Unmanned aerial vehicle auxiliary target positioning and tracking method

Abstract

The invention relates to an unmanned aerial vehicle auxiliary target positioning and tracking method, and belongs to the technical field of unmanned aerial vehicle positioning. The method comprises the following steps: S1, modeling an unmanned aerial vehicle auxiliary target positioning and tracking system model; s2, modeling a sensing channel model; s3, the modeling unmanned aerial vehicle senses a target radar signal and a target echo signal; s4, modeling a target dynamic model; s5, estimating a target arrival angle and arrival time; s6, determining the matching of each time slot target based on a Hungary algorithm; s7, estimating a target position and calculating a Cramer-Rao lower bound based on an extended Kalman filtering algorithm; s8, modeling an auxiliary target positioning and tracking constraint of the unmanned aerial vehicle; s9, modeling an unmanned aerial vehicle target tracking and flight path planning problem as a system cost function minimization problem; and S10, modeling the target tracking and flight path of the unmanned aerial vehicle as a Markov decision process, and solving by adopting a multi-agent DQN algorithm. According to the invention, by optimizing the target tracking strategy and the flight path of multiple unmanned aerial vehicles, the system cost function minimization is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of UAV positioning, and relates to a method for UAV-assisted target positioning and tracking. Background Technique

[0002] With the rapid development of positioning technology, target positioning and tracking, as a key spatial perception technology, has important application values in fields such as military reconnaissance, emergency disaster relief, and environmental monitoring. The UAV-assisted target positioning and tracking technology realizes high-precision continuous tracking of dynamic targets by optimizing the design of UAV target perception strategies and flight trajectories. In recent years, UAV systems, with their advantages such as flexibility and multi-aircraft collaborative operations, have become efficient aerial platforms for wide-area target tracking. However, in UAV-assisted target positioning and tracking systems, how to optimize UAV flight trajectories and design target perception strategies in complex environments to improve the accuracy of target state estimation and reduce system resource consumption has become an urgent problem to be solved.

[0003] Currently, there are already literature studies on UAV-assisted target positioning and tracking problems. For example, some literature estimates the target state based on the Kalman filter method and realizes positioning and tracking accuracy by optimizing the UAV trajectory; some literature determines the target position by estimating the time of arrival. However, existing research rarely considers multi-UAV collaborative target positioning and tracking and long-term system performance optimization. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for UAV-assisted target positioning and tracking. For a target positioning and tracking system including multiple UAVs and multiple moving targets, while satisfying the constraints of target positioning and tracking, with the minimization of system energy consumption and the Cramér-Rao lower bound as the optimization objectives, UAV trajectory planning and tracking target association strategies are realized.

[0005] To achieve the above objective, the present invention provides the following technical solutions:

[0006] A method for UAV-assisted target positioning and tracking, which specifically includes the following steps:

[0007] S1: Model the UAV-assisted target positioning and tracking system model;

[0008] S2: Model the sensing channel model;

[0009] S3: Model the UAV's sensing of the target radar signal and the target echo signal;

[0010] S4: Model the target dynamic model;

[0011] S5: Estimate the angle of arrival and time of arrival of the target;

[0012] S6: Determine the matching of targets in each time slot based on the Hungarian algorithm;

[0013] S7: Estimate the target position based on the extended Kalman filter algorithm and calculate the Cramer-Rao lower bound;

[0014] S8: Model the constraints of UAV-assisted target positioning and tracking;

[0015] S9: Model the UAV target tracking and flight trajectory planning problem as a system cost function minimization problem;

[0016] S10: Model the UAV target tracking and flight trajectory as a Markov decision process (MDP), and solve it using the multi-agent deep Q-network (DQN) algorithm.

[0017] Furthermore, in step S1, model the UAV-assisted target positioning and tracking system model, specifically including: The system includes M multi-antenna UAVs and N moving targets; Assume that the UAVs are equipped with uniform linear antenna arrays, which can send radar sensing signals, receive target echo signals, estimate the angle of arrival and position of the targets, and let L represent the number of antennas of each UAV; The UAVs start from the starting point and perform positioning and tracking on each target during the flight; Divide the system time into T time slots, and the length of each time slot is τ; Let represent the position of UAV m at time slot t, be the flight altitude of UAV m at time slot t, and represent the lowest and highest altitudes of the UAV flight respectively, 1 ≤ m ≤ M; Let q n,t = [x n,t , y n,t , 0] T represent the position of target n at time slot t, 1 ≤ n ≤ N; The state of UAV m at time slot t can be modeled as:

[0018]

[0019] where, let represent the action vector of UAV m at time slot t, which can be modeled as:

[0020]

[0021] where, ε is the moving distance of the UAV between adjacent time slots; e m,t and k m,t are the pitch angle and roll angle orders that UAV m can rotate at time slot t respectively, 1 ≤ e m,t ≤ N φ , 1 ≤ k m,t ≤ N θ , N φ and N θ are the orders of the adjustable pitch angle and roll angle of the UAV respectively; Δ φ= π / N φ is the pitch angle granularity that the UAV can rotate in each time slot; Δ θ = 2π / N θ is the roll angle granularity that the UAV can rotate in each time slot.

[0022] Furthermore, in step S2, the modeling of the sensing channel model specifically includes: assuming that the line-of-sight link is the main between the UAV and the target, let H m,n,t represent the sensing channel model between UAV m and target n at time slot t, which can be modeled as:

[0023]

[0024] where, represents the small-scale gain of the channel between UAV m and target n at time slot t, which can be modeled as a complex Gaussian distributed random variable with a mean of 0 and a variance of 1; ψ m,n,t represents the path loss of the channel between UAV m and target n at time slot t, which can be modeled as:

[0025]

[0026] where, ξ m,n represents the average path loss at a reference distance of 1 meter; represents the departure angle of UAV m sensing target n at time slot t; represents the arrival angle of UAV m sensing target n at time slot t, which can be modeled as:

[0027]

[0028] and respectively represent the receiving antenna steering vector and the transmitting antenna steering vector corresponding to the state of UAV m sensing target n at time slot t, which can be modeled as:

[0029]

[0030] where, d is the spacing between adjacent antennas of the UAV; λ is the wavelength of the transmitted signal.

[0031] Furthermore, in step S3, the modeling of the UAV sensing the target radar signal and the target echo signal specifically includes: let <http: / / www.example.com / represent the radar signal sent by each UAV to each target in each time slot. The value of the l-th antenna of X at the t P sampling point can be modeled as:

[0032]

[0033] where, P T is the transmission power of the UAV; Denote the value of the radar signal transmitted by the l-th antenna at the sampling point t when each UAV senses the state of each target in each time slot P where 1 ≤ t P ≤ T P ; T P is the number of sampling points of the chirp signal transmitted by the UAV in each time slot; Let Y m,t denote the target echo signal received by UAV m in time slot t, which can be modeled as:

[0034]

[0035] where δ m,n,t ∈ {0, 1} is the tracking variable of UAV m in time slot t. If δ m,n,t = 1, it means that UAV m tracks target n in time slot t, otherwise δ m,n,t = 0; N m,t is the echo noise received by UAV m in time slot t, which can be modeled as Gaussian noise with mean 0 and variance ; τ m,n,t′ is the arrival time of UAV m in time slot t' received from target n, which can be modeled as:

[0036]

[0037] where c is the speed of light.

[0038] Furthermore, in step S4, the target dynamic model is modeled, specifically including: Let g n,t denote the dynamic model of target n in time slot t, which can be modeled as:

[0039]

[0040] where and are the velocities of target n in the x, y, and z directions in time slot t, respectively; and are the accelerations of target n in the x, y, and z directions in time slot t, respectively; Let denote the acceleration of target n in time slot t, which can be modeled as:

[0041]

[0042] where is the change coefficient of the acceleration between adjacent time slots; w n,t is the perturbation noise of target n in time slot t, which can be modeled as Gaussian noise with mean 0 and variance ; The state update formula of target n in time slot t can be modeled as:

[0043] g n,t = Φg n,t-1+Γw n,t-1

[0044] Among them, Φ and Γ are the state transition matrix and the transition matrix of the disturbance noise of target n in adjacent time slots, respectively, and can be modeled as:

[0045]

[0046] Among them, and are the state transition matrix and the transition matrix of the disturbance noise of each target in adjacent time slots in the x, y, and z directions, respectively, and can be modeled as:

[0047]

[0048] Furthermore, in step S5, estimating the angle of arrival and time of arrival of the target specifically includes: using the Multiple Signal Classification (MUSIC) algorithm to estimate the angle of arrival of the target, and letting be the covariance matrix of the echo signal received by the UAV m in time slot t, and can be modeled as:

[0049]

[0050] Among them, R m,t is the covariance matrix of the transmitted signal of the UAV m in time slot t, and can be modeled as:

[0051]

[0052] Performing singular value decomposition on the covariance matrix of the target echo signal, we can obtain:

[0053]

[0054] Among them, is the signal eigenvector space of the UAV m in time slot t; is the noise eigenvector space of the UAV m in time slot t; N′ m,t is the number of targets tracked by the UAV m in time slot t, and can be modeled as:

[0055]

[0056] The signal subspace and the noise subspace can be modeled as:

[0057]

[0058] Discretize the angle of arrival of the target, and let Θ represent the set of discretized angles of arrival; let P(θ m,t)Denote the spectral estimation function of UAV m at time slot t based on the MUSIC algorithm, which can be modeled as:

[0059]

[0060] where α(θ m,t ) is the steering vector corresponding to the arrival angle θ m,t ; Let denote the n'-th arrival angle estimated by UAV m at time slot t, which can be modeled as:

[0061]

[0062] Let denote the estimated arrival time of UAV m sensing target n at time slot t, which can be modeled as:

[0063]

[0064] where is the amplitude coefficient of the received signal when UAV m senses target n at time slot t, which can be modeled as:

[0065]

[0066] Furthermore, in step S6, determining the matching of each time slot target based on the Hungarian algorithm specifically includes: Let b m,t denote the observation data matrix of UAV m sensing target at time slot t, which can be modeled as:

[0067]

[0068] where is the arrival time vector of UAV m sensing target at time slot t, which can be modeled as:

[0069]

[0070] is the arrival angle matrix vector of UAV m sensing target at time slot t, which can be modeled as:

[0071]

[0072] Let denote the state prediction value of each UAV sensing target n at time slot t. According to the state transition matrix, we have:

[0073]

[0074] where is the state estimation value of UAVs jointly sensing target n at time slot t; Let d' m,n,n′,tThe cost function representing the matching of UAV m to targets n and n′ at time slot t can be modeled as:

[0075]

[0076] Where, V n,t is the Jacobian matrix of each UAV sensing target n at time slot t, which can be modeled as:

[0077]

[0078] P m,n,t is the covariance matrix of the state estimation error value corresponding to the state of UAV m sensing target n at time slot t, which can be modeled as:

[0079]

[0080] Let represent the target matching variable at time slot t, represent that at UAV m in time slot t, target n and target n′ are matched, otherwise, The target matching problem can be modeled as:

[0081]

[0082] Where, v max and a max are the maximum speed and maximum acceleration of the target movement in adjacent time slots respectively; is the chi-square distribution threshold; Let G m,t be the weighted complete bipartite graph of the target matching problem at time slot t, which can be modeled as:

[0083] G m,t ={B′ m,t ,B″ m,t ,Ω,W}

[0084] Where, B′ m,t is the set of predicted values of UAV m sensing targets at time slot t, which can be modeled as:

[0085]

[0086] B″ m,t is the set of observed values of UAV m sensing targets at time slot t, which can be modeled as:

[0087] B″ m,t ={b m,t}

[0088] Ω is the set of edges connecting two vertices in B′ m,t and B″ m,t , which can be modeled as:

[0089]

[0090] Among them, represents the edge connecting vertex and vertex [b m,t n′,1 ; W is the weight of the set of edges connecting two vertices in B' m,t and B'' m,t , and can be modeled as:

[0091]

[0092] Among them, represents the weight of the edge connecting vertex and vertex [b m,t n′,1 , and can be modeled as:

[0093]

[0094] Based on the Hungarian algorithm to solve the optimization problem, the target matching strategy can be determined.

[0095] Furthermore, in step S7, based on the extended Kalman filter algorithm, the position parameters of the target are estimated and the Cramer-Rao lower bound is calculated. Specifically, let b m,n,t represent the observation model corresponding to the state where the unmanned aerial vehicle m senses the target n at time slot t, and can be modeled as:

[0096] b m,n,t = V m,n,t g m,n,t + n m,n,t

[0097] Among them, n m,n,t is the measurement noise and can be modeled as Gaussian noise with a mean of 0 and a variance of ; let K m,n,t represent the Kalman gain matrix corresponding to the state where the unmanned aerial vehicle m senses the target n at time slot t, and can be modeled as:

[0098]

[0099] Among them, the covariance matrix of the state prediction value of the target n at time slot t, and can be modeled as:

[0100]

[0101] is the covariance matrix of the observation noise corresponding to the state where the unmanned aerial vehicle m senses the target n at time slot t, and can be modeled as:

[0102] ​​

[0103] According to K m,n,t and the state estimation value corresponding to the state of the unmanned aerial vehicle m sensing the target n at time slot t can be obtained, that is:

[0104]

[0105] where υ m,n,t represents the error of the predicted value of the state of the unmanned aerial vehicle m sensing the target n at time slot t, and can be modeled as:

[0106] [[ID=1 + 18]]

[0107] According to K m,n,t and V m,n,t the covariance matrix of the state estimation value corresponding to the state of the unmanned aerial vehicle m sensing the target n at time slot t can be obtained, that is:

[0108] <000>

[0109] Let represent the target position of the unmanned aerial vehicle jointly sensing the target n at time slot t, and can be modeled as:

[0110]

[0111] where ψ m,n represents the weight factor of the unmanned aerial vehicle m sensing the position of the target n, and can be modeled as:

[0112]

[0113] P n,t represents the covariance matrix of the state estimation value of the unmanned aerial vehicle jointly sensing the target n at time slot t, and can be modeled as:

[0114]

[0115] Let η m,t represent the observation data matrix of the unmanned aerial vehicle m sensing the target at time slot t, and can be modeled as:

[0116]

[0117] where τ m,t is the arrival time matrix of the unmanned aerial vehicle m sensing the target at time slot t, and can be modeled as:

[0118]

[0119] θ m,t is the arrival angle matrix of the unmanned aerial vehicle m sensing the target at time slot t, and can be modeled as:

[0120]

[0121] Let \(I(\eta\) m,t ) denote the Fisher information matrix of the observation data of the target by UAV \(m\) at time slot \(t\), which is modeled as:

[0122]

[0123] where \(p(Y\) m,t |\(\eta\) m,t ) is the likelihood function of the observation data of the target sensed by UAV \(m\) at time slot \(t\), which can be modeled as:

[0124]

[0125] Partitioning \(I(\eta\) m,t ) gives:

[0126]

[0127] where \(I_1(\tau\) m,t , \(\tau\) m,t ) is the Fisher information matrix of the arrival time of the target sensed by UAV \(m\) at time slot \(t\), which can be modeled as:

[0128]

[0129] where \(SNR\) m,n,t is the signal-to-noise ratio of the received signal when UAV \(m\) senses target \(n\) at time slot \(t\), which can be modeled as:

[0130]

[0131] \(I_4(\theta\) m,t , \(\theta\) m,t ) is the Fisher information matrix of the angle of arrival of the target sensed by UAV \(m\) at time slot \(t\), which can be modeled as:

[0132]

[0133] \(I_2(\tau\) m,t , \(\theta\) m,t ) and \(I_3(\theta\) m,t , \(\tau\) m,t ) are the cross terms of the Fisher information matrix of the observation data of the target sensed by UAV \(m\) at time slot \(t\), which can be modeled as:

[0134] \(I_2(\tau\) m,t , \(\theta\) m,t ) = \(I_3(\theta\) m,t , \(\tau\) m,t ) \(\approx 0\)

[0135] Let \(I_0(q\) m,n,t ) denote the Fisher information matrix of UAV \(m\) sensing target \(n\) at time slot \(t\), which can be modeled as:

[0136]

[0137] Let \(J(q m,n,t )\) denote the posterior Cramer-Rao lower bound of the position of target \(n\) at time slot \(t\), which can be modeled as:

[0138]

[0139] where, denotes the Bayesian Fisher information matrix of the position of target \(n\) at time slot \(t\), which can be modeled as:

[0140]

[0141] where, is the position matrix of \(M\) UAVs within time slot \(t\), which can be modeled as:

[0142]

[0143] \(\delta n,t \) is the tracking association vector of \(M\) UAVs within time slot \(t\), which can be modeled as:

[0144] \(\delta n,t = [\delta 1,n,t ,…,\delta M,n,t T

[0145] I P (q n,t )\) is the Fisher information matrix of the prior information of target \(n\) at time slot \(t\), which can be modeled as:

[0146]

[0147] is the Fisher information matrix of the observation data of target \(n\) at time slot \(t\), which can be modeled as:

[0148]

[0149] Furthermore, in step S8, the constraints for UAV-assisted target positioning and tracking are modeled, specifically including: UAV target tracking load constraint, UAV flight trajectory constraint, UAV sensing range constraint, UAV energy consumption constraint; Let \(C1\) and \(C2\) denote the UAV target tracking load constraint, which can be modeled as:

[0150] C1:

[0151] C2: ​Among them, C1 indicates that the UAV can sense at most L targets in each time slot; C2 indicates that each target is sensed by at least one UAV in each time slot; Let C3 to C4 represent the UAV flight trajectory constraints, which can be modeled as:

[0152] C3:

[0153] C4: Among them, C3 is the flight distance constraint of UAV m in adjacent time slots; C4 is the collision avoidance constraint between different UAVs in each time slot, and d u represents the minimum safe flight distance between adjacent UAVs; Let C5 represent the sensing range constraint of the UAV, which can be modeled as:

[0154] C5: Among them, S min is the minimum receiver sensitivity of the radar; Let C6 represent the energy consumption constraint of the UAV, which can be modeled as:

[0155] C6: Among them, E m,t is the energy consumption of UAV m in time slot t, which can be modeled as:

[0156]

[0157] Among them, is the energy consumed by UAV m during flight in time slot t, which can be modeled as:

[0158]

[0159] Among them, P0 and P0′ are the constants of the blade profile power and the induced power in the hovering state respectively; can be modeled as:

[0160]

[0161] Among them, U 2 is the square of the tip speed of the rotor blade; is the speed of UAV m in time slot t; can be modeled as:

[0162]

[0163] Among them, v0 is the average rotor induced speed of the UAV in the hovering state; can be modeled as:

[0164]

[0165] Among them, ξ d 、ξ t are the fuselage drag ratio and the rotor reliability respectively; ρ, S Uare the air density and the rotor disk area, respectively; is the energy consumed by the UAV m to track and sense the target at time slot t, which can be modeled as:

[0166]

[0167] Furthermore, in step S9, the UAV target tracking and flight trajectory planning problem is modeled as a system cost function minimization problem, specifically including: Let E t represent the energy consumed by the UAV at time slot t, which can be modeled as:

[0168]

[0169] Let J t ′ represent the Cramér-Rao lower bound of the target position at time slot t, which can be modeled as:

[0170]

[0171] Let C t represent the system cost function at time slot t, which can be modeled as:

[0172] C t = β1E[[ID=:32]] t + β2J t ′

[0173] where β1 and β2 are the weight factors of the total energy consumption of the UAV and the Cramér-Rao lower bound, respectively; under the condition of satisfying the constraint conditions, the UAV flight trajectory and tracking association strategy are determined based on the optimization of the long-term system cost function, that is:

[0174]

[0175] Furthermore, in step S10, the UAV target tracking and flight trajectory planning problem is modeled as an MDP, and the multi-agent DQN algorithm is used to solve it, specifically including: The modeled MDP can be expressed as where s t is the system environment state space of the UAV at time slot t, which can be modeled as:

[0176]

[0177] where is the state of the UAV m at time slot t, which can be modeled as:

[0178]

[0179] is the joint action space of the UAV at time slot t, which can be modeled as:

[0180]

[0181] Among them, The action of unmanned aerial vehicle m at time slot t can be modeled as:

[0182]

[0183] Let r t u represent the reward function obtained by the agent at time slot t, which can be modeled as:

[0184] r t u = {r 1,t ,..., r M,t}

[0185] Among them, r m,t is the reward function of unmanned aerial vehicle m at time slot t, which can be modeled as:

[0186]

[0187] Among them, β1 is the weight factor of E m,t ; β2 is the weight factor of [J t ′] m,m ; η3 > 0 is the penalty constant, indicating that if unmanned aerial vehicle m collides with other unmanned aerial vehicles, it will be punished by η3; η4 > 0 is the penalty constant, indicating that if the moving distance of unmanned aerial vehicle m between adjacent time slots exceeds the threshold, it will be punished by η4; η5 > 0 is the penalty constant, indicating that if there is a target in the current time slot t that is not tracked by at least one unmanned aerial vehicle, it will be punished by η5; η6 > 0 is the penalty constant, indicating that if the number of targets selected by unmanned aerial vehicle m in the current time slot t exceeds the number of antennas, it will be punished by η6; η7 > 0 is the penalty constant, indicating that if the current unmanned aerial vehicle runs out of power and does not return to the landing point, it will be punished by η7; The multi-agent DQN algorithm is used to solve the modeled MDP. Specifically, each unmanned aerial vehicle observes the current system environment, executes actions to obtain the reward function, and stores it in the experience replay pool; In the algorithm training stage, each unmanned aerial vehicle observes the current system environment, executes the action corresponding to the maximum Q value with probability , and randomly selects actions with probability ; Repeat the above process until the algorithm converges, and the optimal unmanned aerial vehicle target tracking and flight trajectory planning can be obtained.

[0188] The beneficial effects of the present invention are as follows: In the unmanned aerial vehicle assisted target positioning and tracking system of the present invention, under the constraints of target positioning and tracking, the flight trajectory of the unmanned aerial vehicle and the tracking target association strategy are jointly optimized, realizing the minimization of system energy consumption and the Cramér-Rao lower bound.

[0189] Other advantages, objects, and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and obtained by the following description of the specification. Description of the Drawings

[0190] In order to make the objects, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably in conjunction with the accompanying drawings, where:

[0191] Figure 1 It is a schematic diagram of the trajectory planning and tracking target allocation scenario of the UAV-assisted target positioning and tracking system of the present invention;

[0192] Figure 2 It is a flowchart of the trajectory planning and tracking target allocation of the UAV-assisted target positioning and tracking system of the present invention. Detailed Embodiments

[0193] The following specific examples illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0194] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and should not be construed as a limitation of the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged, or reduced, and do not represent the dimensions of actual products; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0195] The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as a limitation of the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0196] Please refer to Figures 1 to 2 , the present invention provides a method for drone-assisted target positioning and tracking, Figure 1 which is a schematic diagram of the scenario of the drone-assisted target positioning and tracking system constructed by the present invention. As Figure 1 shown, the positioning and tracking system includes a target positioning and tracking system for multiple drones and multiple moving targets. Under the constraints of target positioning and tracking, with the minimization of system energy consumption and the Cramer-Rao lower bound as the optimization goal, the drone trajectory planning and tracking target association strategy are realized.

[0197] Figure 2 which is a schematic flow diagram of the method for drone-assisted target positioning and tracking of the present invention. As Figure 2 shown, the method specifically includes the following steps:

[0198] Step 1: Scenario modeling of the drone-assisted target positioning and tracking system;

[0199] The scenario modeling of the drone-assisted target positioning and tracking system is specifically as follows: M multi-antenna drones and N moving targets; it is assumed that the drones are equipped with uniform linear antenna arrays, which can send radar sensing signals, receive target echo signals, and estimate the angle of arrival and position of the targets. Let L represent the number of antennas of each drone; the drones start from the starting point and perform positioning and tracking of each target during flight; the system time is divided into T time slots, and the length of each time slot is τ; let represent the position of drone m at time slot t, be the flight altitude of drone m at time slot t, and represent the lowest and highest altitudes of the drone flight respectively, 1 ≤ m ≤ M; let q n,t =[x n,t , y n,t , 0] T represent the position of target n at time slot t, 1 ≤ n ≤ N; the state of drone m at time slot t can be modeled as:

[0200]

[0201] where, let represent the action vector of drone m at time slot t, which can be modeled as:

[0202]

[0203] where, ε is the moving distance of the drone between adjacent time slots; e m,t and k m,t are the pitch angle and roll angle orders that drone m can rotate at time slot t respectively, 1 ≤ e m,t ≤ N φ , 1 ≤ k m,t ≤ Nθ , N φ and N θ are the adjustable orders of the pitch angle and roll angle of the UAV, respectively; Δ φ = π / N φ is the pitch angle granularity that the UAV can rotate in each time slot; Δ θ = 2π / N θ is the roll angle granularity that the UAV can rotate in each time slot.

[0204] Step 2: Modeling of the sensing channel model;

[0205] Modeling of the sensing channel model is specifically as follows: Assume that the line-of-sight link is dominant between the UAV and the target. Let H m,n,t represent the sensing channel model between UAV m and target n at time slot t, which can be modeled as:

[0206]

[0207] Among them, represents the small-scale gain of the channel between UAV m and target n at time slot t, which can be modeled as a complex Gaussian distributed random variable with a mean of 0 and a variance of 1; ψ m,n,t represents the path loss of the channel between UAV m and target n at time slot t, which can be modeled as:

[0208]

[0209] Among them, ξ m,n represents the average path loss at a reference distance of 1 meter; represents the departure angle of UAV m sensing target n at time slot t; represents the arrival angle of UAV m sensing target n at time slot t, which can be modeled as:

[0210]

[0211] and respectively represent the receiving antenna steering vector and transmitting antenna steering vector corresponding to the state of UAV m sensing target n at time slot t, which can be modeled as:

[0212]

[0213] Among them, d is the spacing between adjacent antennas of the UAV; λ is the wavelength of the transmitted signal.

[0214] Step 3: Modeling of the UAV sensing the target radar signal and the target echo signal;

[0215] Let represent the radar signals sent by each UAV to each target in each time slot. The l-th antenna of X at t PThe value of the sampling point can be modeled as:

[0216]

[0217] where P T is the transmission power of the UAV; represents the value of the radar signal transmitted by the l-th antenna when each UAV senses the state of each target in each time slot at the sampling point t P , 1 ≤ t P ≤ T P ; T P is the number of sampling points of the chirp signal transmitted by the UAV in each time slot; Let Y m,t represent the target echo signal received by UAV m in time slot t, which can be modeled as:

[0218]

[0219] where δ m,n,t ∈ {0, 1} is the tracking variable of UAV m in time slot t. If δ m,n,t = 1, it means that UAV m tracks target n in time slot t, otherwise δ m,n,t = 0; N m,t is the echo noise received by UAV m in time slot t, which can be modeled as Gaussian noise with a mean of 0 and a variance of ; τ m,n,t′ is the arrival time of UAV m in time slot t' received from target n, which can be modeled as:

[0220]

[0221] where c is the speed of light.

[0222] Step 4: Modeling of the target dynamic model;

[0223] Modeling of the target dynamic model is specifically as follows: Let g n,t represent the dynamic model of target n in time slot t, which can be modeled as:

[0224]

[0225] where and are the velocities of target n in the x, y, and z directions in time slot t, respectively; and are the accelerations of target n in the x, y, and z directions in time slot t, respectively; Let represent the acceleration of target n in time slot t, which can be modeled as:

[0226]

[0227] where is the change coefficient of the acceleration in adjacent time slots; w n,t is the disturbance noise of target n in time slot t, which can be modeled as Gaussian noise with a mean of 0 and a variance of The state update formula of target n in time slot t can be modeled as:

[0228] g n,t = Φg n,t-1 + Γw n,t-1

[0229] where Φ and Γ are the state transition matrix and the transition matrix of the disturbance noise of target n in adjacent time slots, respectively, and can be modeled as:

[0230]

[0231] where and are the state transition matrix and the transition matrix of the disturbance noise of each target in the x, y, and z directions in adjacent time slots, respectively, and can be modeled as:

[0232]

[0233] Step 5: Estimation of the angle of arrival and time of arrival of the target;

[0234] The estimation of the angle of arrival and time of arrival of the target is specifically as follows: The Multiple Signal Classification (MUSIC) algorithm is used to estimate the angle of arrival of the target. Let be the covariance matrix of the echo signal received by UAV m in time slot t, which can be modeled as:

[0235]

[0236] where R m,t is the covariance matrix of the transmitted signal of UAV m in time slot t, which can be modeled as:

[0237]

[0238] Perform singular value decomposition on the covariance matrix of the target echo signal, and we can get:

[0239]

[0240] where is the signal eigenvector space of UAV m in time slot t; is the noise eigenvector space of UAV m in time slot t; N′ m,t is the number of targets tracked by UAV m in time slot t, which can be modeled as:

[0241]

[0242] The signal subspace and the noise subspace can be respectively modeled as:

[0243]

[0244] Discretize the angle of arrival of the target, and let Θ denote the set of discretized angles of arrival; let P(θ m,t ) denote the spectral estimation function of UAV m at time slot t based on the MUSIC algorithm, which can be modeled as:

[0245]

[0246] where α(θ m,t ) is the steering vector corresponding to the angle of arrival θ m,t ; let denote the n'-th estimated angle of arrival estimated by UAV m at time slot t, which can be modeled as:

[0247]

[0248] Let denote the estimated time of arrival of UAV m sensing target n at time slot t, which can be modeled as:

[0249]

[0250] where is the amplitude coefficient of the received signal when UAV m senses target n at time slot t, which can be modeled as:

[0251]

[0252] Step 6: Determine the matching of targets in each time slot based on the Hungarian algorithm;

[0253] Determine the matching of targets in each time slot based on the Hungarian algorithm, specifically: Let b m,t denote the observation data matrix of UAV m sensing target at time slot t, which can be modeled as:

[0254]

[0255] where is the time of arrival vector of UAV m sensing target at time slot t, which can be modeled as:

[0256]

[0257] is the angle of arrival matrix vector of UAV m sensing target at time slot t, which can be modeled as:

[0258]

[0259] Let represent the predicted value of the state of target n sensed by each UAV in time slot t. According to the state transition matrix, we have:

[0260]

[0261] where is the state estimation value of the joint sensing of target n by the UAVs in time slot t; let d′ m,n,n′,t represent the cost function of UAV m matching target n and n′ in time slot t, which can be modeled as:

[0262]

[0263] where V n,t is the Jacobian matrix of each UAV sensing target n in time slot t, which can be modeled as:

[0264]

[0265] P m,n,t is the covariance matrix of the state estimation error value corresponding to the state of UAV m sensing target n in time slot t, which can be modeled as:

[0266]

[0267] Let represent the target matching variable in time slot t, represent that at UAV m in time slot t, target n is matched with target n′; otherwise, the target matching problem can be modeled as:

[0268]

[0269] where v max and a max are the maximum speed and maximum acceleration of the target movement in adjacent time slots, respectively; is the chi-square distribution threshold; let G m,t be the weighted complete bipartite graph of the target matching problem in time slot t, which can be modeled as:

[0270] G m,t ={B′ m,t ,B″ m,t ,Ω,W}

[0271] where B′ m,t is the set of predicted values of target n sensed by UAV m in time slot t, which can be modeled as:

[0272]

[0273] B″ m,tis the set of observation values of the target perceived by UAV m in time slot t, which can be modeled as:

[0274] B″ m,t ={b m,t}

[0275] Ω is the connection B′ m,t and B″ m,t The set of edges between two vertices in can be modeled as:

[0276]

[0277] in, Represents connected vertices and vertex [b m,t ] n′,1 The edge of W is connected to B′ m,t and B″ m,t The weight of the set of edges between two vertices in can be modeled as:

[0278]

[0279] in, Represents connected vertices and vertex [b m,t ] n′,1 The edge weights of can be modeled as:

[0280]

[0281] The target matching strategy can be determined by solving the optimization problem based on the Hungarian algorithm.

[0282] Step 7: Estimate the target's position parameters and calculate the Cramer-Rao lower bound based on the extended Kalman filter algorithm;

[0283] The target position parameters are estimated based on the extended Kalman filter algorithm and the Cramer-Rao lower bound is calculated as follows: Let b m,n,t The observation model corresponding to the state of the target n when the drone m perceives the target n in time slot t can be modeled as:

[0284] b m,n,t =V m,n,t g m,n,t +n m,n,t

[0285] Among them, n m,n,t For measurement noise, it can be modeled as having a mean of 0 and a variance of Gaussian noise; let K m,n,t The Kalman gain matrix corresponding to the state of the target n when the drone m perceives the target n in time slot t can be modeled as:

[0286]

[0287] Among them, The covariance matrix of the predicted value of the state of target n at time slot t can be modeled as:

[0288]

[0289] It is the covariance matrix of the observation noise corresponding to the state of target n sensed by UAV m at time slot t, and can be modeled as:

[0290]

[0291] According to K m,n,t and The state estimation value corresponding to the state of target n sensed by UAV m at time slot t can be obtained, that is:

[0292]

[0293] Among them, υ m,n,t represents the error of the predicted value of the state of target n sensed by UAV m at time slot t, and can be modeled as:

[0294]

[0295] According to K m,n,t and V m,n,t The covariance matrix of the state estimation value corresponding to the state of target n sensed by UAV m at time slot t can be obtained, that is:

[0296]

[0297] Let represent the target position of UAV joint sensing of target n at time slot t, and can be modeled as:

[0298]

[0299] Among them, ψ m,n represents the weight factor of the position of target n sensed by UAV m, and can be modeled as:

[0300]

[0301] P n,t represents the covariance matrix of the state estimation value of UAV joint sensing of target n at time slot t, and can be modeled as:

[0302]

[0303] Let η m,t represent the observation data matrix of UAV m sensing target at time slot t, and can be modeled as:

[0304]

[0305] Among them, τ m,t is the arrival time matrix of the target sensed by UAV m in time slot t, which can be modeled as:

[0306]

[0307] θ m,t is the arrival angle matrix of the target sensed by UAV m in time slot t, which can be modeled as:

[0308]

[0309] Let I(η m,t ) represent the Fisher information matrix of the observation data of the target by UAV m in time slot t, which is modeled as:

[0310]

[0311] Among them, p(Y m,t |η m,t ) is the likelihood function of the observation data of the target sensed by UAV m in time slot t, which can be modeled as:

[0312]

[0313] Performing block partitioning on I(η m,t ) gives:

[0314]

[0315] Among them, I1(τ m,t ,τ m,t ) is the Fisher information matrix of the arrival time of the target sensed by UAV m in time slot t, which can be modeled as:

[0316]

[0317] Among them, SNR m,n,t is the signal-to-noise ratio of the received signal when UAV m senses target n in time slot t, which can be modeled as:

[0318]

[0319] I4(θ m,t ,θ m,t ) is the Fisher information matrix of the arrival angle of the target sensed by UAV m in time slot t, which can be modeled as:

[0320]

[0321] I2(τ m,t ,θ m,t ) and I3(θm,t , τ m,t ) The cross - term of the Fisher information matrix of the observation data of the target sensed by the UAV m at time slot t can be modeled as:

[0322] I2(τ m,t , θ m,t ) = I3(θ m,t , τ m,t ) ≈ 0

[0323] Let I0(q m,n,t ) denote the Fisher information matrix of the target n sensed by the UAV m at time slot t, which can be modeled as:

[0324]

[0325] Let J(q m,n,t ) denote the posterior Cramer - Rao lower bound of the position of the target n at time slot t, which can be modeled as:

[0326]

[0327] Where, denotes the Bayesian Fisher information matrix of the position of the target n at time slot t, which can be modeled as:

[0328]

[0329] Where, is the position matrix of M UAVs within time slot t, which can be modeled as:

[0330]

[0331] δ n,t is the tracking association vector of M UAVs within time slot t, which can be modeled as:

[0332] δ n,t = [δ 1,n,t , …, δ M,n,t T

[0333] I P (q n,t ) is the Fisher information matrix of the prior information of the target n at time slot t, which can be modeled as:

[0334]

[0335] is the Fisher information matrix of the observation data of the target n at time slot t, which can be modeled as:

[0336]

[0337] ​Step 8: UAV-assisted target positioning and tracking constraint modeling;

[0338] UAV-assisted target positioning and tracking constraint modeling is specifically as follows: UAV target tracking load constraint, UAV flight trajectory constraint, UAV sensing range constraint, UAV energy consumption constraint; Let C1 and C2 represent the UAV target tracking load constraint, which can be modeled as:

[0339] C1:

[0340] C2 Among them, C1 represents that the UAV can sense at most L targets in each time slot; C2 represents that each target is sensed by at least one UAV in each time slot; Let C3 to C4 represent the UAV flight trajectory constraint, which can be modeled as:

[0341] C3:

[0342] C4: Among them, C3 is the flight distance constraint of UAV m in adjacent time slots; C4 is the collision avoidance constraint between different UAVs in each time slot, and d u represents the minimum safe flight distance between adjacent UAVs; Let C5 represent the UAV sensing range constraint, which can be modeled as:

[0343] C5: Among them, S min is the minimum receiver sensitivity of the radar; Let C6 represent the UAV energy consumption constraint, which can be modeled as:

[0344] C6: Among them, E m,t is the energy consumption of UAV m in time slot t, which can be modeled as:

[0345]

[0346] Among them, is the energy consumed by UAV m during flight in time slot t, which can be modeled as:

[0347]

[0348] Among them, P0 and P0' are the constants of the blade profile power and induced power in the hovering state respectively; can be modeled as:

[0349]

[0350] Among them, U 2 is the square of the tip speed of the rotor blade; is the speed of UAV m in time slot t; can be modeled as:

[0351]

[0352] Among them, v0 is the average rotor induced velocity of the UAV in the hovering state; It can be modeled as:

[0353]

[0354] Among them, ξ d and ξ t are the fuselage drag ratio and rotor reliability respectively; ρ, S U are the air density and rotor disk area respectively; is the energy consumed by UAV m to track and sense the target in time slot t, and can be modeled as:

[0355]

[0356] Step 9: Model the UAV target tracking and flight trajectory planning problem as a system cost function minimization problem;

[0357] Model the UAV target tracking and flight trajectory planning problem as a system cost function minimization problem, specifically: Let E t represent the energy consumed by the UAV in time slot t, and can be modeled as:

[0358]

[0359] Let J t ′ represent the Cramer-Rao lower bound of the target position in time slot t, and can be modeled as:

[0360]

[0361] Let C t represent the system cost function in time slot t, and can be modeled as:

[0362] C t = β1E t + β2J t ′

[0363] Among them, β1 and β2 are the weight factors of the total energy consumption of the UAV and the Cramer-Rao lower bound respectively; Under the condition of meeting the constraint conditions, determine the UAV flight trajectory and tracking association strategy based on the long-term system cost function optimization, that is:

[0364]

[0365] Step 10: Model the UAV target tracking and flight trajectory planning problem as an MDP, and use the multi-agent DQN algorithm to solve it;

[0366] Model the UAV target tracking and flight trajectory planning problem as an MDP, and use the multi-agent DQN algorithm to solve it. Specifically: The modeled MDP can be expressed as where, s t is the system environment state space of the UAV at time slot t, which can be modeled as:

[0367]

[0368] where, is the state of UAV m at time slot t, which can be modeled as:

[0369]

[0370] is the joint action space of the UAV at time slot t, which can be modeled as:

[0371]

[0372] where, is the action of UAV m at time slot t, which can be modeled as:

[0373]

[0374] Let r t u represent the reward function obtained by the agent at time slot t, which can be modeled as:

[0375] r t u ={r 1,t ,...,r M,t}

[0376] where, r m,t is the reward function of UAV m at time slot t, which can be modeled as:

[0377]

[0378] where, β1 is the weight factor of E m,t ; β2 is [J t ′] m,mThe weight factor; η3 > 0 is a penalty constant, indicating that if UAV m collides with other UAVs, it will be penalized by η3; η4 > 0 is a penalty constant, indicating that if the moving distance of UAV m in adjacent time slots exceeds the threshold, it will be penalized by η4; η5 > 0 is a penalty constant, indicating that if there is a target that is not tracked by at least one UAV in the current time slot t, it will be penalized by η5; η6 > 0 is a penalty constant, indicating that if the number of targets selected by UAV m to track in the current time slot t exceeds the number of antennas, it will be penalized by η6; η7 > 0 is a penalty constant, indicating that if the current UAV runs out of power and does not return to the landing point, it will be penalized by η7; The multi-agent DQN algorithm is used to solve the modeled MDP. Specifically, each UAV observes the current system environment, executes an action to obtain a reward function, and stores it in the experience replay pool; In the algorithm training stage, each UAV observes the current system environment, and with probability executes the action corresponding to the maximum Q value, and with probability randomly selects an action; Repeat the above process until the algorithm converges, and the optimal UAV target tracking and flight trajectory planning can be obtained.

[0379] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for drone-assisted target positioning and tracking, characterized in that, The method specifically includes the following steps: S1: Model the unmanned aerial vehicle (UAV) - assisted target positioning and tracking system model; S2: Model the sensing channel model; S3: Model the UAV's sensing of the target radar signal and the target echo signal; S4: Model the target dynamic model; S5: Estimate the angle of arrival (AoA) and time of arrival (ToA) of the target; S6: Determine the matching of targets in each time slot based on the Hungarian algorithm; S7: Estimate the target position and calculate the Cramér - Rao lower bound (CRLB) based on the extended Kalman filter algorithm; S8: Model the UAV - assisted target positioning and tracking constraints; S9: Model the UAV target tracking and flight trajectory planning problem as a system cost function minimization problem; S10: Model the UAV target tracking and flight trajectory as a Markov decision process (MDP), and solve it using the multi - agent deep Q - network (DQN) algorithm.

2. The method for unmanned aerial vehicle-assisted target positioning and tracking according to claim 1, wherein In step S1, a model of an unmanned aerial vehicle (UAV) - assisted target positioning and tracking system is built, which specifically includes: The system consists of M multi - antenna UAVs and N moving targets; It is assumed that the UAVs are equipped with uniform linear antenna arrays, which can send radar sensing signals, receive target echo signals, and estimate the angle of arrival and position of the targets. Let L denote the number of antennas of each UAV; The UAVs start from the starting point and perform positioning and tracking on each target during the flight; The system time is divided into T time slots, and the length of each time slot is τ; Let represent the position of UAV m at time slot t, be the flight altitude of UAV m at time slot t, and represent the lowest and highest altitudes of the UAV flight respectively, 1 ≤ m ≤ M; Let q n,t = [x n,t , y n,t , 0] T represent the position of target n at time slot t, 1 ≤ n ≤ N; The state of UAV m at time slot t can be modeled as: where, let represent the action vector of UAV m at time slot t, which can be modeled as: where ε is the moving distance of adjacent - slot UAVs; e m,t and k m,t are the pitch - angle and roll - angle orders that UAV m can rotate at time slot t, respectively, 1 ≤ e m,t ≤ N φ , 1 ≤ k m,t ≤ N θ , N φ and N θ are the adjustable orders of the pitch - angle and roll - angle of the UAV, respectively; Δ φ = π / N φ is the pitch - angle granularity that the UAV can rotate at each time slot; Δ θ = 2π / N θ is the roll - angle granularity that the UAV can rotate at each time slot.

3. The method for drone-assisted target positioning and tracking according to claim 3, wherein In step S2, a modeling perception channel model is specifically as follows: Assume that the line-of-sight link is dominant between the UAV and the target, and let H m,n,t represent the perception channel model between UAV m and target n at time slot t, which can be modeled as: Among them, represents the small-scale gain of the channel between the UAV m and the target n at time slot t, which can be modeled as a complex Gaussian distributed random variable with a mean of 0 and a variance of 1; ψ m,n,t represents the path loss of the channel between the UAV m and the target n at time slot t, which can be modeled as: Among them, ξ m,n represents the average path loss at a reference distance of 1 meter; represents the departure angle of the UAV m sensing the target n at time slot t; represents the arrival angle of the UAV m sensing the target n at time slot t, which can be modeled as: and respectively represent the receiving antenna steering vector and the transmitting antenna steering vector corresponding to the state where the unmanned aerial vehicle m senses the target n at time slot t, and can be modeled as: Where, d is the spacing between adjacent antennas of the UAV; λ is the wavelength of the transmitted signal.

4. The method for drone-assisted target positioning and tracking according to claim 4, wherein In step S3, the modeling UAV senses the target radar signal and the target echo signal, specifically including: Let represent the radar signals sent by each UAV to each target in each time slot. The value of the l-th antenna of X at t P sampling points can be modeled as: Among them, P T is the transmission power of the UAV; represents the value of the radar signal transmitted by the l-th antenna when each UAV senses the state of each target at each time slot at the sampling point t P where 1 ≤ t P ≤ T P ; T P is the number of sampling points of the chirp signal transmitted by the UAV within each time slot; Let Y m,t represent the target echo signal received by UAV m at time slot t, which can be modeled as: where, δ m,n,t ∈ {0, 1} is the tracking variable of UAV m in time slot t. If δ m,n,t = 1, it means that UAV m tracks target n in time slot t. Otherwise, δ m,n,t = 0; N m,t is the echo noise received by UAV m in time slot t, which can be modeled as Gaussian noise with a mean of 0 and a variance of ; τ m,n,t′ is the time of arrival of UAV m received from target n in time slot t', which can be modeled as: Where, c is the speed of light.

5. The method for drone-assisted target positioning and tracking according to claim 5, wherein In step S4, a dynamic model of the modeling objective, specifically including: Let g n,t represent the dynamic model of target n at time slot t, which can be modeled as: Among them, and are the velocities of target n in the x, y, and z directions at time slot t, respectively; and are the accelerations of target n in the x, y, and z directions at time slot t, respectively. Let represent the acceleration of target n at time slot t, which can be modeled as: Among them, is the change coefficient of the acceleration in adjacent time slots; w n,t is the disturbance noise of target n at time slot t, which can be modeled as Gaussian noise with a mean of 0 and a variance of ; the state update formula of target n at time slot t can be modeled as: g n,t = Φg n,t-1 + Γw n,t-1 Where, Φ and Γ are the state transition matrix and the transition matrix of the perturbation noise of target n in adjacent time slots respectively, and can be modeled as: Among them, and are the state transition matrices of each target in adjacent time slots in the x, y, and z directions and the transition matrix of the disturbance noise, respectively, and can be modeled as:

6. The method for unmanned aerial vehicle-assisted target positioning and tracking according to claim 6, characterized in that In step S5, the angle of arrival (AoA) and time of arrival (ToA) of the target are estimated, which specifically includes: using the Multiple Signal Classification (MUSIC) algorithm to estimate the AoA of the target, and letting be the covariance matrix of the echo signal received by the UAV m at time slot t, which can be modeled as: Among them, R m,t is the covariance matrix of the transmission signal of the UAV m in time slot t, and can be modeled as: Covariance matrix of the target echo signal Performing singular value decomposition, we can obtain: Among them, is the signal feature vector space of unmanned aerial vehicle m at time slot t; is the noise feature vector space of unmanned aerial vehicle m at time slot t; N′ m,t is the number of targets tracked by unmanned aerial vehicle m at time slot t, which can be modeled as: The signal subspace and the noise subspace can be modeled respectively as: Discretize the angle of arrival of the target, and let Θ denote the set of discretized angles of arrival; let P(θ m,t ) represent the spectral estimation function of UAV m based on the MUSIC algorithm in time slot t, which can be modeled as: where, α(θ m,t ) is the steering vector corresponding to the arrival angle of θ m,t ; Let denote the n'-th arrival angle estimated by the UAV m at time slot t, which can be modeled as: Let denote the estimated arrival time of the target n sensed by the UAV m at time slot t, which can be modeled as: wherein, is the amplitude coefficient of the received signal when the UAV m senses the target n at time slot t, and can be modeled as:

7. The method for unmanned aerial vehicle-assisted target positioning and tracking according to claim 6, wherein, In step S6, determining the matching of each time-slot target based on the Hungarian algorithm specifically includes: Let b m,t represent the observation data matrix of the UAV m sensing the target at time slot t, which can be modeled as: Among them, is the arrival time vector of the target sensed by the UAV m at time slot t, which can be modeled as: The matrix vector of the arrival angle for the UAV m to sense the target at time slot t can be modeled as: Let represent the predicted value of the state of each UAV sensing target n at time slot t. According to the state transition matrix, we have: Among them, is the state estimation value of the UAV jointly sensing target n at time slot t; let d′ m,n,n′,t represents the cost function of UAV m matching targets n and n′ at time slot t, which can be modeled as: Among them, V n,t is the Jacobian matrix of each UAV sensing target n at time slot t, which can be modeled as: P m,n,t The covariance matrix of the state estimation error value corresponding to the state when the UAV m senses the target n at time slot t can be modeled as: Let denote the target matching variable at time slot t, denote that at the UAV m at time slot t, target n and target n' are matched; otherwise, the target matching problem can be modeled as: where v max and a max are respectively the maximum speed and maximum acceleration of the target motion in adjacent time slots; is the chi-square distribution threshold; let G m,t be the weighted complete bipartite graph of the target matching problem in time slot t, which can be modeled as: G m,t = {B′ m,t , B″ m,t , Ω, W} Among them, B' m,t is the set of predicted values for the target sensed by the UAV m at time slot t, and can be modeled as: B″ m,t The set of observed values for the UAV m to sense the target at time slot t can be modeled as: B″ m,t = {b m,t} Ω is the set of edges connecting two vertices among B′ m,t and B″ m,t and can be modeled as: Among them, represents the connecting vertex and vertex [b m,t n′,1 ; W is the weight of the set of edges connecting two vertices in B' m,t and B'' m,t , which can be modeled as:​ Among them, represents the connection vertex and vertex [b m,t n′,1 The weight of the edge can be modeled as:​ Solving the optimization problem based on the Hungarian algorithm can determine the target matching strategy.

8. The method for unmanned aerial vehicle-assisted target positioning and tracking according to claim 7, characterized in that, In step S7, the position parameters of the target are estimated and the Cramer-Rao lower bound is calculated based on the extended Kalman filter algorithm, which specifically includes: Let b m,n,t represent the observation model corresponding to the state where the unmanned aerial vehicle m senses the target n at time slot t, which can be modeled as: b m,n,t = V m,n,t g m,n,t + n m,n,t where n m,n,t is the measurement noise, which can be modeled as Gaussian noise with a mean of 0 and a variance of ; let K m,n,t denote the Kalman gain matrix corresponding to the state when the UAV m senses the target n at time slot t, which can be modeled as: Among them, The covariance matrix of the predicted value of the state of target n at time slot t can be modeled as: The covariance matrix of the observation noise corresponding to the state of target n sensed by UAV m at time slot t can be modeled as: According to K m,n,t and the state estimate value corresponding to the state when the UAV m senses the target n at time slot t can be obtained, that is: where, υ m,n,t represents the error of the predicted value of the state of the target n sensed by the UAV m in time slot t, and can be modeled as: According to K m,n,t and V m,n,t the covariance matrix of the state estimation value corresponding to the state when the UAV m senses the target n at time slot t can be obtained, that is: Let represent the target location of the UAV jointly sensing target n at time slot t, which can be modeled as: Among them, ψ m,n represents the weight factor for the UAV m to sense the position of the target n, and can be modeled as: P n,t It represents the covariance matrix of the state estimation value of the UAV jointly sensing target n at time slot t, which can be modeled as: Let η m,t represent the observation data matrix of the target sensed by UAV m at time slot t, which can be modeled as: where τ m,t is the arrival time matrix of the target sensed by the UAV m at time slot t and can be modeled as: θ m,t The angle-of-arrival matrix for the UAV m to sense the target at time slot t, which can be modeled as: Let \(I(\eta m,t )\) denote the Fisher information matrix of the observation data of the target by the UAV \(m\) in time slot \(t\), which is modeled as: where p(Y m,t | η m,t ) is the likelihood function of the observation data of the target sensed by the UAV m in time slot t, which can be modeled as: For I(η m,t ), the chunking results in: Among them, I1(τ m,t , τ m,t ) is the Fisher information matrix of the arrival time of the target sensed by the UAV m in time slot t, which can be modeled as: where, SNR m,n,t is the signal-to-noise ratio of the received signal when UAV m senses target n at time slot t, and can be modeled as: I4(θ m,t ,θ m,t ) is the Fisher information matrix of the arrival angle of the target sensed by the UAV m in time slot t, which can be modeled as: I2(τ m,t ,θ m,t ) and I3(θ m,t ,τ m,t ) The cross-term of the Fisher information matrix of the observation data of the target sensed by the UAV m in time slot t can be modeled as: I2(τ m,t ,θ m,t ) = I3(θ m,t ,τ m,t ) ≈ 0 Let \(I_0(q m,n,t )\) denote the Fisher information matrix for UAV \(m\) to sense target \(n\) at time slot \(t\), which can be modeled as: Let \(J(q m,n,t )\) denote the posterior Cramer-Rao lower bound of the position of target \(n\) in time slot \(t\), which can be modeled as: Among them, The Bayesian Fisher information matrix representing the position of target n at time slot t can be modeled as: Among them, is the position matrix of M UAVs within time slot t, which can be modeled as: δ n,t The tracking association vector of M UAVs within time slot t can be modeled as: δ n,t = [δ 1,n,t , …, δ M,n,t T ​ I P (q n,t ) is the Fisher information matrix of the prior information of target n at time slot t and can be modeled as: The Fisher information matrix for the observed data of time slot t and target n can be modeled as follows:

9. A method for drone-assisted target positioning and tracking according to claim 8, characterized in that, In step S8, modeling the UAV - assisted target positioning and tracking constraints specifically includes: UAV target tracking load constraint, UAV flight trajectory constraint, UAV sensing range constraint, UAV energy consumption constraint; Let C1 and C2 represent the UAV target tracking load constraint, and can be modeled as: Where, C1 represents that the UAV can sense at most L targets in each time slot; C2 represents that each target is sensed by at least one UAV in each time slot; Let C3 - C4 represent the UAV flight trajectory constraint, and can be modeled as: Among them, C3 is the flight distance constraint of UAV m in adjacent time slots; C4 is the collision avoidance constraint between different UAVs in each time slot, and d u represents the minimum safe flight distance between adjacent UAVs; let C5 represent the sensing range constraint of the UAV, which can be modeled as: Among them, S min is the minimum receiver sensitivity of the radar; let C6 represent the energy consumption constraint of the UAV, which can be modeled as: Among them, E m,t is the energy consumption of UAV m at time slot t, which can be modeled as: Among them, is the energy consumed by UAV m during flight at time slot t, which can be modeled as: where P0 and P0′ are constants of the blade profile power and the induced power in the hovering state, respectively; can be modeled as: where U 2 is the square of the tip speed of the rotor blade; is the speed of the UAV m at time slot t; can be modeled as: where, v0 is the average rotor induced velocity of the UAV in the hovering state; It can be modeled as: Among them, ξ d , ξ t are the fuselage drag ratio and the rotor reliability respectively; ρ, S U are the air density and the rotor disk area respectively; is the energy consumed by the UAV m to track and sense the target during the time slot t, which can be modeled as:

10. The method for drone-assisted target positioning and tracking according to claim 9, characterized in that, In step S9, the problem of UAV target tracking and flight trajectory planning is modeled as a system cost function minimization problem, which specifically includes: Let E t represent the energy consumed by the UAV in time slot t, which can be modeled as: Let J t ′ denote the Cramer-Rao lower bound of the target position at time slot t, which can be modeled as: Let C t represent the cost function of the system at time slot t, which can be modeled as: C t = β1E t + β2J′ t Where, β1 and β2 are the weight factors of the total energy consumption of the UAV and the Cramér - Rao lower bound respectively; Under the condition of meeting the constraint conditions, determine the UAV flight trajectory and tracking association strategy based on the optimization of the long - term system cost function, that is:

11. A method for drone-assisted target positioning and tracking according to claim 10, characterized in that, In step S10, the problem of UAV target tracking and flight trajectory planning is modeled as an MDP, and the multi-agent DQN algorithm is used to solve it, specifically including: the modeled MDP can be expressed as where s t is the system environment state space of the UAV at time slot t, which can be modeled as: Among them, The state of UAV m at time slot t can be modeled as: The joint action space for the UAV at time slot t can be modeled as: Among them, The action of UAV m at time slot t can be modeled as: Let r t u represent the reward function obtained by the agent at time slot t, which can be modeled as: r t u ＝{r 1,t ,...,r M,t} where r m,t is the reward function of UAV m at time slot t and can be modeled as: Among them, β1 is the weight factor of E m,t ; β2 is the weight factor of [J t ′] m,m ; η3 > 0 is a penalty constant, indicating that if UAV m collides with other UAVs, it will be penalized by η3; η4 > 0 is a penalty constant, indicating that if the moving distance of UAV m in adjacent time slots exceeds the threshold, it will be penalized by η4; η5 > 0 is a penalty constant, indicating that if there is a target in the current time slot t that is not tracked by at least one UAV, it will be penalized by η5; η6 > 0 is a penalty constant, indicating that if the number of targets selected by UAV m in the current time slot t exceeds the number of antennas, it will be penalized by η6; η7 > 0 is a penalty constant, indicating that if the current UAV runs out of power and does not return to the landing point, it will be penalized by η7; The multi-agent DQN algorithm is used to solve the modeled MDP. Specifically, each UAV observes the current system environment, executes an action to obtain a reward function, and stores in the experience replay pool; In the algorithm training stage, each UAV observes the current system environment, executes the action corresponding to the maximum Q value with probability θ, and randomly selects an action with probability 1 - θ; Repeat the above process until the algorithm converges, and the optimal UAV target tracking and flight trajectory planning can be obtained.

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