k)] T The radar or sensor is located at the origin of the coordinate system, and the information it observes is the polar coordinate information of the target (range and angle information), i.e., h(k) = [l(k), θ(k)]. T Therefore, a target measurement model can be constructed:

[0155]

[0156] Where δl and δθ represent the ranging error and angular measurement error of the sensor, respectively. The target's process noise matrix is ​​also defined. Where θ = 5 is the process noise density, T = 1s is the sampling interval, and I2 is the second-order identity matrix.

[0157] Depending on the target's maneuvering state and prior information, the embodiments of the present invention are simulated and compared with existing commonly used maneuvering target tracking algorithms in two scenarios. The algorithms compared include the standard IMM algorithm and the traditional AGIMM algorithm. Scenario 1: Target with weak maneuvering + prior information known; Scenario 2: Target with strong maneuvering + prior information unknown.

[0158] Simulation Experiment 1: Target with Weak Maneuvering + Prior Information Known

[0159] Important note: The prior information at this point includes: ① the model parameters and types in the model set; ② the covariance matrix of the measurement noise.

[0160] Simulation conditions:

[0161] In Simulation 1, since the prior information is known, we can directly assume:

[0162] The measurement covariance matrix is ​​R = diag

[40] 2 0.02 2 (That is, the sensor ranging error is 40m and the angle measurement error is 0.02°).

[0163] The model set includes approximate CV models and ordinary CT models; therefore, the state transition matrix of the target can be represented as:

[0164]

[0165] Where i is the model index in the model set, w i These are the parameters corresponding to model i. In this simulation, the model set is set to have three models, namely... Furthermore, there are counterclockwise CT models with w1 = 18°, approximate CV models with w2 = 0.01°, and clockwise CT models with w3 = -18°.

[0166] Simulation content and results:

[0167] The total simulation time step for Simulation 1 is set to 100 seconds, with a sampling interval of 1 second, resulting in 100 simulation time points. The target's motion comprises four stages:

[0168] Phase 1: 1–40 seconds, uniform linear motion;

[0169] Phase Two: 41–60s, counter-clockwise turning motion, turning angular velocity ω = 18° / s;

[0170] Phase 3: 61–65 seconds, uniform linear motion;

[0171] Phase 4: 66-100s, clockwise turning motion, turning angular velocity ω=-18° / s.

[0172] The target's trajectory is shown in Figure 2(a). The initial transition probability matrix is ​​set as follows:

[0173]

[0174] The initial probabilities for each model are:

[0175]

[0176] The initial spacing of the adaptive fence partitioning is G0 = 0.2°, and the partitioning threshold is M = 7. A high-speed, high-maneuverability target tracking method combining adaptive fence partitioning and multi-model hazard-sensitive filtering is used to track the target. The results are as follows: Figures 2(b) to 2(d) As shown: Figure 2(b) shows a comparison of the filtered trajectories after tracking using the three algorithms; Figure 2(c) shows a comparison of the RMSE (root mean square error) of the three algorithms; Figure 2(d) shows a comparison of the computation time of the three algorithms.

[0177] Simulation Result Analysis

[0178] Figure 2(b) shows the filtered trajectory diagrams obtained by tracking a maneuvering target with weak maneuverability and known prior information using a maneuvering target tracking method based on adaptive fence partitioning and multi-model hazard-sensitive filtering, as well as two comparative methods and theoretical data association. It can be seen that all three methods can effectively track the target. Among them, the filtered trajectory of the AG-IMM algorithm and the algorithm proposed in this invention is closer to the actual motion trajectory of the maneuvering target than the traditional IMM algorithm.

[0179] Figure 2(c) shows the RMSE (distance RMSE and speed RMSE) for tracking the maneuvering target using three algorithms. It can be seen that the RMSE of the AG-IMM algorithm and the algorithm proposed in this embodiment are not much different. This is because, under known prior conditions, the effect of hazard-sensitive filtering is actually inferior to that of standard Kalman filtering. However, based on the above-mentioned "output fusion" process, the algorithm proposed in this embodiment will be approximately transformed into the AGIMM algorithm in this case. Therefore, there is no significant difference in the tracking effect between the two algorithms. In addition, the RMSE of both algorithms is smaller than that of the traditional IMM algorithm, indicating that the two algorithms can achieve more accurate tracking of maneuvering targets than the traditional IMM algorithm.

[0180] Figure 2(d) shows the time consumption (in seconds) for tracking the maneuvering target using three algorithms. It can be seen that since the time complexity of the hazard-sensitive filtering and Kalman filtering algorithms is the same (the hazard-sensitive filtering is slightly higher), there is no significant difference in the computational cost between the two algorithms. At the same time, both algorithms add an adaptive fence partitioning process to the traditional IMM algorithm, so their computational cost is higher than that of the traditional IMM algorithm.

[0181] Simulation Experiment 2: Target with Strong Maneuvering + Unknown Prior Information

[0182] Simulation conditions:

[0183] In Simulation 2, since the prior information is unknown, we can assume that:

[0184] The measurement covariance matrix is ​​R = diag

[80] 2 0.02 2 (That is, the sensor ranging error is 80m and the angle measurement error is 0.02°). However, when generating measurements based on the measurement model, δl = 40m and δθ = 0.04° are set to ensure that the prior information is consistent.

[0185] Similarly, assume the model set contains approximate CV models and ordinary CT models. In this simulation, the model set is set to have three models, namely... Furthermore, there are counterclockwise CT models with w1 = 4.5°, approximate CV models with w2 = 0.01°, and clockwise CT models with w3 = -4.5°.

[0186] Simulation content and results:

[0187] The total simulation time step for Simulation 2 is set to 100 seconds, with a sampling interval of 1 second, resulting in 100 simulation time points. The target's motion comprises six stages:

[0188] Phase 1: 1-20s, uniform linear motion;

[0189] Phase Two: 21–40 seconds, counter-clockwise turning motion, turning angular velocity ω = 14° / s;

[0190] Phase 3: 41–60s, counter-clockwise turning motion, turning angular velocity ω=5° / s;

[0191] Phase 4: 66–100s, clockwise turning motion, turning angular velocity ω=-14° / s;

[0192] Phase 5: 71–80s, uniform linear motion;

[0193] Phase Six: 71–80s, clockwise turning motion, turning angular velocity ω=-4° / s;

[0194] The target's maneuvering is more intense than in Simulation 1, and the motion model used is completely different from the pre-set model set, thus ensuring the unknown nature of the prior model set information.

[0195] The target's trajectory is shown in Figure 3(a), and other parameters are set consistently as in Simulation 1. A high-speed, high-maneuverability target tracking method based on adaptive fence partitioning and multi-model hazard-sensitive filtering was used to track the target, and the results are shown in Figure 3(a). Figures 3(b) to 3(d) As shown: Figure 3(b) shows a comparison of the filtered trajectories after tracking using the three algorithms; Figure 3(c) shows a comparison of the RMSE (root mean square error) of the three algorithms; Figure 3(d) shows a comparison of the computation time of the three algorithms.

[0196] Simulation Result Analysis

[0197] Figure 3(b) shows the filtered trajectory diagrams obtained by tracking a maneuvering target with strong maneuverability and unknown prior information using a maneuvering target tracking method that combines adaptive fence partitioning and multi-model hazard-sensitive filtering, as well as two comparative methods and theoretical data association. It can be seen that all three methods can effectively track the target. Among them, the filtered trajectory of the algorithm proposed in this invention is closer to the actual motion trajectory of the maneuvering target than the AG-IMM algorithm and the traditional IMM algorithm.

[0198] Figure 3(c) shows the RMSE indices (distance RMSE and velocity RMSE) corresponding to the tracking of the maneuvering target using three algorithms. It can be seen that the algorithm proposed in this embodiment is significantly superior to the AGIMM algorithm and the traditional IMM algorithm. This is because in the tracking environment where the prior conditions or model parameters are unknown, the danger-sensitive filter is more robust than the standard Kalman filter, thus ensuring the tracking accuracy of the algorithm and making the proposed algorithm more adaptable to the complex and ever-changing motion patterns of highly maneuvering targets.

[0199] Figure 3(d) shows the time consumption (in seconds) for tracking the maneuvering target using three algorithms. Similar to Simulation 1, the proposed algorithm and the AGIMM algorithm have higher time complexity than the traditional IMM algorithm, thus taking longer. However, it is worth noting that in Simulation 2, the proposed algorithm employs more hazard-sensitive filtering, which has a slightly higher time cost than the standard Kalman filter, resulting in the proposed algorithm taking longer than the AGIMM algorithm.

[0200] Based on the results of the two simulation experiments above, it can be seen that in scenarios with unknown parameters, such as tracking of highly maneuverable targets, the tracking algorithm proposed in this embodiment of the invention can track the target well and has a significant advantage in tracking accuracy compared to the traditional IMM algorithm. Therefore, the tracking algorithm proposed in this embodiment of the invention can meet the tracking requirements of high-speed, highly maneuverable targets and is innovative.

[0201] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0202] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0203] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A tracking method for high-speed, high-mobility moving targets, characterized in that, include: Step 1: Obtain target measurement information of the moving target detected by the detection device within the detection range at the previous moment, and extract the state vector of the moving target at the previous moment from the target measurement information; Step 2: Using the unscented transformation method, based on the set of interaction models used when tracking the maneuvering target in the previous moment, the model-related parameters of each motion model, and the target-related parameters of the maneuvering target, solve the filtered information state at the current moment. Then, using the filtered information state at the current moment, solve the state vector of the target predicted by each motion model at the current moment and the prediction covariance matrix corresponding to each motion model. Step 2 includes: Step 21: Using the danger-sensitive filter estimation result from the previous moment, solve for the filter information state at the current moment; the filter information state at the current moment is represented as: Among them, pure saturation This is called the hazard sensitivity coefficient; The current moment; The previous moment; The weight matrix is ​​positive definite. yes Measurement of maneuvering targets at any given time; Indicates the first A unit vector with one 1 and the rest 0 is used to represent the index of a model in the set of interaction models; This represents the danger-sensitive filter estimation result from the previous moment; Indicates the intermediate information status; This represents the transition probability distribution between models. This is the index of each model in the interaction model set, and it has... ; Let be the Markov chain transition probability matrix at the previous time step; Indicates measurement The prior probability density; Indicates measurement The likelihood probability density; Represents a positive definite weight matrix; This indicates the number of models in the interaction model set; Represents an n-dimensional real vector or space; express Model index at time step; {·} represents conditional probability; express Target coordinate information at any given time; Step 22: Based on the current filtered information state, obtain the state vector of the maneuvering target predicted by each motion model at the current time and the prediction covariance matrix corresponding to each motion model; The danger-sensitive filter estimation result from the previous time step is obtained by performing an unscented transform. Then, the state vector of the maneuvering target predicted by each motion model at the current time is represented as: The prediction covariance matrix for each motion model is: in, , , express Point index, Indicating the selection in the infinite transformation Point weights; Indicating the selection in the infinite transformation The total number of points; This represents the scaling factor and is set to a positive number. express Time-of-flight model Dependency state prediction; For parameters model The corresponding state transition matrix, For parameters model The corresponding observation matrix; Indicates the first The process noise matrix of each model; Representation of process noise matrix Dimensionally compatible process control matrix; This indicates finding the transpose of a matrix. Perform a first unscented transform on the integral part of the filtered information state at the current moment to obtain... The state of the filter information at any time It can be represented as: in, Measurement under hazardous sensitivity conditions The probability density function, for The residual covariance matrix that the model at time j depends on. Both are Gaussian probability density functions; The interaction model set includes multiple motion models, and the model-related parameters include: functional parameters that fully describe the motion model, model probabilities, error covariance matrix, and Markov chain transition probability matrix between each motion model; the target-related parameters of the maneuvering target include process noise matrix and measurement noise matrix. Step 3: Based on the current state vector and the prediction covariance matrix corresponding to each motion model, calculate the innovation residual, residual covariance matrix, updated target state vector, and corresponding updated covariance matrix for each model at the current time. Step 4: Calculate the model probability of each motion model at the current time based on the information residuals of each motion model at the current time, the updated covariance matrix, and the model probability of each motion model at the previous time. Step 5: The model probabilities, updated target state vectors, and updated covariance matrices of each motion model at the current time are fused separately for each motion model, so as to obtain the model fusion probability, fusion state vector and fusion covariance matrix at the current time. The fusion state vector at the current time is used as the danger-sensitive filter estimation result at the current time. Step 6: Using the information residuals and residual covariance matrices of each model at the current time, perform fence partitioning on each model to adjust the functional parameters of each model in the interactive model set. Step 7: Using the adjusted set of interaction models, calculate the Markov chain transition probability matrix at the current time. Step 8: When the next moment arrives, the process of steps 1 to 7 is repeated, taking the next moment as the current moment, to predict the state vector of the maneuvering target in the time series, thereby realizing the continuous tracking of the maneuvering target.

2. The tracking method for high-speed, high-velocity moving targets according to claim 1, characterized in that, Step 1 includes: Step 11: Obtain target measurement information from the previous moment when the radar or other sensors were within detection range and detected the moving target; Step 12: Extract the state vector of the maneuvering target at the previous moment from the target measurement information; The state vector includes the coordinate position and velocity of the maneuvering target in the Cartesian coordinate system.

3. The tracking method for high-speed, high-velocity moving targets according to claim 1, characterized in that, Step 3 includes: Step 31: For The state of the filter information at any time The product of the Gaussian density functions is subjected to a second unscented transformation to obtain the output of the model-dependent unscented transformation. ; Step 32: Based on the unscented transformation results in Step 31, calculate the innovation residual of each model, the residual covariance matrix of each model, and the state-measurement cross-covariance matrix of each model at the current moment, using the state vector of the maneuvering target and the corresponding prediction covariance matrix. Step 33: Based on the residual covariance matrix and the state-measurement cross-covariance matrix at the current time, calculate the updated target state vector and the updated covariance matrix at the current time.

4. The tracking method for high-speed, high-velocity moving targets according to claim 3, characterized in that, In step 31 The state of the filtered information at time t is represented as follows: The residual covariance matrix in step 32 is: The state-measurement cross-covariance matrix in step 32 is: The new information residual in step 32 is: In step 33, the updated target state vector at the current time is represented as: The updated covariance matrix at the current time in step 33 is represented as follows: in, , Indicates the first A motion model in The model probability at time step [time]. Represents the measurement function; Represents the measurement noise matrix; Representation and measurement noise matrix Dimensionally compatible measurement control matrix; Indicates the first A motion model in The residual covariance matrix at time t. Indicates the first A motion model in The residual covariance matrix at time step 1.

5. The tracking method for high-speed, high-velocity moving targets according to claim 4, characterized in that, Step 4 includes: Step 41: Calculate the likelihood value of each motion model at the current time based on the new residuals of each motion model and the updated covariance matrix; The likelihood values ​​of each motion model at the current time are expressed as: Step 42: Calculate the model probability of each motion model at the current time based on the likelihood value of each motion model at the current time and the model probability of each motion model at the previous time. The model probabilities of each motion model at the current time are expressed as follows: in, express The model probability at time step [time]. express The model fusion probability at time step.

6. The tracking method for high-speed, high-velocity moving targets according to claim 5, characterized in that, The model fusion probability in step 5 is expressed as: The state vector after model fusion is represented as: The covariance matrix after model fusion is expressed as: Where M represents the number of motion models in the interaction set model.

7. The tracking method for high-speed, high-velocity moving targets according to claim 6, characterized in that, Step 6 includes: Step 61: Calculate the distance function of each motion model based on the innovation residuals and residual covariance matrix of each motion model at the current time; The distance function is expressed as: ; Step 62: Based on the likelihood values ​​of each motion model at the current time, calculate the cross-likelihood matrix among the motion models at the current time; The mutual likelihood matrix is ​​expressed as: ; Step 63: For each motion model, determine whether the distance function of the motion model is greater than the threshold. If it is, adjust the functional parameters of the motion model adaptively according to the update formula that includes the adaptive fence step size. The update formula that includes the adaptive fence step size is as follows: in, , This is the initial fence step size. The step size limit parameter is scalar. This is the index value of the motion model with the highest transition probability in the Markov chain within the set of interaction models; , All represent the index values ​​of the model; Step 63: If the distance function is not greater than the threshold, then the functional parameters of the motion model are adaptively adjusted according to the update formula that does not include the adaptive fence step size; The update formula, excluding the adaptive fence step size, is as follows: Among them, the set of functional parameters , Indicates the first Functional parameters of a motion model.

8. The tracking method for high-speed, high-velocity moving targets according to claim 7, characterized in that, Step 7 includes: Step 71: Calculate the merging probability of the motion models based on the model probability of each motion model at the current time and the fusion model probability; Step 72: Based on the mutual likelihood matrix, merging interaction probability, and Markov chain transition probability matrix of the motion models at the current time, calculate the Markov chain transition probability matrix of each motion model at the current time. Wherein, the merging probability is expressed as The Markov chain transition probability matrix at the current moment is expressed as: , intermediate probability .

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