A tracking trajectory optimization method for task-oriented hierarchical goal motion characteristics

Abstract

The application relates to a task-oriented tracking trajectory optimization method for hierarchical target motion characteristics, which adopts BCRLB as a resource allocation model for a measurement function of target tracking performance, considers different threat degrees of targets and possible cutting-off situations of the targets when moving, sets threat degrees for targets with different threat degrees, sets an attenuation factor for the possible cutting-off situations which seriously affect the target tracking performance, takes the steady flight speed and the turning speed of the wingman as optimization variables, takes minimizing the target estimated state error as a target, establishes a resource allocation model under the premise of meeting various constraints, obtains the motion state of each wingman at each time and further obtains the flight trajectory of each wingman, finally completes the task of the tracking trajectory optimization oriented to the task hierarchy and the target motion characteristics, and realizes the highest-precision tracking.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a tracking trajectory optimization method based on the target motion characteristics of a mission-level target. Background Technology

[0002] In modern battlefield environments, integrating radar networks onto UAV swarm platforms is an increasingly common reconnaissance and counter-reconnaissance tactic. When airborne radar performs reconnaissance missions, it must not only conduct a complete search of the target area but also continuously track high-threat key targets within that area. However, when the radar cuts off from the target (radial velocity is 0), the echo signal is lost in clutter, severely impacting target tracking performance. Therefore, establishing a reasonable resource allocation mechanism for distributed radar networks and optimizing the trajectories of wingman swarms are crucial for improving target tracking accuracy.

[0003] Since the 1980s, many countries have been dedicated to research on automated trajectory planning systems and the collaborative optimization allocation of networked radar transmission resources. NASA has developed the ANOE (Automatic Novel Orientation and Pathfinding) real-time route planning system. To adapt to 3D environments, Majumder et al. proposed an algorithm for incremental path search throughout the entire flight. Princeton University scholar Godrich proposed a power allocation method based on a Multiple-Input Multiple-Output (MIMO) radar platform, reducing transmission power while meeting target positioning accuracy requirements. Domestically, Zeng Yong et al. from Southeast University used UAVs as a communication platform and proposed a trajectory planning scheme to improve communication performance. For multi-target localization and tracking tasks, Professor Yi Wei from the University of Electronic Science and Technology of China proposed an on-demand resource allocation algorithm for MIMO radar, aiming to achieve multi-target tracking with minimal transmission power while maintaining accuracy. Professor Yan Junkun of Xidian University has constructed a vector optimization model with the goal of minimizing total resource consumption and multi-target positioning / tracking errors. This model can allocate and manage system launch resources on demand. He also proposed a network radar power allocation method, which can effectively extend the target tracking distance in clutter backgrounds. For single-target tracking tasks under asynchronous working conditions, he proposed a corresponding network radar resource allocation method, which can significantly improve the target tracking accuracy.

[0004] In general, many scholars at home and abroad have conducted a lot of research on optimizing the trajectory direction of wingman swarms to improve tracking accuracy and system resource allocation under different application conditions. However, current trajectory optimization work has only explored specific and simple scenarios. The working method of wingman swarms is simply a replication of individual wingmen. It is not well integrated with the distributed detection background of wingman swarms and the resource allocation of each wingman is not precise enough under the condition of limited total resources. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a tracking trajectory optimization method based on the motion characteristics of target targets categorized by task hierarchy. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a tracking trajectory optimization method based on the motion characteristics of a task-level target, comprising:

[0007] Step 1: Establish the target motion model based on the Singer motion model;

[0008] Step 2: Establish a wingman motion model, where the level flight speed of the i-th wingman at time k is... and angular velocity As the motor control variable to be optimized

[0009] Step 3: Establish a measurement model based on the target motion model and the wingman motion model;

[0010] Step 4: Based on the measurement model, determine the resource allocation model using BCRLB, wherein at least one of a threat coefficient and a decay factor is added to the resource allocation model;

[0011] Step 5: Solve for the optimal solution of the resource allocation model to obtain the optimal values ​​of the maneuver control variables of each wingman at each time point, and complete the tracking trajectory optimization based on the target motion characteristics of the mission hierarchy.

[0012] In one embodiment of the present invention, step 1 includes:

[0013] Suppose there are Q targets moving in arbitrary ways in the plane, and establish the state of target q at time k as follows:

[0014]

[0015] Among them, (x T,q,k ,y T,q,k () represents the position coordinates of target q at time k. This represents the velocity component of target q at time k. This represents the acceleration component of target q at time k;

[0016] Using the dynamic equations of the Singer model and the state of target q at time k, the target motion model is established as follows:

[0017] x T,q,k+1 =f T (x T,q,k ,t k+1 -t k )+u(t k+1 -t k );

[0018] Among them, f T (.) denotes the state transition function for objective q. Indicates the target at fusion time t k The process of fusion vectors, Follows a pattern with a mean of 0 and a covariance of 0. Gaussian distribution;

[0019]

[0020] Where I2 represents the 2D identity matrix, This represents the direct product operation, T0 = t k+1 -t k α represents the fusion time interval, α represents the maneuver frequency, and T represents the sampling period.

[0021] In one embodiment of the present invention, step 2 includes:

[0022] Suppose N wingmen are flying in a two-dimensional plane, and the state of the i-th wingman at time k is:

[0023]

[0024] in, Let represent the position coordinates of the i-th wingman at time k. Let x represent the angle between the flight direction of the i-th wingman at time k and the x-axis;

[0025] Based on the state of the i-th wingman at time k, the following state transition equation for the i-th wingman at the next time step is obtained:

[0026]

[0027] Based on the following state transition equation for the i-th wingman at the next moment, the wingman motion model is established as follows:

[0028]

[0029] in, Let d represent the state vector of all wingmen at time k-1. k This represents the maneuver control variables for all wingmen at time k. The noise represents the process noise, which follows a mean of 0 and a covariance of 0. The Gaussian distribution.

[0030] In one embodiment of the present invention, step 3 includes:

[0031] Based on the state of the i-th wingman at time k and the state of the target q at time k, the measurement function is established as follows:

[0032]

[0033] Among them, R i,k,q Let θ represent the distance measurement between the i-th wingman and target q at time k. i,k,q Let represent the azimuth angle measurement of the i-th wingman relative to target q at time k;

[0034] Based on the measurement function, the measurement model is established as follows:

[0035]

[0036] Among them, w i,k,q Let denot be the measurement noise of the i-th wingman's measurement of target q at time k, with a mean of 0 and a covariance of Σ. i,k,q Gaussian distribution;

[0037]

[0038]

[0039] in, Let represent the measurement variance of the distance measurement value between the i-th wingman and the target q at time k. Let β represent the measurement variance of the azimuth angle measurement of the i-th wingman towards the target q at time k. i B represents the transmission signal bandwidth of the radar of the i-th wingman. i Let S and R represent the 3dB receive beamwidth of the radar of the i-th wingman, respectively. i,k,m Let represent the signal-to-noise ratio of the radar echo signal of the i-th wingman at time k.

[0040] In one embodiment of the present invention, step 4 includes:

[0041] Based on the measurement model and the target motion model, the normalized estimate BCRLB of the target q state is obtained as follows:

[0042] F(d i,k )=Tr(Λ·(B- 1 (x T,q,k+1 )) 4×4 ·Λ T );

[0043] Where Tr(·) represents the trace, 4×4 represents taking the first 4×4 dimensions of the target state estimate, Λ is the normalization matrix, and B -1 (x T,q,k+1 ) denotes the lower bound of the variance of the filtered estimate;

[0044] The normalized BCRLB estimate of the target state q is supplemented with a threat coefficient to classify the tracking task, resulting in the BCRLB with added threat coefficient:

[0045]

[0046] Where, ω q This represents the threat level coefficient of target q;

[0047] The normalized estimate of the target q-state, BCRLB, is obtained by adding a decay factor to avoid flyaway phenomenon. The BCRLB with the decay factor is:

[0048]

[0049] Where, α i,q,k+1 Indicates the attenuation factor.

[0050] The resource allocation model is determined based on the addition of a threat coefficient or a decay factor to the BCRLB:

[0051]

[0052] In one embodiment of the present invention, step 5 includes:

[0053] The optimal solution of the resource allocation model at time k is obtained by using a genetic algorithm, and the optimal values ​​of the maneuver control variables of each wingman at time k are obtained.

[0054] Based on the measured value of the measurement model at time k and the optimal solution of the resource allocation model at time k, the predicted state of target q at time k+1 and the prediction covariance matrix corresponding to the predicted state are calculated.

[0055] Based on the predicted state and the predicted covariance matrix, the extended Kalman filter algorithm is used to perform state recursion estimation to obtain the state estimate of target q at time k+1 and the covariance matrix corresponding to the state estimate.

[0056] Let k = k + 1, and perform iterative loops to obtain the optimal values ​​of the maneuver control variables for each wingman at each time step.

[0057] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0058] 1. The tracking trajectory optimization method of the present invention, which is based on the motion characteristics of target under different task levels, takes into account targets with different threat levels, distinguishes between key tracking targets and non-key tracking targets, and allocates different resources to them, so that the tracking accuracy of the former is improved and the tracking accuracy of the latter is reduced to adapt to different working scenarios;

[0059] 2. The tracking trajectory optimization method of this invention, based on the target motion characteristics categorized by task level, considers the scenario of target and wingman aircraft cutting off from each other. When this happens, the echo signal is annihilated in clutter, severely affecting target tracking performance. By incorporating an attenuation factor into the resource allocation model, the tracking path of the wingman cluster can be rationally planned, avoiding the cutting-off phenomenon at its source and enabling the wingman cluster to efficiently complete the tracking task.

[0060] 3. The tracking trajectory optimization method of the present invention, which is based on the target motion characteristics of the mission hierarchy, optimizes the level flight speed and turning speed of each wingman in the context of a multi-radar multi-target system, so as to achieve the maximum tracking accuracy under the condition of limited resources.

[0061] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0062] Figure 1 This is a flowchart of a tracking trajectory optimization method based on the motion characteristics of a task-level target provided in an embodiment of the present invention;

[0063] Figure 2 This is a wingman flight status diagram provided in an embodiment of the present invention;

[0064] Figure 3 This is the trajectory diagram without optimization provided in the embodiments of the present invention;

[0065] Figure 4 This is an optimized trajectory diagram provided in an embodiment of the present invention;

[0066] Figure 5 This is a comparison chart of tracking accuracy before and after optimization provided in an embodiment of the present invention;

[0067] Figure 6 This is a trajectory comparison diagram obtained under the task classification scenario provided in the embodiments of the present invention;

[0068] Figure 7 This is a comparison chart of the tracking accuracy after grading provided in the embodiments of the present invention;

[0069] Figure 8 This is a comparison diagram of the wingman's trajectory before and after considering the target characteristics, provided in an embodiment of the present invention.

[0070] Figure 9 This is a comparison chart of tracking accuracy before and after adding an attenuation factor, provided in an embodiment of the present invention. Detailed Implementation

[0071] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail, with reference to the accompanying drawings and specific embodiments, a tracking trajectory optimization method based on the task-level target motion characteristics proposed in this invention.

[0072] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0073] Example 1

[0074] Please see Figure 1 , Figure 1 This is a flowchart of a tracking trajectory optimization method based on the motion characteristics of a task-level target provided in this embodiment of the invention. As shown in the figure, the tracking trajectory optimization method based on the motion characteristics of a task-level target in this embodiment includes:

[0075] Step 1: Establish the target motion model based on the Singer motion model;

[0076] Suppose there is a target q, q = 1, ... Q, in a plane, which can move in any way. Based on the Singer motion model, the motion model of the target is established as follows:

[0077] x T,q,k+1 =f T (x T,q,k ,t k+1 -t k )+u(t k+1 -t k (1);

[0078] Among them, f T (.) denotes the state transition function for objective q. Indicates the target at fusion time t k The process of fusion vectors, Follows a pattern with a mean of 0 and a covariance of 0. The Gaussian distribution of x. T,q,k The state of target q at time k is expressed as:

[0079]

[0080] Among them, (x T,q,k ,y T,q,k () represents the position coordinates of target q at time k. This represents the velocity component of target q at time k. This represents the acceleration component of target q at time k.

[0081] The Singer model is a standard model for describing maneuvers, covering target motion patterns between uniform linear motion (CV) and uniformly accelerated linear motion (CA). Treating the acceleration a(t) as a stationary stochastic process, the autocorrelation function is:

[0082]

[0083] Where α is the maneuver frequency, It is the variance of the target acceleration.

[0084] The kinetic acceleration a(t) is described by a first-order time-dependent model with white noise as input:

[0085]

[0086] The dynamic equations of the continuous-time Singer model can then be expressed as:

[0087]

[0088] Where ω(t) represents white noise with zero mean and variance is... After discretizing equation (5) according to the sampling period T, the discrete state equation of the Singer model can be obtained as follows:

[0089]

[0090] Where I2 represents the 2D identity matrix, This represents the direct product operation, T0 = t k+1 -t k This represents the fusion time interval. When αT→∞, the target tends to CV motion; when αT→1, the target tends to CA motion.

[0091] The noise covariance matrix is:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] The Singer model proposes a three-dimensional uniform symmetric distribution to model acceleration, which can relatively well describe the instantaneous maneuvering characteristics of a maneuvering target, specifically the target maneuver amplitude σ. 2 The probability density function can be expressed as:

[0100]

[0101] Step 2: Establish a wingman motion model, where the level flight speed of the i-th wingman at time k is... and angular velocity As the motor control variable to be optimized

[0102] Suppose N wingmen are flying in a two-dimensional plane, and let the state of the i-th wingman at time k be:

[0103]

[0104] in, Let represent the position coordinates of the i-th wingman at time k. Let represent the angle between the flight direction of the i-th wingman at time k and the x-axis, and let represent the flight direction of the wingman, such as... Figure 2 The diagram shown is a wingman flight status diagram provided by an embodiment of the present invention.

[0105] The level flight speed of the i-th wingman at time k and angular velocity As a control variable for maneuver resources to be optimized

[0106]

[0107] Level flight speed and angular velocity Limited by the wingman platform, level flight speed The range is angular velocity The range is The following equation can be used to obtain the following state transition equation for the i-th wingman at the next moment:

[0108]

[0109] Define the state vector of all wingmen as The maneuver resource control variables of all wingmen at time k. The state transition equations for all wingmen are:

[0110]

[0111] Similarly, by adding process noise, the wingman motion model is obtained as follows:

[0112]

[0113] in, The noise represents the process noise, which follows a mean of 0 and a covariance of 0. The Gaussian distribution.

[0114] Step 3: Establish a measurement model based on the target motion model and the wingman motion model;

[0115] The measurement model is used to combine the wingman's motion with the target's motion to represent the radar's target tracking process. Let x represent the state of the i-th wingman at time k. T,q,k Let the measurement function represent the state of target q at time k:

[0116]

[0117] Among them, R i,k,q Let θ represent the distance measurement between the i-th wingman and target q at time k. i,k,q Let represent the azimuth angle measurement of the i-th wingman relative to target q at time k. Therefore, the measurement equation for the i-th wingman relative to target q at time k is:

[0118]

[0119] Among them, w i,k,q Let denot be the measurement noise of the i-th wingman's measurement of target q at time k, with a mean of 0 and a covariance of Σ. i,k,q The Gaussian distribution.

[0120] use Let represent the measurement variance of the distance measurement value between the i-th wingman and the target at time k. Let represent the measurement variance of the azimuth angle measurement of the i-th wingman relative to the target at time k.

[0121]

[0122] Where, β i B represents the transmission signal bandwidth of the radar of the i-th wingman. i Let S and R represent the 3dB receive beamwidth of the radar of the i-th wingman, respectively. i,k,m Let represent the signal-to-noise ratio of the radar echo signal of the i-th wingman at time k.

[0123] As can be seen from the formula, due to the unoptimized maneuver control variable d i,k This determines the wingman's flight direction and speed, alters the wingman's observation and position, and affects the signal-to-noise ratio (SNR) of the radar echo signals from each wingman.i,k,m Related. Therefore, covariance Σ i,k,q It can be written as a block diagonal matrix of the two:

[0124]

[0125] In summary, the target motion model is based on the Singer model, including state transition functions and process noise. In the wingman motion model, the position and flight direction of each wingman are taken as the state, and the level flight speed and angular velocity of the wingmen are taken as the maneuver control variables to be optimized. i,k Similarly, process noise is incorporated. The measurement model is used to combine the wingman's motion with the target's motion, representing the wingman's tracking process of the target, including the measurement function and measurement noise. Due to the maneuver control variable d to be optimized... i,k It determines the flight direction and speed of the wingman, can change the radar's observation and position, and affects the signal-to-noise ratio (SNR) of the radar echo signals of each wingman. i,k,m This relates to changing the accuracy of target tracking.

[0126] Step 4: Based on the measurement model, determine the resource allocation model using BCRLB, wherein at least one of the threat level coefficient and the attenuation factor is added to the resource allocation model;

[0127] In a resource-constrained system, how to allocate resources to each wingman to maximize the target tracking accuracy is the problem this embodiment aims to solve. A key metric related to target tracking accuracy is the Bayesian Cramér-Rao Lower Bound (BCRB), which provides a lower bound for the mean square error of the target tracking state estimation. Therefore, this embodiment will use the BCRLB as the metric for target tracking performance in the resource allocation model, optimizing the maneuver control variable d under various constraints. i,k To achieve optimal target tracking performance.

[0128] The BCRLB inequality can be written as:

[0129]

[0130] Among them, B -1 (x T,q,k+1 ) is the lower bound of the variance of the filter estimate (i.e., BCRLB); It is state x T,q,k+1 Bayesian information matrix (i.e., BIM) and the other two are inversely related. This represents finding the expected value of x. T,q,k+1 This represents the true value of the extended state at time k+1. Let represent the extended state estimate at time k+1. The BIM calculation formula is:

[0131]

[0132] in, p(z) represents the second-order partial guide coefficient. k ,x T,q,k+1 ) represents (z k ,x T,q,k+1 The joint probability density function of ). J p (x T,q,k+1 J represents the Fisher information matrix (FIM) representing prior information, combined with the target motion model. p (x T,q,k+1 ) can be written as

[0133]

[0134]

[0135] in, The covariance matrix F represents the process noise. k+1 The Jacobian matrix of the state transition of the target state vector at time k.

[0136] J r (x T,q,k+1 ) represents the FIM of the observed data at the current time, which can be simplified for calculation purposes and written as:

[0137]

[0138]

[0139] Where, Σ i,k,q H represents the noise covariance matrix of the measurement set. i,k,q Let represent the Jacobian matrix of the measurements taken by the i-th wingman against the q-th target at time k.

[0140] Therefore, the Bayesian information matrix can be approximated as follows:

[0141]

[0142] B -1 (x T，q，k The elements on the diagonal provide a lower bound for the estimated variance of each component of the extended state vector, reflecting the tracking performance. However, since the elements on the diagonal are not on the same scale unit, normalization is required. The normalized estimate BCRLB of the target q-state is as follows:

[0143] F(d i,k )=Tr(Λ·(B -1 (x T,q,k+1 )) 4×4·Λ T (25);

[0144] Where Tr(·) represents the trace, 4×4 represents taking the first 4×4 dimensions of the target state estimate, and Λ is the normalization matrix.

[0145] To differentiate targets with different threat levels, a threat coefficient ω = [ω1, ..., ω] is introduced. Q This allows for the classification of tracking tasks. More resources are allocated to targets with higher threat levels in hopes of achieving higher tracking accuracy and reducing the mean square error of the target tracking estimation state. The threat coefficient ω = [1,...,1] for each target before task classification, and equation (25) after task classification can be rewritten as:

[0146]

[0147] In radar moving target detection and display, when a moving target cuts off from the radar (radial velocity is 0), the weak echo signal is obscured by clutter, severely affecting target tracking performance. Considering the maneuverability of wingman formations, the zero-frequency problem caused by cut-offs can be solved at its source by changing the wingman's flight angle.

[0148] Define the attenuation factor as

[0149]

[0150] At this point, equation (26) can be further written as:

[0151]

[0152] When the radial velocity is 0 At that time, α i,q,k =∞. Because it is necessary to minimize the tracking performance metric function, adding an attenuation factor will change the level flight speed or turning speed where zero frequency might have previously occurred, in order to avoid flight cut-off phenomenon at the cost of a small portion of tracking accuracy.

[0153] Equation (28) can be regarded as the control variable d of the mobility resources. i,k As a function of the independent variable, the control variables of the wingman group affect the radar's signal-to-noise ratio to the target, thus affecting the lower bound of the estimation error. Therefore, in this embodiment, equation (28) is chosen as the target tracking performance measurement function of the distributed radar system. This can achieve the task of tracking trajectory optimization that is mission-oriented and takes into account the target motion characteristics. The optimal target tracking performance is obtained by optimizing the control variables. The resource allocation model of the system is as follows:

[0154]

[0155] It should be noted that in practical applications, you can choose to add only the threat coefficient or the attenuation factor to the resource allocation model, or you can choose to add both the threat coefficient and the attenuation factor to the resource allocation model.

[0156] Step 5: Solve for the optimal solution of the resource allocation model to obtain the optimal values ​​of the maneuver control variables of each wingman at each time step, and complete the tracking trajectory optimization based on the target motion characteristics of the mission hierarchy.

[0157] As can be seen from equations (28) and (29), the optimization problem of this resource allocation model is a non-convex and nonlinear optimization problem. Genetic Algorithm (GA) is a general algorithm for solving optimization problems. This algorithm finds the optimal solution through a probabilistic search method and has a wide range of applications. Therefore, this embodiment uses the genetic algorithm to calculate the optimal solution and obtains the optimal values ​​of the maneuver resource control variables of each wingman at each time step.

[0158] Specifically, step 5 includes:

[0159] Step a: Use a genetic algorithm to solve for the optimal solution of the resource allocation model at time k, and obtain the optimal values ​​of the maneuver control variables of each wingman at time k;

[0160] Step b: Based on the measurement values ​​of the measurement model at time k and the optimal solution of the resource allocation model at time k, calculate the predicted state of target q at time k+1 and the prediction covariance matrix corresponding to the predicted state.

[0161] Step c: Based on the predicted state and the predicted covariance matrix, use the extended Kalman filter to perform state recursive estimation, and obtain the state estimate of target q at time k+1 and the corresponding covariance matrix.

[0162] Step d: Let k = k + 1, perform iterative loops to obtain the optimal values ​​of the maneuver control variables for each wingman at each time step.

[0163] Due to uncontrollable factors such as system disturbances, the observation equations and target state transition equations also exhibit uncertainty. During target tracking, filtering algorithms are needed to perform recursive estimation using the current state values. Traditional Kalman filtering is primarily used to solve linear problems; however, the system proposed in this embodiment is nonlinear, so an Extended Kalman Filter (EKF) is employed for state estimation.

[0164] Specifically, the extended Kalman filter algorithm is explained, and the algorithm process can be divided into prediction, recursion, and update parts. For the prediction part...

[0165]

[0166]

[0167] Where F is the state transition matrix, P represents the state estimate at time k. T,q,k|k This represents the corresponding covariance matrix; and P T,q,k+1|k This represents the predicted state and the predicted covariance matrix at time k+1.

[0168] For the recursive part, the predicted state and the predicted covariance matrix are used as recursion factors in the iteration.

[0169]

[0170]

[0171] S T,q,k+1|k =HP T,q,k+1|k H T +Σ i,k,q (34);

[0172] Where H is the observation matrix, v represents the predicted measurement value at time k+1. k+1 Represents the measurement value obtained at time k+1 The news brought by S T,q,k+1|k This represents the corresponding information covariance matrix, which is typically used to measure the uncertainty of information.

[0173] For the update part, the gain matrix of the filter is introduced.

[0174] K T,q,k+1 =P T,q,k+1|k H T S T,q,k+1|k -1 (35);

[0175] The updated target state and covariance matrix are obtained as follows

[0176]

[0177] P T,q,k+1|k+1 =P T,q,k+1|k -K T,q,k+1 S T,q,k+1|k K T,q,k+1 T (37);

[0178] As can be seen from equations (35) and (36), EKF actually determines the value of the filter gain by evaluating the process noise and measurement noise of the system, so that the final target state is optimally estimated.

[0179] This embodiment of the tracking trajectory optimization method based on the target motion characteristics of task-level classification takes into account targets of different threat levels, distinguishes between key and non-key tracking targets, and allocates different resources to them. This improves the tracking accuracy of the former and reduces the tracking accuracy of the latter to adapt to different working scenarios. It also considers the scenario of target and wingman aircraft cutting off each other. When this happens, the echo signal is annihilated in clutter, severely affecting target tracking performance. By incorporating an attenuation factor into the resource allocation model, the tracking path of the wingman cluster can be rationally planned, avoiding the cutting-off phenomenon at its source and enabling the wingman cluster to complete the tracking task efficiently.

[0180] Example 2

[0181] This embodiment uses simulation experiments to verify and illustrate the effectiveness of the tracking trajectory optimization method for task-oriented hierarchical target motion characteristics in Embodiment 1.

[0182] 1. Simulation conditions:

[0183] The simulation system is an Intel(R) Core(TM) i7-8750 CPU@2.2GHz, a 64-bit Windows 10 operating system, and the simulation software is MATLAB (R2022b).

[0184] 2. Simulation content and result analysis:

[0185] Assume there are four enemy targets within a 300km x 200km mission area. Targets 1, 2, and 4 are maneuvering targets with varying speeds and accelerations at different times, exhibiting irregular motion. Target 3 moves at a constant speed in a straight line. Assume eight wingmen equipped with distributed airborne radars are tasked with tracking these four targets. The initial signal-to-noise ratio is set to 12dB at a reference range of 150km. The Singer model is used for target tracking. The maneuvering time constants on both the x and y axes are set to 60. The probability of maneuvering acceleration being 0 is P0 = 0, and the probability of maneuvering acceleration reaching its maximum value is P... max =0.3, the maximum acceleration a of the target on the x and y axes max Both are 10m / s 2 The target and initial radar coordinates are shown in Tables 1 and 2.

[0186] Table 1 Initial coordinates of the target

[0187] Target 1 Target 2 Target 3 Target 4 (60km, 60km) (-100km, 20km) (60km, 70km) (-50km, 20km)

[0188] Table 2. Initial Radar Coordinates

[0189] Radar 1 Radar 2 Radar 3 Radar 4 (-140km, 100km) (-100km, -100km) (-60km, -100km) (-20km, -100km) Radar 5 Radar 6 Radar 7 Radar 8 (20km, -100km) (60km, -100km) (100km, -100km) (140km, -100km)

[0190] Figure 3This refers to the wingman's trajectory before optimization. Each radar flies at a constant speed from bottom to top, and at this time, the radar can only track the target in a fixed direction.

[0191] Figure 4 The wingman trajectories were obtained through a genetic algorithm. It can be seen that after optimization, the flight paths of the wingman group are longer, meaning that each wingman is allocated a higher flight speed, enabling them to close the distance between the target and the radar more quickly, improving the radar's echo signal-to-noise ratio, and thus improving tracking accuracy. At the same time, the wingman trajectories no longer follow a fixed direction. The improvements in angular velocity obtained through optimization cause the trajectories to exhibit a divergent phenomenon, providing the radar network with more diverse angular observation information. The fusion of multi-source information improves the target tracking accuracy.

[0192] Figure 5 The goal is to minimize tracking accuracy. The results show that the tracking accuracy before and after optimization are significantly lower after optimization, which proves the feasibility and effectiveness of the optimization scheme.

[0193] When dealing with task classification, different threat levels are set for targets in the optimized scenario. The threat levels are shown in Table 3. Targets 1 and 4 become high-threat targets, and their tracking accuracy needs to be increased; targets 2 and 3 become low-threat targets, and can be given lower tracking weights and allocated fewer resources.

[0194] Table 3 Threat Level Settings Before and After

[0195] Target 1 Target 2 Target 3 Target 4 Before grading 5 5 5 5 After classification 7 3 3 7

[0196] Figure 6 This involves comparing and analyzing the results without classification with those after classification. When all targets have the same threat level, the trajectories of the wingmen approach the targets relatively evenly; after classification, it is clear that the wingmen's trajectories are moving closer to the central key targets 1 and 4, the four radars on the left are moving closer to target 4, and the four radars on the right are moving closer to target 1.

[0197] Figure 7 This is a comparison of tracking accuracy before and after the classification. Under the same threat level, the tracking accuracy of the target is similar. After the threat level changes, the tracking objective function of high threat target 1 becomes smaller, that is, more resources are allocated to obtain higher tracking accuracy; the tracking objective function of low threat target 2 becomes larger, that is, more resources are not needed to maintain a lower accuracy within a certain range.

[0198] Figure 8 The image shows the wingman's tracking trajectory before and after considering the target's characteristics. The trajectory becomes more tortuous, indicating that the wingman avoids cutting off from the maneuvering target when tracking it, verifying the effectiveness of introducing an attenuation factor in preventing such cutoffs.

[0199] Figure 9 The comparison of tracking accuracy before and after considering the target characteristics shows that the tracking accuracy after adding the attenuation factor is still much higher than before optimization, proving the efficiency of the algorithm.

[0200] The tracking trajectory optimization method based on the mission-level target motion characteristics in this embodiment optimizes the level flight speed and turning speed of each wingman in the context of a multi-radar multi-target system, so as to achieve the maximum tracking accuracy under limited resources.

[0201] It should be noted that, in this document, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device that includes said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0202] 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 trajectory optimization method based on the motion characteristics of a task-level target, characterized in that, include: Step 1: Establish the target motion model based on the Singer motion model; Step 2: Establish a wingman motion model, where the first... i Wingman k Level flight speed at any moment and angular velocity As the motor control variable to be optimized ; Step 3: Establish a measurement model based on the target motion model and the wingman motion model; Step 4: Based on the measurement model, determine the resource allocation model using BCRLB, wherein at least one of a threat coefficient and a decay factor is added to the resource allocation model; Step 4 includes: Based on the measurement model and the target motion model, the target is obtained. q The normalized estimate of the state, BCRLB, is: ； in, To find the trace, Indicates taking the preceding part Part of the objective state estimation, For the normalized matrix, This represents the lower bound of the variance of the filtered estimate. express k+ The actual value of the extended state at time 1; For the target q The normalized state estimate BCRLB, with the addition of a threat coefficient, is used to classify the tracking task, resulting in the BCRLB with the threat coefficient added: ； in, Indicate target q Threat level coefficient; For the target q The normalized state estimate BCRLB, with the addition of a decay factor to avoid flyaway phenomenon, yields the BCRLB with the decay factor: ； in, Indicates the attenuation factor. , For the number of wingmen, For the number of targets, express k Time of the first i Wingman aircraft targeting q The azimuth measurement value; The resource allocation model is determined based on the addition of a threat coefficient or a decay factor to the BCRLB: ； Step 5: Solve for the optimal solution of the resource allocation model to obtain the optimal values ​​of the maneuver control variables of each wingman at each time point, and complete the tracking trajectory optimization based on the target motion characteristics of the mission hierarchy.

2. The tracking trajectory optimization method based on the motion characteristics of a task-level target according to claim 1, characterized in that, Step 1 includes: Suppose there exists in the plane Q Establish a target that moves in any way. q exist k The state at that moment is: ， in, Indicate target q exist k Position coordinates at that moment Indicate target q exist k The velocity component at time t, Indicate target q exist k The acceleration component at time t; Using the dynamic equations and objective of the Singer model q exist k The state at time t is used to establish the target motion model as follows: ； in, Indicate target q State transition function, Indicates the target at the fusion moment The process of fusion vectors, Follows a pattern with a mean of 0 and a covariance of 0. Gaussian distribution; ； in, Represents a 2D identity matrix. This represents the direct product operation. Indicates the fusion time interval. Indicates the frequency of maneuvering. T Indicates the sampling period.

3. The tracking trajectory optimization method based on the motion characteristics of a task-level target according to claim 2, characterized in that, Step 2 includes: set up N One wingman flies in a two-dimensional plane, the first... i Wingman k The state at that moment is: ， in, Indicates the first i Wingman k Position coordinates at that moment Indicates the first i The wingman k Flight direction at any time and x The included angle of the axis; According to the i Wingman k The state at time t, obtain the first i The following equation represents the transition state of the wingman at the next moment: ； According to the i The following equations for the wingman's state transition at the next moment are used to establish the wingman's motion model: ； in, Indicates in k The state vector of all wingmen at time -1. express k The constant maneuver control variables of all wingmen. The noise represents the process noise, which follows a mean of 0 and a covariance of 0. The Gaussian distribution.

4. The tracking trajectory optimization method based on the motion characteristics of a task-level target according to claim 3, characterized in that, Step 3 includes: According to the i Wingman k The state of being at any given moment, and the goal q exist k The state at time t is used to establish the measurement function as follows: ； in, express k Time of the first i Wingman aircraft targeting q The distance measurement value, express k Time of the first i Wingman aircraft targeting q The azimuth measurement value; Based on the measurement function, the measurement model is established as follows: ； in, express k Time of the first i Wingman aircraft targeting q The measurement noise of the measured values ​​follows a mean of 0 and a covariance of . Gaussian distribution; ； ； in, express k Time of the first i Wingman aircraft targeting q The measurement variance of the distance measurement values, express k Time of the first i Wingman aircraft targeting q The measurement variance of the azimuth angle measurement value Indicates the first i The bandwidth of the radar transmission signal of the wingman aircraft. They represent the first i The wingman's radar has a 3dB receiving beamwidth. express k Time of the first i The signal-to-noise ratio of the radar echo signal of the wingman aircraft.

5. The tracking trajectory optimization method based on the motion characteristics of a task-level target according to claim 1, characterized in that, Step 5 includes: Using a genetic algorithm to solve the problem of the first... k The optimal solution of the resource allocation model at time t is obtained. k The optimal values ​​of the maneuver control variables for each wingman at any given time; According to the k The measured values ​​of the measurement model at time and the first k The optimal solution of the resource allocation model at time t is calculated to obtain the target. q In the k The predicted state at time +1 and the prediction covariance matrix corresponding to the predicted state; Based on the predicted state and the predicted covariance matrix, the extended Kalman filter algorithm is used to perform recursive state estimation to obtain the target. q In the k The state estimate at time +1 and the covariance matrix corresponding to the state estimate; make k = k +1, perform iterative loops to obtain the optimal values ​​of the maneuver control variables for each wingman at each time point.

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