Multi-unmanned aerial vehicle multi-target search and tracking trajectory optimization method

Abstract

The invention discloses a multi-unmanned aerial vehicle multi-target search and tracking trajectory optimization method, which comprises the following steps of: modeling unknown target density in a search area under a framework of joint integration probability data association filtering; according to the predicted posterior unknown target density and the predicted posterior known target tracking error covariance, creating dimensionless evaluation indexes, weighting the two indexes as a trajectory optimization criterion of the unmanned aerial vehicle, and obtaining an expected state vector of the unmanned aerial vehicle at the next moment; and then the unmanned aerial vehicle is controlled to reach the state of the expected state vector at the next moment, and optimization of the trajectory of the unmanned aerial vehicle is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control when unmanned aerial vehicles search for targets, and in particular to a method for optimizing multi-unmanned aerial vehicle multi-target search and tracking trajectories. Background Art

[0002] In actual application environments, the number of targets that need to be searched by drones is generally unknown. Therefore, drones need to track discovered targets while searching the surveillance area to promptly discover potential targets in order to grasp the overall situation information in a timely manner. For drones equipped with sensors such as cameras, their detection range is limited and cannot cover the entire area to be searched at the same time. Therefore, when drones go to unexplored areas to search for targets, they may leave the tracked targets and cause the loss of maintained targets. Therefore, it is necessary to plan and design the detection flight trajectory of drones in the most reasonable way to balance the search of undetected areas and the tracking of identified targets as much as possible.

[0003] Based on the above problems, the inventors have conducted in-depth research on the UAV multi-target search and tracking trajectory optimization method, in the hope of designing a multi-UAV multi-target search and tracking trajectory optimization method that can solve the above problems. Summary of the invention

[0004] In order to overcome the above problems, the inventors have conducted intensive research and designed a multi-UAV multi-target search and tracking trajectory optimization method. In this method, under the framework of joint integrated probabilistic data association filtering, the unknown target density in the search area is modeled, and dimensionless evaluation indicators are created according to the predicted a posteriori unknown target density and the tracking error covariance of the a posteriori known target. After weighting the two, they are used as the trajectory optimization criterion of the UAV to obtain the expected UAV state vector at the next moment, and then the UAV is controlled to reach the state of the expected state vector at the next moment, thereby realizing the optimization of the UAV trajectory, thereby completing the present invention.

[0005] Specifically, the purpose of the present invention is to provide a multi-UAV multi-target search and tracking trajectory optimization method, the method comprising the following steps:

[0006] Step 1, keeping the output power of the drone unchanged, based on the drone's own position information and the drone's maximum turning angle, obtaining all possible state vectors of the drone at the next moment in real time to form a state vector set; preferably, the state vector includes a position component and a velocity component;

[0007] Step 2: Obtain the cost function of the multi-target search part in real time in the drone And the cost function of the known target tracking part

[0008] Step 3: Obtain the objective function of the search and tracking problem through the following formula (1):

[0009]

[0010] Among them, J k Represents the objective function of the search and tracking problem;

[0011] η represents the weight parameter;

[0012] Step 4: Select from the state vector set of step 1 the objective function J that can solve the search and tracking problem k The state vector with the maximum value is taken as the desired state vector of the drone at the next moment, and the drone flight is controlled accordingly.

[0013] The beneficial effects of the present invention include:

[0014] (1) According to the multi-UAV multi-target search and tracking trajectory optimization method provided by the present invention, the method models the unknown target density in the search area and updates it according to the UAV trajectory, guiding the UAV to move to the area with high density of unknown targets;

[0015] (2) According to the multi-UAV multi-target search and tracking trajectory optimization method provided by the present invention, the unknown target density is considered in the process of calculating the external source density by the joint integrated probabilistic data association filtering algorithm, thereby increasing the probability of the sensor measurement value being associated with the unknown target, which is helpful for the initialization process of the potential unknown target, that is, the process from no target to confirming that it is a target;

[0016] (3) According to the multi-UAV multi-target search and tracking trajectory optimization method provided by the present invention, dimensionless evaluation indicators are created respectively by predicting the posterior unknown target density and the tracking error covariance of the posterior known target, and the two are weighted as the trajectory optimization criterion of the UAV, thereby solving the trajectory optimization problem of the detection UAV. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A schematic diagram showing an application scenario of the multi-UAV multi-target search and tracking trajectory optimization method of the present application;

[0018] Figure 2 The overall logic diagram of the multi-UAV multi-target search and tracking trajectory optimization method of the present application is shown;

[0019] Figure 3 A schematic diagram showing scene 1 in embodiment 1 is shown;

[0020] Figure 4 A schematic diagram showing the motion trajectories of the four UAVs obtained in Example 1 is shown;

[0021] Figure 5 A schematic diagram of the position estimation OSPA error obtained in Example 1 is shown;

[0022] Figure 6 A schematic diagram showing scene 2 in embodiment 2 is shown;

[0023] Figure 7 A schematic diagram showing the motion trajectories of the four UAVs obtained in Example 2 is shown;

[0024] Figure 8 A schematic diagram of the position estimation OSPA error obtained in Example 2 is shown;

[0025] Fig. 9 A schematic diagram showing scene 3 in embodiment 3 is shown;

[0026] Fig.10 A schematic diagram showing the motion trajectories of the four UAVs obtained in Example 3 is shown;

[0027] Fig.11 A schematic diagram of the position estimation OSPA error obtained in Example 3 is shown. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0029] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0030] When UAVs carrying bearing-only sensors cooperate to search and track an unknown number of targets in a surveillance area, the model of multi-target cooperative search and tracking is as follows: Figure 1 As shown, the union of the field of view of each airborne sensor cannot cover the entire search area, so it is necessary to guide the drone to search for undiscovered targets. On the other hand, due to the poor observability of the azimuth-only sensor, it is also necessary to optimize the flight path of the drone to ensure the tracking accuracy of the discovered target. The drones in this application all fly on a horizontal plane at a fixed height.

[0031] In order to better control the UAV and design the most optimized flight route for the UAV, the present invention provides a multi-UAV multi-target search and tracking trajectory optimization method, such as Figure 2 As shown in , the method comprises the following steps:

[0032] Step 1, keeping the output power of the drone unchanged, based on the drone's own position information and the drone's maximum turning angle, obtaining all possible state vectors of the drone at the next moment in real time to form a state vector set; preferably, the state vector includes a position component and a velocity component. Since the drone flies at a fixed horizontal altitude, the position component and the velocity component only include two-dimensional information of the plane state, and do not include information in the height direction;

[0033] Step 2: Obtain the cost function of the multi-target search part in real time in the drone And the cost function of the known target tracking part

[0034] Step 3: Obtain the objective function of the search and tracking problem through the following formula (1):

[0035]

[0036] Among them, J k Represents the objective function of the search and tracking problem;

[0037] η represents a weight parameter; preferably, the value of the weight parameter is 1;

[0038] Step 4: Select from the state vector set of step 1 the objective function J that can solve the search and tracking problem k The state vector with the maximum value is taken as the desired state vector of the drone at the next moment, and the drone flight is controlled accordingly, that is, the drone is controlled to reach the desired state vector at the next moment.

[0039] When multiple drones are deployed in the surveillance area at the same time, each drone follows the above control scheme, and when multiple drones are deployed, the initial travel directions of the multiple drones are different, so that they can search for targets in different directions. Generally speaking, in order to improve efficiency and ensure the success rate of search and monitoring, at least 4 drones will be deployed in a surveillance search area at the same time.

[0040] In a preferred embodiment, in step 1, the cost function of the multi-objective search part is Obtained by the following formula (II):

[0041]

[0042] Among them, n g represents the number of grids obtained by grid discretization of the search area, i represents the th grid, in this application, the discrete grid is a square grid, the actual length of the ground corresponding to the grid side length is related to the height of the drone and the recognition accuracy, and preferably the grid size is set to 16mX16m;

[0043] represents the number of unknown targets at time k+1,

[0044] Represents the prior value of the number of unknown targets at time k+1.

[0045] Preferably, the number of unknown targets at time k+1 in the i-th grid is Obtained by the following formula (III):

[0046]

[0047] in, represents the posterior unknown target density,

[0048] Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid.

[0049] Represents the state vector The posterior unknown target density at ,

[0050] s(gi) represents the area of ​​the i-th grid,

[0051] (u,v) represents the velocity component in the state vector.

[0052] Preferably, the posterior unknown target density at the position corresponding to the state vector x at time k+1 is Obtained by the following formula (IV): represents the a priori unknown target density at the center point of the i-th grid gi at time k+1, which can be calculated by substituting the coordinates of the center point of gi into formula (4).

[0053]

[0054] Among them, N S Represents the number of sensors, including optical cameras and infrared cameras. Various cameras on each drone are counted as one sensor. S The value of is consistent with the number of drones, that is, each drone is equipped with a sensor. S It can be 2-10.

[0055] l represents the lth sensor,

[0056] Indicates that the lth sensor is at x k+1 The detection probability at is preferably 0.95.

[0057] Represents the a priori unknown target density at the position corresponding to the state vector x at time k+1.

[0058] Preferably, the prior value of the number of unknown targets at time k+1 in the i-th grid is Obtained by the following formula (V):

[0059]

[0060] in, represents the a priori unknown target density at time k+1,

[0061] Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid.

[0062] represents the a priori unknown target density at the center point of the i-th grid gi at time k+1,

[0063] s(gi) represents the area of ​​the i-th grid,

[0064] (u,v) represents the velocity component in the state vector.

[0065] Preferably, the Obtained by the following formula (VI): represents the a priori unknown target density at the center point of the i-th grid gi at time k+1, which can be calculated by substituting the coordinates of the center point of gi into formula (VI);

[0066]

[0067] in, represents the number of Gaussian components in the unknown target density distribution,

[0068] represents the number of Gaussian components in the new target density distribution,

[0069] t represents the tth Gaussian component in the target density distribution,

[0070] represents the weight of the t-th Gaussian component in the posterior unknown target density at time k, which is predicted and updated by jointly integrating probabilistic data association filtering.

[0071] represents the weight of the t-th Gaussian component in the new target density at time k+1, which is obtained by setting the new target distribution model.

[0072] P S It represents the survival probability of the target. It is preferably set to 0.99 according to the actual scenario.

[0073] Represents x k+1 The mean is The covariance matrix is Gaussian distribution,

[0074] x k+1 Represents the state value at time k+1, and its mean is The covariance matrix is Gaussian distribution,

[0075] represents the mean of the t-th Gaussian component in the a priori unknown target density distribution at time k+1,

[0076] represents the covariance matrix of the t-th Gaussian component in the a priori unknown target density distribution at time k+1,

[0077] Represents x k+1 The mean is The covariance matrix is Gaussian distribution,

[0078] represents the mean of the t-th Gaussian component in the new target density distribution at time k+1,

[0079] Represents the covariance matrix of the tth Gaussian component in the new target density distribution at time k+1.

[0080] In a preferred embodiment, in step 1, the cost function of the known target tracking part is Obtained by the following formula (VII):

[0081]

[0082] in, It indicates that the number of targets confirmed to exist at the predicted k+1 time is equal to the number of targets confirmed to exist at the k time.

[0083] i indicates the serial number of the target to be confirmed.

[0084] represents the posterior error covariance matrix of the i-th confirmed target,

[0085] Represents the prediction error covariance matrix of the i-th confirmed target.

[0086] Preferably, the It is obtained by jointly integrating the update calculation of the covariance matrix in the probabilistic data association filter.

[0087] Preferably, the Obtained by predictive computation of the covariance matrix in a jointly integrated probabilistic data association filter.

[0088] Example 1

[0089] Set the search area of ​​800m×800m, the number of grids divided when calculating the unknown target density is 50×50, and set the field of view range of 4 drones with a radius of 150m. The detection probability of the airborne sensor to the target in its field of view is P d =0.95, the standard deviation of the angle measurement noise is σ a = 1°, the expected number of environmental clutter contained in each frame of measurement value of each sensor is N FA =3.

[0090] The four drones are moving at a constant speed, and the sampling time interval of the sensors on the drones is T. S =1s, process noise δ v The standard deviation is 0.08m / s 2 , the target survival probability is P S =0.99. The maximum permissible turning rate of the drone is set to ω max =40° / s, the speed is 15m / s.

[0091] Figure 3 This is scene 1. The black diamond in the figure represents the positions of the four UAVs at the initial moment, that is, the initial positions of the four UAVs are the same, but they are facing the four directions of southeast, northwest, and northeast respectively. The green circular area represents the field of view of the sensor at the initial moment. The black solid line is the target motion trajectory when process noise is not considered. The hollow circles at both ends of the trajectory represent the starting position of the target trajectory, and the hollow triangles represent the ending position of the target trajectory. The time mark near each trajectory is the time when the target appears and disappears in the search area.

[0092] Scene 1 is the target reverse motion scene: from the initial moment, there are two groups of targets moving in opposite directions in the area, one of which is within the sensor's field of view. The setting of this simulation scene is to examine whether the trajectory optimization method of the drone can explore and discover potential targets in other areas based on tracking existing targets. The initial coordinates of the drone are (350m, 650m);

[0093] All drones follow the same control scheme, which is:

[0094] Step 1: Keep the output power of the drone unchanged, and obtain all possible state vectors of the drone at the next moment in real time based on the drone's own position information and the drone's maximum turning angle to form a state vector set, wherein the state vector includes a position component and a velocity component;

[0095] Step 2: Obtain the cost function of the multi-target search part in real time in the drone And the cost function of the known target tracking part

[0096] Step 3: Obtain the objective function of the search and tracking problem through the following formula (1):

[0097]

[0098] Among them, J k Represents the objective function of the search and tracking problem;

[0099] η represents the weight parameter, and its value is 1;

[0100] Step 4: Select from the state vector set of step 1 the objective function J that can solve the search and tracking problem k The state vector with the maximum value is taken as the desired state vector of the drone at the next moment, and the drone flight is controlled accordingly.

[0101] Among them, in step 1, the cost function J of the multi-objective search part is k s Obtained by the following formula (II):

[0102]

[0103] Among them, n g It represents the number of grids obtained by grid discretization of the search area, and its value is 2500. i represents the grid.

[0104] represents the number of unknown targets at time k+1,

[0105] Represents the prior value of the number of unknown targets at time k+1.

[0106] The number of unknown targets in the i-th grid at time k+1 Obtained by the following formula (III):

[0107]

[0108] in, represents the unknown target posterior density,

[0109] Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid.

[0110] Represents the state vector The unknown target posterior density at ,

[0111] s(gi) represents the area of ​​the ith grid, which is 16mX16m.

[0112] (u,v) represents the velocity component in the state vector.

[0113] The posterior unknown target density at the position corresponding to the state vector x at time k+1 Obtained by the following formula (IV):

[0114]

[0115] Among them, N S Indicates the number of sensors, the value is 4.

[0116] l represents the lth sensor,

[0117] Indicates that the lth sensor is at x k+1 The detection probability at

[0118] Represents the a priori unknown target density at the position corresponding to the state vector x at time k+1.

[0119] The prior value of the number of unknown targets at time k+1 in the i-th grid Obtained by the following formula (V):

[0120]

[0121] in, represents the a priori unknown target density at the position corresponding to the state vector x at time k+1,

[0122] Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid.

[0123] represents the a priori unknown target density at the center point of the i-th grid gi at time k+1,

[0124] s(gi) represents the area of ​​the i-th grid,

[0125] (u,v) represents the velocity component in the state vector.

[0126] Said Obtained by the following formula (VI):

[0127]

[0128] in, represents the number of Gaussian components in the unknown target density distribution,

[0129] represents the number of Gaussian components in the new target density distribution,

[0130] t represents the tth Gaussian component in the target density distribution,

[0131] represents the weight of the t-th Gaussian component in the posterior unknown target density at time k, which is predicted and updated by jointly integrating probabilistic data association filtering.

[0132] represents the weight of the t-th Gaussian component in the new target density at time k+1, which is obtained by setting the new target distribution model.

[0133] P S represents the target survival probability, P S =0.99,

[0134] Represents x k+1 The mean is The covariance matrix is Gaussian distribution,

[0135] Represents x k+1 The mean is The covariance matrix is Gaussian distribution.

[0136] In step 1, the cost function of the known target tracking part is Obtained by the following formula (VII):

[0137]

[0138] in, It indicates that the number of targets confirmed to exist at the predicted k+1 time is equal to the number of targets confirmed to exist at the k time.

[0139] i indicates the serial number of the target to be confirmed.

[0140] represents the posterior error covariance matrix of the i-th confirmed target,

[0141] Represents the prediction error covariance matrix of the i-th confirmed target.

[0142] Said It is obtained by the update calculation of the covariance matrix in the joint integrated probabilistic data association filter;

[0143] Said The covariance matrix in the joint integrated probability data association filter is obtained by predictive calculation. The covariance matrix in the joint integrated probability data association filter is the covariance matrix in the joint integrated probability data association filter recorded in Williams J L. Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA, and association-based MeMBer [J]. IEEE Transactions on Aerospace and Electronic Systems, 2015, 51 (3): 1664-1687.

[0144] Under the control of the above control method, the results obtained in scenario 1 are as follows Figure 4 and Figure 5 As shown in Figure 4 The motion trajectories of the four UAVs are shown in FIG. 1 , where the purple scattered points are the target positions estimated by the multi-UAV multi-target search and tracking trajectory optimization method. Figure 5 is the position estimation OSPA error for multi-target tracking. It can be seen from the figure that although there is a group of targets in the sensor field of view at the initial moment, in order to balance the two purposes of search and tracking, the first and second drones leave the area to search other areas, and the first drone discovers the remaining three targets in turn between t=15s and t=25s, and continues to track this group of targets. The second drone continues to search the area that has not been reached, and the second group of targets has not appeared in the field of view. At t=30s, the three targets in the upper left corner disappear, and the third and fourth drones begin to search other areas. From the simulation results of scenario 1, it can be seen that the multi-drone multi-target search and tracking trajectory optimization method can better balance the two purposes of target search and tracking.

[0145] Example 2

[0146] Set the search area and drone exactly the same as in Example 1.

[0147] Set as Figure 6 In the second scene shown in the figure, the black diamond represents the position of the four UAVs at the initial moment, that is, the initial positions of the four UAVs are the same, but they are facing the four directions of southeast, northwest, and northeast respectively. The green circular area represents the field of view of the sensor at the initial moment, and the black solid line is the target motion trajectory when the process noise is not considered. The hollow circles at both ends of the trajectory represent the starting position of the target trajectory, and the hollow triangles represent the ending position of the target trajectory. The time mark near each trajectory is the time when the target appears and disappears in the search area.

[0148] Scenario 2 is a priori search information scenario: Assuming that the target can only enter the region through the left edge of the region, the new target density model

[0149]

[0150] The number of Gaussian components in is set to The interval between the position means of adjacent Gaussian components is 80m, and the mean coordinates of the position components are p i ∈0m×{0m,100m,···,800m}. Figure 4 As shown in the figure, at the initial moment, six targets enter the area from the left edge of the search area, and the initial coordinates of the UAV are (300m, 400m); the setting of this simulation scene is intended to examine whether the trajectory optimization method of the UAV can keep tracking the discovered targets while searching the area with high unknown target density after searching for the targets.

[0151] The drone is controlled using a control method that is completely consistent with that in Example 1.

[0152] Under the control of the above control method, the results obtained in scenario 2 are as follows Figure 7 and Figure 8 As shown in Figure 7 The motion trajectories of the four UAVs are shown in the figure. At the initial moment, there are no targets in the sensor field of view of the four UAVs, so they search for targets from different directions in the area with high density of unknown targets on the left. It can be observed from the figure that the UAVs successively found six targets entering the search area from the left edge between t=15s and t=30s, and the OSPA error was maintained within 20m. When t=50s, the three targets in the lower area disappeared. Since it takes a while to judge that the trajectory disappears, the OSPA error corresponding to this moment increases. When t=60s, the second UAV starts to move downward to reduce the density of unknown targets in the area with a vertical coordinate range of 600m to 700m, resulting in the loss of the target at the top. However, 5s later, the fourth UAV covers the area, and the second UAV returns to the upper left area to continue tracking the two targets above. From the simulation results, it can be seen that the multi-UAV multi-target search and tracking trajectory optimization method can track known targets while maintaining monitoring of the high unknown target density area by coordinating the movement of each UAV, and keep the multi-target tracking error within a certain range.

[0153] Example 3

[0154] Set the search area and drones that are completely consistent with those in Example 1 and Example 2.

[0155] Set as Fig. 9In the scene three shown in the figure, the black diamond represents the position of the four UAVs at the initial moment, that is, the initial positions of the four UAVs are the same, but they are facing the four directions of southeast, northwest, and northeast respectively. The green circular area represents the field of view of the sensor at the initial moment, and the black solid line is the target motion trajectory when the process noise is not considered. The hollow circles at both ends of the trajectory represent the starting position of the target trajectory, and the hollow triangles represent the ending position of the target trajectory. The time mark near each trajectory is the time when the target appears and disappears in the search area.

[0156] Scene 3 is the target random appearance scene: Fig. 9 As shown in the figure, consider the scenario where 4 drones search and track 10 targets in the search area. There is no prior information about new targets. The 10 targets appear in sequence at different times. The initial position of the drone is (400m, 400m). The setting of this simulation scenario is intended to comprehensively examine the search and tracking capabilities of the drone trajectory optimization method for targets in the search area.

[0157] The drone is controlled using a control method that is completely consistent with that in Example 1 and Example 2.

[0158] Under the control of the above control method, the results obtained in scenario 3 are as follows Fig.10 and Fig.11 As shown in Fig.10 The trajectories of the four UAVs are shown in the figure. The target at (500m, 500m) generated at the initial moment is within the detection range of the four UAVs. To balance the performance of the search and estimation tasks, the first and second UAVs move toward the target to reduce the tracking error, while the third and fourth UAVs move to the other half of the area to find more potential targets. The first UAV detects the target at (300m, 600m) while tracking the target, and then moves toward the newly discovered target. The second UAV continues to track the target that appears in the first frame. The fourth UAV successfully discovers the two targets starting at (200m, 300m) in turn and maintains a high estimation accuracy. It is worth noting that the third UAV failed to successfully start the track at the coordinates that appeared at the 30th second. The possible reason is that at the 30th second, the target was close to another target that ended at (500m, 200m), and the new target was not successfully started during the data association process. The multi-UAV multi-target search and tracking trajectory optimization method failed to enhance its observability. Fig.11 This is the variation curve of the OSPA error of position estimation for multi-target tracking in the simulation. It can be seen that the error converges well. When a new target appears in the area or a target disappears, the OSPA error at the corresponding moment will increase. This is because the search and start of new targets and the confirmation of the disappearance of old targets require the measurement of multiple frames of sensors.

[0159] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A multi-UAV multi-target search and tracking trajectory optimization method, characterized in that: The method comprises the following steps: Step 1, keeping the output power of the drone unchanged, based on the drone's own position information and the drone's maximum turning angle, obtaining all possible state vectors of the drone at the next moment in real time to form a state vector set; preferably, the state vector includes a position component and a velocity component; Step 2: Obtain the cost function of the multi-target search part in real time in the drone And the cost function of the known target tracking part Step 3: Obtain the objective function of the search and tracking problem through the following formula (1): Among them, J k Represents the objective function of the search and tracking problem; η represents the weight parameter; Step 4: Select from the state vector set of step 1 the objective function J that can solve the search and tracking problem k The state vector with the maximum value is taken as the desired state vector of the drone at the next moment, and the drone flight is controlled accordingly.

2. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 1 is characterized in that: In step 1, the cost function of the multi-objective search part is Obtained by the following formula (II): Among them, n g represents the number of grids obtained by grid discretization of the search area, i represents the th grid, represents the number of unknown targets at time k+1, Represents the prior value of the number of unknown targets at time k+1.

3. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 2 is characterized in that: The number of unknown targets in the i-th grid at time k+1 Obtained by the following formula (III): in, represents the posterior unknown target density, Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid. Represents the state vector The posterior unknown target density at , s(gi) represents the area of ​​the i-th grid, (u,v) represents the velocity component in the state vector.

4. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 3 is characterized in that: The posterior unknown target density at the position corresponding to the state vector x at time k+1 Obtained by the following formula (IV): Among them, N S represents the number of sensors, l represents the lth sensor, Indicates that the lth sensor is at x k+1 The detection probability at Represents the a priori unknown target density at the position corresponding to the state vector x at time k+1.

5. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 2 is characterized in that: The prior value of the number of unknown targets at time k+1 in the i-th grid Obtained by the following formula (V): in, represents the a priori unknown target density at time k+1, Represents the state vector, the position component of which is consistent with the coordinate value of the center point of the i-th grid. represents the a priori unknown target density at the center point of the i-th grid gi at time k+1, s(gi) represents the area of ​​the i-th grid, (u,v) represents the velocity component in the state vector.

6. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 4 or 5, characterized in that: Said Obtained by the following formula (VI): in, represents the number of Gaussian components in the unknown target density distribution, represents the number of Gaussian components in the new target density distribution, t represents the tth Gaussian component in the target density distribution, represents the weight of the t-th Gaussian component in the posterior unknown target density at time k, represents the weight of the tth Gaussian component in the new target density at time k+1, P S represents the target survival probability, Represents x k+1 The mean is The covariance matrix is Gaussian distribution, Represents x k+1 The mean is The covariance matrix is Gaussian distribution.

7. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 1 is characterized in that: In step 1, the cost function of the known target tracking part is Obtained by the following formula (VII): in, It indicates that the number of targets confirmed to exist at the predicted k+1 time is equal to the number of targets confirmed to exist at the k time. i indicates the serial number of the target to be confirmed. represents the posterior error covariance matrix of the i-th confirmed target, Represents the prediction error covariance matrix of the i-th confirmed target.

8. The multi-UAV multi-target search and tracking trajectory optimization method according to claim 1, characterized in that: In step 3, the value of the weight parameter η is 1.

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