Maneuvering multi-target data association and tracking method based on chaos optimization NSGA-Ⅱ algorithm

Abstract

The application discloses a kind of based on chaotic optimization NSGA-Ⅱ algorithm's maneuvering multi-target data association and tracking method, it includes by maneuvering target motion modeling and state prediction, according to the motion state information of target last time obtains the motion state information prediction result of target in next time;Establish maneuvering multi-target data association optimization model;By chaotic theory, improve NSGA-Ⅱ algorithm, and utilize the CONSGA-Ⅱ algorithm obtained after improvement to the maneuvering multi-target data association optimization model more optimal solution, obtain multi-target data association result;Using multi-target data association result, using EKF filtering algorithm completes the track filtering and plot update of all targets.The application enhances the robustness of tracking algorithm, improves tracking precision and real-time performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-target data association and tracking, in particular to a method for maneuvering multi-target data association and tracking based on chaotic optimization NSGA-II algorithm. BACKGROUND

[0002] Data association is one of the key problems and difficult steps of multi-target tracking. Data association is to correctly and accurately match multiple measurements with multiple targets to ensure the accuracy of target data association. However, with the acceleration of the battlefield rhythm, the real-time and accuracy of target association and tracking are constantly increasing. At the same time, with the rapid development of scientific materials and the rapid rise of new technologies, the maneuverability of radar tracking targets is becoming stronger and stronger, the types are becoming more and more complex, and the motion state is more and more complex, which makes the multi-target data association and track tracking technology more flexible to adapt to changes in all aspects. Especially in complex environments, when the number of targets is large, the number of association hypotheses between targets and echoes will increase, and the combination explosion problem of calculation amount may occur; when the maneuverability of the target is strong, the cross and bifurcation may occur, and the false tracking and lost tracking phenomenon is easy to occur. Therefore, further exploring the association problem between targets and radar measurements is still a strong demand in the military field.

[0003] Researchers at home and abroad have conducted in-depth exploration on data association algorithms, such as nearest neighbor method (NNDA). This algorithm only relies on distance to match measurement data and targets. This method is simple in principle, but has low reliability and is more likely to cause false association. Delayed decision multi-hypothesis method (MHT). This algorithm matches all measurements with existing tracks through traversal, and selects the measurement with the highest association probability as the best match. This method is simple to operate and has high accuracy, but the calculation amount will increase exponentially with the number of tracked targets, and real-time tracking cannot be achieved. Joint probability data association method (JPDA). This method is based on Bayesian theory, gives different association weights to each candidate observation, and uses all measurements for track updating. However, the calculation complexity increases dramatically with the increase of the number of targets. In recent years, with the development of many bionic optimization algorithms such as genetic algorithm, neural network, ant colony algorithm, and iterative updating algorithms based on them, a series of innovations and breakthroughs have been made in multi-target data association and tracking. However, in actual use, there are problems such as falling into local optimum, slow convergence speed, and dependence on prior information. There is a certain distance from the actual demand of the current battlefield. Therefore, how to accurately, reliably and quickly perform data association and tracking of maneuvering multi-targets needs further research. SUMMARY

[0004] In view of this, the present application provides a method for maneuvering multi-target data association and tracking based on chaotic optimization NSGA-II algorithm to solve the above technical problems.

[0005] The application discloses a method for maneuvering multi-target data association and tracking based on a chaotic optimization NSGA-II algorithm, which comprises the following steps:

[0006] Step 1: obtaining a motion state information prediction result of a target at a next moment according to motion state information of the target at a last moment through maneuvering target motion modeling and state prediction;

[0007] Step 2: establishing a maneuvering multi-target data association optimization model;

[0008] Step 3: improving the NSGA-II algorithm through a chaotic theory, and performing more optimal solution on the maneuvering multi-target data association optimization model by using the CONSGA-II algorithm obtained after the improvement, so as to obtain a multi-target data association result;

[0009] Step 4: using the multi-target data association result to complete track filtering and plot updating of all targets by using an EKF filtering algorithm.

[0010] Further, the step 1 comprises the following steps:

[0011] Supposing that a target motion state vector is X(k) at an arbitrary moment k, and a covariance matrix corresponding to the target motion state vector is P(k), according to an EKF algorithm, one-step prediction results of the state motion vector and the covariance matrix are as follows:

[0012]

[0013] In the formula, F represents a state transition matrix, G represents a process noise covariance matrix, and Q(k) represents process noise.

[0014] If the measurement information of a radar is Z(k), then one-step prediction of the state equation can be expressed as:

[0015] Z(k+1) = HX(k+1) + W(k+1) (2)

[0016] In the formula, W(k) is measurement noise, and H is a measurement matrix.

[0017] Further, the step 2 comprises the following steps:

[0018] Supposing that m target track information is established at the moment k, and a prediction result corresponding to the track at the moment k+1 is obtained by prediction At the moment k+1, n targets are observed by the radar, and a real measurement result value of the n targets is judging an optimal corresponding relation of , and establishing a multi-target data association combination optimization model; in the formula, i = 1, 2, …, m, and j = 1, 2, …, n.

[0019] Furthermore, the establishment of the multi-target data association and combination optimization model includes: combining the trajectory results Z1(k), Z2(k), ..., Z of m targets at time k. m (k) is considered as integers 1, 2, ..., m, corresponding to random permutations i1, i2, ..., i m The actual measurement results of n targets at time k+1 are... Consider the integers 1, 2, ..., n as per ascending order, corresponding to j1, j2, ..., j n ; and use d ij Indicates the target predicted value and the true value The residual distance between them is then expressed as the sum of the residual distances of all targets at time k+1:

[0020]

[0021] Equation (3) is taken as the objective function for data association, and the following assumptions are made: an objective has one and only one measurement associated with it; a measurement is associated with at most one objective; the constraint condition for obtaining the objective function for data association is n≥m; under the constraint condition, when D=D min When this condition is met, the optimal correspondence between the actual measurement results of n targets and the trajectory results of m targets at time k+1 is: Where i = 1, 2, ..., m, j = 1, 2, ..., n.

[0022] Further, step 3 includes:

[0023] Step 31: Define the vector for each chromosome in the initial population;

[0024] Step 32: Generate the initial chaotic optimization vector and map it to the range of values ​​of the decision variable n, thus obtaining R(t,j);

[0025] Step 33: Calculate the objective function values ​​of all vectors in R(t,j), and select the top L vectors with the minimum objective function values ​​as chromosome vectors to obtain the optimized initial population Q. k+1 ;

[0026] Step 34: Let Q represent the initial population. g Calculate Q g The objective function values ​​of each chromosome were calculated; and two individuals were randomly selected into the mating pool using a two-branch competitive selection method for rapid non-dominated sorting and crowding calculation.

[0027] Step 35: Employ a simulated binary crossover algorithm, and use P... C Crossover operations are performed using the crossover probability as the selection crossover probability; a multinomial mutation algorithm is employed, with P...M Mutation operation is performed for mutation probability to obtain offspring population P g ;

[0028] Step 36: merging parent population Q g and offspring population P g to obtain population Z g , based on population Z g , parent population Q g+1 is obtained;

[0029] Step 37: judging whether the iteration number meets the condition, if yes, going to step 38; if not, going to step 310;

[0030] Step 38: repeating step 33 and step 34 to generate L chaotic vectors C L ;

[0031] Step 39: discarding L chromosomes in Q g+1 in a roulette manner; and replacing the discarded part with C L chaotic vector to complete the update of parent population Q g+1 ;

[0032] Step 310: judging whether the iteration number is less than or equal to a preset value; if yes, going to step 311, otherwise, the iteration number is increased by 1 and going to step 35;

[0033] Step 311: completing the output of optimal solution and ending the CONSGA-II algorithm process.

[0034] Further, the step 31 comprises:

[0035] Step 311: determining initial population parameters; assuming that the real measurement number at k+1 moment is n and the predicted target number is m; determining population size L and maximum evolution generation g max ;

[0036] Step 312: defining initial population Q k+1 ; according to the maneuvering multi-target data association optimization model, each chromosome vector is defined as:

[0037] C(l,j)=randperm(n) (4)

[0038] wherein, l=1,2,…L, C(l) represents the lth chromosome; the dimension of the decision vector in each chromosome is n, and n is the measurement number; randperm(·) represents a random rearrangement function; the elements greater than m in C(l) are set to zero, which represents that the measurement corresponding to the false alarm.

[0039] Further, the step 32 comprises:

[0040] Step 321: generating initial chaotic optimization vectors; generating T chaotic vectors of n dimensions as initial values by using Tent method, n being the number of real measurements; and restricting the number of chaotic vectors T to be at least twice the number of chromosomes, i.e. T≥2N;

[0041]

[0042] wherein t = 1, 2, …T, represents the chaotic vector number; X(t) represents the chaotic vector of the tth chromosome; and the t+1th chaotic vector X(t+1) is defined as:

[0043]

[0044] Through equation (6), t n-dimensional variables X(T, n) with chaotic characteristics are obtained;

[0045] Step 322: mapping the chaotic variables X(T, n) into the value range of the decision variables n, and the specific mapping relationship is as follows:

[0046] R(t, j) = int(mX j (t, n)) j = 1, 2, …, n (7)

[0047] Wherein int(·) represents the integer function, and m represents the number of prediction targets.

[0048] Further, the step 36 comprises:

[0049] Step 361: merging the parent population Q g and the offspring population P g to obtain a population Z g with a number of 2L;

[0050] Step 362: performing fast non-dominated sorting and crowdedness calculation on the population Z g , and sorting;

[0051] Step 363: selecting the first 2L chromosomes in the population Z g as the parent population Q g+1 .

[0052] Further, in the step 37: judging whether the iteration number meets the condition, i.e. judging whether g is equal to C*g max / 50; wherein C is a positive integer.

[0053] Further, the step 4 comprises:

[0054] Step 41: calculating the innovation covariance matrix:

[0055] S n(k) = h x n (k) P n (k|k-1) (h x n (k)) T + R(k) (9)

[0056] where n is the number of targets, h x (k) is the Jacobian matrix of the measurement matrix H(k); R(k) is the covariance matrix of the measurement noise W(k);

[0057] Step 42: Calculate the Kalman gain:

[0058] K n (k) = P n (k|k-1) (h x n (k)) T |S n (k)| -1 (10)

[0059] Step 43: Update the state vector:

[0060] X n (k|k) = X n (k|k-1) + K n (k) v n (k) (11)

[0061] Step 44: Update the covariance matrix:

[0062] P n (k|k) = P n (k|k-1) - K n (k) S n (k) (K n (k)) T (12)

[0063] Repeat steps 41 to 44 until the track filtering and plot updating for all targets are completed.

[0064] Due to the adoption of the above technical solutions, the present application has the following advantages:

[0065] The application solves the problems of the NSGA-II algorithm falling into local optimum and slow convergence speed, and the problems of the traditional maneuvering multi-target data association and tracking algorithm, such as large amount of calculation, low association accuracy, etc., by using the ergodicity, randomness and regularity of chaotic variables in chaotic motion. The application has the advantages of fast convergence speed, high operation efficiency, strong robustness, good algorithm applicability, etc., can optimize the maneuvering multi-target data association model with high performance, can not only obtain high association accuracy, but also effectively improve the association speed, and further improve the maneuvering multi-target track tracking result. BRIEF DESCRIPTION OF DRAWINGS

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the application, the drawings needed to be used in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments described in the embodiments of the application, and other drawings can also be obtained by those skilled in the art according to these drawings.

[0067] Figure 1 A flowchart of a maneuvering multi-target data association and tracking method based on a chaotic optimization NSGA-II algorithm of the application;

[0068] Figure 2 A flowchart of a multi-maneuvering target data association algorithm based on CONSGA-II of the application;

[0069] Figure 3 A schematic diagram of a multi-target real motion track in the specific embodiment of the application;

[0070] Fig. 4(a) and Fig. 4(b) are the Pareto optimal solution space distribution of the ZDT1 test function in the specific embodiment of the application; wherein, Fig. 4(a) corresponds to the 10th data association result, and Fig. 4(b) corresponds to the 34th data association result;

[0071] Figure 5 A schematic diagram of a maneuvering multi-target data association result in the specific embodiment of the application;

[0072] Figure 6 A schematic diagram of a target track tracking result in the specific embodiment of the application;

[0073] Figure 7 A schematic diagram of a filter error result of each target in the x-axis and y-axis in the specific embodiment of the application;

[0074] Figure 8 A schematic diagram of an RMSE error result of each target in the x-axis and y-axis in the specific embodiment of the application. DETAILED DESCRIPTION

[0075] With the aid of the drawings and embodiments, it is obvious that the embodiments described are only a part of the embodiments of the present application and are not all the embodiments. All other embodiments obtained by a person of ordinary skill in the art shall belong to the scope of protection of the embodiments of the present application.

[0076] In order to solve the problems in the prior art, the embodiments of the present application provide a maneuvering multi-target data association and tracking method based on a chaotic optimization NSGA-II algorithm, first, a combination optimization model of maneuvering multi-target measurement data association is established; then the initialization process and the elite reservation process of the NSGA-II algorithm are improved through the chaos theory, the search space is expanded, the algorithm is prevented from falling into local optimization, the convergence speed of the algorithm is accelerated, and the improved CONSGA-II algorithm is used for data association of the model, so that better solutions of the multi-target optimization model are realized; finally, based on the EKF algorithm, the associated measurement data are filtered and tracked to obtain smooth and stable track tracking results of the maneuvering multi-target. Figure 1 The specific technical solutions adopted by the embodiments are as follows:

[0077] Step one: maneuvering target motion modeling and state prediction.

[0078] Target maneuverability describes that the target suddenly changes the motion direction and motion speed during the motion process. Establishing an accurate target motion mathematical model is a basic prerequisite and direct factor for realizing accurate tracking.

[0079] Suppose that at any time k, the target motion state vector is X(k), and the corresponding covariance matrix is P(k), according to the EKF algorithm, one-step prediction results of the state motion vector and the covariance matrix are obtained as follows:

[0080]

[0081] Wherein, F represents a state transition matrix, G represents a process noise covariance matrix, and Q(k) represents process noise.

[0082] Since the radar detection system is a nonlinear system, the detection results are generally distance, speed, azimuth angle, pitch angle and the like. If the measurement information is Z(k), one-step prediction of the state equation can be represented as:

[0083] Z(k+1)=HX(k+1)+W(k+1) (2)

[0084] Wherein, W(k) is measurement noise. H is a measurement matrix.

[0085] Through step one, after the radar detection information is processed, the motion state information prediction result of the target at the next time can be obtained according to the motion state information of the target at the last time.

[0086] Step 2: Establish a multi-objective data association optimization model for maneuvering.

[0087] Suppose that at time k, track information has been established for m targets, and the predicted track information for time k+1 is: At time k+1, the radar observes n targets, and the actual measurement result is... The multi-target data association problem is to determine how the n measurement points at time k+1 relate to the track states Z1(k), Z2(k), ..., Z of the m targets at the previous time. m (k) is paired to complete the tracking of the tracks of m targets at time k+1. To determine... The optimal correspondence (where (i = 1, 2, ..., m, j = 1, 2, ..., n)) is used to establish a multi-objective data association combination optimization model as follows.

[0088] The trajectory results Z1(k), Z2(k), ..., Zn(k) of m targets at time k. m (k) can be considered as a random permutation of integers 1, 2, ..., m, j1, j2, ..., jm. m The actual measurement results of n targets at time k+1 are... Consider the integers 1, 2, ..., n as an ascending sequence of natural numbers i1, i2, ..., i... n ; and use d ij Indicates the target predicted value and the true value The residual distance between them is then expressed as the sum of the residual distances of all targets at time k+1:

[0089]

[0090] Using the above formula as the objective function for data association, we make the following assumptions: (1) Each objective has one and only one measurement associated with it. (2) Each measurement is associated with at most one objective. From these assumptions, we can derive the constraint condition for the data association objective function: n ≥ m. Under these constraints, when D = D... min When (n≥m) holds true, the optimal correspondence between the actual measurement results of n targets and the trajectory results of m targets at time k+1 is: Where i = 1, 2, ..., n.

[0091] Step 3: Implementation of the multi-maneuver target data association algorithm based on CONSGA-Ⅱ.

[0092] The objective function constructed by the method is a multi-objective optimization problem. Therefore, the NSGA-II algorithm widely used in the field of multi-objective optimization is introduced. The algorithm reduces the complexity of non-dominated sorting genetic algorithm by combining the population grading mechanism of non-dominated sorting and the elite retention strategy, and has the advantages of fast running speed and good convergence of solution set. The formula derivation process of the traditional NSGA-II algorithm is described in detail in the reference (Improved multi-objective genetic algorithm based on NSGA-II); Although the NSGA-II algorithm has been widely used in the field of multi-objective optimization, there is still a significant local optimal problem. Therefore, the method uses a chaos optimization algorithm to improve its adaptability to achieve better solutions to the maneuvering multi-target data association model and obtain multi-maneuvering target data association results. The complete algorithm implementation steps of CONSGA-II can be summarized as follows:

[0093] Step 3.1: Determine the initial population parameters. Assume that the number of real measurements at time k+1 is n, and the number of predicted targets is m; under the condition of considering the operation efficiency and population diversity, determine the population size L and the maximum evolution generation g max .

[0094] Step 3.2: Define the initial population Q k+1 According to the maneuvering multi-target data association optimization model in step two, define each chromosome vector as

[0095] C(l,j)=randperm(n) (4)

[0096] Where l=1,2,…L, C(l) represents the lth chromosome; the dimension of the decision vector in each chromosome is n, and n is the number of measurements; randperm(·) represents a random rearrangement function; since n≥m, set the elements greater than m in C(l) to zero, indicating that the corresponding measurement is a false alarm.

[0097] Step 3.3: Generate initial chaos optimization vectors. This method uses the Tent method to generate T n-dimensional chaos vectors with initial values, where n is the number of real measurements; to meet the optimization theory, the number of chaos vectors T is at least twice the number of chromosomes, i.e. T≥2N; each element is randomly selected between 0 and 1, and the specific operation formula is as follows:

[0098]

[0099] Where t=1,2,…T represents the chaos vector number; X(t) represents the tth chaos vector of the chromosome. Define the t+1th chaos vector X(t+1) as:

[0100]

[0101] Through the above formula, t n-dimensional variables X(T, n) with chaotic characteristics are obtained.

[0102] Step 3.4: Map the chaotic variable X(T, n) into the value range of the decision variable n, and the specific mapping relationship is as follows:

[0103] R(t, j) = int(mX j (t, n)) j = 1, 2,..., n (7)

[0104] Where int(·) represents the integer function, and m represents the prediction target number.

[0105] Step 3.5: Calculate the objective function value of all vectors in R(t, j), and select the top L vectors as chromosome vectors according to the minimum objective function value, thereby obtaining the optimized initial population Q k+1 .

[0106] Step 3.6: Calculate the objective function value of each chromosome in the initial population Q g , and randomly select two individuals into the mating pool through the double-branch bidding selection method, and perform fast non-dominated sorting and crowding calculation.

[0107] Step 3.7: Adopt the simulated binary crossover algorithm, and perform crossover operation with P C as the selection and crossover probability; adopt the polynomial mutation algorithm, and perform mutation operation with P M as the mutation probability, to obtain the offspring population P g .

[0108] Step 3.8: Merge the parent population Q g and the offspring population P g to obtain the population Z g with a size of 2L.

[0109] Step 3.9: Perform fast non-dominated sorting and crowding calculation on the population Z g , and sort.

[0110] Step 3.10: Select the top 2L chromosomes in the population Z g as the parent population Q g+1 .

[0111] Step 3.11: By judging whether the iteration number meets the condition, the chaotic vector is introduced again to expand the solution space of the population Q g+1 , to avoid the algorithm falling into local optimum, and the judgment condition is as follows:

[0112] g = C * g max / 50? (8)

[0113] where C is a positive integer; if the above formula is true, go to the next step; if the above formula is not true, go to step 3.14.

[0114] Step 3.12: repeat steps five and six to generate L chaotic vectors C L .

[0115] Step 3.13: discard Q in a roulette manner g+1 of L chromosomes. And replace the discarded part with C L chaotic vectors to complete the update of the parent population Q g+1 .

[0116] Step 3.14: determine whether g≤g max is true. If true, go to the next step. If not true, update g to g = g + 1, and go to step 3.7.

[0117] Step 3.15: complete the output of the optimal solution, and end the CONSGA-II algorithm process.

[0118] The flow chart of the multi-maneuvering target data association algorithm based on CONSGA-II is shown in Figure 2 Fig. 4. At the same time, in order to verify the performance of the CONSGA-II algorithm, the classical target test function ZDT1 is used as the test function, and the Pareto solution space distribution is shown in Fig. 4(a) and Fig. 4(b). As can be seen from Fig. 4(a) and Fig. 4(b), the Pareto solution distribution of the CONSGA-II algorithm has uniformity and stability, thereby illustrating the feasibility of the algorithm.

[0119] Step four: use the multi-target data association results to complete the track filtering and plot updating of all targets by using the EKF filtering algorithm.

[0120] According to the data association results of the M known maneuvering targets by using the CONSGA-II algorithm in step three, the EKF filtering algorithm is used to complete the track filtering and plot updating of all targets, and the specific tracking process is as follows:

[0121] (1) Calculate the innovation covariance matrix

[0122] S n (k) = h x n (k)P n (k|k-1)(h x n (k)) T + R(k) (9)

[0123] where n is the number of targets, h x(k) is the Jacobian matrix of the measurement matrix H(k); R(k) is the covariance matrix of the measurement noise W(k).

[0124] (2) Calculate the Kalman gain

[0125] K n (k) = P n (k|k-1) (h x n (k)) T |S n (k)| -1 (10)

[0126] (3) Update the state vector

[0127] X n (k|k) = X n (k|k-1) + K n (k)v n (k) (11)

[0128] (4) Update the covariance matrix

[0129] P n (k|k) = P n (k|k-1) - K n (k)S n (k)(K n (k)) T (12)

[0130] Repeat step four to complete the track filtering and plot update of all targets.

[0131] In order to facilitate understanding, a more specific embodiment of the application is given:

[0132] The application mainly adopts simulation experiment method for verification, and all steps and conclusions are verified correct on MATLAB R2019b. The method of the application is further described below in combination with the drawings and specific embodiments.

[0133] Step one: maneuvering target motion modeling and state prediction.

[0134] This embodiment carries out multi-target data association and track tracking on two high-speed maneuvering targets. It is assumed that the position of the radar is the coordinate origin, and the target moves in the three-dimensional plane xoy. The total time of time simulation is 80s, and the sampling interval time is T=1s. In order to simulate the high maneuverability of multi-target flight, the target arbitrarily switches between uniform motion and turning motion within 80s. The initial state of the target is X a =[0, 100, 10000, 100], X b=[0, 200, 800, 200], respectively represent the distance and velocity of the target along the x-axis and the distance and velocity along the y-axis. Assume that the detection probability p of the sensor is 90%, the clutter density obeys the Poisson distribution with parameter λ=4; the system noise and observation noise both obey the Gaussian distribution with mean value 0. The system noise variance and observation noise variance are Q=diag([20 d 20 2 20 2 ]) and R=diag([50 2 50 2 ]) respectively. The state transition matrix of the target moving at a constant speed is F1=[1 T 0 0; 0 1 0 0; 0 0 1 T; 0 0 0 1], and the process noise covariance matrix is G1=[T 2 / 2 0; T 0; 0 T 2 / 2; 0 T]. The state transition matrix of the target moving at a constant speed with turning is F2=[f1 f2 0-f3; 0f4 0-f5; 0f3 f1 f2; 0f5 0f4], where f1=1, f2=sin(ωT) / ω, f3=1-cos(ωT) / ω, f4=cos(ωT), f5=sin(ωT), the left turning angular velocity ω1=3 rad / s, the right turning angular velocity ω2=-4 rad / s, and the process noise covariance matrix is G2=G1. The schematic diagram of the real motion trajectory of the target in the embodiment is shown in Figure 3 .

[0135] Step two: establishment of the multi-target data association optimization model.

[0136] Suppose that at time k, target a and target b have established track information, and the prediction results of the corresponding tracks at time k+1 are At time k+1, the radar observes n measurement data, respectively The residual distance between the target prediction value and the real value is calculated, and the sum D of the residual distances of all targets at time k+1 is calculated.

[0137] Under the constraint condition, when D=D min (n≥m) is established, the optimal corresponding relationship between the real measurement value of the n targets at time k+1 and the track results of target a and target b is where i=1, 2, …, n.

[0138] Step three: implementation of the multi-maneuvering target data association algorithm based on CONSGA-II.

[0139] In the embodiment, the main parameters in the CONSGA-II algorithm are set as follows: (1) the population size L is 200, the maximum evolution generation g max is 200; (2) the length of each chromosome is the number of measurements n at the moment; (3) in order to meet the optimization theory, the scale of the chaotic vector generated by the Tent method is 400; (4) the crossover probability P C is 0.9, the mutation probability P M is 0.1; (5) in order to avoid the algorithm falling into local optimum, the judgment condition g = C * g max / 50? In the embodiment, the positive integer C is set as 1, 3, 5, and 7.

[0140] According to step three in the summary, the multi-maneuvering target is data-associated to obtain the multi-target data association result of the multi-maneuvering target at any moment in the embodiment. The multi-target data association result is shown in Fig. 3. Figure 5

[0141] Step four: the track of the target is further completed based on the EKF algorithm by using the multi-target data association result.

[0142] In the embodiment, the Monte Carlo method is used for simulation experiment, and the simulation times are MC = 50. It is assumed that the initial predicted state of the target is the same as the actual initial state, and the initial state covariance is P0 = diag([200 2 200 2 400 2 400 2 ]). According to step four in the summary, the multi-target data association result is tracked to obtain the filter result of the aircraft in the embodiment, and the specific case is shown in Fig. 4. Figure 6

[0143] Further, in order to verify the effectiveness of the application, the root mean square error (RMSE) is used to evaluate the experimental results of the multiple simulation experiments, and the distance filtering error and the RMSE error of each target in the x-axis and y-axis are obtained, respectively, and the specific case is shown in Figs. 5 and 6. Figure 7 Figure 8

[0144] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application but not to limit the same, and although the application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the specific embodiments of the application can be modified or replaced equivalently without departing from the spirit and scope of the application, and any modification or equivalent replacement without departing from the spirit and scope of the application should be covered in the protection scope of the claims of the application.​​​​

Claims

1. A method for maneuvering multi-target data association and tracking based on chaotic optimization NSGA-II algorithm, characterized in that, The application relates to a multi-target data association method based on improved NSGA-Ⅱ algorithm and EKF filtering algorithm. The method comprises the following steps: Step 1: obtaining the motion state information prediction result of a target at a next moment according to the motion state information of the target at a previous moment through motor target motion modeling and state prediction; Step 2: establishing a motor multi-target data association optimization model; Step 3: improving the NSGA-Ⅱ algorithm through a chaos theory, and using the improved CONSGA-Ⅱ algorithm to solve the motor multi-target data association optimization model to obtain a multi-target data association result; Step 4: using the multi-target data association result to complete track filtering and plot updating of all targets through an EKF filtering algorithm. The step 3 comprises: Step 31: defining each chromosome vector in an initial population; Step 33: Calculate the objective function value of all vectors in R(t,j), and select the first L vectors as chromosome vectors according to the minimum objective function value, thereby obtaining the optimized initial population Q k+1 ; Step 34: record the initialization population as Q g , calculate the objective function value of each chromosome in Q g ; and randomly select two individuals into the mating pool by double tournament selection method, and perform fast non-dominated sorting and crowdedness calculation; Step 35: adopt analog binary crossover algorithm, and take P C as the crossover probability to perform crossover operation; adopt polynomial mutation algorithm, and take P M as the mutation probability to perform mutation operation, to obtain offspring population P g ; Step 36: merging the parent population Q g and the offspring population P g to obtain the population Z g , based on the population Z g obtaining the parent population Q g+1 ; Step 32: generating an initial chaos optimization vector and mapping the initial chaos optimization vector to the value range of the decision variable n, that is, obtaining R(t,j); Step 38: Repeat Step 33 and Step 34 to generate L chaotic vectors C L ; Step 39: Eliminate Q in roulette g+1 chromosomes; and use C L chaotic vector instead of the eliminated part to complete the update of the parent population Q g+1 ; Step 37: judging whether the iteration number meets a condition, if yes, turning to step 38; if not, turning to step 310; Step 310: judging whether the iteration number is less than or equal to a preset value; if yes, turning to step 311; otherwise, increasing the iteration number by 1 and turning to step 35; Step 311: completing the output of the optimal solution and ending the CONSGA-Ⅱ algorithm process. Step 311: determining initial population parameters; assuming that the real number of measurements at time k+1 is n, the predicted target number is m; determining the population size L and the maximum evolution generation g max ; Step 312: defining the initial population Q k+1 According to the optimization model of motorized multi-target data association, each chromosome vector is defined as: The step 31 comprises: C(l,j) = randperm(n) (4) Wherein, l = 1, 2,..., L, C(l) represents the lth chromosome; the dimension of the decision vector in each chromosome is n, and n is the number of measurements; randperm(·) represents a random rearrangement function; the elements greater than m in C(l) are set to zero, which represents that the corresponding measurement is a false alarm; The step 32 comprises: Step 321: generating an initial chaos optimization vector; T tent n-dimensional chaos vectors are generated by using a tent method, and n is the number of real measurements; the number of chaos vectors T is constrained to be at least twice the number of chromosomes, that is, T >= 2N; Wherein, t = 1, 2,..., T, represents the chaos vector number; X(t) represents the tth chaos vector of the chromosome; the t+1th chaos vector X(t+1) is defined as: Through formula (6), t n-dimensional variables X(T,n) with chaos characteristics are obtained; R(t,j) = int(m X j (t,n)) j = 1,2,"...,n (7) Step 322: mapping the chaos variable X(T,n) to the value range of the decision variable n, and the specific mapping relationship is as follows:

2. The method of claim 1, wherein, Wherein, int(·) represents an integer function, and m represents the number of predicted targets. The step 1 comprises: Supposing that the target motion state vector is X(k) at any moment k, and the corresponding covariance matrix is P(k), according to the EKF algorithm, one-step prediction results of the state motion vector and the covariance matrix are as follows: Wherein, F represents a state transition matrix, G represents a process noise covariance matrix, and Q(k) represents process noise; If the measurement information of the radar is Z(k), one-step prediction of the state equation can be expressed as: Z(k+1) = HX(k+1) + W(k+1) (2) 3. The method of claim 1, wherein, Wherein, W(k) is measurement noise, and H is a measurement matrix. Assume that m targets have established track information at time k, and the predicted result of the corresponding track at time k+1 is At time k+1, the radar observes n targets, and the true measurement value of the targets is Determine the optimal correspondence relationship of , i = 1, 2", m, j = 1, 2", n.

4. The method of claim 3, wherein, The step 2 comprises: The track results of m targets at time k, Z1(k), Z2(k), …, Zm(k) are regarded as integers 1, 2, …, m, and the corresponding random permutation i1, i2, …, im is denoted as m (k) is regarded as integers 1, 2, …, m, and the corresponding random permutation i1, i2, …, im is denoted as m The real measurement value of n targets at time k+1 is regarded as integers 1, 2, …, n, and the corresponding permutation j1, j2, …, jn from small to large is denoted as The real measurement value of n targets at time k+1 is regarded as integers 1, 2, …, n, and the corresponding permutation j1, j2, …, jn from small to large is denoted as n The residual distance between the predicted value of the target and the real value is denoted as d ij The residual distance between the predicted value of the target and the real value is denoted as d The residual distance between the predicted value of the target and the real value is denoted as d The sum of the residual distances of all targets at time k+1 is denoted as The formula (3) is taken as a target function of data association, and the following assumptions are made: one target has and only has one measurement associated therewith; one measurement is at most associated with one target; the constraint condition of the target function of data association is n≥m; and when D=D min is established, the optimal corresponding relation between the n target real measurement results at the k+1 time and the track results of the m targets is where i=1, 2", m, and j=1, 2", n.

5. The method of claim 1, wherein, The step 2 comprises: Step 361: Merge parent population Q g Offspring population P g Population Z g Number size 2L; Step 362: Selecting a population Z from the population Y g Perform fast non-dominated sorting and crowdedness calculation and sort Step 363: Selecting population Z g Top 2L chromosomes as parent population Q g+1 .

6. The method of claim 1, wherein, In step 37: judging whether the iteration number meets the condition, i.e. judging whether g is equal to C*g max / 50; wherein C is a positive integer.

7. The method of claim 1, wherein, The step 36 comprises: The step 4 comprises: Step 41: Compute innovation covariance matrix: S n (k) = h x n (k) P n (k|k-1) (h x n (k)) T + R(k) (9) where n is the target number, h x (k) is the Jacobian matrix of the measurement matrix H(k); R(k) is the covariance matrix of the measurement noise W(k); Step 42: Compute Kalman gain: K n (k) = P n (k|k-1)(h x n (k)) T |S n (k)| -1 (10) Step 43: Update state vector: X n (k|k) = X n (k|k-1) + K n (k) v n (k) (11) Step 44: Update covariance matrix: P n (k|k) = P n (k|k-1) - K n (k) S n (k) (K n (k)) T (12) Repeat steps 41 to 44 until track filtering and plot updating for all targets are completed.

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